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https://www.bartleby.com/solution-answer/chapter-11-problem-32p-college-physics-11th-edition/9781305952300/how-much-energy-is-required-to-change-a-40-g-ice-cube-from-ice-at-10-c-to-steam-at-110c/fab00c0b-98d4-11e8-ada4-0ee91056875a
[ "", null, "", null, "", null, "Chapter 11, Problem 32P\n\nChapter\nSection\nTextbook Problem\n\nHow much energy is required to change a 40.-g ice cube from ice at −10. °C to steam at 110.°C?\n\nTo determine\nThe energy required to change a 40 g ice cube from ice at 10°C to steam at 110°C .\n\nExplanation\n\nGiven Info: Mass of ice cube is 40 g, initial temperature of ice cube is 10°C , temperature of steam is 110°C ,\n\nExplanation:\n\nEnergy supplied must lower the temperature of ice from 10°C   to 0°C , then melt the ice to cold water at 0°C , then it has to raise the temperature of water to 100°C , then transform the water to steam at 100°C and then increase the temperature of steam to 110°C .\n\nFormula to calculate the heat required to raise the temperature of ice 0°C is,\n\nQice=micecice(Tf,iceTi,ice) (I)\n\n• Qice is the heat required to raise the temperature of ice to 0°C ,\n• mice is the mass of the ice,\n• Ti,ice is the initial temperature of ice,\n• Tf,ice is the final temperature of ice,\n\nFormula to calculate the heat required to melt the ice to cold water is,\n\nQmelt=miceLf (II)\n\n• Qmelt is the energy required to melt the ice to cold water,\n• mice is the mass of the ice,\n• Lf is the latent heat of fusion of ice,\n\nFormula to calculate the heat required to raise the temperature of cold water to hot water at 100°C is,\n\nQboil=mwatercwater(Tf,waterTi,water) (III)\n\n• Qboil is the heat required to raise the temperature of cold water to hot water.\n• cwater is the specific heat of water,\n• Ti,water is the initial temperature of cold water from ice,\n• Tf is the boiling temperature of water,\n\nFormula to calculate the heat required to transform water to steam at 100°C is,\n\nQsteam=msteamLv (IV)\n\n• Qsteam is the energy required to transform water to steam,\n• msteam is the mass of the steam,\n• Lv is the latent heat of vaporization,\n\nFormula to calculate the heat required to raise the temperature of steam to 110°C is,\n\nQsteam=msteamcsteam(Tf,steamTi,steam) (V)\n\n• Qsteam is the heat required to raise the temperature of steam,\n• msteam is the mass of steam,\n• csteam is the specific heat of steam,\n• Ti,steam is the initial temperature of steam,\n• Tf,steam is the final temperature of steam,\n\nFormula to calculate the energy required to change 40 g ice cube from ice at 10°C to steam at 110°C is,\n\nQ=Qice+Qmelt+Qboil+Qsteam+Qsteam (VI)\n\nSubstitute equation (I), (II), (III) (IV) (V) in equation (VI) to calculate Qtran\n\nStill sussing out bartleby?\n\nCheck out a sample textbook solution.\n\nSee a sample solution\n\nThe Solution to Your Study Problems\n\nBartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!\n\nGet Started", null, "" ]
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https://www.brainkart.com/article/Torque--Speed-Charactersistics-of-BLPM-SQM-DC-Motor_11777/
[ "Home | | Special Electrical Machines | Torque- Speed Charactersistics of BLPM SQM DC Motor\n\n# Torque- Speed Charactersistics of BLPM SQM DC Motor\n\nLet the supply voltage V be constant. A family of torque speed characteristics for various constant supply voltages is as shown in figure 4.20\n\nTORQUE- SPEED CHARACTERSISTICS OF BLPM SQM DC MOTOR\n\nLet the supply voltage V be constant. A family of torque speed characteristics for various constant supply voltages is as shown in figure 4.20", null, "Fig 4.20 T-ωm curve for various supply voltages\n\nPermissible region of operation in T-ωm plane\n\nTorque speed characteristics of BLPM square wave motor is shown in fig.4.21. The constraints are\n\n1.     The continues current should not exceed the permissible current limit In (i.e) Torques should not exceed Kt In.\n\n2.     The maximum permissible supply voltage = Vn.\n\n3.     The speed should not exceed ωmn.", null, "Line AB\n\nParallel to X-axis represents maximum permissible torque line which corresponds to maximum permissible current In.\n\nLine FG\n\nIt represents T-ωm characteristics corresponding to the maximum permissible Vn. B and C are points in Fg. B is the point of intersection between AB and FG.\n\nLine DH\n\nIt represents constant maximum permissible speed line (i.e) ωmn is constant. DH intersects FG and x axis at D.\n\nThe area OABCDO is the permissible region of operation. To obtain a particular point P corresponding to given load-torque and speed condition the only way to operate the motor at P is by suitably adjusting the supply voltage fed to the motor.", null, "v   If the phase resistance is small as it should be in an efficient design, then the characteristics to that of a shunt dc motor. The speed is essentially controlled by the voltage V and may be changed by changing the supply voltage. Then the current drawn just to drive the torque at its speed.\n\nv   As the load torque is increased, the speed drops and the drop is directly proportional to the phase resistance and the torque.\n\nv   The voltage is usually controlled by chopping or PWM. This gives rise to a family of torque speed characteristics as shown in fig. 4.22. The boundaries of continuous and intermittent limits are shown.\n\nContinuous limit - determined by the heat transfer and temperature rise.\n\nIntermittent limit – determined by the maximum ratings of semiconductor devices in circuit.\n\nIn practice the torque speed characteristics deviates from the ideal form because of the effects of inductance and other parasitic influences.\n\nAlso the speed range can be extended by increasing the dwell of conduction period relative to the rotor position.\n\nStudy Material, Lecturing Notes, Assignment, Reference, Wiki description explanation, brief detail\n\nRelated Topics" ]
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https://www.teachoo.com/11008/3130/Question-35-OR-1st-question/category/CBSE-Class-10-Sample-Paper-for-2020-Boards---Maths-Standard/
[ "CBSE Class 10 Sample Paper for 2020 Boards - Maths Standard\n\nClass 10\nSolutions of Sample Papers for Class 10 Boards\n\n## Draw a triangle ABC with side BC = 6.5 cm, ∠B = 30°, ∠A = 105°. Then construct another triangle whose sides are 3/4 times the corresponding sides of the triangle ABC.", null, "", null, "", null, "", null, "", null, "", null, "Note : This is similar to Ex 11.1, 6 of NCERT – Chapter 11 Class 10\n\n### Transcript\n\nQuestion 35 (OR 1st question) Draw a triangle ABC with side BC = 6.5 cm, ∠B = 30°, ∠A = 105°. Then construct another triangle whose sides are 3/4 times the corresponding sides of the triangle ABC. Let’s first draw a rough diagram To construct Δ ABC, we first need to find ∠ C Finding ∠ C In Δ ABC ∠A + ∠B + ∠C = 180° 105° + 30° + ∠C = 180° 135° + ∠C = 180° ∠C = 180° − 135° ∠C = 45° Steps to draw Δ ABC Draw base BC of side 6.5 cm Draw ∠ B = 30° Draw ∠ C = 45° 4. Let point A be the point where the two rays intersect ∴ Δ ABC is the required triangle Now, we need to make a triangle which is 3/4 times its size ∴ Scale factor = 3/4 < 1 Steps of construction Draw any ray BX making an acute angle with BC on the side opposite to the vertex A. Mark 4 (the greater of 4 and 3 in 3/4 ) points 𝐵_1, 𝐵_2, 𝐵_3,𝐵_4 on BX so that 〖𝐵𝐵〗_1=𝐵_1 𝐵_2=𝐵_2 𝐵_3=𝐵_3 𝐵_4 Join 𝐵_4C and draw a line through 𝐵_3 (the 3rd point, 3 being smaller of 3 and 4 in 3/4) parallel to 𝐵_4 𝐶, to intersect BC at C′. Draw a line through C′ parallel to the line AC to intersect AB at A′. Thus, Δ A′BC′ is the required triangle", null, "" ]
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https://pocketteacher.ru/eng/different/five-equations
[ "# 5 equations that the entire internet is puzzling over\n\nMany scientists recommend training your brain by solving mathematical equations. Thanks to modern technologies, on the Internet you can find a large number of different puzzles that help you develop your abilities. The more you exercise, the faster you can calculate algebra in the future.\n\n## Examples and ways to solve them\n\nThe five most popular puzzles are:\n\n• An example in two steps without parentheses. Netizens argue over the result of the problem: 230-220 * 0.5. Someone thinks that the answer is 120, while others are sure that the result is 5. In fact both are right. Only in the second case, the result is 5 with an exclamation mark, that is five with a factorial. 5! = 5 * 4 * 3 * 2 * 1 = 120.\n• Equation with brackets. Another subject of controversy on the Internet is the example: 8/2 * (2 + 2). Spread in significant answers: some believe that the result will be 1, while others - 16. If you follow the rules of mathematics, then first the action in brackets is performed, that is, 2 + 2 = 4, and then everything is performed in order. This means 8/2 * 4 = 16. If the author of the example would put one more parentheses before 2, then 2 would be multiplied by 4, and then 8 would be divisible by 8, and in the end the answer would be 1.\n• Mindfulness puzzle. In front of users is a picture showing tracks for racing cars, each of which has numbers: 16, 06, 68, 88, one more is closed by a car, and the last one is 98. You are asked to calculate what number is hidden under the car. To solve the problem, you do not need to apply math skills. It is enough just to turn the image over and understand that it is upside down 16 is 91, 06-90, and so on. So the number under the car is 87.\n• The principle of constructing examples. Problems of this kind are often encountered. For example, 6 + 4 = 210 or 8 + 5 = 313. The solution is pretty easy. The authors simply first subtracted the number 4 from 6, and then added. It turned out 6-4 = 2 and 6 + 4 = 10, and together 210. Other similar examples are constructed in the same way.\n• Equations with pictures. On the Internet you can find many pictures, where, for example, multiply first 3 ice cream cones and the answer is 27, then two full ice creams are added with white vanilla, which is 10 and other actions. You are asked to determine the numbers that inserted by the author instead of pictures. To determine, you must first solve the first example and then substitute this figure in the rest to solve the whole problem.\n\nIf you don’t have time to think long and you don’t know, how to solve math , you can do it using our website.", null, "Our artificial intelligence solves complex math problems in seconds.\n\nWe will solve your exam, homework, olympiad problems with detailed steps. You will need just to copy the solution." ]
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https://dev.opencascade.org/doc/occt-7.0.0/refman/html/class_bnd___box2d.html
[ "Open CASCADE Technology  7.0.0\n\n# Bnd_Box2d Class Reference\n\nDescribes a bounding box in 2D space. A bounding box is parallel to the axes of the coordinates system. If it is finite, it is defined by the two intervals: More...\n\n`#include <Bnd_Box2d.hxx>`\n\n## Public Member Functions\n\nBnd_Box2d ()\nCreates an empty 2D bounding box. The constructed box is qualified Void. Its gap is null. More...\n\nvoid SetWhole ()\nSets this bounding box so that it covers the whole 2D space, i.e. it is infinite in all directions. More...\n\nvoid SetVoid ()\nSets this 2D bounding box so that it is empty. All points are outside a void box. More...\n\nvoid Set (const gp_Pnt2d &P)\nSets this 2D bounding box so that it bounds the point P. This involves first setting this bounding box to be void and then adding the point PThe rectangle bounds the point. More...\n\nvoid Set (const gp_Pnt2d &P, const gp_Dir2d &D)\nSets this 2D bounding box so that it bounds the half-line defined by point P and direction D, i.e. all points M defined by M=P+u*D, where u is greater than or equal to 0, are inside the bounding area. This involves first setting this 2D box to be void and then adding the half-line. More...\n\nvoid Update (const Standard_Real aXmin, const Standard_Real aYmin, const Standard_Real aXmax, const Standard_Real aYmax)\nEnlarges this 2D bounding box, if required, so that it contains at least: More...\n\nvoid Update (const Standard_Real X, const Standard_Real Y)\nAdds a point of coordinates (X,Y) to this bounding box. More...\n\nStandard_Real GetGap () const\nReturns the gap of this 2D bounding box. More...\n\nvoid SetGap (const Standard_Real Tol)\nSet the gap of this 2D bounding box to abs(Tol). More...\n\nvoid Enlarge (const Standard_Real Tol)\nEnlarges the box with a tolerance value. This means that the minimum values of its X and Y intervals of definition, when they are finite, are reduced by the absolute value of Tol, while the maximum values are increased by the same amount. More...\n\nvoid Get (Standard_Real &aXmin, Standard_Real &aYmin, Standard_Real &aXmax, Standard_Real &aYmax) const\nReturns the bounds of this 2D bounding box. The gap is included. If this bounding box is infinite (i.e. \"open\"), returned values may be equal to +/- Precision::Infinite(). if IsVoid() More...\n\nvoid OpenXmin ()\nThe Box will be infinitely long in the Xmin direction. More...\n\nvoid OpenXmax ()\nThe Box will be infinitely long in the Xmax direction. More...\n\nvoid OpenYmin ()\nThe Box will be infinitely long in the Ymin direction. More...\n\nvoid OpenYmax ()\nThe Box will be infinitely long in the Ymax direction. More...\n\nStandard_Boolean IsOpenXmin () const\nReturns true if this bounding box is open in the Xmin direction. More...\n\nStandard_Boolean IsOpenXmax () const\nReturns true if this bounding box is open in the Xmax direction. More...\n\nStandard_Boolean IsOpenYmin () const\nReturns true if this bounding box is open in the Ymin direction. More...\n\nStandard_Boolean IsOpenYmax () const\nReturns true if this bounding box is open in the Ymax direction. More...\n\nStandard_Boolean IsWhole () const\nReturns true if this bounding box is infinite in all 4 directions (Whole Space flag). More...\n\nStandard_Boolean IsVoid () const\nReturns true if this 2D bounding box is empty (Void flag). More...\n\nBnd_Box2d Transformed (const gp_Trsf2d &T) const\nReturns a bounding box which is the result of applying the transformation T to this bounding box. Warning Applying a geometric transformation (for example, a rotation) to a bounding box generally increases its dimensions. This is not optimal for algorithms which use it. More...\n\nvoid Add (const Bnd_Box2d &Other)\nAdds the 2d box <Other> to <me>. More...\n\nvoid Add (const gp_Pnt2d &P)\nAdds the 2d pnt. More...\n\nvoid Add (const gp_Pnt2d &P, const gp_Dir2d &D)\nExtends <me> from the Pnt. More...\n\nvoid Add (const gp_Dir2d &D)\nExtends the Box in the given Direction, i.e. adds a half-line. The box may become infinite in 1 or 2 directions. More...\n\nStandard_Boolean IsOut (const gp_Pnt2d &P) const\nReturns True if the 2d pnt. More...\n\nStandard_Boolean IsOut (const Bnd_Box2d &Other) const\nReturns True if <Box2d> is out <me>. More...\n\nStandard_Boolean IsOut (const Bnd_Box2d &Other, const gp_Trsf2d &T) const\nReturns True if transformed <Box2d> is out <me>. More...\n\nStandard_Boolean IsOut (const gp_Trsf2d &T1, const Bnd_Box2d &Other, const gp_Trsf2d &T2) const\nCompares a transformed bounding with a transformed bounding. The default implementation is to make a copy of <me> and <Other>, to transform them and to test. More...\n\nvoid Dump () const\n\nStandard_Real SquareExtent () const\nComputes the squared diagonal of me. More...\n\n## Detailed Description\n\nDescribes a bounding box in 2D space. A bounding box is parallel to the axes of the coordinates system. If it is finite, it is defined by the two intervals:\n\n• [ Xmin,Xmax ], and\n• [ Ymin,Ymax ]. A bounding box may be infinite (i.e. open) in one or more directions. It is said to be:\n• OpenXmin if it is infinite on the negative side of the \"X Direction\";\n• OpenXmax if it is infinite on the positive side of the \"X Direction\";\n• OpenYmin if it is infinite on the negative side of the \"Y Direction\";\n• OpenYmax if it is infinite on the positive side of the \"Y Direction\";\n• WholeSpace if it is infinite in all four directions. In this case, any point of the space is inside the box;\n• Void if it is empty. In this case, there is no point included in the box. A bounding box is defined by four bounds (Xmin, Xmax, Ymin and Ymax) which limit the bounding box if it is finite, six flags (OpenXmin, OpenXmax, OpenYmin, OpenYmax, WholeSpace and Void) which describe the bounding box if it is infinite or empty, and\n• a gap, which is included on both sides in any direction when consulting the finite bounds of the box.\n\n## Constructor & Destructor Documentation\n\n Bnd_Box2d::Bnd_Box2d ( )\n\nCreates an empty 2D bounding box. The constructed box is qualified Void. Its gap is null.\n\n## Member Function Documentation\n\n void Bnd_Box2d::Add ( const Bnd_Box2d & Other )\n\nAdds the 2d box <Other> to <me>.\n\n void Bnd_Box2d::Add ( const gp_Pnt2d & P )\n\nAdds the 2d pnt.\n\nto <me>.\n\n void Bnd_Box2d::Add ( const gp_Pnt2d & P, const gp_Dir2d & D )\n\nExtends <me> from the Pnt.\n\nin the direction <D>.\n\n void Bnd_Box2d::Add ( const gp_Dir2d & D )\n\nExtends the Box in the given Direction, i.e. adds a half-line. The box may become infinite in 1 or 2 directions.\n\n void Bnd_Box2d::Dump ( ) const\n void Bnd_Box2d::Enlarge ( const Standard_Real Tol )\n\nEnlarges the box with a tolerance value. This means that the minimum values of its X and Y intervals of definition, when they are finite, are reduced by the absolute value of Tol, while the maximum values are increased by the same amount.\n\n void Bnd_Box2d::Get ( Standard_Real & aXmin, Standard_Real & aYmin, Standard_Real & aXmax, Standard_Real & aYmax ) const\n\nReturns the bounds of this 2D bounding box. The gap is included. If this bounding box is infinite (i.e. \"open\"), returned values may be equal to +/- Precision::Infinite(). if IsVoid()\n\n Standard_Real Bnd_Box2d::GetGap ( ) const\n\nReturns the gap of this 2D bounding box.\n\n Standard_Boolean Bnd_Box2d::IsOpenXmax ( ) const\n\nReturns true if this bounding box is open in the Xmax direction.\n\n Standard_Boolean Bnd_Box2d::IsOpenXmin ( ) const\n\nReturns true if this bounding box is open in the Xmin direction.\n\n Standard_Boolean Bnd_Box2d::IsOpenYmax ( ) const\n\nReturns true if this bounding box is open in the Ymax direction.\n\n Standard_Boolean Bnd_Box2d::IsOpenYmin ( ) const\n\nReturns true if this bounding box is open in the Ymin direction.\n\n Standard_Boolean Bnd_Box2d::IsOut ( const gp_Pnt2d & P ) const\n\nReturns True if the 2d pnt.\n\nis out <me>.\n\n Standard_Boolean Bnd_Box2d::IsOut ( const Bnd_Box2d & Other ) const\n\nReturns True if <Box2d> is out <me>.\n\n Standard_Boolean Bnd_Box2d::IsOut ( const Bnd_Box2d & Other, const gp_Trsf2d & T ) const\n\nReturns True if transformed <Box2d> is out <me>.\n\n Standard_Boolean Bnd_Box2d::IsOut ( const gp_Trsf2d & T1, const Bnd_Box2d & Other, const gp_Trsf2d & T2 ) const\n\nCompares a transformed bounding with a transformed bounding. The default implementation is to make a copy of <me> and <Other>, to transform them and to test.\n\n Standard_Boolean Bnd_Box2d::IsVoid ( ) const\n\nReturns true if this 2D bounding box is empty (Void flag).\n\n Standard_Boolean Bnd_Box2d::IsWhole ( ) const\n\nReturns true if this bounding box is infinite in all 4 directions (Whole Space flag).\n\n void Bnd_Box2d::OpenXmax ( )\n\nThe Box will be infinitely long in the Xmax direction.\n\n void Bnd_Box2d::OpenXmin ( )\n\nThe Box will be infinitely long in the Xmin direction.\n\n void Bnd_Box2d::OpenYmax ( )\n\nThe Box will be infinitely long in the Ymax direction.\n\n void Bnd_Box2d::OpenYmin ( )\n\nThe Box will be infinitely long in the Ymin direction.\n\n void Bnd_Box2d::Set ( const gp_Pnt2d & P )\n\nSets this 2D bounding box so that it bounds the point P. This involves first setting this bounding box to be void and then adding the point PThe rectangle bounds the point.\n\n.\n\n void Bnd_Box2d::Set ( const gp_Pnt2d & P, const gp_Dir2d & D )\n\nSets this 2D bounding box so that it bounds the half-line defined by point P and direction D, i.e. all points M defined by M=P+u*D, where u is greater than or equal to 0, are inside the bounding area. This involves first setting this 2D box to be void and then adding the half-line.\n\n void Bnd_Box2d::SetGap ( const Standard_Real Tol )\n\nSet the gap of this 2D bounding box to abs(Tol).\n\n void Bnd_Box2d::SetVoid ( )\n\nSets this 2D bounding box so that it is empty. All points are outside a void box.\n\n void Bnd_Box2d::SetWhole ( )\n\nSets this bounding box so that it covers the whole 2D space, i.e. it is infinite in all directions.\n\n Standard_Real Bnd_Box2d::SquareExtent ( ) const\n\nComputes the squared diagonal of me.\n\n Bnd_Box2d Bnd_Box2d::Transformed ( const gp_Trsf2d & T ) const\n\nReturns a bounding box which is the result of applying the transformation T to this bounding box. Warning Applying a geometric transformation (for example, a rotation) to a bounding box generally increases its dimensions. This is not optimal for algorithms which use it.\n\n void Bnd_Box2d::Update ( const Standard_Real aXmin, const Standard_Real aYmin, const Standard_Real aXmax, const Standard_Real aYmax )\n\nEnlarges this 2D bounding box, if required, so that it contains at least:\n\n• interval [ aXmin,aXmax ] in the \"X Direction\",\n• interval [ aYmin,aYmax ] in the \"Y Direction\"\n void Bnd_Box2d::Update ( const Standard_Real X, const Standard_Real Y )\n\nAdds a point of coordinates (X,Y) to this bounding box.\n\nThe documentation for this class was generated from the following file:" ]
[ null ]
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https://mathoverflow.net/questions/383039/equivalent-definitions-of-normality-for-complex-algebraic-varieties
[ "# Equivalent definitions of normality for complex algebraic varieties\n\nIn Kollár's article The structure of algebraic threefolds: an introduction to Mori's program he gives the following definition of a normal variety:\n\nDefinition 5.4. Let $$V \\subset \\mathbb{C}^n$$ be an algebraic variety and $$v \\in V$$. We say $$V$$ is normal at $$v$$ if every rational function bounded in some neighborhood of $$v$$ is regular at $$v$$.\n\nThis is in contrast to the definition of normal which I have seen everywhere else: the point $$v \\in V$$ is normal if the local ring $$\\mathcal{O}_{V,v}$$ is integrally closed. Of course the first question that came to mind is whether these two concepts are equivalent. I intuitively see that if for the rational function $$g/h$$ we have that $$|(g/h)(w)| \\to \\infty$$ as $$w \\to v$$, then said function cannot satisfy a monic polynomial relation with regular coefficients (although I am not 100% sure how to prove this). However the converse seems very misterious to me. Is this the way to prove they are equivalent or am I following the wrong path? Are they equivalent at all?\n\n• Welcome new contributor. I recommend that you search for the key phrase \"Zariski's Main Theorem\". The discussion in Mumford's \"Red Book\" is particularly useful. Feb 3 at 20:44\n• One thing which is relevant is that on normal varieties rational functions are regular away from their divisors of poles (see `Structure theorem' in III.8 in Mumford's red book), hence if a rational function is bounded on an open set, this set does not intersect the divisors of poles, and the function is regular. Feb 3 at 22:36\n• See also Exercise 4.25 on page 141 in Eisenbud's book on commutative algebra. Feb 3 at 22:55\n\nThe fact that the integral closure is contained in the weakly holomorphic functions follows from an elementary property of roots of monic polynomials. The proof of the other inclusion uses the local parametrization theorem (which corresponds to the Noether normalization in the algebraic setting) and the Riemann extension theorem which says that that any function which is holomorphic on $$U \\setminus A$$ and locally bounded near $$A$$, where $$U \\subseteq \\mathbb{C}^n$$ is open, and $$A$$ is an analytic subset of positive codimension." ]
[ null ]
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https://grinebiter.com/Calculators/Factors/Factors-of-642.html
[ "Factors of 642\n\nHere we have calculated and created a list of all the factors of six hundred forty-two.\nThe factors of 642 are:\n\n1, 2, 3, 6, 107, 214, 321, 642\n\nFactors of 642 are integers that you can multiply together to get 642. Here are all the combinations of factors of 642 that you can multiply together to get 642:\n\n1 x 642 = 642\n2 x 321 = 642\n3 x 214 = 642\n6 x 107 = 642\n107 x 6 = 642\n214 x 3 = 642\n321 x 2 = 642\n642 x 1 = 642\n\nIf you divide 642 by a factor of 642, you will get one of the other factors of 642. Here are all combinations of dividing 642 by its factors:\n\n642 / 1 = 642\n642 / 2 = 321\n642 / 3 = 214\n642 / 6 = 107\n642 / 107 = 6\n642 / 214 = 3\n642 / 321 = 2\n642 / 642 = 1\n\nIn summary, we have not only listed all the factors of 642, but also illustrated that our solution is correct by multiplying and dividing the factors of six hundred forty-two.\n\nFactoring Calculator\nDo you need the factors for another number? No problem - just enter it below and press \"Factor\".\n\nFactors of 643\nHere is the next number on our list for which we have calculated the factors." ]
[ null ]
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https://imagen.holoviz.org/Reference_Manual/imagen.html
[ "# imagen.imagen Package¶\n\n## imagen Package¶", null, "Objects capable of generating a two-dimensional array of values.\n\nSuch patterns can be used as input to machine learning, neural network, or compuatational neuroscience algorithms, or for any other purpose where a two-dimensional pattern may be needed. Any new PatternGenerator classes can be derived from these, and can then be combined with the existing classes easily.\n\nclass imagen.__init__.Angle(**params)[source]\n\nAngle composed of two line segments.\n\nparam Number x (allow_None=False, bounds=None, constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.2, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nX-coordinate location of pattern center.\nparam Number scale (allow_None=False, bounds=None, constant=False, default=1.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.1, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nMultiplicative strength of input pattern, defaulting to 1.0\nparam String group (allow_None=False, basestring=<type ‘basestring’>, constant=False, default=Pattern, instantiate=False, pickle_default_value=True, precedence=-1, readonly=False)\nThe group name assigned to the returned HoloViews object.\nparam Number angle (allow_None=False, bounds=(0.0, None), constant=False, default=0.785398163397, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.63, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nAngle between the two line segments.\nparam Number orientation (allow_None=False, bounds=None, constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.4, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nPolar angle of pattern, i.e., the orientation in the Cartesian coordinate system, with zero at 3 o’clock and increasing counterclockwise.\nparam ClassSelector z (allow_None=True, constant=False, default=None, instantiate=True, is_instance=True, pickle_default_value=True, precedence=-1, readonly=False)\nThe Dimension object associated with the z-values generated by the PatternGenerator . If None, uses the default set by HoloViews.Image.\nOptional object (expected to be an array) with which to multiply the pattern array after it has been created, before any output_fns are applied. This can be used to shape the pattern.\nBoundingBox of the area in which the pattern is generated.\nparam Parameter operator (allow_None=False, constant=False, default=<ufunc ‘maximum’>, instantiate=False, pickle_default_value=True, precedence=0.98, readonly=False)\nBinary Numpy function used to combine the individual patterns. Any binary Numpy array “ufunc” returning the same type of array as the operands and supporting the reduce operator is allowed here. Supported ufuncs include:: add subtract multiply divide maximum minimum remainder power The most useful ones are probably add and maximum, but there are uses for at least some of the others as well (e.g. to remove pieces of other patterns). You can also write your own operators, by making a class that has a static method named “reduce” that returns an array of the same size and type as the arrays in the list. For example:: class return_first(object): @staticmethod def reduce(x): return x\nparam Number thickness (allow_None=False, bounds=(0.0, None), constant=False, default=0.05, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.6, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nThickness of the rectangle.\nparam Number xdensity (allow_None=False, bounds=(0, None), constant=False, default=256, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=-1, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nDensity (number of samples per 1.0 length) in the x direction.\nparam Number y (allow_None=False, bounds=None, constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.21, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nY-coordinate location of pattern center.\nparam HookList output_fns (allow_None=False, bounds=(0, None), constant=False, default=[], instantiate=True, pickle_default_value=True, precedence=0.08, readonly=False)\nOptional function(s) to apply to the pattern array after it has been created. Can be used for normalization, thresholding, etc.\nparam List generators (allow_None=False, bounds=(1, None), constant=False, default=[Constant(bounds=BoundingBox(radius=0.5), group=’Pattern’, mask=None, mask_shape=None, name=’Constant01030’, offset=0.0, orientation=0.0, output_fns=[], position=[0.0, 0.0], scale=0.0, size=1.0, x=0.0, xdensity=256, y=0.0, ydensity=256, z=None)], instantiate=True, pickle_default_value=True, precedence=0.97, readonly=False)\nList of patterns to combine or select from. The default pattern is a blank pattern, and thus should be overridden for any useful work.\nparam Number offset (allow_None=False, bounds=None, constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.11, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nAdditive offset to input pattern, defaulting to 0.0\nOptional PatternGenerator used to construct a mask to be applied to the pattern.\nparam Composite position (allow_None=True, attribs=[‘x’, ‘y’], constant=False, default=None, instantiate=False, objtype=<class ‘imagen.patterngenerator.PatternGenerator’>, pickle_default_value=True, precedence=-1, readonly=False)\nCoordinates of location of pattern center. Provides a convenient way to set the x and y parameters together as a tuple (x,y), but shares the same actual storage as x and y (and thus only position OR x and y need to be specified).\nparam Number smoothing (allow_None=False, bounds=(0.0, None), constant=False, default=0.015, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.61, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nWidth of the Gaussian fall-off around the rectangles.\nparam Number ydensity (allow_None=False, bounds=(0, None), constant=False, default=256, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=-1, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nDensity (number of samples per 1.0 length) in the y direction. Typically the same as the xdensity.\nparam Number size (allow_None=False, bounds=(0.01, None), constant=False, default=0.5, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.62, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nOverall diameter of the pattern, if angle=pi.\nanim(duration, offset=0, timestep=1, label=None, unit=None, time_fn=Time(label='Time', name='Time00001', time_type=<type 'int'>, timestep=1.0, unit=None, until=Infinity()))\n\nduration: The temporal duration to animate in the units defined on the global time function.\n\noffset: The temporal offset from which the animation is generated given the supplied pattern\n\ntimestep: The time interval between successive frames. The duration must be an exact multiple of the timestep.\n\nlabel: A label string to override the label of the global time function (if not None).\n\nunit: The unit string to override the unit value of the global time function (if not None).\n\ntime_fn: The global time function object that is shared across the time-varying objects that are being sampled.\n\nNote that the offset, timestep and time_fn only affect patterns parameterized by time-dependent number generators. Otherwise, the frames are generated by successive call to the pattern which may or may not be varying (e.g to view the patterns contained within a Selector).\n\nchannels(use_cached=False, **params_to_override)\n\nChannels() adds a shared interface for single channel and multichannel structures. It will always return an ordered dict: its first element is the single channel of the pattern (if single-channel) or the channel average (if multichannel); the successive elements are the individual channels’ arrays (key: 0,1,..N-1).\n\ndebug(msg, *args, **kw)\n\nPrint msg merged with args as a debugging statement.\n\nSee Python’s logging module for details of message formatting.\n\ndefaults()\n\nReturn {parameter_name:parameter.default} for all non-constant Parameters.\n\nNote that a Parameter for which instantiate==True has its default instantiated.\n\nforce_new_dynamic_value = <functools.partial object at 0x2adfbaf6d4c8>\nget_param_values(onlychanged=False)\n\nReturn a list of name,value pairs for all Parameters of this object.\n\nIf onlychanged is True, will only return values that are not equal to the default value.\n\nget_value_generator = <functools.partial object at 0x2adfbaf6d368>\ninspect_value = <functools.partial object at 0x2adfbaf6d520>\nmessage(msg, *args, **kw)\n\nPrint msg merged with args as a message.\n\nSee Python’s logging module for details of message formatting.\n\nnum_channels()\n\nQuery the number of channels implemented by the PatternGenerator. In case of single-channel generators this will return 1; in case of multichannel, it will return the number of channels (eg, in the case of RGB images it would return ‘3’, Red-Green-Blue, even though the OrderedDict returned by channels() will have 4 elements – the 3 channels + their average).\n\noperator = <ufunc 'maximum'>\nclassmethod params(parameter_name=None)\n\nReturn the Parameters of this class as the dictionary {name: parameter_object}\n\nIncludes Parameters from this class and its superclasses.\n\npprint(imports=None, prefix=' ', unknown_value='<?>', qualify=False, separator='')\n\n(Experimental) Pretty printed representation that may be evaluated with eval. See pprint() function for more details.\n\nclassmethod print_param_defaults()\n\nPrint the default values of all cls’s Parameters.\n\nprint_param_values()\n\nPrint the values of all this object’s Parameters.\n\nscript_repr(imports=, []prefix=' ')\n\nVariant of __repr__ designed for generating a runnable script.\n\nclassmethod set_default(param_name, value)\n\nSet the default value of param_name.\n\nEquivalent to setting param_name on the class.\n\nset_dynamic_time_fn = <functools.partial object at 0x2adfbaf6d5d0>\nset_matrix_dimensions(bounds, xdensity, ydensity)\n\nChange the dimensions of the matrix into which the pattern will be drawn. Users of this class should call this method rather than changing the bounds, xdensity, and ydensity parameters directly. Subclasses can override this method to update any internal data structures that may depend on the matrix dimensions.\n\nset_param = <functools.partial object at 0x2adfbaf6d3c0>\nstate_pop()\n\nPop the state of all generators\n\nstate_push()\n\nPush the state of all generators\n\nverbose(msg, *args, **kw)\n\nPrint msg merged with args as a verbose message.\n\nSee Python’s logging module for details of message formatting.\n\nwarning(msg, *args, **kw)\n\nPrint msg merged with args as a warning, unless module variable warnings_as_exceptions is True, then raise an Exception containing the arguments.\n\nSee Python’s logging module for details of message formatting.\n\nclass imagen.__init__.OrientationContrast(**params)[source]\n\nCircular pattern for testing responses to differences in contrast.\n\nThe pattern contains a sine grating ring surrounding a sine grating disk, each with parameters (orientation, size, scale and offset) that can be changed independently.\n\nparam Number orientationsurround (allow_None=False, bounds=(-6.283185307179586, 6.283185307179586), constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=None, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nOrientation of the surround grating, either absolute or relative to the central grating.\nparam Number orientation (allow_None=False, bounds=None, constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.4, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nPolar angle of pattern, i.e., the orientation in the Cartesian coordinate system, with zero at 3 o’clock and increasing counterclockwise.\nparam Number frequency (allow_None=False, bounds=(0.0, None), constant=False, default=2.4, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.5, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nFrequency of the sine grating.\nparam Number orientationcenter (allow_None=False, bounds=(0.0, 6.283185307179586), constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=None, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nOrientation of the center grating.\nparam Number smoothing (allow_None=False, bounds=(0.0, None), constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=None, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nWidth of the Gaussian fall-off inside and outside the ring.\nparam Number ydensity (allow_None=False, bounds=(0, None), constant=False, default=256, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=-1, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nDensity (number of samples per 1.0 length) in the y direction. Typically the same as the xdensity.\nparam Number scale (allow_None=False, bounds=None, constant=False, default=1.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.1, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nMultiplicative strength of input pattern, defaulting to 1.0\nparam String group (allow_None=False, basestring=<type ‘basestring’>, constant=False, default=Pattern, instantiate=False, pickle_default_value=True, precedence=-1, readonly=False)\nThe group name assigned to the returned HoloViews object.\nparam Number scalesurround (allow_None=False, bounds=(0.0, None), constant=False, default=1.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=None, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nScale of the surround grating.\nparam Number scalecenter (allow_None=False, bounds=(0.0, None), constant=False, default=1.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=None, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nScale of the center grating.\nparam Composite position (allow_None=True, attribs=[‘x’, ‘y’], constant=False, default=None, instantiate=False, objtype=<class ‘imagen.patterngenerator.PatternGenerator’>, pickle_default_value=True, precedence=-1, readonly=False)\nCoordinates of location of pattern center. Provides a convenient way to set the x and y parameters together as a tuple (x,y), but shares the same actual storage as x and y (and thus only position OR x and y need to be specified).\nparam Number offsetsurround (allow_None=False, bounds=(0.0, None), constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=None, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nOffset of the surround grating.\nparam Number thickness (allow_None=False, bounds=(0.0, None), constant=False, default=0.3, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=None, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nThickness (line width) of the ring.\nparam Number xdensity (allow_None=False, bounds=(0, None), constant=False, default=256, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=-1, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nDensity (number of samples per 1.0 length) in the x direction.\nparam Number sizecenter (allow_None=False, bounds=(0.0, None), constant=False, default=0.5, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=None, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nSize of the center grating.\nparam Number size (allow_None=False, bounds=(0.0, None), constant=False, default=0.5, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.3, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nDetermines the overall size of the pattern.\nparam Number sizesurround (allow_None=False, bounds=(0.0, None), constant=False, default=1.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=None, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nSize of the surround grating.\nOptional PatternGenerator used to construct a mask to be applied to the pattern.\nparam Number offset (allow_None=False, bounds=None, constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.11, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nAdditive offset to input pattern, defaulting to 0.0\nparam Number phase (allow_None=False, bounds=(0.0, None), constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.51, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nPhase of the sine grating.\nparam Number aspect_ratio (allow_None=False, bounds=(0.0, None), constant=False, default=1.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=None, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nRatio of width to height; size*aspect_ratio gives the overall width.\nOptional object (expected to be an array) with which to multiply the pattern array after it has been created, before any output_fns are applied. This can be used to shape the pattern.\nBoundingBox of the area in which the pattern is generated.\nparam Number offsetcenter (allow_None=False, bounds=(0.0, None), constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=None, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nOffset of the center grating.\nparam HookList output_fns (allow_None=False, bounds=(0, None), constant=False, default=[], instantiate=True, pickle_default_value=True, precedence=0.08, readonly=False)\nOptional function(s) to apply to the pattern array after it has been created. Can be used for normalization, thresholding, etc.\nparam Number y (allow_None=False, bounds=None, constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.21, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nY-coordinate location of pattern center.\nparam Number x (allow_None=False, bounds=None, constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.2, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nX-coordinate location of pattern center.\nparam ClassSelector z (allow_None=True, constant=False, default=None, instantiate=True, is_instance=True, pickle_default_value=True, precedence=-1, readonly=False)\nThe Dimension object associated with the z-values generated by the PatternGenerator . If None, uses the default set by HoloViews.Image.\nparam Boolean surround_orientation_relative (allow_None=False, bounds=(0, 1), constant=False, default=False, instantiate=False, pickle_default_value=True, precedence=None, readonly=False)\nDetermines whether the surround grating is relative to the central grating.\nanim(duration, offset=0, timestep=1, label=None, unit=None, time_fn=Time(label='Time', name='Time00001', time_type=<type 'int'>, timestep=1.0, unit=None, until=Infinity()))\n\nduration: The temporal duration to animate in the units defined on the global time function.\n\noffset: The temporal offset from which the animation is generated given the supplied pattern\n\ntimestep: The time interval between successive frames. The duration must be an exact multiple of the timestep.\n\nlabel: A label string to override the label of the global time function (if not None).\n\nunit: The unit string to override the unit value of the global time function (if not None).\n\ntime_fn: The global time function object that is shared across the time-varying objects that are being sampled.\n\nNote that the offset, timestep and time_fn only affect patterns parameterized by time-dependent number generators. Otherwise, the frames are generated by successive call to the pattern which may or may not be varying (e.g to view the patterns contained within a Selector).\n\nchannels(use_cached=False, **params_to_override)\n\nChannels() adds a shared interface for single channel and multichannel structures. It will always return an ordered dict: its first element is the single channel of the pattern (if single-channel) or the channel average (if multichannel); the successive elements are the individual channels’ arrays (key: 0,1,..N-1).\n\ndebug(msg, *args, **kw)\n\nPrint msg merged with args as a debugging statement.\n\nSee Python’s logging module for details of message formatting.\n\ndefaults()\n\nReturn {parameter_name:parameter.default} for all non-constant Parameters.\n\nNote that a Parameter for which instantiate==True has its default instantiated.\n\nforce_new_dynamic_value = <functools.partial object at 0x2adfbaf6d0a8>\nfunction(p)\n\nReturn a sine grating pattern (two-dimensional sine wave).\n\nget_param_values(onlychanged=False)\n\nReturn a list of name,value pairs for all Parameters of this object.\n\nIf onlychanged is True, will only return values that are not equal to the default value.\n\nget_value_generator = <functools.partial object at 0x2adfbaf6d1b0>\ninspect_value = <functools.partial object at 0x2adfbaf6d578>\nmessage(msg, *args, **kw)\n\nPrint msg merged with args as a message.\n\nSee Python’s logging module for details of message formatting.\n\nnum_channels()\n\nQuery the number of channels implemented by the PatternGenerator. In case of single-channel generators this will return 1; in case of multichannel, it will return the number of channels (eg, in the case of RGB images it would return ‘3’, Red-Green-Blue, even though the OrderedDict returned by channels() will have 4 elements – the 3 channels + their average).\n\nclassmethod params(parameter_name=None)\n\nReturn the Parameters of this class as the dictionary {name: parameter_object}\n\nIncludes Parameters from this class and its superclasses.\n\npprint(imports=None, prefix=' ', unknown_value='<?>', qualify=False, separator='')\n\n(Experimental) Pretty printed representation that may be evaluated with eval. See pprint() function for more details.\n\nclassmethod print_param_defaults()\n\nPrint the default values of all cls’s Parameters.\n\nprint_param_values()\n\nPrint the values of all this object’s Parameters.\n\nscript_repr(imports=, []prefix=' ')\n\nVariant of __repr__ designed for generating a runnable script.\n\nclassmethod set_default(param_name, value)\n\nSet the default value of param_name.\n\nEquivalent to setting param_name on the class.\n\nset_dynamic_time_fn = <functools.partial object at 0x2adfbaf6d628>\nset_matrix_dimensions(bounds, xdensity, ydensity)\n\nChange the dimensions of the matrix into which the pattern will be drawn. Users of this class should call this method rather than changing the bounds, xdensity, and ydensity parameters directly. Subclasses can override this method to update any internal data structures that may depend on the matrix dimensions.\n\nset_param = <functools.partial object at 0x2adfbaf6d260>\nstate_pop()\n\nRestore the state of the output functions saved by state_push.\n\nstate_push()\n\nSave the state of the output functions, to be restored with state_pop.\n\nverbose(msg, *args, **kw)\n\nPrint msg merged with args as a verbose message.\n\nSee Python’s logging module for details of message formatting.\n\nwarning(msg, *args, **kw)\n\nPrint msg merged with args as a warning, unless module variable warnings_as_exceptions is True, then raise an Exception containing the arguments.\n\nSee Python’s logging module for details of message formatting.\n\nclass imagen.__init__.Spiral(**params)[source]\n\nArchimedean spiral. Successive turnings of the spiral have a constant separation distance.\n\nSpiral is defined by polar equation r=size*angle plotted in Gaussian plane.\n\nparam Number x (allow_None=False, bounds=None, constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.2, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nX-coordinate location of pattern center.\nparam Number scale (allow_None=False, bounds=None, constant=False, default=1.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.1, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nMultiplicative strength of input pattern, defaulting to 1.0\nparam String group (allow_None=False, basestring=<type ‘basestring’>, constant=False, default=Pattern, instantiate=False, pickle_default_value=True, precedence=-1, readonly=False)\nThe group name assigned to the returned HoloViews object.\nparam Number orientation (allow_None=False, bounds=None, constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.4, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nPolar angle of pattern, i.e., the orientation in the Cartesian coordinate system, with zero at 3 o’clock and increasing counterclockwise.\nparam Number aspect_ratio (allow_None=False, bounds=(0.0, None), constant=False, default=1.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.31, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nRatio of width to height.\nparam ClassSelector z (allow_None=True, constant=False, default=None, instantiate=True, is_instance=True, pickle_default_value=True, precedence=-1, readonly=False)\nThe Dimension object associated with the z-values generated by the PatternGenerator . If None, uses the default set by HoloViews.Image.\nOptional object (expected to be an array) with which to multiply the pattern array after it has been created, before any output_fns are applied. This can be used to shape the pattern.\nBoundingBox of the area in which the pattern is generated.\nparam Number thickness (allow_None=False, bounds=(0.0, None), constant=False, default=0.02, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.6, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nThickness (line width) of the spiral.\nparam Number xdensity (allow_None=False, bounds=(0, None), constant=False, default=256, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=-1, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nDensity (number of samples per 1.0 length) in the x direction.\nparam Number y (allow_None=False, bounds=None, constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.21, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nY-coordinate location of pattern center.\nparam HookList output_fns (allow_None=False, bounds=(0, None), constant=False, default=[], instantiate=True, pickle_default_value=True, precedence=0.08, readonly=False)\nOptional function(s) to apply to the pattern array after it has been created. Can be used for normalization, thresholding, etc.\nparam Number turning (allow_None=False, bounds=(0.01, None), constant=False, default=0.05, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.62, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nDensity of turnings; turning*angle gives the actual radius.\nparam Number offset (allow_None=False, bounds=None, constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.11, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nAdditive offset to input pattern, defaulting to 0.0\nOptional PatternGenerator used to construct a mask to be applied to the pattern.\nparam Composite position (allow_None=True, attribs=[‘x’, ‘y’], constant=False, default=None, instantiate=False, objtype=<class ‘imagen.patterngenerator.PatternGenerator’>, pickle_default_value=True, precedence=-1, readonly=False)\nCoordinates of location of pattern center. Provides a convenient way to set the x and y parameters together as a tuple (x,y), but shares the same actual storage as x and y (and thus only position OR x and y need to be specified).\nparam Number smoothing (allow_None=False, bounds=(0.0, None), constant=False, default=0.05, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.61, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nWidth of the Gaussian fall-off inside and outside the spiral.\nparam Number ydensity (allow_None=False, bounds=(0, None), constant=False, default=256, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=-1, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nDensity (number of samples per 1.0 length) in the y direction. Typically the same as the xdensity.\nparam Number size (allow_None=False, bounds=(0.0, None), constant=False, default=1.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.3, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nDetermines the overall size of the pattern.\nanim(duration, offset=0, timestep=1, label=None, unit=None, time_fn=Time(label='Time', name='Time00001', time_type=<type 'int'>, timestep=1.0, unit=None, until=Infinity()))\n\nduration: The temporal duration to animate in the units defined on the global time function.\n\noffset: The temporal offset from which the animation is generated given the supplied pattern\n\ntimestep: The time interval between successive frames. The duration must be an exact multiple of the timestep.\n\nlabel: A label string to override the label of the global time function (if not None).\n\nunit: The unit string to override the unit value of the global time function (if not None).\n\ntime_fn: The global time function object that is shared across the time-varying objects that are being sampled.\n\nNote that the offset, timestep and time_fn only affect patterns parameterized by time-dependent number generators. Otherwise, the frames are generated by successive call to the pattern which may or may not be varying (e.g to view the patterns contained within a Selector).\n\nchannels(use_cached=False, **params_to_override)\n\nChannels() adds a shared interface for single channel and multichannel structures. It will always return an ordered dict: its first element is the single channel of the pattern (if single-channel) or the channel average (if multichannel); the successive elements are the individual channels’ arrays (key: 0,1,..N-1).\n\ndebug(msg, *args, **kw)\n\nPrint msg merged with args as a debugging statement.\n\nSee Python’s logging module for details of message formatting.\n\ndefaults()\n\nReturn {parameter_name:parameter.default} for all non-constant Parameters.\n\nNote that a Parameter for which instantiate==True has its default instantiated.\n\nforce_new_dynamic_value = <functools.partial object at 0x2adfbaf6d158>\nget_param_values(onlychanged=False)\n\nReturn a list of name,value pairs for all Parameters of this object.\n\nIf onlychanged is True, will only return values that are not equal to the default value.\n\nget_value_generator = <functools.partial object at 0x2adfbaf6d5d0>\ninspect_value = <functools.partial object at 0x2adfbaf6d310>\nmessage(msg, *args, **kw)\n\nPrint msg merged with args as a message.\n\nSee Python’s logging module for details of message formatting.\n\nnum_channels()\n\nQuery the number of channels implemented by the PatternGenerator. In case of single-channel generators this will return 1; in case of multichannel, it will return the number of channels (eg, in the case of RGB images it would return ‘3’, Red-Green-Blue, even though the OrderedDict returned by channels() will have 4 elements – the 3 channels + their average).\n\nclassmethod params(parameter_name=None)\n\nReturn the Parameters of this class as the dictionary {name: parameter_object}\n\nIncludes Parameters from this class and its superclasses.\n\npprint(imports=None, prefix=' ', unknown_value='<?>', qualify=False, separator='')\n\n(Experimental) Pretty printed representation that may be evaluated with eval. See pprint() function for more details.\n\nclassmethod print_param_defaults()\n\nPrint the default values of all cls’s Parameters.\n\nprint_param_values()\n\nPrint the values of all this object’s Parameters.\n\nscript_repr(imports=, []prefix=' ')\n\nVariant of __repr__ designed for generating a runnable script.\n\nclassmethod set_default(param_name, value)\n\nSet the default value of param_name.\n\nEquivalent to setting param_name on the class.\n\nset_dynamic_time_fn = <functools.partial object at 0x2adfbaf6d4c8>\nset_matrix_dimensions(bounds, xdensity, ydensity)\n\nChange the dimensions of the matrix into which the pattern will be drawn. Users of this class should call this method rather than changing the bounds, xdensity, and ydensity parameters directly. Subclasses can override this method to update any internal data structures that may depend on the matrix dimensions.\n\nset_param = <functools.partial object at 0x2adfbaf6d470>\nstate_pop()\n\nRestore the state of the output functions saved by state_push.\n\nstate_push()\n\nSave the state of the output functions, to be restored with state_pop.\n\nverbose(msg, *args, **kw)\n\nPrint msg merged with args as a verbose message.\n\nSee Python’s logging module for details of message formatting.\n\nwarning(msg, *args, **kw)\n\nPrint msg merged with args as a warning, unless module variable warnings_as_exceptions is True, then raise an Exception containing the arguments.\n\nSee Python’s logging module for details of message formatting.\n\nclass imagen.__init__.SigmoidedDoLG(**params)[source]\n\nSigmoid multiplicatively combined with a difference of Log Gaussians, such that one part of the plane can be the mirror image of the other, and the peaks of the gaussians are movable.\n\nparam Number positive_size (allow_None=False, bounds=(0.0, None), constant=False, default=0.5, inclusive_bounds=(True, False), instantiate=False, pickle_default_value=True, precedence=None, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nSize of the positive LogGaussian pattern.\nparam Number positive_scale (allow_None=False, bounds=(0.0, None), constant=False, default=1.5, inclusive_bounds=(True, False), instantiate=False, pickle_default_value=True, precedence=None, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nMultiplicative scale for the positive LogGaussian pattern.\nparam Number orientation (allow_None=False, bounds=None, constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.4, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nPolar angle of pattern, i.e., the orientation in the Cartesian coordinate system, with zero at 3 o’clock and increasing counterclockwise.\nparam Number sigmoid_position (allow_None=False, bounds=(None, None), constant=False, default=0.05, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=None, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nX position of the transition between the two regions.\nparam Number negative_scale (allow_None=False, bounds=(0.0, None), constant=False, default=1.0, inclusive_bounds=(True, False), instantiate=False, pickle_default_value=True, precedence=None, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nMultiplicative scale for the negative LogGaussian pattern.\nparam Number ydensity (allow_None=False, bounds=(0, None), constant=False, default=256, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=-1, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nDensity (number of samples per 1.0 length) in the y direction. Typically the same as the xdensity.\nparam Number negative_x_shape (allow_None=False, bounds=(0.0, None), constant=False, default=0.8, inclusive_bounds=(False, False), instantiate=False, pickle_default_value=True, precedence=None, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nThe length of the tail along the x axis for the negative LogGaussian pattern.\nparam Number scale (allow_None=False, bounds=None, constant=False, default=1.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.1, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nMultiplicative strength of input pattern, defaulting to 1.0\nparam String group (allow_None=False, basestring=<type ‘basestring’>, constant=False, default=Pattern, instantiate=False, pickle_default_value=True, precedence=-1, readonly=False)\nThe group name assigned to the returned HoloViews object.\nparam Composite position (allow_None=True, attribs=[‘x’, ‘y’], constant=False, default=None, instantiate=False, objtype=<class ‘imagen.patterngenerator.PatternGenerator’>, pickle_default_value=True, precedence=-1, readonly=False)\nCoordinates of location of pattern center. Provides a convenient way to set the x and y parameters together as a tuple (x,y), but shares the same actual storage as x and y (and thus only position OR x and y need to be specified).\nparam Number negative_y_shape (allow_None=False, bounds=(0.0, None), constant=False, default=0.35, inclusive_bounds=(False, False), instantiate=False, pickle_default_value=True, precedence=None, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nThe length of the tail along the y axis for the negative LogGaussian pattern.\nparam Number positive_aspect_ratio (allow_None=False, bounds=(0.0, None), constant=False, default=0.5, inclusive_bounds=(True, False), instantiate=False, pickle_default_value=True, precedence=None, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nRatio of width to height for the positive LogGaussian pattern.\nparam Number xdensity (allow_None=False, bounds=(0, None), constant=False, default=256, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=-1, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nDensity (number of samples per 1.0 length) in the x direction.\nparam Number negative_aspect_ratio (allow_None=False, bounds=(0.0, None), constant=False, default=0.3, inclusive_bounds=(True, False), instantiate=False, pickle_default_value=True, precedence=None, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nRatio of width to height for the negative LogGaussian pattern.\nparam Number size (allow_None=False, bounds=(0.0, None), constant=False, default=1.5, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.3, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nDetermines the overall size of the pattern.\nparam Number positive_y_shape (allow_None=False, bounds=(0.0, None), constant=False, default=0.35, inclusive_bounds=(False, False), instantiate=False, pickle_default_value=True, precedence=None, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nThe length of the tail along the y axis for the positive LogGaussian pattern.\nparam Number negative_size (allow_None=False, bounds=(0.0, None), constant=False, default=0.8, inclusive_bounds=(True, False), instantiate=False, pickle_default_value=True, precedence=None, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nSize of the negative LogGaussian pattern.\nOptional PatternGenerator used to construct a mask to be applied to the pattern.\nparam Number offset (allow_None=False, bounds=None, constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.11, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nAdditive offset to input pattern, defaulting to 0.0\nparam Number sigmoid_slope (allow_None=False, bounds=(None, None), constant=False, default=50.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=None, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nParameter controlling the smoothness of the transition between the two regions; high values give a sharp transition.\nparam Number positive_x_shape (allow_None=False, bounds=(0.0, None), constant=False, default=0.8, inclusive_bounds=(False, False), instantiate=False, pickle_default_value=True, precedence=None, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nThe length of the tail along the x axis for the positive LogGaussian pattern.\nOptional object (expected to be an array) with which to multiply the pattern array after it has been created, before any output_fns are applied. This can be used to shape the pattern.\nBoundingBox of the area in which the pattern is generated.\nparam HookList output_fns (allow_None=False, bounds=(0, None), constant=False, default=[], instantiate=True, pickle_default_value=True, precedence=0.08, readonly=False)\nOptional function(s) to apply to the pattern array after it has been created. Can be used for normalization, thresholding, etc.\nparam Number y (allow_None=False, bounds=None, constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.21, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nY-coordinate location of pattern center.\nparam Number x (allow_None=False, bounds=None, constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.2, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nX-coordinate location of pattern center.\nparam ClassSelector z (allow_None=True, constant=False, default=None, instantiate=True, is_instance=True, pickle_default_value=True, precedence=-1, readonly=False)\nThe Dimension object associated with the z-values generated by the PatternGenerator . If None, uses the default set by HoloViews.Image.\nanim(duration, offset=0, timestep=1, label=None, unit=None, time_fn=Time(label='Time', name='Time00001', time_type=<type 'int'>, timestep=1.0, unit=None, until=Infinity()))\n\nduration: The temporal duration to animate in the units defined on the global time function.\n\noffset: The temporal offset from which the animation is generated given the supplied pattern\n\ntimestep: The time interval between successive frames. The duration must be an exact multiple of the timestep.\n\nlabel: A label string to override the label of the global time function (if not None).\n\nunit: The unit string to override the unit value of the global time function (if not None).\n\ntime_fn: The global time function object that is shared across the time-varying objects that are being sampled.\n\nNote that the offset, timestep and time_fn only affect patterns parameterized by time-dependent number generators. Otherwise, the frames are generated by successive call to the pattern which may or may not be varying (e.g to view the patterns contained within a Selector).\n\nchannels(use_cached=False, **params_to_override)\n\nChannels() adds a shared interface for single channel and multichannel structures. It will always return an ordered dict: its first element is the single channel of the pattern (if single-channel) or the channel average (if multichannel); the successive elements are the individual channels’ arrays (key: 0,1,..N-1).\n\ndebug(msg, *args, **kw)\n\nPrint msg merged with args as a debugging statement.\n\nSee Python’s logging module for details of message formatting.\n\ndefaults()\n\nReturn {parameter_name:parameter.default} for all non-constant Parameters.\n\nNote that a Parameter for which instantiate==True has its default instantiated.\n\nforce_new_dynamic_value = <functools.partial object at 0x2adfbaf6d628>\nget_param_values(onlychanged=False)\n\nReturn a list of name,value pairs for all Parameters of this object.\n\nIf onlychanged is True, will only return values that are not equal to the default value.\n\nget_value_generator = <functools.partial object at 0x2adfbaf6d470>\ninspect_value = <functools.partial object at 0x2adfbaf6d520>\nmessage(msg, *args, **kw)\n\nPrint msg merged with args as a message.\n\nSee Python’s logging module for details of message formatting.\n\nnum_channels()\n\nQuery the number of channels implemented by the PatternGenerator. In case of single-channel generators this will return 1; in case of multichannel, it will return the number of channels (eg, in the case of RGB images it would return ‘3’, Red-Green-Blue, even though the OrderedDict returned by channels() will have 4 elements – the 3 channels + their average).\n\nclassmethod params(parameter_name=None)\n\nReturn the Parameters of this class as the dictionary {name: parameter_object}\n\nIncludes Parameters from this class and its superclasses.\n\npprint(imports=None, prefix=' ', unknown_value='<?>', qualify=False, separator='')\n\n(Experimental) Pretty printed representation that may be evaluated with eval. See pprint() function for more details.\n\nclassmethod print_param_defaults()\n\nPrint the default values of all cls’s Parameters.\n\nprint_param_values()\n\nPrint the values of all this object’s Parameters.\n\nscript_repr(imports=, []prefix=' ')\n\nVariant of __repr__ designed for generating a runnable script.\n\nclassmethod set_default(param_name, value)\n\nSet the default value of param_name.\n\nEquivalent to setting param_name on the class.\n\nset_dynamic_time_fn = <functools.partial object at 0x2adfbaf6d368>\nset_matrix_dimensions(bounds, xdensity, ydensity)\n\nChange the dimensions of the matrix into which the pattern will be drawn. Users of this class should call this method rather than changing the bounds, xdensity, and ydensity parameters directly. Subclasses can override this method to update any internal data structures that may depend on the matrix dimensions.\n\nset_param = <functools.partial object at 0x2adfbaf6d0a8>\nstate_pop()\n\nRestore the state of the output functions saved by state_push.\n\nstate_push()\n\nSave the state of the output functions, to be restored with state_pop.\n\nverbose(msg, *args, **kw)\n\nPrint msg merged with args as a verbose message.\n\nSee Python’s logging module for details of message formatting.\n\nwarning(msg, *args, **kw)\n\nPrint msg merged with args as a warning, unless module variable warnings_as_exceptions is True, then raise an Exception containing the arguments.\n\nSee Python’s logging module for details of message formatting.\n\nclass imagen.__init__.Spectrogram(**params)[source]\n\nExtends PowerSpectrum to provide a temporal buffer, yielding a 2D representation of a fixed-width spectrogram.\n\nparam Number orientation (allow_None=False, bounds=None, constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=-1, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nPolar angle of pattern, i.e., the orientation in the Cartesian coordinate system, with zero at 3 o’clock and increasing counterclockwise.\nparam Integer min_latency (allow_None=False, bounds=(0, None), constant=False, default=0, inclusive_bounds=(True, False), instantiate=False, pickle_default_value=True, precedence=1, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nSmallest latency (in milliseconds) for which to return amplitudes.\nparam Integer max_frequency (allow_None=False, bounds=(0, None), constant=False, default=9999, inclusive_bounds=(False, False), instantiate=False, pickle_default_value=True, precedence=None, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nLargest frequency for which to return an amplitude.\nparam Number ydensity (allow_None=False, bounds=(0, None), constant=False, default=256, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=-1, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nDensity (number of samples per 1.0 length) in the y direction. Typically the same as the xdensity.\nparam Number scale (allow_None=False, bounds=(0, None), constant=False, default=0.01, inclusive_bounds=(False, False), instantiate=False, pickle_default_value=True, precedence=0.1, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nThe amount by which to scale amplitudes by. This is useful if we want to rescale to say a range [0:1]. Note: Constant scaling is preferable to dynamic scaling so as not to artificially ramp down loud sounds while ramping up hiss and other background interference.\nparam String group (allow_None=False, basestring=<type ‘basestring’>, constant=False, default=Pattern, instantiate=False, pickle_default_value=True, precedence=-1, readonly=False)\nThe group name assigned to the returned HoloViews object.\nparam Composite position (allow_None=True, attribs=[‘x’, ‘y’], constant=False, default=None, instantiate=False, objtype=<class ‘imagen.patterngenerator.PatternGenerator’>, pickle_default_value=True, precedence=-1, readonly=False)\nCoordinates of location of pattern center. Provides a convenient way to set the x and y parameters together as a tuple (x,y), but shares the same actual storage as x and y (and thus only position OR x and y need to be specified).\nparam Number xdensity (allow_None=False, bounds=(0, None), constant=False, default=256, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=-1, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nDensity (number of samples per 1.0 length) in the x direction.\nparam Number size (allow_None=False, bounds=(0.0, None), constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=-1, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nDetermines the overall size of the pattern.\nparam Integer min_frequency (allow_None=False, bounds=(0, None), constant=False, default=0, inclusive_bounds=(True, False), instantiate=False, pickle_default_value=True, precedence=None, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nSmallest frequency for which to return an amplitude.\nparam Parameter windowing_function (allow_None=True, constant=False, default=None, instantiate=False, pickle_default_value=True, precedence=None, readonly=False)\nThis function is multiplied with the current interval, i.e. the most recent portion of the waveform interval of a signal, before performing the Fourier transform. It thus shapes the interval, which is otherwise always rectangular. The function chosen here dictates the tradeoff between resolving comparable signal strengths with similar frequencies, and resolving disparate signal strengths with dissimilar frequencies. numpy provides a number of options, e.g. bartlett, blackman, hamming, hanning, kaiser; see http://docs.scipy.org/doc/numpy/reference/routines.window.html You may also supply your own.\nOptional PatternGenerator used to construct a mask to be applied to the pattern.\nparam Number offset (allow_None=False, bounds=None, constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.11, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nAdditive offset to input pattern, defaulting to 0.0\nparam Integer max_latency (allow_None=False, bounds=(0, None), constant=False, default=500, inclusive_bounds=(False, False), instantiate=False, pickle_default_value=True, precedence=2, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nLargest latency (in milliseconds) for which to return amplitudes.\nparam TimeSeriesParam signal (allow_None=False, constant=False, default=<TimeSeries TimeSeries01037>, instantiate=True, is_instance=True, pickle_default_value=True, precedence=None, readonly=False)\nA TimeSeries object on which to perfom the Fourier Transform.\nOptional object (expected to be an array) with which to multiply the pattern array after it has been created, before any output_fns are applied. This can be used to shape the pattern.\nBoundingBox of the area in which the pattern is generated.\nparam HookList output_fns (allow_None=False, bounds=(0, None), constant=False, default=[], instantiate=True, pickle_default_value=True, precedence=0.08, readonly=False)\nOptional function(s) to apply to the pattern array after it has been created. Can be used for normalization, thresholding, etc.\nparam Number y (allow_None=False, bounds=None, constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=-1, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nY-coordinate location of pattern center.\nparam Number x (allow_None=False, bounds=None, constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=-1, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nX-coordinate location of pattern center.\nparam ClassSelector z (allow_None=True, constant=False, default=None, instantiate=True, is_instance=True, pickle_default_value=True, precedence=-1, readonly=False)\nThe Dimension object associated with the z-values generated by the PatternGenerator . If None, uses the default set by HoloViews.Image.\nanim(duration, offset=0, timestep=1, label=None, unit=None, time_fn=Time(label='Time', name='Time00001', time_type=<type 'int'>, timestep=1.0, unit=None, until=Infinity()))\n\nduration: The temporal duration to animate in the units defined on the global time function.\n\noffset: The temporal offset from which the animation is generated given the supplied pattern\n\ntimestep: The time interval between successive frames. The duration must be an exact multiple of the timestep.\n\nlabel: A label string to override the label of the global time function (if not None).\n\nunit: The unit string to override the unit value of the global time function (if not None).\n\ntime_fn: The global time function object that is shared across the time-varying objects that are being sampled.\n\nNote that the offset, timestep and time_fn only affect patterns parameterized by time-dependent number generators. Otherwise, the frames are generated by successive call to the pattern which may or may not be varying (e.g to view the patterns contained within a Selector).\n\nchannels(use_cached=False, **params_to_override)\n\nChannels() adds a shared interface for single channel and multichannel structures. It will always return an ordered dict: its first element is the single channel of the pattern (if single-channel) or the channel average (if multichannel); the successive elements are the individual channels’ arrays (key: 0,1,..N-1).\n\ndebug(msg, *args, **kw)\n\nPrint msg merged with args as a debugging statement.\n\nSee Python’s logging module for details of message formatting.\n\ndefaults()\n\nReturn {parameter_name:parameter.default} for all non-constant Parameters.\n\nNote that a Parameter for which instantiate==True has its default instantiated.\n\nforce_new_dynamic_value = <functools.partial object at 0x2adfbaf6d158>\nfunction(p)\n\nFunction to draw a pattern that will then be scaled and rotated.\n\nInstead of implementing __call__ directly, PatternGenerator subclasses will typically implement this helper function used by __call__, because that way they can let __call__ handle the scaling and rotation for them. Alternatively, __call__ itself can be reimplemented entirely by a subclass (e.g. if it does not need to do any scaling or rotation), in which case this function will be ignored.\n\nget_param_values(onlychanged=False)\n\nReturn a list of name,value pairs for all Parameters of this object.\n\nIf onlychanged is True, will only return values that are not equal to the default value.\n\nget_value_generator = <functools.partial object at 0x2adfbaf6d208>\ninspect_value = <functools.partial object at 0x2adfbaf6d4c8>\nmessage(msg, *args, **kw)\n\nPrint msg merged with args as a message.\n\nSee Python’s logging module for details of message formatting.\n\nnum_channels()\n\nQuery the number of channels implemented by the PatternGenerator. In case of single-channel generators this will return 1; in case of multichannel, it will return the number of channels (eg, in the case of RGB images it would return ‘3’, Red-Green-Blue, even though the OrderedDict returned by channels() will have 4 elements – the 3 channels + their average).\n\nclassmethod params(parameter_name=None)\n\nReturn the Parameters of this class as the dictionary {name: parameter_object}\n\nIncludes Parameters from this class and its superclasses.\n\npprint(imports=None, prefix=' ', unknown_value='<?>', qualify=False, separator='')\n\n(Experimental) Pretty printed representation that may be evaluated with eval. See pprint() function for more details.\n\nclassmethod print_param_defaults()\n\nPrint the default values of all cls’s Parameters.\n\nprint_param_values()\n\nPrint the values of all this object’s Parameters.\n\nscript_repr(imports=, []prefix=' ')\n\nVariant of __repr__ designed for generating a runnable script.\n\nclassmethod set_default(param_name, value)\n\nSet the default value of param_name.\n\nEquivalent to setting param_name on the class.\n\nset_dynamic_time_fn = <functools.partial object at 0x2adfbaf6d260>\nset_param = <functools.partial object at 0x2adfbaf6d310>\nstate_pop()\n\nRestore the state of the output functions saved by state_push.\n\nstate_push()\n\nSave the state of the output functions, to be restored with state_pop.\n\nverbose(msg, *args, **kw)\n\nPrint msg merged with args as a verbose message.\n\nSee Python’s logging module for details of message formatting.\n\nwarning(msg, *args, **kw)\n\nPrint msg merged with args as a warning, unless module variable warnings_as_exceptions is True, then raise an Exception containing the arguments.\n\nSee Python’s logging module for details of message formatting.\n\nclass imagen.__init__.SpiralGrating(**params)[source]\n\nGrating pattern made from overlaid spirals.\n\nparam Number orientation (allow_None=False, bounds=None, constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.4, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nPolar angle of pattern, i.e., the orientation in the Cartesian coordinate system, with zero at 3 o’clock and increasing counterclockwise.\nparam Parameter operator (allow_None=False, constant=False, default=<ufunc ‘maximum’>, instantiate=False, pickle_default_value=True, precedence=0.98, readonly=False)\nBinary Numpy function used to combine the individual patterns. Any binary Numpy array “ufunc” returning the same type of array as the operands and supporting the reduce operator is allowed here. Supported ufuncs include:: add subtract multiply divide maximum minimum remainder power The most useful ones are probably add and maximum, but there are uses for at least some of the others as well (e.g. to remove pieces of other patterns). You can also write your own operators, by making a class that has a static method named “reduce” that returns an array of the same size and type as the arrays in the list. For example:: class return_first(object): @staticmethod def reduce(x): return x\nparam Number smoothing (allow_None=False, bounds=(0.0, None), constant=False, default=0.05, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.61, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nWidth of the Gaussian fall-off inside and outside the spiral.\nparam Number ydensity (allow_None=False, bounds=(0, None), constant=False, default=256, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=-1, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nDensity (number of samples per 1.0 length) in the y direction. Typically the same as the xdensity.\nparam Number scale (allow_None=False, bounds=None, constant=False, default=1.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.1, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nMultiplicative strength of input pattern, defaulting to 1.0\nparam String group (allow_None=False, basestring=<type ‘basestring’>, constant=False, default=Pattern, instantiate=False, pickle_default_value=True, precedence=-1, readonly=False)\nThe group name assigned to the returned HoloViews object.\nparam Composite position (allow_None=True, attribs=[‘x’, ‘y’], constant=False, default=None, instantiate=False, objtype=<class ‘imagen.patterngenerator.PatternGenerator’>, pickle_default_value=True, precedence=-1, readonly=False)\nCoordinates of location of pattern center. Provides a convenient way to set the x and y parameters together as a tuple (x,y), but shares the same actual storage as x and y (and thus only position OR x and y need to be specified).\nparam Number thickness (allow_None=False, bounds=(0.0, None), constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.6, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nThickness (line width) of the spiral.\nparam Number xdensity (allow_None=False, bounds=(0, None), constant=False, default=256, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=-1, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nDensity (number of samples per 1.0 length) in the x direction.\nparam Integer parts (allow_None=False, bounds=(1, None), constant=False, default=2, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.31, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nNumber of parts in the grating.\nparam List generators (allow_None=False, bounds=(1, None), constant=False, default=[Constant(bounds=BoundingBox(radius=0.5), group=’Pattern’, mask=None, mask_shape=None, name=’Constant01030’, offset=0.0, orientation=0.0, output_fns=[], position=[0.0, 0.0], scale=0.0, size=1.0, x=0.0, xdensity=256, y=0.0, ydensity=256, z=None)], instantiate=True, pickle_default_value=True, precedence=0.97, readonly=False)\nList of patterns to combine or select from. The default pattern is a blank pattern, and thus should be overridden for any useful work.\nparam Number size (allow_None=False, bounds=(0.0, None), constant=False, default=1.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.3, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nScaling factor applied to all sub-patterns.\nparam Number turning (allow_None=False, bounds=(0.01, None), constant=False, default=0.05, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.62, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nDensity of turnings; turning*angle gives the actual radius.\nOptional PatternGenerator used to construct a mask to be applied to the pattern.\nparam Number offset (allow_None=False, bounds=None, constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.11, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nAdditive offset to input pattern, defaulting to 0.0\nOptional object (expected to be an array) with which to multiply the pattern array after it has been created, before any output_fns are applied. This can be used to shape the pattern.\nBoundingBox of the area in which the pattern is generated.\nparam HookList output_fns (allow_None=False, bounds=(0, None), constant=False, default=[], instantiate=True, pickle_default_value=True, precedence=0.08, readonly=False)\nOptional function(s) to apply to the pattern array after it has been created. Can be used for normalization, thresholding, etc.\nparam Number y (allow_None=False, bounds=None, constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.21, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nY-coordinate location of pattern center.\nparam Number x (allow_None=False, bounds=None, constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.2, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nX-coordinate location of pattern center.\nparam ClassSelector z (allow_None=True, constant=False, default=None, instantiate=True, is_instance=True, pickle_default_value=True, precedence=-1, readonly=False)\nThe Dimension object associated with the z-values generated by the PatternGenerator . If None, uses the default set by HoloViews.Image.\nanim(duration, offset=0, timestep=1, label=None, unit=None, time_fn=Time(label='Time', name='Time00001', time_type=<type 'int'>, timestep=1.0, unit=None, until=Infinity()))\n\nduration: The temporal duration to animate in the units defined on the global time function.\n\noffset: The temporal offset from which the animation is generated given the supplied pattern\n\ntimestep: The time interval between successive frames. The duration must be an exact multiple of the timestep.\n\nlabel: A label string to override the label of the global time function (if not None).\n\nunit: The unit string to override the unit value of the global time function (if not None).\n\ntime_fn: The global time function object that is shared across the time-varying objects that are being sampled.\n\nNote that the offset, timestep and time_fn only affect patterns parameterized by time-dependent number generators. Otherwise, the frames are generated by successive call to the pattern which may or may not be varying (e.g to view the patterns contained within a Selector).\n\nchannels(use_cached=False, **params_to_override)\n\nChannels() adds a shared interface for single channel and multichannel structures. It will always return an ordered dict: its first element is the single channel of the pattern (if single-channel) or the channel average (if multichannel); the successive elements are the individual channels’ arrays (key: 0,1,..N-1).\n\ndebug(msg, *args, **kw)\n\nPrint msg merged with args as a debugging statement.\n\nSee Python’s logging module for details of message formatting.\n\ndefaults()\n\nReturn {parameter_name:parameter.default} for all non-constant Parameters.\n\nNote that a Parameter for which instantiate==True has its default instantiated.\n\nforce_new_dynamic_value = <functools.partial object at 0x2adfbaf6d1b0>\nget_param_values(onlychanged=False)\n\nReturn a list of name,value pairs for all Parameters of this object.\n\nIf onlychanged is True, will only return values that are not equal to the default value.\n\nget_value_generator = <functools.partial object at 0x2adfbaf6d2b8>\ninspect_value = <functools.partial object at 0x2adfbaf6d520>\nmessage(msg, *args, **kw)\n\nPrint msg merged with args as a message.\n\nSee Python’s logging module for details of message formatting.\n\nnum_channels()\n\nQuery the number of channels implemented by the PatternGenerator. In case of single-channel generators this will return 1; in case of multichannel, it will return the number of channels (eg, in the case of RGB images it would return ‘3’, Red-Green-Blue, even though the OrderedDict returned by channels() will have 4 elements – the 3 channels + their average).\n\noperator = <ufunc 'maximum'>\nclassmethod params(parameter_name=None)\n\nReturn the Parameters of this class as the dictionary {name: parameter_object}\n\nIncludes Parameters from this class and its superclasses.\n\npprint(imports=None, prefix=' ', unknown_value='<?>', qualify=False, separator='')\n\n(Experimental) Pretty printed representation that may be evaluated with eval. See pprint() function for more details.\n\nclassmethod print_param_defaults()\n\nPrint the default values of all cls’s Parameters.\n\nprint_param_values()\n\nPrint the values of all this object’s Parameters.\n\nscript_repr(imports=, []prefix=' ')\n\nVariant of __repr__ designed for generating a runnable script.\n\nclassmethod set_default(param_name, value)\n\nSet the default value of param_name.\n\nEquivalent to setting param_name on the class.\n\nset_dynamic_time_fn = <functools.partial object at 0x2adfbaf6d628>\nset_matrix_dimensions(bounds, xdensity, ydensity)\n\nChange the dimensions of the matrix into which the pattern will be drawn. Users of this class should call this method rather than changing the bounds, xdensity, and ydensity parameters directly. Subclasses can override this method to update any internal data structures that may depend on the matrix dimensions.\n\nset_param = <functools.partial object at 0x2adfbaf6d470>\nstate_pop()\n\nPop the state of all generators\n\nstate_push()\n\nPush the state of all generators\n\nverbose(msg, *args, **kw)\n\nPrint msg merged with args as a verbose message.\n\nSee Python’s logging module for details of message formatting.\n\nwarning(msg, *args, **kw)\n\nPrint msg merged with args as a warning, unless module variable warnings_as_exceptions is True, then raise an Exception containing the arguments.\n\nSee Python’s logging module for details of message formatting.\n\nclass imagen.__init__.ArcCentered(**params)[source]\n\nBases: imagen.__init__.Arc\n\n2D arc pattern generator (centered at the middle of the arc).\n\nDraws an arc (partial ring) of the specified size (radius*2), with middle at radian 0.0 and starting at arc_length/2 and ending at -arc_length/2. The pattern is centered at the middle of the arc.\n\nSee the Disk class for a note about the Gaussian fall-off.\n\nparam Number x (allow_None=False, bounds=None, constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.2, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nX-coordinate location of pattern center.\nparam Number scale (allow_None=False, bounds=None, constant=False, default=1.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.1, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nMultiplicative strength of input pattern, defaulting to 1.0\nparam String group (allow_None=False, basestring=<type ‘basestring’>, constant=False, default=Pattern, instantiate=False, pickle_default_value=True, precedence=-1, readonly=False)\nThe group name assigned to the returned HoloViews object.\nparam Number orientation (allow_None=False, bounds=None, constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.4, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nPolar angle of pattern, i.e., the orientation in the Cartesian coordinate system, with zero at 3 o’clock and increasing counterclockwise.\nparam Number aspect_ratio (allow_None=False, bounds=(0.0, None), constant=False, default=1.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.31, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nRatio of width to height; size*aspect_ratio gives the overall width.\nparam ClassSelector z (allow_None=True, constant=False, default=None, instantiate=True, is_instance=True, pickle_default_value=True, precedence=-1, readonly=False)\nThe Dimension object associated with the z-values generated by the PatternGenerator . If None, uses the default set by HoloViews.Image.\nOptional object (expected to be an array) with which to multiply the pattern array after it has been created, before any output_fns are applied. This can be used to shape the pattern.\nBoundingBox of the area in which the pattern is generated.\nparam Number thickness (allow_None=False, bounds=(0.0, None), constant=False, default=0.015, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.6, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nThickness (line width) of the ring.\nparam Number smoothing (allow_None=False, bounds=(0.0, None), constant=False, default=0.05, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.61, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nWidth of the Gaussian fall-off inside and outside the ring.\nparam Number xdensity (allow_None=False, bounds=(0, None), constant=False, default=256, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=-1, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nDensity (number of samples per 1.0 length) in the x direction.\nparam Number y (allow_None=False, bounds=None, constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.21, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nY-coordinate location of pattern center.\nparam HookList output_fns (allow_None=False, bounds=(0, None), constant=False, default=[], instantiate=True, pickle_default_value=True, precedence=0.08, readonly=False)\nOptional function(s) to apply to the pattern array after it has been created. Can be used for normalization, thresholding, etc.\nparam Number arc_length (allow_None=False, bounds=(0.0, None), constant=False, default=3.14159265359, inclusive_bounds=(True, False), instantiate=False, pickle_default_value=True, precedence=0.62, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nLength of the arc, in radians, starting from orientation 0.0.\nparam Number offset (allow_None=False, bounds=None, constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.11, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nAdditive offset to input pattern, defaulting to 0.0\nOptional PatternGenerator used to construct a mask to be applied to the pattern.\nparam Composite position (allow_None=True, attribs=[‘x’, ‘y’], constant=False, default=None, instantiate=False, objtype=<class ‘imagen.patterngenerator.PatternGenerator’>, pickle_default_value=True, precedence=-1, readonly=False)\nCoordinates of location of pattern center. Provides a convenient way to set the x and y parameters together as a tuple (x,y), but shares the same actual storage as x and y (and thus only position OR x and y need to be specified).\nparam Number ydensity (allow_None=False, bounds=(0, None), constant=False, default=256, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=-1, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nDensity (number of samples per 1.0 length) in the y direction. Typically the same as the xdensity.\nparam Number size (allow_None=False, bounds=(0.0, None), constant=False, default=0.5, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.3, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nDetermines the overall size of the pattern.\nanim(duration, offset=0, timestep=1, label=None, unit=None, time_fn=Time(label='Time', name='Time00001', time_type=<type 'int'>, timestep=1.0, unit=None, until=Infinity()))\n\nduration: The temporal duration to animate in the units defined on the global time function.\n\noffset: The temporal offset from which the animation is generated given the supplied pattern\n\ntimestep: The time interval between successive frames. The duration must be an exact multiple of the timestep.\n\nlabel: A label string to override the label of the global time function (if not None).\n\nunit: The unit string to override the unit value of the global time function (if not None).\n\ntime_fn: The global time function object that is shared across the time-varying objects that are being sampled.\n\nNote that the offset, timestep and time_fn only affect patterns parameterized by time-dependent number generators. Otherwise, the frames are generated by successive call to the pattern which may or may not be varying (e.g to view the patterns contained within a Selector).\n\nchannels(use_cached=False, **params_to_override)\n\nChannels() adds a shared interface for single channel and multichannel structures. It will always return an ordered dict: its first element is the single channel of the pattern (if single-channel) or the channel average (if multichannel); the successive elements are the individual channels’ arrays (key: 0,1,..N-1).\n\ndebug(msg, *args, **kw)\n\nPrint msg merged with args as a debugging statement.\n\nSee Python’s logging module for details of message formatting.\n\ndefaults()\n\nReturn {parameter_name:parameter.default} for all non-constant Parameters.\n\nNote that a Parameter for which instantiate==True has its default instantiated.\n\nforce_new_dynamic_value = <functools.partial object at 0x2adfbaf6d310>\nget_param_values(onlychanged=False)\n\nReturn a list of name,value pairs for all Parameters of this object.\n\nIf onlychanged is True, will only return values that are not equal to the default value.\n\nget_value_generator = <functools.partial object at 0x2adfbaf6d260>\ninspect_value = <functools.partial object at 0x2adfbaf6d520>\nmessage(msg, *args, **kw)\n\nPrint msg merged with args as a message.\n\nSee Python’s logging module for details of message formatting.\n\nnum_channels()\n\nQuery the number of channels implemented by the PatternGenerator. In case of single-channel generators this will return 1; in case of multichannel, it will return the number of channels (eg, in the case of RGB images it would return ‘3’, Red-Green-Blue, even though the OrderedDict returned by channels() will have 4 elements – the 3 channels + their average).\n\nclassmethod params(parameter_name=None)\n\nReturn the Parameters of this class as the dictionary {name: parameter_object}\n\nIncludes Parameters from this class and its superclasses.\n\npprint(imports=None, prefix=' ', unknown_value='<?>', qualify=False, separator='')\n\n(Experimental) Pretty printed representation that may be evaluated with eval. See pprint() function for more details.\n\nclassmethod print_param_defaults()\n\nPrint the default values of all cls’s Parameters.\n\nprint_param_values()\n\nPrint the values of all this object’s Parameters.\n\nscript_repr(imports=, []prefix=' ')\n\nVariant of __repr__ designed for generating a runnable script.\n\nclassmethod set_default(param_name, value)\n\nSet the default value of param_name.\n\nEquivalent to setting param_name on the class.\n\nset_dynamic_time_fn = <functools.partial object at 0x2adfbaf6d470>\nset_matrix_dimensions(bounds, xdensity, ydensity)\n\nChange the dimensions of the matrix into which the pattern will be drawn. Users of this class should call this method rather than changing the bounds, xdensity, and ydensity parameters directly. Subclasses can override this method to update any internal data structures that may depend on the matrix dimensions.\n\nset_param = <functools.partial object at 0x2adfbaf6d208>\nstate_pop()\n\nRestore the state of the output functions saved by state_push.\n\nstate_push()\n\nSave the state of the output functions, to be restored with state_pop.\n\nverbose(msg, *args, **kw)\n\nPrint msg merged with args as a verbose message.\n\nSee Python’s logging module for details of message formatting.\n\nwarning(msg, *args, **kw)\n\nPrint msg merged with args as a warning, unless module variable warnings_as_exceptions is True, then raise an Exception containing the arguments.\n\nSee Python’s logging module for details of message formatting.\n\nclass imagen.__init__.PatternGenerator(**params)\n\nA class hierarchy for callable objects that can generate 2D patterns.\n\nOnce initialized, PatternGenerators can be called to generate a value or a matrix of values from a 2D function, typically accepting at least x and y.\n\nA PatternGenerator’s Parameters can make use of Parameter’s precedence attribute to specify the order in which they should appear, e.g. in a GUI. The precedence attribute has a nominal range of 0.0 to 1.0, with ordering going from 0.0 (first) to 1.0 (last), but any value is allowed.\n\nThe orientation and layout of the pattern matrices is defined by the SheetCoordinateSystem class, which see.\n\nNote that not every parameter defined for a PatternGenerator will be used by every subclass. For instance, a Constant pattern will ignore the x, y, orientation, and size parameters, because the pattern does not vary with any of those parameters. However, those parameters are still defined for all PatternGenerators, even Constant patterns, to allow PatternGenerators to be scaled, rotated, translated, etc. uniformly.\n\nparam Number x (allow_None=False, bounds=None, constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.2, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nX-coordinate location of pattern center.\nparam Number scale (allow_None=False, bounds=None, constant=False, default=1.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.1, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nMultiplicative strength of input pattern, defaulting to 1.0\nparam String group (allow_None=False, basestring=<type ‘basestring’>, constant=False, default=Pattern, instantiate=False, pickle_default_value=True, precedence=-1, readonly=False)\nThe group name assigned to the returned HoloViews object.\nparam Number orientation (allow_None=False, bounds=None, constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.4, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nPolar angle of pattern, i.e., the orientation in the Cartesian coordinate system, with zero at 3 o’clock and increasing counterclockwise.\nparam ClassSelector z (allow_None=True, constant=False, default=None, instantiate=True, is_instance=True, pickle_default_value=True, precedence=-1, readonly=False)\nThe Dimension object associated with the z-values generated by the PatternGenerator . If None, uses the default set by HoloViews.Image.\nOptional object (expected to be an array) with which to multiply the pattern array after it has been created, before any output_fns are applied. This can be used to shape the pattern.\nBoundingBox of the area in which the pattern is generated.\nparam Number xdensity (allow_None=False, bounds=(0, None), constant=False, default=256, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=-1, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nDensity (number of samples per 1.0 length) in the x direction.\nparam Number y (allow_None=False, bounds=None, constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.21, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nY-coordinate location of pattern center.\nparam HookList output_fns (allow_None=False, bounds=(0, None), constant=False, default=[], instantiate=True, pickle_default_value=True, precedence=0.08, readonly=False)\nOptional function(s) to apply to the pattern array after it has been created. Can be used for normalization, thresholding, etc.\nparam Number offset (allow_None=False, bounds=None, constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.11, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nAdditive offset to input pattern, defaulting to 0.0\nOptional PatternGenerator used to construct a mask to be applied to the pattern.\nparam Composite position (allow_None=True, attribs=[‘x’, ‘y’], constant=False, default=None, instantiate=False, objtype=<class ‘imagen.patterngenerator.PatternGenerator’>, pickle_default_value=True, precedence=-1, readonly=False)\nCoordinates of location of pattern center. Provides a convenient way to set the x and y parameters together as a tuple (x,y), but shares the same actual storage as x and y (and thus only position OR x and y need to be specified).\nparam Number ydensity (allow_None=False, bounds=(0, None), constant=False, default=256, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=-1, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nDensity (number of samples per 1.0 length) in the y direction. Typically the same as the xdensity.\nparam Number size (allow_None=False, bounds=(0.0, None), constant=False, default=1.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.3, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nDetermines the overall size of the pattern.\nanim(duration, offset=0, timestep=1, label=None, unit=None, time_fn=Time(label='Time', name='Time00001', time_type=<type 'int'>, timestep=1.0, unit=None, until=Infinity()))\n\nduration: The temporal duration to animate in the units defined on the global time function.\n\noffset: The temporal offset from which the animation is generated given the supplied pattern\n\ntimestep: The time interval between successive frames. The duration must be an exact multiple of the timestep.\n\nlabel: A label string to override the label of the global time function (if not None).\n\nunit: The unit string to override the unit value of the global time function (if not None).\n\ntime_fn: The global time function object that is shared across the time-varying objects that are being sampled.\n\nNote that the offset, timestep and time_fn only affect patterns parameterized by time-dependent number generators. Otherwise, the frames are generated by successive call to the pattern which may or may not be varying (e.g to view the patterns contained within a Selector).\n\nchannels(use_cached=False, **params_to_override)\n\nChannels() adds a shared interface for single channel and multichannel structures. It will always return an ordered dict: its first element is the single channel of the pattern (if single-channel) or the channel average (if multichannel); the successive elements are the individual channels’ arrays (key: 0,1,..N-1).\n\ndebug(msg, *args, **kw)\n\nPrint msg merged with args as a debugging statement.\n\nSee Python’s logging module for details of message formatting.\n\ndefaults()\n\nReturn {parameter_name:parameter.default} for all non-constant Parameters.\n\nNote that a Parameter for which instantiate==True has its default instantiated.\n\nforce_new_dynamic_value = <functools.partial object at 0x2adfbaf6d520>\nfunction(p)\n\nFunction to draw a pattern that will then be scaled and rotated.\n\nInstead of implementing __call__ directly, PatternGenerator subclasses will typically implement this helper function used by __call__, because that way they can let __call__ handle the scaling and rotation for them. Alternatively, __call__ itself can be reimplemented entirely by a subclass (e.g. if it does not need to do any scaling or rotation), in which case this function will be ignored.\n\nget_param_values(onlychanged=False)\n\nReturn a list of name,value pairs for all Parameters of this object.\n\nIf onlychanged is True, will only return values that are not equal to the default value.\n\nget_value_generator = <functools.partial object at 0x2adfbaf6d0a8>\ninspect_value = <functools.partial object at 0x2adfbaf6d4c8>\nmessage(msg, *args, **kw)\n\nPrint msg merged with args as a message.\n\nSee Python’s logging module for details of message formatting.\n\nnum_channels()\n\nQuery the number of channels implemented by the PatternGenerator. In case of single-channel generators this will return 1; in case of multichannel, it will return the number of channels (eg, in the case of RGB images it would return ‘3’, Red-Green-Blue, even though the OrderedDict returned by channels() will have 4 elements – the 3 channels + their average).\n\nclassmethod params(parameter_name=None)\n\nReturn the Parameters of this class as the dictionary {name: parameter_object}\n\nIncludes Parameters from this class and its superclasses.\n\npprint(imports=None, prefix=' ', unknown_value='<?>', qualify=False, separator='')\n\n(Experimental) Pretty printed representation that may be evaluated with eval. See pprint() function for more details.\n\nclassmethod print_param_defaults()\n\nPrint the default values of all cls’s Parameters.\n\nprint_param_values()\n\nPrint the values of all this object’s Parameters.\n\nscript_repr(imports=, []prefix=' ')\n\nVariant of __repr__ designed for generating a runnable script.\n\nclassmethod set_default(param_name, value)\n\nSet the default value of param_name.\n\nEquivalent to setting param_name on the class.\n\nset_dynamic_time_fn = <functools.partial object at 0x2adfbaf6d628>\nset_matrix_dimensions(bounds, xdensity, ydensity)\n\nChange the dimensions of the matrix into which the pattern will be drawn. Users of this class should call this method rather than changing the bounds, xdensity, and ydensity parameters directly. Subclasses can override this method to update any internal data structures that may depend on the matrix dimensions.\n\nset_param = <functools.partial object at 0x2adfbaf6d208>\nstate_pop()\n\nRestore the state of the output functions saved by state_push.\n\nstate_push()\n\nSave the state of the output functions, to be restored with state_pop.\n\nverbose(msg, *args, **kw)\n\nPrint msg merged with args as a verbose message.\n\nSee Python’s logging module for details of message formatting.\n\nwarning(msg, *args, **kw)\n\nPrint msg merged with args as a warning, unless module variable warnings_as_exceptions is True, then raise an Exception containing the arguments.\n\nSee Python’s logging module for details of message formatting.\n\nclass imagen.__init__.Rectangle(**params)[source]\n\n2D rectangle pattern, with Gaussian smoothing around the edges.\n\nparam Number x (allow_None=False, bounds=None, constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.2, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nX-coordinate location of pattern center.\nparam Number scale (allow_None=False, bounds=None, constant=False, default=1.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.1, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nMultiplicative strength of input pattern, defaulting to 1.0\nparam String group (allow_None=False, basestring=<type ‘basestring’>, constant=False, default=Pattern, instantiate=False, pickle_default_value=True, precedence=-1, readonly=False)\nThe group name assigned to the returned HoloViews object.\nparam Number orientation (allow_None=False, bounds=None, constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.4, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nPolar angle of pattern, i.e., the orientation in the Cartesian coordinate system, with zero at 3 o’clock and increasing counterclockwise.\nparam Number aspect_ratio (allow_None=False, bounds=(0.0, None), constant=False, default=1.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.31, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nRatio of width to height; size*aspect_ratio gives the width of the rectangle.\nparam ClassSelector z (allow_None=True, constant=False, default=None, instantiate=True, is_instance=True, pickle_default_value=True, precedence=-1, readonly=False)\nThe Dimension object associated with the z-values generated by the PatternGenerator . If None, uses the default set by HoloViews.Image.\nOptional object (expected to be an array) with which to multiply the pattern array after it has been created, before any output_fns are applied. This can be used to shape the pattern.\nBoundingBox of the area in which the pattern is generated.\nparam Number smoothing (allow_None=False, bounds=(0.0, None), constant=False, default=0.05, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.61, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nWidth of the Gaussian fall-off outside the rectangle.\nparam Number xdensity (allow_None=False, bounds=(0, None), constant=False, default=256, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=-1, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nDensity (number of samples per 1.0 length) in the x direction.\nparam Number y (allow_None=False, bounds=None, constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.21, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nY-coordinate location of pattern center.\nparam HookList output_fns (allow_None=False, bounds=(0, None), constant=False, default=[], instantiate=True, pickle_default_value=True, precedence=0.08, readonly=False)\nOptional function(s) to apply to the pattern array after it has been created. Can be used for normalization, thresholding, etc.\nparam Number offset (allow_None=False, bounds=None, constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.11, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nAdditive offset to input pattern, defaulting to 0.0\nOptional PatternGenerator used to construct a mask to be applied to the pattern.\nparam Composite position (allow_None=True, attribs=[‘x’, ‘y’], constant=False, default=None, instantiate=False, objtype=<class ‘imagen.patterngenerator.PatternGenerator’>, pickle_default_value=True, precedence=-1, readonly=False)\nCoordinates of location of pattern center. Provides a convenient way to set the x and y parameters together as a tuple (x,y), but shares the same actual storage as x and y (and thus only position OR x and y need to be specified).\nparam Number ydensity (allow_None=False, bounds=(0, None), constant=False, default=256, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=-1, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nDensity (number of samples per 1.0 length) in the y direction. Typically the same as the xdensity.\nparam Number size (allow_None=False, bounds=(0.0, None), constant=False, default=0.5, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.3, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nHeight of the rectangle.\nanim(duration, offset=0, timestep=1, label=None, unit=None, time_fn=Time(label='Time', name='Time00001', time_type=<type 'int'>, timestep=1.0, unit=None, until=Infinity()))\n\nduration: The temporal duration to animate in the units defined on the global time function.\n\noffset: The temporal offset from which the animation is generated given the supplied pattern\n\ntimestep: The time interval between successive frames. The duration must be an exact multiple of the timestep.\n\nlabel: A label string to override the label of the global time function (if not None).\n\nunit: The unit string to override the unit value of the global time function (if not None).\n\ntime_fn: The global time function object that is shared across the time-varying objects that are being sampled.\n\nNote that the offset, timestep and time_fn only affect patterns parameterized by time-dependent number generators. Otherwise, the frames are generated by successive call to the pattern which may or may not be varying (e.g to view the patterns contained within a Selector).\n\nchannels(use_cached=False, **params_to_override)\n\nChannels() adds a shared interface for single channel and multichannel structures. It will always return an ordered dict: its first element is the single channel of the pattern (if single-channel) or the channel average (if multichannel); the successive elements are the individual channels’ arrays (key: 0,1,..N-1).\n\ndebug(msg, *args, **kw)\n\nPrint msg merged with args as a debugging statement.\n\nSee Python’s logging module for details of message formatting.\n\ndefaults()\n\nReturn {parameter_name:parameter.default} for all non-constant Parameters.\n\nNote that a Parameter for which instantiate==True has its default instantiated.\n\nforce_new_dynamic_value = <functools.partial object at 0x2adfbaf6d680>\nget_param_values(onlychanged=False)\n\nReturn a list of name,value pairs for all Parameters of this object.\n\nIf onlychanged is True, will only return values that are not equal to the default value.\n\nget_value_generator = <functools.partial object at 0x2adfbaf6d310>\ninspect_value = <functools.partial object at 0x2adfbaf6d260>\nmessage(msg, *args, **kw)\n\nPrint msg merged with args as a message.\n\nSee Python’s logging module for details of message formatting.\n\nnum_channels()\n\nQuery the number of channels implemented by the PatternGenerator. In case of single-channel generators this will return 1; in case of multichannel, it will return the number of channels (eg, in the case of RGB images it would return ‘3’, Red-Green-Blue, even though the OrderedDict returned by channels() will have 4 elements – the 3 channels + their average).\n\nclassmethod params(parameter_name=None)\n\nReturn the Parameters of this class as the dictionary {name: parameter_object}\n\nIncludes Parameters from this class and its superclasses.\n\npprint(imports=None, prefix=' ', unknown_value='<?>', qualify=False, separator='')\n\n(Experimental) Pretty printed representation that may be evaluated with eval. See pprint() function for more details.\n\nclassmethod print_param_defaults()\n\nPrint the default values of all cls’s Parameters.\n\nprint_param_values()\n\nPrint the values of all this object’s Parameters.\n\nscript_repr(imports=, []prefix=' ')\n\nVariant of __repr__ designed for generating a runnable script.\n\nclassmethod set_default(param_name, value)\n\nSet the default value of param_name.\n\nEquivalent to setting param_name on the class.\n\nset_dynamic_time_fn = <functools.partial object at 0x2adfbaf6d2b8>\nset_matrix_dimensions(bounds, xdensity, ydensity)\n\nChange the dimensions of the matrix into which the pattern will be drawn. Users of this class should call this method rather than changing the bounds, xdensity, and ydensity parameters directly. Subclasses can override this method to update any internal data structures that may depend on the matrix dimensions.\n\nset_param = <functools.partial object at 0x2adfbaf6d6d8>\nstate_pop()\n\nRestore the state of the output functions saved by state_push.\n\nstate_push()\n\nSave the state of the output functions, to be restored with state_pop.\n\nverbose(msg, *args, **kw)\n\nPrint msg merged with args as a verbose message.\n\nSee Python’s logging module for details of message formatting.\n\nwarning(msg, *args, **kw)\n\nPrint msg merged with args as a warning, unless module variable warnings_as_exceptions is True, then raise an Exception containing the arguments.\n\nSee Python’s logging module for details of message formatting.\n\nclass imagen.__init__.Sweeper(**params)[source]\n\nPatternGenerator that sweeps a supplied PatternGenerator in a direction perpendicular to its orientation. Each time step, the supplied PatternGenerator is sweeped further at a fixed speed, and after reset_period time steps a new pattern is drawn.\n\nparam Number step_offset (allow_None=False, bounds=None, constant=False, default=0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=None, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nThe number of steps to offset the sweeper by.\nparam Number orientation (allow_None=False, bounds=None, constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.4, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nPolar angle of pattern, i.e., the orientation in the Cartesian coordinate system, with zero at 3 o’clock and increasing counterclockwise.\nparam Number speed (allow_None=False, bounds=(0.0, None), constant=False, default=0.0833333333333, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=None, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nThe speed with which the pattern should move, in sheet coordinates per time_fn unit.\nparam Number ydensity (allow_None=False, bounds=(0, None), constant=False, default=256, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=-1, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nDensity (number of samples per 1.0 length) in the y direction. Typically the same as the xdensity.\nparam Number scale (allow_None=False, bounds=None, constant=False, default=1.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.1, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nMultiplicative strength of input pattern, defaulting to 1.0\nparam String group (allow_None=False, basestring=<type ‘basestring’>, constant=False, default=Pattern, instantiate=False, pickle_default_value=True, precedence=-1, readonly=False)\nThe group name assigned to the returned HoloViews object.\nparam ClassSelector generator (allow_None=False, constant=False, default=<Gaussian Gaussian01036>, instantiate=True, is_instance=True, pickle_default_value=True, precedence=0.97, readonly=False)\nPattern to sweep.\nparam Composite position (allow_None=True, attribs=[‘x’, ‘y’], constant=False, default=None, instantiate=False, objtype=<class ‘imagen.patterngenerator.PatternGenerator’>, pickle_default_value=True, precedence=-1, readonly=False)\nCoordinates of location of pattern center. Provides a convenient way to set the x and y parameters together as a tuple (x,y), but shares the same actual storage as x and y (and thus only position OR x and y need to be specified).\nparam Number xdensity (allow_None=False, bounds=(0, None), constant=False, default=256, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=-1, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nDensity (number of samples per 1.0 length) in the x direction.\nparam Number size (allow_None=False, bounds=(0.0, None), constant=False, default=1.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.3, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nDetermines the overall size of the pattern.\nparam Number relative_motion_orientation (allow_None=False, bounds=(0, 6.283185307179586), constant=False, default=1.57079632679, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=None, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nThe direction in which the pattern should be moved, relative to the orientation of the supplied generator\nOptional PatternGenerator used to construct a mask to be applied to the pattern.\nparam Number offset (allow_None=False, bounds=None, constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.11, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nAdditive offset to input pattern, defaulting to 0.0\nparam HookList channel_transforms (allow_None=False, bounds=(0, None), constant=False, default=[], instantiate=True, pickle_default_value=True, precedence=None, readonly=False)\nOptional functions to apply post processing to the set of channels.\nOptional object (expected to be an array) with which to multiply the pattern array after it has been created, before any output_fns are applied. This can be used to shape the pattern.\nBoundingBox of the area in which the pattern is generated.\nparam HookList output_fns (allow_None=False, bounds=(0, None), constant=False, default=[], instantiate=True, pickle_default_value=True, precedence=0.08, readonly=False)\nOptional function(s) to apply to the pattern array after it has been created. Can be used for normalization, thresholding, etc.\nparam Callable time_fn (allow_None=False, constant=False, default=<Time Time00001>, instantiate=False, pickle_default_value=True, precedence=None, readonly=False)\nFunction to generate the time used as a base for translation.\nparam Number reset_period (allow_None=False, bounds=(0, None), constant=False, default=4, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=None, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nPeriod between generating each new translation episode.\nparam Number y (allow_None=False, bounds=None, constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.21, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nY-coordinate location of pattern center.\nparam Number x (allow_None=False, bounds=None, constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.2, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nX-coordinate location of pattern center.\nparam ClassSelector z (allow_None=True, constant=False, default=None, instantiate=True, is_instance=True, pickle_default_value=True, precedence=-1, readonly=False)\nThe Dimension object associated with the z-values generated by the PatternGenerator . If None, uses the default set by HoloViews.Image.\nparam Number time_offset (allow_None=False, bounds=None, constant=False, default=0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=None, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nThe time offset from which frames are generated given the supplied pattern.\nanim(duration, offset=0, timestep=1, label=None, unit=None, time_fn=Time(label='Time', name='Time00001', time_type=<type 'int'>, timestep=1.0, unit=None, until=Infinity()))\n\nduration: The temporal duration to animate in the units defined on the global time function.\n\noffset: The temporal offset from which the animation is generated given the supplied pattern\n\ntimestep: The time interval between successive frames. The duration must be an exact multiple of the timestep.\n\nlabel: A label string to override the label of the global time function (if not None).\n\nunit: The unit string to override the unit value of the global time function (if not None).\n\ntime_fn: The global time function object that is shared across the time-varying objects that are being sampled.\n\nNote that the offset, timestep and time_fn only affect patterns parameterized by time-dependent number generators. Otherwise, the frames are generated by successive call to the pattern which may or may not be varying (e.g to view the patterns contained within a Selector).\n\ndebug(msg, *args, **kw)\n\nPrint msg merged with args as a debugging statement.\n\nSee Python’s logging module for details of message formatting.\n\ndefaults()\n\nReturn {parameter_name:parameter.default} for all non-constant Parameters.\n\nNote that a Parameter for which instantiate==True has its default instantiated.\n\nforce_new_dynamic_value = <functools.partial object at 0x2adfbaf6d4c8>\nget_param_values(onlychanged=False)\n\nReturn a list of name,value pairs for all Parameters of this object.\n\nIf onlychanged is True, will only return values that are not equal to the default value.\n\nget_value_generator = <functools.partial object at 0x2adfbaf6d628>\ninspect_value = <functools.partial object at 0x2adfbaf6d470>\nmessage(msg, *args, **kw)\n\nPrint msg merged with args as a message.\n\nSee Python’s logging module for details of message formatting.\n\nclassmethod params(parameter_name=None)\n\nReturn the Parameters of this class as the dictionary {name: parameter_object}\n\nIncludes Parameters from this class and its superclasses.\n\npprint(imports=None, prefix=' ', unknown_value='<?>', qualify=False, separator='')\n\n(Experimental) Pretty printed representation that may be evaluated with eval. See pprint() function for more details.\n\nclassmethod print_param_defaults()\n\nPrint the default values of all cls’s Parameters.\n\nprint_param_values()\n\nPrint the values of all this object’s Parameters.\n\nscript_repr(imports=, []prefix=' ')\n\nVariant of __repr__ designed for generating a runnable script.\n\nclassmethod set_default(param_name, value)\n\nSet the default value of param_name.\n\nEquivalent to setting param_name on the class.\n\nset_dynamic_time_fn = <functools.partial object at 0x2adfbaf6d1b0>\nset_matrix_dimensions(bounds, xdensity, ydensity)\n\nChange the dimensions of the matrix into which the pattern will be drawn. Users of this class should call this method rather than changing the bounds, xdensity, and ydensity parameters directly. Subclasses can override this method to update any internal data structures that may depend on the matrix dimensions.\n\nset_param = <functools.partial object at 0x2adfbaf6d0a8>\nstate_pop()\n\nRestore the state of the output functions saved by state_push.\n\nstate_push()\n\nSave the state of the output functions, to be restored with state_pop.\n\nverbose(msg, *args, **kw)\n\nPrint msg merged with args as a verbose message.\n\nSee Python’s logging module for details of message formatting.\n\nwarning(msg, *args, **kw)\n\nPrint msg merged with args as a warning, unless module variable warnings_as_exceptions is True, then raise an Exception containing the arguments.\n\nSee Python’s logging module for details of message formatting.\n\nclass imagen.__init__.DifferenceOfGaussians(**params)[source]\n\nTwo-dimensional difference of Gaussians pattern.\n\nparam Number positive_size (allow_None=False, bounds=(0.0, None), constant=False, default=0.1, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=1, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nSize of the positive region of the pattern.\nparam Number orientation (allow_None=False, bounds=None, constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.4, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nPolar angle of pattern, i.e., the orientation in the Cartesian coordinate system, with zero at 3 o’clock and increasing counterclockwise.\nparam Number positive_x (allow_None=False, bounds=(None, None), constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=3, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nX position for the central peak of the positive region.\nparam Number positive_y (allow_None=False, bounds=(None, None), constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=4, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nY position for the central peak of the positive region.\nparam Number ydensity (allow_None=False, bounds=(0, None), constant=False, default=256, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=-1, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nDensity (number of samples per 1.0 length) in the y direction. Typically the same as the xdensity.\nparam Number negative_x (allow_None=False, bounds=(None, None), constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=7, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nX position for the central peak of the negative region.\nparam Number scale (allow_None=False, bounds=None, constant=False, default=1.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.1, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nMultiplicative strength of input pattern, defaulting to 1.0\nparam String group (allow_None=False, basestring=<type ‘basestring’>, constant=False, default=Pattern, instantiate=False, pickle_default_value=True, precedence=-1, readonly=False)\nThe group name assigned to the returned HoloViews object.\nparam Composite position (allow_None=True, attribs=[‘x’, ‘y’], constant=False, default=None, instantiate=False, objtype=<class ‘imagen.patterngenerator.PatternGenerator’>, pickle_default_value=True, precedence=-1, readonly=False)\nCoordinates of location of pattern center. Provides a convenient way to set the x and y parameters together as a tuple (x,y), but shares the same actual storage as x and y (and thus only position OR x and y need to be specified).\nparam Number xdensity (allow_None=False, bounds=(0, None), constant=False, default=256, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=-1, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nDensity (number of samples per 1.0 length) in the x direction.\nparam Number negative_aspect_ratio (allow_None=False, bounds=(0.0, None), constant=False, default=1.5, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=6, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nRatio of width to height for the negative region of the pattern.\nparam Number size (allow_None=False, bounds=(0.0, None), constant=False, default=1.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.3, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nDetermines the overall size of the pattern.\nparam Number negative_size (allow_None=False, bounds=(0.0, None), constant=False, default=0.3, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=5, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nSize of the negative region of the pattern.\nOptional PatternGenerator used to construct a mask to be applied to the pattern.\nparam Number negative_y (allow_None=False, bounds=(None, None), constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=8, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nY position for the central peak of the negative region.\nparam Number offset (allow_None=False, bounds=None, constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.11, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nAdditive offset to input pattern, defaulting to 0.0\nparam Number positive_aspect_ratio (allow_None=False, bounds=(0.0, None), constant=False, default=1.5, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=2, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nRatio of width to height for the positive region of the pattern.\nOptional object (expected to be an array) with which to multiply the pattern array after it has been created, before any output_fns are applied. This can be used to shape the pattern.\nBoundingBox of the area in which the pattern is generated.\nparam HookList output_fns (allow_None=False, bounds=(0, None), constant=False, default=[], instantiate=True, pickle_default_value=True, precedence=0.08, readonly=False)\nOptional function(s) to apply to the pattern array after it has been created. Can be used for normalization, thresholding, etc.\nparam Number y (allow_None=False, bounds=None, constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.21, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nY-coordinate location of pattern center.\nparam Number x (allow_None=False, bounds=None, constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.2, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nX-coordinate location of pattern center.\nparam ClassSelector z (allow_None=True, constant=False, default=None, instantiate=True, is_instance=True, pickle_default_value=True, precedence=-1, readonly=False)\nThe Dimension object associated with the z-values generated by the PatternGenerator . If None, uses the default set by HoloViews.Image.\nanim(duration, offset=0, timestep=1, label=None, unit=None, time_fn=Time(label='Time', name='Time00001', time_type=<type 'int'>, timestep=1.0, unit=None, until=Infinity()))\n\nduration: The temporal duration to animate in the units defined on the global time function.\n\noffset: The temporal offset from which the animation is generated given the supplied pattern\n\ntimestep: The time interval between successive frames. The duration must be an exact multiple of the timestep.\n\nlabel: A label string to override the label of the global time function (if not None).\n\nunit: The unit string to override the unit value of the global time function (if not None).\n\ntime_fn: The global time function object that is shared across the time-varying objects that are being sampled.\n\nNote that the offset, timestep and time_fn only affect patterns parameterized by time-dependent number generators. Otherwise, the frames are generated by successive call to the pattern which may or may not be varying (e.g to view the patterns contained within a Selector).\n\nchannels(use_cached=False, **params_to_override)\n\nChannels() adds a shared interface for single channel and multichannel structures. It will always return an ordered dict: its first element is the single channel of the pattern (if single-channel) or the channel average (if multichannel); the successive elements are the individual channels’ arrays (key: 0,1,..N-1).\n\ndebug(msg, *args, **kw)\n\nPrint msg merged with args as a debugging statement.\n\nSee Python’s logging module for details of message formatting.\n\ndefaults()\n\nReturn {parameter_name:parameter.default} for all non-constant Parameters.\n\nNote that a Parameter for which instantiate==True has its default instantiated.\n\nforce_new_dynamic_value = <functools.partial object at 0x2adfbaf6d310>\nget_param_values(onlychanged=False)\n\nReturn a list of name,value pairs for all Parameters of this object.\n\nIf onlychanged is True, will only return values that are not equal to the default value.\n\nget_value_generator = <functools.partial object at 0x2adfbaf6d2b8>\ninspect_value = <functools.partial object at 0x2adfbaf6d5d0>\nmessage(msg, *args, **kw)\n\nPrint msg merged with args as a message.\n\nSee Python’s logging module for details of message formatting.\n\nnum_channels()\n\nQuery the number of channels implemented by the PatternGenerator. In case of single-channel generators this will return 1; in case of multichannel, it will return the number of channels (eg, in the case of RGB images it would return ‘3’, Red-Green-Blue, even though the OrderedDict returned by channels() will have 4 elements – the 3 channels + their average).\n\nclassmethod params(parameter_name=None)\n\nReturn the Parameters of this class as the dictionary {name: parameter_object}\n\nIncludes Parameters from this class and its superclasses.\n\npprint(imports=None, prefix=' ', unknown_value='<?>', qualify=False, separator='')\n\n(Experimental) Pretty printed representation that may be evaluated with eval. See pprint() function for more details.\n\nclassmethod print_param_defaults()\n\nPrint the default values of all cls’s Parameters.\n\nprint_param_values()\n\nPrint the values of all this object’s Parameters.\n\nscript_repr(imports=, []prefix=' ')\n\nVariant of __repr__ designed for generating a runnable script.\n\nclassmethod set_default(param_name, value)\n\nSet the default value of param_name.\n\nEquivalent to setting param_name on the class.\n\nset_dynamic_time_fn = <functools.partial object at 0x2adfbaf6daa0>\nset_matrix_dimensions(bounds, xdensity, ydensity)\n\nChange the dimensions of the matrix into which the pattern will be drawn. Users of this class should call this method rather than changing the bounds, xdensity, and ydensity parameters directly. Subclasses can override this method to update any internal data structures that may depend on the matrix dimensions.\n\nset_param = <functools.partial object at 0x2adfbaf6dc00>\nstate_pop()\n\nRestore the state of the output functions saved by state_push.\n\nstate_push()\n\nSave the state of the output functions, to be restored with state_pop.\n\nverbose(msg, *args, **kw)\n\nPrint msg merged with args as a verbose message.\n\nSee Python’s logging module for details of message formatting.\n\nwarning(msg, *args, **kw)\n\nPrint msg merged with args as a warning, unless module variable warnings_as_exceptions is True, then raise an Exception containing the arguments.\n\nSee Python’s logging module for details of message formatting.\n\nclass imagen.__init__.Composite(**params)\n\nPatternGenerator that accepts a list of other PatternGenerators. To create a new pattern, asks each of the PatternGenerators in the list to create a pattern, then it combines the patterns to create a single pattern that it returns.\n\nparam Number x (allow_None=False, bounds=None, constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.2, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nX-coordinate location of pattern center.\nparam Number scale (allow_None=False, bounds=None, constant=False, default=1.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.1, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nMultiplicative strength of input pattern, defaulting to 1.0\nparam String group (allow_None=False, basestring=<type ‘basestring’>, constant=False, default=Pattern, instantiate=False, pickle_default_value=True, precedence=-1, readonly=False)\nThe group name assigned to the returned HoloViews object.\nparam Number orientation (allow_None=False, bounds=None, constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.4, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nPolar angle of pattern, i.e., the orientation in the Cartesian coordinate system, with zero at 3 o’clock and increasing counterclockwise.\nparam ClassSelector z (allow_None=True, constant=False, default=None, instantiate=True, is_instance=True, pickle_default_value=True, precedence=-1, readonly=False)\nThe Dimension object associated with the z-values generated by the PatternGenerator . If None, uses the default set by HoloViews.Image.\nOptional object (expected to be an array) with which to multiply the pattern array after it has been created, before any output_fns are applied. This can be used to shape the pattern.\nBoundingBox of the area in which the pattern is generated.\nparam Parameter operator (allow_None=False, constant=False, default=<ufunc ‘maximum’>, instantiate=False, pickle_default_value=True, precedence=0.98, readonly=False)\nBinary Numpy function used to combine the individual patterns. Any binary Numpy array “ufunc” returning the same type of array as the operands and supporting the reduce operator is allowed here. Supported ufuncs include:: add subtract multiply divide maximum minimum remainder power The most useful ones are probably add and maximum, but there are uses for at least some of the others as well (e.g. to remove pieces of other patterns). You can also write your own operators, by making a class that has a static method named “reduce” that returns an array of the same size and type as the arrays in the list. For example:: class return_first(object): @staticmethod def reduce(x): return x\nparam Number xdensity (allow_None=False, bounds=(0, None), constant=False, default=256, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=-1, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nDensity (number of samples per 1.0 length) in the x direction.\nparam Number y (allow_None=False, bounds=None, constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.21, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nY-coordinate location of pattern center.\nparam HookList output_fns (allow_None=False, bounds=(0, None), constant=False, default=[], instantiate=True, pickle_default_value=True, precedence=0.08, readonly=False)\nOptional function(s) to apply to the pattern array after it has been created. Can be used for normalization, thresholding, etc.\nparam List generators (allow_None=False, bounds=(1, None), constant=False, default=[Constant(bounds=BoundingBox(radius=0.5), group=’Pattern’, mask=None, mask_shape=None, name=’Constant01030’, offset=0.0, orientation=0.0, output_fns=[], position=[0.0, 0.0], scale=0.0, size=1.0, x=0.0, xdensity=256, y=0.0, ydensity=256, z=None)], instantiate=True, pickle_default_value=True, precedence=0.97, readonly=False)\nList of patterns to combine or select from. The default pattern is a blank pattern, and thus should be overridden for any useful work.\nparam Number offset (allow_None=False, bounds=None, constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.11, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nAdditive offset to input pattern, defaulting to 0.0\nOptional PatternGenerator used to construct a mask to be applied to the pattern.\nparam Composite position (allow_None=True, attribs=[‘x’, ‘y’], constant=False, default=None, instantiate=False, objtype=<class ‘imagen.patterngenerator.PatternGenerator’>, pickle_default_value=True, precedence=-1, readonly=False)\nCoordinates of location of pattern center. Provides a convenient way to set the x and y parameters together as a tuple (x,y), but shares the same actual storage as x and y (and thus only position OR x and y need to be specified).\nparam Number ydensity (allow_None=False, bounds=(0, None), constant=False, default=256, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=-1, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nDensity (number of samples per 1.0 length) in the y direction. Typically the same as the xdensity.\nparam Number size (allow_None=False, bounds=(0.0, None), constant=False, default=1.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.3, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nScaling factor applied to all sub-patterns.\nanim(duration, offset=0, timestep=1, label=None, unit=None, time_fn=Time(label='Time', name='Time00001', time_type=<type 'int'>, timestep=1.0, unit=None, until=Infinity()))\n\nduration: The temporal duration to animate in the units defined on the global time function.\n\noffset: The temporal offset from which the animation is generated given the supplied pattern\n\ntimestep: The time interval between successive frames. The duration must be an exact multiple of the timestep.\n\nlabel: A label string to override the label of the global time function (if not None).\n\nunit: The unit string to override the unit value of the global time function (if not None).\n\ntime_fn: The global time function object that is shared across the time-varying objects that are being sampled.\n\nNote that the offset, timestep and time_fn only affect patterns parameterized by time-dependent number generators. Otherwise, the frames are generated by successive call to the pattern which may or may not be varying (e.g to view the patterns contained within a Selector).\n\nchannels(use_cached=False, **params_to_override)\n\nChannels() adds a shared interface for single channel and multichannel structures. It will always return an ordered dict: its first element is the single channel of the pattern (if single-channel) or the channel average (if multichannel); the successive elements are the individual channels’ arrays (key: 0,1,..N-1).\n\ndebug(msg, *args, **kw)\n\nPrint msg merged with args as a debugging statement.\n\nSee Python’s logging module for details of message formatting.\n\ndefaults()\n\nReturn {parameter_name:parameter.default} for all non-constant Parameters.\n\nNote that a Parameter for which instantiate==True has its default instantiated.\n\nforce_new_dynamic_value = <functools.partial object at 0x2adfbaf6d260>\nfunction(p)\n\nConstructs combined pattern out of the individual ones.\n\nget_param_values(onlychanged=False)\n\nReturn a list of name,value pairs for all Parameters of this object.\n\nIf onlychanged is True, will only return values that are not equal to the default value.\n\nget_value_generator = <functools.partial object at 0x2adfbaf6d100>\ninspect_value = <functools.partial object at 0x2adfbaf6d5d0>\nmessage(msg, *args, **kw)\n\nPrint msg merged with args as a message.\n\nSee Python’s logging module for details of message formatting.\n\nnum_channels()\n\nQuery the number of channels implemented by the PatternGenerator. In case of single-channel generators this will return 1; in case of multichannel, it will return the number of channels (eg, in the case of RGB images it would return ‘3’, Red-Green-Blue, even though the OrderedDict returned by channels() will have 4 elements – the 3 channels + their average).\n\noperator = <ufunc 'maximum'>\nclassmethod params(parameter_name=None)\n\nReturn the Parameters of this class as the dictionary {name: parameter_object}\n\nIncludes Parameters from this class and its superclasses.\n\npprint(imports=None, prefix=' ', unknown_value='<?>', qualify=False, separator='')\n\n(Experimental) Pretty printed representation that may be evaluated with eval. See pprint() function for more details.\n\nclassmethod print_param_defaults()\n\nPrint the default values of all cls’s Parameters.\n\nprint_param_values()\n\nPrint the values of all this object’s Parameters.\n\nscript_repr(imports=, []prefix=' ')\n\nVariant of __repr__ designed for generating a runnable script.\n\nclassmethod set_default(param_name, value)\n\nSet the default value of param_name.\n\nEquivalent to setting param_name on the class.\n\nset_dynamic_time_fn = <functools.partial object at 0x2adfbaf6d310>\nset_matrix_dimensions(bounds, xdensity, ydensity)\n\nChange the dimensions of the matrix into which the pattern will be drawn. Users of this class should call this method rather than changing the bounds, xdensity, and ydensity parameters directly. Subclasses can override this method to update any internal data structures that may depend on the matrix dimensions.\n\nset_param = <functools.partial object at 0x2adfbaf6d578>\nstate_pop()\n\nPop the state of all generators\n\nstate_push()\n\nPush the state of all generators\n\nverbose(msg, *args, **kw)\n\nPrint msg merged with args as a verbose message.\n\nSee Python’s logging module for details of message formatting.\n\nwarning(msg, *args, **kw)\n\nPrint msg merged with args as a warning, unless module variable warnings_as_exceptions is True, then raise an Exception containing the arguments.\n\nSee Python’s logging module for details of message formatting.\n\nclass imagen.__init__.Asterisk(**params)[source]\n\nAsterisk-like object composed of radial rectangular lines. Also makes crosses and tripods.\n\nparam Number x (allow_None=False, bounds=None, constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.2, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nX-coordinate location of pattern center.\nparam Integer parts (allow_None=False, bounds=(1, None), constant=False, default=3, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.31, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nNumber of parts in the asterisk.\nparam Number scale (allow_None=False, bounds=None, constant=False, default=1.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.1, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nMultiplicative strength of input pattern, defaulting to 1.0\nparam String group (allow_None=False, basestring=<type ‘basestring’>, constant=False, default=Pattern, instantiate=False, pickle_default_value=True, precedence=-1, readonly=False)\nThe group name assigned to the returned HoloViews object.\nparam Number orientation (allow_None=False, bounds=None, constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.4, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nPolar angle of pattern, i.e., the orientation in the Cartesian coordinate system, with zero at 3 o’clock and increasing counterclockwise.\nparam ClassSelector z (allow_None=True, constant=False, default=None, instantiate=True, is_instance=True, pickle_default_value=True, precedence=-1, readonly=False)\nThe Dimension object associated with the z-values generated by the PatternGenerator . If None, uses the default set by HoloViews.Image.\nOptional object (expected to be an array) with which to multiply the pattern array after it has been created, before any output_fns are applied. This can be used to shape the pattern.\nBoundingBox of the area in which the pattern is generated.\nparam Parameter operator (allow_None=False, constant=False, default=<ufunc ‘maximum’>, instantiate=False, pickle_default_value=True, precedence=0.98, readonly=False)\nBinary Numpy function used to combine the individual patterns. Any binary Numpy array “ufunc” returning the same type of array as the operands and supporting the reduce operator is allowed here. Supported ufuncs include:: add subtract multiply divide maximum minimum remainder power The most useful ones are probably add and maximum, but there are uses for at least some of the others as well (e.g. to remove pieces of other patterns). You can also write your own operators, by making a class that has a static method named “reduce” that returns an array of the same size and type as the arrays in the list. For example:: class return_first(object): @staticmethod def reduce(x): return x\nparam Number thickness (allow_None=False, bounds=(0.0, None), constant=False, default=0.05, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.6, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nThickness of the rectangle.\nparam Number xdensity (allow_None=False, bounds=(0, None), constant=False, default=256, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=-1, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nDensity (number of samples per 1.0 length) in the x direction.\nparam Number y (allow_None=False, bounds=None, constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.21, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nY-coordinate location of pattern center.\nparam HookList output_fns (allow_None=False, bounds=(0, None), constant=False, default=[], instantiate=True, pickle_default_value=True, precedence=0.08, readonly=False)\nOptional function(s) to apply to the pattern array after it has been created. Can be used for normalization, thresholding, etc.\nparam List generators (allow_None=False, bounds=(1, None), constant=False, default=[Constant(bounds=BoundingBox(radius=0.5), group=’Pattern’, mask=None, mask_shape=None, name=’Constant01030’, offset=0.0, orientation=0.0, output_fns=[], position=[0.0, 0.0], scale=0.0, size=1.0, x=0.0, xdensity=256, y=0.0, ydensity=256, z=None)], instantiate=True, pickle_default_value=True, precedence=0.97, readonly=False)\nList of patterns to combine or select from. The default pattern is a blank pattern, and thus should be overridden for any useful work.\nparam Number offset (allow_None=False, bounds=None, constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.11, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nAdditive offset to input pattern, defaulting to 0.0\nOptional PatternGenerator used to construct a mask to be applied to the pattern.\nparam Composite position (allow_None=True, attribs=[‘x’, ‘y’], constant=False, default=None, instantiate=False, objtype=<class ‘imagen.patterngenerator.PatternGenerator’>, pickle_default_value=True, precedence=-1, readonly=False)\nCoordinates of location of pattern center. Provides a convenient way to set the x and y parameters together as a tuple (x,y), but shares the same actual storage as x and y (and thus only position OR x and y need to be specified).\nparam Number smoothing (allow_None=False, bounds=(0.0, None), constant=False, default=0.015, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.61, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nWidth of the Gaussian fall-off around the rectangles.\nparam Number ydensity (allow_None=False, bounds=(0, None), constant=False, default=256, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=-1, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nDensity (number of samples per 1.0 length) in the y direction. Typically the same as the xdensity.\nparam Number size (allow_None=False, bounds=(0.01, None), constant=False, default=0.5, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.62, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nOverall diameter of the pattern.\nanim(duration, offset=0, timestep=1, label=None, unit=None, time_fn=Time(label='Time', name='Time00001', time_type=<type 'int'>, timestep=1.0, unit=None, until=Infinity()))\n\nduration: The temporal duration to animate in the units defined on the global time function.\n\noffset: The temporal offset from which the animation is generated given the supplied pattern\n\ntimestep: The time interval between successive frames. The duration must be an exact multiple of the timestep.\n\nlabel: A label string to override the label of the global time function (if not None).\n\nunit: The unit string to override the unit value of the global time function (if not None).\n\ntime_fn: The global time function object that is shared across the time-varying objects that are being sampled.\n\nNote that the offset, timestep and time_fn only affect patterns parameterized by time-dependent number generators. Otherwise, the frames are generated by successive call to the pattern which may or may not be varying (e.g to view the patterns contained within a Selector).\n\nchannels(use_cached=False, **params_to_override)\n\nChannels() adds a shared interface for single channel and multichannel structures. It will always return an ordered dict: its first element is the single channel of the pattern (if single-channel) or the channel average (if multichannel); the successive elements are the individual channels’ arrays (key: 0,1,..N-1).\n\ndebug(msg, *args, **kw)\n\nPrint msg merged with args as a debugging statement.\n\nSee Python’s logging module for details of message formatting.\n\ndefaults()\n\nReturn {parameter_name:parameter.default} for all non-constant Parameters.\n\nNote that a Parameter for which instantiate==True has its default instantiated.\n\nforce_new_dynamic_value = <functools.partial object at 0x2adfbaf6d680>\nget_param_values(onlychanged=False)\n\nReturn a list of name,value pairs for all Parameters of this object.\n\nIf onlychanged is True, will only return values that are not equal to the default value.\n\nget_value_generator = <functools.partial object at 0x2adfbaf6d3c0>\ninspect_value = <functools.partial object at 0x2adfbaf6d890>\nmessage(msg, *args, **kw)\n\nPrint msg merged with args as a message.\n\nSee Python’s logging module for details of message formatting.\n\nnum_channels()\n\nQuery the number of channels implemented by the PatternGenerator. In case of single-channel generators this will return 1; in case of multichannel, it will return the number of channels (eg, in the case of RGB images it would return ‘3’, Red-Green-Blue, even though the OrderedDict returned by channels() will have 4 elements – the 3 channels + their average).\n\noperator = <ufunc 'maximum'>\nclassmethod params(parameter_name=None)\n\nReturn the Parameters of this class as the dictionary {name: parameter_object}\n\nIncludes Parameters from this class and its superclasses.\n\npprint(imports=None, prefix=' ', unknown_value='<?>', qualify=False, separator='')\n\n(Experimental) Pretty printed representation that may be evaluated with eval. See pprint() function for more details.\n\nclassmethod print_param_defaults()\n\nPrint the default values of all cls’s Parameters.\n\nprint_param_values()\n\nPrint the values of all this object’s Parameters.\n\nscript_repr(imports=, []prefix=' ')\n\nVariant of __repr__ designed for generating a runnable script.\n\nclassmethod set_default(param_name, value)\n\nSet the default value of param_name.\n\nEquivalent to setting param_name on the class.\n\nset_dynamic_time_fn = <functools.partial object at 0x2adfbaf6d520>\nset_matrix_dimensions(bounds, xdensity, ydensity)\n\nChange the dimensions of the matrix into which the pattern will be drawn. Users of this class should call this method rather than changing the bounds, xdensity, and ydensity parameters directly. Subclasses can override this method to update any internal data structures that may depend on the matrix dimensions.\n\nset_param = <functools.partial object at 0x2adfbaf6d578>\nstate_pop()\n\nPop the state of all generators\n\nstate_push()\n\nPush the state of all generators\n\nverbose(msg, *args, **kw)\n\nPrint msg merged with args as a verbose message.\n\nSee Python’s logging module for details of message formatting.\n\nwarning(msg, *args, **kw)\n\nPrint msg merged with args as a warning, unless module variable warnings_as_exceptions is True, then raise an Exception containing the arguments.\n\nSee Python’s logging module for details of message formatting.\n\nclass imagen.__init__.Selector(**params)[source]\n\nPatternGenerator that selects from a list of other PatternGenerators.\n\nparam Number x (allow_None=False, bounds=None, constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.2, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nX-coordinate location of pattern center.\nparam Number scale (allow_None=False, bounds=None, constant=False, default=1.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.1, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nMultiplicative strength of input pattern, defaulting to 1.0\nparam String group (allow_None=False, basestring=<type ‘basestring’>, constant=False, default=Pattern, instantiate=False, pickle_default_value=True, precedence=-1, readonly=False)\nThe group name assigned to the returned HoloViews object.\nparam Number index (allow_None=False, bounds=(-1.0, 1.0), constant=False, default=<UniformRandom UniformRandom01035>, inclusive_bounds=(True, True), instantiate=True, pickle_default_value=True, precedence=0.2, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nIndex into the list of pattern generators, on a scale from 0 (start of the list) to 1.0 (end of the list). Typically a random value or other number generator, to allow a different item to be selected each time.\nparam Number orientation (allow_None=False, bounds=None, constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.4, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nPolar angle of pattern, i.e., the orientation in the Cartesian coordinate system, with zero at 3 o’clock and increasing counterclockwise.\nparam ClassSelector z (allow_None=True, constant=False, default=None, instantiate=True, is_instance=True, pickle_default_value=True, precedence=-1, readonly=False)\nThe Dimension object associated with the z-values generated by the PatternGenerator . If None, uses the default set by HoloViews.Image.\nOptional object (expected to be an array) with which to multiply the pattern array after it has been created, before any output_fns are applied. This can be used to shape the pattern.\nBoundingBox of the area in which the pattern is generated.\nparam Number xdensity (allow_None=False, bounds=(0, None), constant=False, default=256, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=-1, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nDensity (number of samples per 1.0 length) in the x direction.\nparam Number y (allow_None=False, bounds=None, constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.21, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nY-coordinate location of pattern center.\nparam HookList output_fns (allow_None=False, bounds=(0, None), constant=False, default=[], instantiate=True, pickle_default_value=True, precedence=0.08, readonly=False)\nOptional function(s) to apply to the pattern array after it has been created. Can be used for normalization, thresholding, etc.\nparam List generators (allow_None=False, bounds=(1, None), constant=False, default=[Constant(bounds=BoundingBox(radius=0.5), group=’Pattern’, mask=None, mask_shape=None, name=’Constant01030’, offset=0.0, orientation=0.0, output_fns=[], position=[0.0, 0.0], scale=0.0, size=1.0, x=0.0, xdensity=256, y=0.0, ydensity=256, z=None)], instantiate=True, pickle_default_value=True, precedence=0.97, readonly=False)\nList of patterns to combine or select from. The default pattern is a blank pattern, and thus should be overridden for any useful work.\nparam Number offset (allow_None=False, bounds=None, constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.11, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nAdditive offset to input pattern, defaulting to 0.0\nOptional PatternGenerator used to construct a mask to be applied to the pattern.\nparam Composite position (allow_None=True, attribs=[‘x’, ‘y’], constant=False, default=None, instantiate=False, objtype=<class ‘imagen.patterngenerator.PatternGenerator’>, pickle_default_value=True, precedence=-1, readonly=False)\nCoordinates of location of pattern center. Provides a convenient way to set the x and y parameters together as a tuple (x,y), but shares the same actual storage as x and y (and thus only position OR x and y need to be specified).\nparam Number ydensity (allow_None=False, bounds=(0, None), constant=False, default=256, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=-1, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nDensity (number of samples per 1.0 length) in the y direction. Typically the same as the xdensity.\nparam Number size (allow_None=False, bounds=(0.0, None), constant=False, default=1.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.3, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nScaling factor applied to all sub-patterns.\nanim(duration, offset=0, timestep=1, label=None, unit=None, time_fn=Time(label='Time', name='Time00001', time_type=<type 'int'>, timestep=1.0, unit=None, until=Infinity()))\n\nduration: The temporal duration to animate in the units defined on the global time function.\n\noffset: The temporal offset from which the animation is generated given the supplied pattern\n\ntimestep: The time interval between successive frames. The duration must be an exact multiple of the timestep.\n\nlabel: A label string to override the label of the global time function (if not None).\n\nunit: The unit string to override the unit value of the global time function (if not None).\n\ntime_fn: The global time function object that is shared across the time-varying objects that are being sampled.\n\nNote that the offset, timestep and time_fn only affect patterns parameterized by time-dependent number generators. Otherwise, the frames are generated by successive call to the pattern which may or may not be varying (e.g to view the patterns contained within a Selector).\n\nchannels(use_cached=False, **params_to_override)[source]\n\nGet channel data from the current generator. use_cached is not supported at the moment, though it must be forced to be True in the current_generator in order to avoid generating the same data twice (the first time by self() and the second with current_generator.channels() ).\n\ndebug(msg, *args, **kw)\n\nPrint msg merged with args as a debugging statement.\n\nSee Python’s logging module for details of message formatting.\n\ndefaults()\n\nReturn {parameter_name:parameter.default} for all non-constant Parameters.\n\nNote that a Parameter for which instantiate==True has its default instantiated.\n\nforce_new_dynamic_value = <functools.partial object at 0x2adfbaf6d5d0>\nfunction(p)[source]\n\nSelects and returns one of the patterns in the list.\n\nget_current_generator()[source]\n\nReturn the current generator (as specified by self.index).\n\nget_param_values(onlychanged=False)\n\nReturn a list of name,value pairs for all Parameters of this object.\n\nIf onlychanged is True, will only return values that are not equal to the default value.\n\nget_value_generator = <functools.partial object at 0x2adfbaf6d890>\ninspect_value = <functools.partial object at 0x2adfbaf6d260>\nmessage(msg, *args, **kw)\n\nPrint msg merged with args as a message.\n\nSee Python’s logging module for details of message formatting.\n\nnum_channels()[source]\n\nGet the number of channels in the input generators.\n\nclassmethod params(parameter_name=None)\n\nReturn the Parameters of this class as the dictionary {name: parameter_object}\n\nIncludes Parameters from this class and its superclasses.\n\npprint(imports=None, prefix=' ', unknown_value='<?>', qualify=False, separator='')\n\n(Experimental) Pretty printed representation that may be evaluated with eval. See pprint() function for more details.\n\nclassmethod print_param_defaults()\n\nPrint the default values of all cls’s Parameters.\n\nprint_param_values()\n\nPrint the values of all this object’s Parameters.\n\nscript_repr(imports=, []prefix=' ')\n\nVariant of __repr__ designed for generating a runnable script.\n\nclassmethod set_default(param_name, value)\n\nSet the default value of param_name.\n\nEquivalent to setting param_name on the class.\n\nset_dynamic_time_fn = <functools.partial object at 0x2adfbaf6d578>\nset_matrix_dimensions(bounds, xdensity, ydensity)\n\nChange the dimensions of the matrix into which the pattern will be drawn. Users of this class should call this method rather than changing the bounds, xdensity, and ydensity parameters directly. Subclasses can override this method to update any internal data structures that may depend on the matrix dimensions.\n\nset_param = <functools.partial object at 0x2adfbaf6d838>\nstate_pop()\n\nRestore the state of the output functions saved by state_push.\n\nstate_push()\n\nSave the state of the output functions, to be restored with state_pop.\n\nverbose(msg, *args, **kw)\n\nPrint msg merged with args as a verbose message.\n\nSee Python’s logging module for details of message formatting.\n\nwarning(msg, *args, **kw)\n\nPrint msg merged with args as a warning, unless module variable warnings_as_exceptions is True, then raise an Exception containing the arguments.\n\nSee Python’s logging module for details of message formatting.\n\nclass imagen.__init__.ChannelGenerator(**params)\n\nAbstract base class for patterns supporting multiple channels natively.\n\nparam Number x (allow_None=False, bounds=None, constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.2, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nX-coordinate location of pattern center.\nparam Number scale (allow_None=False, bounds=None, constant=False, default=1.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.1, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nMultiplicative strength of input pattern, defaulting to 1.0\nparam String group (allow_None=False, basestring=<type ‘basestring’>, constant=False, default=Pattern, instantiate=False, pickle_default_value=True, precedence=-1, readonly=False)\nThe group name assigned to the returned HoloViews object.\nparam Number orientation (allow_None=False, bounds=None, constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.4, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nPolar angle of pattern, i.e., the orientation in the Cartesian coordinate system, with zero at 3 o’clock and increasing counterclockwise.\nparam HookList channel_transforms (allow_None=False, bounds=(0, None), constant=False, default=[], instantiate=True, pickle_default_value=True, precedence=None, readonly=False)\nOptional functions to apply post processing to the set of channels.\nparam ClassSelector z (allow_None=True, constant=False, default=None, instantiate=True, is_instance=True, pickle_default_value=True, precedence=-1, readonly=False)\nThe Dimension object associated with the z-values generated by the PatternGenerator . If None, uses the default set by HoloViews.Image.\nOptional object (expected to be an array) with which to multiply the pattern array after it has been created, before any output_fns are applied. This can be used to shape the pattern.\nBoundingBox of the area in which the pattern is generated.\nparam Number xdensity (allow_None=False, bounds=(0, None), constant=False, default=256, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=-1, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nDensity (number of samples per 1.0 length) in the x direction.\nparam Number y (allow_None=False, bounds=None, constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.21, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nY-coordinate location of pattern center.\nparam HookList output_fns (allow_None=False, bounds=(0, None), constant=False, default=[], instantiate=True, pickle_default_value=True, precedence=0.08, readonly=False)\nOptional function(s) to apply to the pattern array after it has been created. Can be used for normalization, thresholding, etc.\nparam Number offset (allow_None=False, bounds=None, constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.11, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nAdditive offset to input pattern, defaulting to 0.0\nOptional PatternGenerator used to construct a mask to be applied to the pattern.\nparam Composite position (allow_None=True, attribs=[‘x’, ‘y’], constant=False, default=None, instantiate=False, objtype=<class ‘imagen.patterngenerator.PatternGenerator’>, pickle_default_value=True, precedence=-1, readonly=False)\nCoordinates of location of pattern center. Provides a convenient way to set the x and y parameters together as a tuple (x,y), but shares the same actual storage as x and y (and thus only position OR x and y need to be specified).\nparam Number ydensity (allow_None=False, bounds=(0, None), constant=False, default=256, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=-1, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nDensity (number of samples per 1.0 length) in the y direction. Typically the same as the xdensity.\nparam Number size (allow_None=False, bounds=(0.0, None), constant=False, default=1.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.3, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nDetermines the overall size of the pattern.\nanim(duration, offset=0, timestep=1, label=None, unit=None, time_fn=Time(label='Time', name='Time00001', time_type=<type 'int'>, timestep=1.0, unit=None, until=Infinity()))\n\nduration: The temporal duration to animate in the units defined on the global time function.\n\noffset: The temporal offset from which the animation is generated given the supplied pattern\n\ntimestep: The time interval between successive frames. The duration must be an exact multiple of the timestep.\n\nlabel: A label string to override the label of the global time function (if not None).\n\nunit: The unit string to override the unit value of the global time function (if not None).\n\ntime_fn: The global time function object that is shared across the time-varying objects that are being sampled.\n\nNote that the offset, timestep and time_fn only affect patterns parameterized by time-dependent number generators. Otherwise, the frames are generated by successive call to the pattern which may or may not be varying (e.g to view the patterns contained within a Selector).\n\ndebug(msg, *args, **kw)\n\nPrint msg merged with args as a debugging statement.\n\nSee Python’s logging module for details of message formatting.\n\ndefaults()\n\nReturn {parameter_name:parameter.default} for all non-constant Parameters.\n\nNote that a Parameter for which instantiate==True has its default instantiated.\n\nforce_new_dynamic_value = <functools.partial object at 0x2adfbaf6d520>\nfunction(p)\n\nFunction to draw a pattern that will then be scaled and rotated.\n\nInstead of implementing __call__ directly, PatternGenerator subclasses will typically implement this helper function used by __call__, because that way they can let __call__ handle the scaling and rotation for them. Alternatively, __call__ itself can be reimplemented entirely by a subclass (e.g. if it does not need to do any scaling or rotation), in which case this function will be ignored.\n\nget_param_values(onlychanged=False)\n\nReturn a list of name,value pairs for all Parameters of this object.\n\nIf onlychanged is True, will only return values that are not equal to the default value.\n\nget_value_generator = <functools.partial object at 0x2adfbaf6d3c0>\ninspect_value = <functools.partial object at 0x2adfbaf6d2b8>\nmessage(msg, *args, **kw)\n\nPrint msg merged with args as a message.\n\nSee Python’s logging module for details of message formatting.\n\nclassmethod params(parameter_name=None)\n\nReturn the Parameters of this class as the dictionary {name: parameter_object}\n\nIncludes Parameters from this class and its superclasses.\n\npprint(imports=None, prefix=' ', unknown_value='<?>', qualify=False, separator='')\n\n(Experimental) Pretty printed representation that may be evaluated with eval. See pprint() function for more details.\n\nclassmethod print_param_defaults()\n\nPrint the default values of all cls’s Parameters.\n\nprint_param_values()\n\nPrint the values of all this object’s Parameters.\n\nscript_repr(imports=, []prefix=' ')\n\nVariant of __repr__ designed for generating a runnable script.\n\nclassmethod set_default(param_name, value)\n\nSet the default value of param_name.\n\nEquivalent to setting param_name on the class.\n\nset_dynamic_time_fn = <functools.partial object at 0x2adfbaf6d838>\nset_matrix_dimensions(bounds, xdensity, ydensity)\n\nChange the dimensions of the matrix into which the pattern will be drawn. Users of this class should call this method rather than changing the bounds, xdensity, and ydensity parameters directly. Subclasses can override this method to update any internal data structures that may depend on the matrix dimensions.\n\nset_param = <functools.partial object at 0x2adfbaf6d890>\nstate_pop()\n\nRestore the state of the output functions saved by state_push.\n\nstate_push()\n\nSave the state of the output functions, to be restored with state_pop.\n\nverbose(msg, *args, **kw)\n\nPrint msg merged with args as a verbose message.\n\nSee Python’s logging module for details of message formatting.\n\nwarning(msg, *args, **kw)\n\nPrint msg merged with args as a warning, unless module variable warnings_as_exceptions is True, then raise an Exception containing the arguments.\n\nSee Python’s logging module for details of message formatting.\n\nclass imagen.__init__.ComposeChannels(**params)\n\nCreate a multi-channel PatternGenerator from a list of PatternGenerators, with the specified channel_transforms applied.\n\nparam Number x (allow_None=False, bounds=None, constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.2, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nX-coordinate location of pattern center.\nparam Number scale (allow_None=False, bounds=None, constant=False, default=1.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.1, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nMultiplicative strength of input pattern, defaulting to 1.0\nparam String group (allow_None=False, basestring=<type ‘basestring’>, constant=False, default=Pattern, instantiate=False, pickle_default_value=True, precedence=-1, readonly=False)\nThe group name assigned to the returned HoloViews object.\nparam Number orientation (allow_None=False, bounds=None, constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.4, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nPolar angle of pattern, i.e., the orientation in the Cartesian coordinate system, with zero at 3 o’clock and increasing counterclockwise.\nparam HookList channel_transforms (allow_None=False, bounds=(0, None), constant=False, default=[], instantiate=True, pickle_default_value=True, precedence=None, readonly=False)\nOptional functions to apply post processing to the set of channels.\nparam ClassSelector z (allow_None=True, constant=False, default=None, instantiate=True, is_instance=True, pickle_default_value=True, precedence=-1, readonly=False)\nThe Dimension object associated with the z-values generated by the PatternGenerator . If None, uses the default set by HoloViews.Image.\nOptional object (expected to be an array) with which to multiply the pattern array after it has been created, before any output_fns are applied. This can be used to shape the pattern.\nBoundingBox of the area in which the pattern is generated.\nparam Number xdensity (allow_None=False, bounds=(0, None), constant=False, default=256, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=-1, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nDensity (number of samples per 1.0 length) in the x direction.\nparam Number y (allow_None=False, bounds=None, constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.21, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nY-coordinate location of pattern center.\nparam HookList output_fns (allow_None=False, bounds=(0, None), constant=False, default=[], instantiate=True, pickle_default_value=True, precedence=0.08, readonly=False)\nOptional function(s) to apply to the pattern array after it has been created. Can be used for normalization, thresholding, etc.\nparam List generators (allow_None=False, bounds=(1, None), constant=False, default=[Constant(bounds=BoundingBox(radius=0.5), group=’Pattern’, mask=None, mask_shape=None, name=’Constant01031’, offset=0.0, orientation=0.0, output_fns=[], position=[0.0, 0.0], scale=0.0, size=1.0, x=0.0, xdensity=256, y=0.0, ydensity=256, z=None)], instantiate=True, pickle_default_value=True, precedence=None, readonly=False)\nList of patterns to use for each channel. Generators which already have more than one channel will only contribute to a single channel of ComposeChannels.\nparam Number offset (allow_None=False, bounds=None, constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.11, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nAdditive offset to input pattern, defaulting to 0.0\nOptional PatternGenerator used to construct a mask to be applied to the pattern.\nparam Composite position (allow_None=True, attribs=[‘x’, ‘y’], constant=False, default=None, instantiate=False, objtype=<class ‘imagen.patterngenerator.PatternGenerator’>, pickle_default_value=True, precedence=-1, readonly=False)\nCoordinates of location of pattern center. Provides a convenient way to set the x and y parameters together as a tuple (x,y), but shares the same actual storage as x and y (and thus only position OR x and y need to be specified).\nparam Number ydensity (allow_None=False, bounds=(0, None), constant=False, default=256, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=-1, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nDensity (number of samples per 1.0 length) in the y direction. Typically the same as the xdensity.\nparam Number size (allow_None=False, bounds=(0.0, None), constant=False, default=1.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.3, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nDetermines the overall size of the pattern.\nanim(duration, offset=0, timestep=1, label=None, unit=None, time_fn=Time(label='Time', name='Time00001', time_type=<type 'int'>, timestep=1.0, unit=None, until=Infinity()))\n\nduration: The temporal duration to animate in the units defined on the global time function.\n\noffset: The temporal offset from which the animation is generated given the supplied pattern\n\ntimestep: The time interval between successive frames. The duration must be an exact multiple of the timestep.\n\nlabel: A label string to override the label of the global time function (if not None).\n\nunit: The unit string to override the unit value of the global time function (if not None).\n\ntime_fn: The global time function object that is shared across the time-varying objects that are being sampled.\n\nNote that the offset, timestep and time_fn only affect patterns parameterized by time-dependent number generators. Otherwise, the frames are generated by successive call to the pattern which may or may not be varying (e.g to view the patterns contained within a Selector).\n\ndebug(msg, *args, **kw)\n\nPrint msg merged with args as a debugging statement.\n\nSee Python’s logging module for details of message formatting.\n\ndefaults()\n\nReturn {parameter_name:parameter.default} for all non-constant Parameters.\n\nNote that a Parameter for which instantiate==True has its default instantiated.\n\nforce_new_dynamic_value = <functools.partial object at 0x2adfbaf6d158>\nfunction(p)\n\nFunction to draw a pattern that will then be scaled and rotated.\n\nInstead of implementing __call__ directly, PatternGenerator subclasses will typically implement this helper function used by __call__, because that way they can let __call__ handle the scaling and rotation for them. Alternatively, __call__ itself can be reimplemented entirely by a subclass (e.g. if it does not need to do any scaling or rotation), in which case this function will be ignored.\n\nget_param_values(onlychanged=False)\n\nReturn a list of name,value pairs for all Parameters of this object.\n\nIf onlychanged is True, will only return values that are not equal to the default value.\n\nget_value_generator = <functools.partial object at 0x2adfbaf6d730>\ninspect_value = <functools.partial object at 0x2adfbaf6d2b8>\nmessage(msg, *args, **kw)\n\nPrint msg merged with args as a message.\n\nSee Python’s logging module for details of message formatting.\n\nclassmethod params(parameter_name=None)\n\nReturn the Parameters of this class as the dictionary {name: parameter_object}\n\nIncludes Parameters from this class and its superclasses.\n\npprint(imports=None, prefix=' ', unknown_value='<?>', qualify=False, separator='')\n\n(Experimental) Pretty printed representation that may be evaluated with eval. See pprint() function for more details.\n\nclassmethod print_param_defaults()\n\nPrint the default values of all cls’s Parameters.\n\nprint_param_values()\n\nPrint the values of all this object’s Parameters.\n\nscript_repr(imports=, []prefix=' ')\n\nVariant of __repr__ designed for generating a runnable script.\n\nclassmethod set_default(param_name, value)\n\nSet the default value of param_name.\n\nEquivalent to setting param_name on the class.\n\nset_dynamic_time_fn = <functools.partial object at 0x2adfbaf6dcb0>\nset_matrix_dimensions(bounds, xdensity, ydensity)\n\nChange the dimensions of the matrix into which the pattern will be drawn. Users of this class should call this method rather than changing the bounds, xdensity, and ydensity parameters directly. Subclasses can override this method to update any internal data structures that may depend on the matrix dimensions.\n\nset_param = <functools.partial object at 0x2adfbaf6d680>\nstate_pop()\n\nRestore the state of the output functions saved by state_push.\n\nstate_push()\n\nSave the state of the output functions, to be restored with state_pop.\n\nverbose(msg, *args, **kw)\n\nPrint msg merged with args as a verbose message.\n\nSee Python’s logging module for details of message formatting.\n\nwarning(msg, *args, **kw)\n\nPrint msg merged with args as a warning, unless module variable warnings_as_exceptions is True, then raise an Exception containing the arguments.\n\nSee Python’s logging module for details of message formatting.\n\nclass imagen.__init__.ExponentialDecay(**params)[source]\n\n2D Exponential pattern generator.\n\nExponential decay based on distance from a central peak, i.e. exp(-d), where d is the distance from the center (assuming size=1.0 and aspect_ratio==1.0). More generally, the size and aspect ratio determine the scaling of x and y dimensions:\n\nyscale=size/2 xscale=yscale*aspect_ratio\n\nThe exponential is then computed for the given (x,y) values as:\n\nexp(-sqrt((x/xscale)^2 - (y/yscale)^2))\n\nparam Number x (allow_None=False, bounds=None, constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.2, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nX-coordinate location of pattern center.\nparam Number scale (allow_None=False, bounds=None, constant=False, default=1.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.1, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nMultiplicative strength of input pattern, defaulting to 1.0\nparam String group (allow_None=False, basestring=<type ‘basestring’>, constant=False, default=Pattern, instantiate=False, pickle_default_value=True, precedence=-1, readonly=False)\nThe group name assigned to the returned HoloViews object.\nparam Number orientation (allow_None=False, bounds=None, constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.4, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nPolar angle of pattern, i.e., the orientation in the Cartesian coordinate system, with zero at 3 o’clock and increasing counterclockwise.\nparam Number aspect_ratio (allow_None=False, bounds=(0.0, None), constant=False, default=3.22580645161, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.31, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nRatio of the width to the height.\nparam ClassSelector z (allow_None=True, constant=False, default=None, instantiate=True, is_instance=True, pickle_default_value=True, precedence=-1, readonly=False)\nThe Dimension object associated with the z-values generated by the PatternGenerator . If None, uses the default set by HoloViews.Image.\nOptional object (expected to be an array) with which to multiply the pattern array after it has been created, before any output_fns are applied. This can be used to shape the pattern.\nBoundingBox of the area in which the pattern is generated.\nparam Number xdensity (allow_None=False, bounds=(0, None), constant=False, default=256, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=-1, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nDensity (number of samples per 1.0 length) in the x direction.\nparam Number y (allow_None=False, bounds=None, constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.21, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nY-coordinate location of pattern center.\nparam HookList output_fns (allow_None=False, bounds=(0, None), constant=False, default=[], instantiate=True, pickle_default_value=True, precedence=0.08, readonly=False)\nOptional function(s) to apply to the pattern array after it has been created. Can be used for normalization, thresholding, etc.\nparam Number offset (allow_None=False, bounds=None, constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.11, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nAdditive offset to input pattern, defaulting to 0.0\nOptional PatternGenerator used to construct a mask to be applied to the pattern.\nparam Composite position (allow_None=True, attribs=[‘x’, ‘y’], constant=False, default=None, instantiate=False, objtype=<class ‘imagen.patterngenerator.PatternGenerator’>, pickle_default_value=True, precedence=-1, readonly=False)\nCoordinates of location of pattern center. Provides a convenient way to set the x and y parameters together as a tuple (x,y), but shares the same actual storage as x and y (and thus only position OR x and y need to be specified).\nparam Number ydensity (allow_None=False, bounds=(0, None), constant=False, default=256, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=-1, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nDensity (number of samples per 1.0 length) in the y direction. Typically the same as the xdensity.\nparam Number size (allow_None=False, bounds=(0.0, None), constant=False, default=0.155, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.3, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nOverall scaling of the x and y dimensions.\nanim(duration, offset=0, timestep=1, label=None, unit=None, time_fn=Time(label='Time', name='Time00001', time_type=<type 'int'>, timestep=1.0, unit=None, until=Infinity()))\n\nduration: The temporal duration to animate in the units defined on the global time function.\n\noffset: The temporal offset from which the animation is generated given the supplied pattern\n\ntimestep: The time interval between successive frames. The duration must be an exact multiple of the timestep.\n\nlabel: A label string to override the label of the global time function (if not None).\n\nunit: The unit string to override the unit value of the global time function (if not None).\n\ntime_fn: The global time function object that is shared across the time-varying objects that are being sampled.\n\nNote that the offset, timestep and time_fn only affect patterns parameterized by time-dependent number generators. Otherwise, the frames are generated by successive call to the pattern which may or may not be varying (e.g to view the patterns contained within a Selector).\n\nchannels(use_cached=False, **params_to_override)\n\nChannels() adds a shared interface for single channel and multichannel structures. It will always return an ordered dict: its first element is the single channel of the pattern (if single-channel) or the channel average (if multichannel); the successive elements are the individual channels’ arrays (key: 0,1,..N-1).\n\ndebug(msg, *args, **kw)\n\nPrint msg merged with args as a debugging statement.\n\nSee Python’s logging module for details of message formatting.\n\ndefaults()\n\nReturn {parameter_name:parameter.default} for all non-constant Parameters.\n\nNote that a Parameter for which instantiate==True has its default instantiated.\n\nforce_new_dynamic_value = <functools.partial object at 0x2adfbaf6d208>\nget_param_values(onlychanged=False)\n\nReturn a list of name,value pairs for all Parameters of this object.\n\nIf onlychanged is True, will only return values that are not equal to the default value.\n\nget_value_generator = <functools.partial object at 0x2adfbaf6d838>\ninspect_value = <functools.partial object at 0x2adfbaf6d890>\nmessage(msg, *args, **kw)\n\nPrint msg merged with args as a message.\n\nSee Python’s logging module for details of message formatting.\n\nnum_channels()\n\nQuery the number of channels implemented by the PatternGenerator. In case of single-channel generators this will return 1; in case of multichannel, it will return the number of channels (eg, in the case of RGB images it would return ‘3’, Red-Green-Blue, even though the OrderedDict returned by channels() will have 4 elements – the 3 channels + their average).\n\nclassmethod params(parameter_name=None)\n\nReturn the Parameters of this class as the dictionary {name: parameter_object}\n\nIncludes Parameters from this class and its superclasses.\n\npprint(imports=None, prefix=' ', unknown_value='<?>', qualify=False, separator='')\n\n(Experimental) Pretty printed representation that may be evaluated with eval. See pprint() function for more details.\n\nclassmethod print_param_defaults()\n\nPrint the default values of all cls’s Parameters.\n\nprint_param_values()\n\nPrint the values of all this object’s Parameters.\n\nscript_repr(imports=, []prefix=' ')\n\nVariant of __repr__ designed for generating a runnable script.\n\nclassmethod set_default(param_name, value)\n\nSet the default value of param_name.\n\nEquivalent to setting param_name on the class.\n\nset_dynamic_time_fn = <functools.partial object at 0x2adfbaf6d520>\nset_matrix_dimensions(bounds, xdensity, ydensity)\n\nChange the dimensions of the matrix into which the pattern will be drawn. Users of this class should call this method rather than changing the bounds, xdensity, and ydensity parameters directly. Subclasses can override this method to update any internal data structures that may depend on the matrix dimensions.\n\nset_param = <functools.partial object at 0x2adfbaf6d158>\nstate_pop()\n\nRestore the state of the output functions saved by state_push.\n\nstate_push()\n\nSave the state of the output functions, to be restored with state_pop.\n\nverbose(msg, *args, **kw)\n\nPrint msg merged with args as a verbose message.\n\nSee Python’s logging module for details of message formatting.\n\nwarning(msg, *args, **kw)\n\nPrint msg merged with args as a warning, unless module variable warnings_as_exceptions is True, then raise an Exception containing the arguments.\n\nSee Python’s logging module for details of message formatting.\n\nclass imagen.__init__.HyperbolicGrating(**params)[source]\n\nConcentric rectangular hyperbolas with Gaussian fall-off which share the same asymptotes. abs(x^2/a^2 - y^2/a^2) = 1, where a mod size = 0\n\nparam Number x (allow_None=False, bounds=None, constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.2, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nX-coordinate location of pattern center.\nparam Number scale (allow_None=False, bounds=None, constant=False, default=1.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.1, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nMultiplicative strength of input pattern, defaulting to 1.0\nparam String group (allow_None=False, basestring=<type ‘basestring’>, constant=False, default=Pattern, instantiate=False, pickle_default_value=True, precedence=-1, readonly=False)\nThe group name assigned to the returned HoloViews object.\nparam Number orientation (allow_None=False, bounds=None, constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.4, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nPolar angle of pattern, i.e., the orientation in the Cartesian coordinate system, with zero at 3 o’clock and increasing counterclockwise.\nparam Number aspect_ratio (allow_None=False, bounds=(0.0, None), constant=False, default=1.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.31, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nRatio of width to height.\nparam ClassSelector z (allow_None=True, constant=False, default=None, instantiate=True, is_instance=True, pickle_default_value=True, precedence=-1, readonly=False)\nThe Dimension object associated with the z-values generated by the PatternGenerator . If None, uses the default set by HoloViews.Image.\nOptional object (expected to be an array) with which to multiply the pattern array after it has been created, before any output_fns are applied. This can be used to shape the pattern.\nBoundingBox of the area in which the pattern is generated.\nparam Number thickness (allow_None=False, bounds=(0.0, None), constant=False, default=0.05, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.6, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nThickness of the hyperbolas.\nparam Number xdensity (allow_None=False, bounds=(0, None), constant=False, default=256, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=-1, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nDensity (number of samples per 1.0 length) in the x direction.\nparam Number y (allow_None=False, bounds=None, constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.21, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nY-coordinate location of pattern center.\nparam HookList output_fns (allow_None=False, bounds=(0, None), constant=False, default=[], instantiate=True, pickle_default_value=True, precedence=0.08, readonly=False)\nOptional function(s) to apply to the pattern array after it has been created. Can be used for normalization, thresholding, etc.\nparam Number offset (allow_None=False, bounds=None, constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.11, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nAdditive offset to input pattern, defaulting to 0.0\nOptional PatternGenerator used to construct a mask to be applied to the pattern.\nparam Composite position (allow_None=True, attribs=[‘x’, ‘y’], constant=False, default=None, instantiate=False, objtype=<class ‘imagen.patterngenerator.PatternGenerator’>, pickle_default_value=True, precedence=-1, readonly=False)\nCoordinates of location of pattern center. Provides a convenient way to set the x and y parameters together as a tuple (x,y), but shares the same actual storage as x and y (and thus only position OR x and y need to be specified).\nparam Number smoothing (allow_None=False, bounds=(0.0, None), constant=False, default=0.05, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.61, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nWidth of the Gaussian fall-off inside and outside the hyperbolas.\nparam Number ydensity (allow_None=False, bounds=(0, None), constant=False, default=256, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=-1, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nDensity (number of samples per 1.0 length) in the y direction. Typically the same as the xdensity.\nparam Number size (allow_None=False, bounds=(0.0, None), constant=False, default=0.5, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.62, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nSize as distance of inner hyperbola vertices from the centre.\nanim(duration, offset=0, timestep=1, label=None, unit=None, time_fn=Time(label='Time', name='Time00001', time_type=<type 'int'>, timestep=1.0, unit=None, until=Infinity()))\n\nduration: The temporal duration to animate in the units defined on the global time function.\n\noffset: The temporal offset from which the animation is generated given the supplied pattern\n\ntimestep: The time interval between successive frames. The duration must be an exact multiple of the timestep.\n\nlabel: A label string to override the label of the global time function (if not None).\n\nunit: The unit string to override the unit value of the global time function (if not None).\n\ntime_fn: The global time function object that is shared across the time-varying objects that are being sampled.\n\nNote that the offset, timestep and time_fn only affect patterns parameterized by time-dependent number generators. Otherwise, the frames are generated by successive call to the pattern which may or may not be varying (e.g to view the patterns contained within a Selector).\n\nchannels(use_cached=False, **params_to_override)\n\nChannels() adds a shared interface for single channel and multichannel structures. It will always return an ordered dict: its first element is the single channel of the pattern (if single-channel) or the channel average (if multichannel); the successive elements are the individual channels’ arrays (key: 0,1,..N-1).\n\ndebug(msg, *args, **kw)\n\nPrint msg merged with args as a debugging statement.\n\nSee Python’s logging module for details of message formatting.\n\ndefaults()\n\nReturn {parameter_name:parameter.default} for all non-constant Parameters.\n\nNote that a Parameter for which instantiate==True has its default instantiated.\n\nforce_new_dynamic_value = <functools.partial object at 0x2adfbaf6dcb0>\nget_param_values(onlychanged=False)\n\nReturn a list of name,value pairs for all Parameters of this object.\n\nIf onlychanged is True, will only return values that are not equal to the default value.\n\nget_value_generator = <functools.partial object at 0x2adfbaf6d730>\ninspect_value = <functools.partial object at 0x2adfbaf6d578>\nmessage(msg, *args, **kw)\n\nPrint msg merged with args as a message.\n\nSee Python’s logging module for details of message formatting.\n\nnum_channels()\n\nQuery the number of channels implemented by the PatternGenerator. In case of single-channel generators this will return 1; in case of multichannel, it will return the number of channels (eg, in the case of RGB images it would return ‘3’, Red-Green-Blue, even though the OrderedDict returned by channels() will have 4 elements – the 3 channels + their average).\n\nclassmethod params(parameter_name=None)\n\nReturn the Parameters of this class as the dictionary {name: parameter_object}\n\nIncludes Parameters from this class and its superclasses.\n\npprint(imports=None, prefix=' ', unknown_value='<?>', qualify=False, separator='')\n\n(Experimental) Pretty printed representation that may be evaluated with eval. See pprint() function for more details.\n\nclassmethod print_param_defaults()\n\nPrint the default values of all cls’s Parameters.\n\nprint_param_values()\n\nPrint the values of all this object’s Parameters.\n\nscript_repr(imports=, []prefix=' ')\n\nVariant of __repr__ designed for generating a runnable script.\n\nclassmethod set_default(param_name, value)\n\nSet the default value of param_name.\n\nEquivalent to setting param_name on the class.\n\nset_dynamic_time_fn = <functools.partial object at 0x2adfbaf6d260>\nset_matrix_dimensions(bounds, xdensity, ydensity)\n\nChange the dimensions of the matrix into which the pattern will be drawn. Users of this class should call this method rather than changing the bounds, xdensity, and ydensity parameters directly. Subclasses can override this method to update any internal data structures that may depend on the matrix dimensions.\n\nset_param = <functools.partial object at 0x2adfbaf6d208>\nstate_pop()\n\nRestore the state of the output functions saved by state_push.\n\nstate_push()\n\nSave the state of the output functions, to be restored with state_pop.\n\nverbose(msg, *args, **kw)\n\nPrint msg merged with args as a verbose message.\n\nSee Python’s logging module for details of message formatting.\n\nwarning(msg, *args, **kw)\n\nPrint msg merged with args as a warning, unless module variable warnings_as_exceptions is True, then raise an Exception containing the arguments.\n\nSee Python’s logging module for details of message formatting.\n\nclass imagen.__init__.Line(**params)[source]\n\n2D line pattern generator.\n\nparam Number x (allow_None=False, bounds=None, constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.2, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nX-coordinate location of pattern center.\nparam Number scale (allow_None=False, bounds=None, constant=False, default=1.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.1, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nMultiplicative strength of input pattern, defaulting to 1.0\nparam String group (allow_None=False, basestring=<type ‘basestring’>, constant=False, default=Pattern, instantiate=False, pickle_default_value=True, precedence=-1, readonly=False)\nThe group name assigned to the returned HoloViews object.\nparam Boolean enforce_minimal_thickness (allow_None=False, bounds=(0, 1), constant=False, default=False, instantiate=False, pickle_default_value=True, precedence=0.6, readonly=False)\nIf True, ensure that the line is at least one pixel in width even for small thicknesses where the line could otherwise fall in between pixel centers and thus disappear at some orientations.\nparam Number orientation (allow_None=False, bounds=None, constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.4, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nPolar angle of pattern, i.e., the orientation in the Cartesian coordinate system, with zero at 3 o’clock and increasing counterclockwise.\nparam ClassSelector z (allow_None=True, constant=False, default=None, instantiate=True, is_instance=True, pickle_default_value=True, precedence=-1, readonly=False)\nThe Dimension object associated with the z-values generated by the PatternGenerator . If None, uses the default set by HoloViews.Image.\nOptional object (expected to be an array) with which to multiply the pattern array after it has been created, before any output_fns are applied. This can be used to shape the pattern.\nBoundingBox of the area in which the pattern is generated.\nparam Number thickness (allow_None=False, bounds=(0.0, None), constant=False, default=0.006, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.6, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nThickness (width) of the solid central part of the line.\nparam Number smoothing (allow_None=False, bounds=(0.0, None), constant=False, default=0.05, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.61, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nWidth of the Gaussian fall-off.\nparam Number xdensity (allow_None=False, bounds=(0, None), constant=False, default=256, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=-1, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nDensity (number of samples per 1.0 length) in the x direction.\nparam Number y (allow_None=False, bounds=None, constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.21, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nY-coordinate location of pattern center.\nparam HookList output_fns (allow_None=False, bounds=(0, None), constant=False, default=[], instantiate=True, pickle_default_value=True, precedence=0.08, readonly=False)\nOptional function(s) to apply to the pattern array after it has been created. Can be used for normalization, thresholding, etc.\nparam Number offset (allow_None=False, bounds=None, constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.11, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nAdditive offset to input pattern, defaulting to 0.0\nOptional PatternGenerator used to construct a mask to be applied to the pattern.\nparam Composite position (allow_None=True, attribs=[‘x’, ‘y’], constant=False, default=None, instantiate=False, objtype=<class ‘imagen.patterngenerator.PatternGenerator’>, pickle_default_value=True, precedence=-1, readonly=False)\nCoordinates of location of pattern center. Provides a convenient way to set the x and y parameters together as a tuple (x,y), but shares the same actual storage as x and y (and thus only position OR x and y need to be specified).\nparam Number ydensity (allow_None=False, bounds=(0, None), constant=False, default=256, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=-1, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nDensity (number of samples per 1.0 length) in the y direction. Typically the same as the xdensity.\nparam Number size (allow_None=False, bounds=(0.0, None), constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=-1.0, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nDetermines the overall size of the pattern.\nanim(duration, offset=0, timestep=1, label=None, unit=None, time_fn=Time(label='Time', name='Time00001', time_type=<type 'int'>, timestep=1.0, unit=None, until=Infinity()))\n\nduration: The temporal duration to animate in the units defined on the global time function.\n\noffset: The temporal offset from which the animation is generated given the supplied pattern\n\ntimestep: The time interval between successive frames. The duration must be an exact multiple of the timestep.\n\nlabel: A label string to override the label of the global time function (if not None).\n\nunit: The unit string to override the unit value of the global time function (if not None).\n\ntime_fn: The global time function object that is shared across the time-varying objects that are being sampled.\n\nNote that the offset, timestep and time_fn only affect patterns parameterized by time-dependent number generators. Otherwise, the frames are generated by successive call to the pattern which may or may not be varying (e.g to view the patterns contained within a Selector).\n\nchannels(use_cached=False, **params_to_override)\n\nChannels() adds a shared interface for single channel and multichannel structures. It will always return an ordered dict: its first element is the single channel of the pattern (if single-channel) or the channel average (if multichannel); the successive elements are the individual channels’ arrays (key: 0,1,..N-1).\n\ndebug(msg, *args, **kw)\n\nPrint msg merged with args as a debugging statement.\n\nSee Python’s logging module for details of message formatting.\n\ndefaults()\n\nReturn {parameter_name:parameter.default} for all non-constant Parameters.\n\nNote that a Parameter for which instantiate==True has its default instantiated.\n\nforce_new_dynamic_value = <functools.partial object at 0x2adfbaf6d890>\nget_param_values(onlychanged=False)\n\nReturn a list of name,value pairs for all Parameters of this object.\n\nIf onlychanged is True, will only return values that are not equal to the default value.\n\nget_value_generator = <functools.partial object at 0x2adfbaf6d3c0>\ninspect_value = <functools.partial object at 0x2adfbaf6d100>\nmessage(msg, *args, **kw)\n\nPrint msg merged with args as a message.\n\nSee Python’s logging module for details of message formatting.\n\nnum_channels()\n\nQuery the number of channels implemented by the PatternGenerator. In case of single-channel generators this will return 1; in case of multichannel, it will return the number of channels (eg, in the case of RGB images it would return ‘3’, Red-Green-Blue, even though the OrderedDict returned by channels() will have 4 elements – the 3 channels + their average).\n\nclassmethod params(parameter_name=None)\n\nReturn the Parameters of this class as the dictionary {name: parameter_object}\n\nIncludes Parameters from this class and its superclasses.\n\npprint(imports=None, prefix=' ', unknown_value='<?>', qualify=False, separator='')\n\n(Experimental) Pretty printed representation that may be evaluated with eval. See pprint() function for more details.\n\nclassmethod print_param_defaults()\n\nPrint the default values of all cls’s Parameters.\n\nprint_param_values()\n\nPrint the values of all this object’s Parameters.\n\nscript_repr(imports=, []prefix=' ')\n\nVariant of __repr__ designed for generating a runnable script.\n\nclassmethod set_default(param_name, value)\n\nSet the default value of param_name.\n\nEquivalent to setting param_name on the class.\n\nset_dynamic_time_fn = <functools.partial object at 0x2adfbaf6d838>\nset_matrix_dimensions(bounds, xdensity, ydensity)\n\nChange the dimensions of the matrix into which the pattern will be drawn. Users of this class should call this method rather than changing the bounds, xdensity, and ydensity parameters directly. Subclasses can override this method to update any internal data structures that may depend on the matrix dimensions.\n\nset_param = <functools.partial object at 0x2adfbaf6d260>\nstate_pop()\n\nRestore the state of the output functions saved by state_push.\n\nstate_push()\n\nSave the state of the output functions, to be restored with state_pop.\n\nverbose(msg, *args, **kw)\n\nPrint msg merged with args as a verbose message.\n\nSee Python’s logging module for details of message formatting.\n\nwarning(msg, *args, **kw)\n\nPrint msg merged with args as a warning, unless module variable warnings_as_exceptions is True, then raise an Exception containing the arguments.\n\nSee Python’s logging module for details of message formatting.\n\nclass imagen.__init__.LogGaussian(**params)[source]\n\n2D Log Gaussian pattern generator allowing standard gaussian patterns but with the added advantage of movable peaks.\n\nThe spread governs decay rates from the peak of the Gaussian, mathematically this is the sigma term.\n\nThe center governs the peak position of the Gaussian, mathematically this is the mean term.\n\nparam Number x_shape (allow_None=False, bounds=(0.0, None), constant=False, default=0.8, inclusive_bounds=(False, False), instantiate=False, pickle_default_value=True, precedence=None, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nThe length of the tail along the x axis.\nparam Number x (allow_None=False, bounds=None, constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.2, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nX-coordinate location of pattern center.\nparam Number scale (allow_None=False, bounds=None, constant=False, default=1.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.1, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nMultiplicative strength of input pattern, defaulting to 1.0\nparam String group (allow_None=False, basestring=<type ‘basestring’>, constant=False, default=Pattern, instantiate=False, pickle_default_value=True, precedence=-1, readonly=False)\nThe group name assigned to the returned HoloViews object.\nparam Number orientation (allow_None=False, bounds=None, constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.4, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nPolar angle of pattern, i.e., the orientation in the Cartesian coordinate system, with zero at 3 o’clock and increasing counterclockwise.\nparam Number y_shape (allow_None=False, bounds=(0.0, None), constant=False, default=0.35, inclusive_bounds=(False, False), instantiate=False, pickle_default_value=True, precedence=None, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nThe length of the tail along the y axis.\nparam ClassSelector z (allow_None=True, constant=False, default=None, instantiate=True, is_instance=True, pickle_default_value=True, precedence=-1, readonly=False)\nThe Dimension object associated with the z-values generated by the PatternGenerator . If None, uses the default set by HoloViews.Image.\nOptional object (expected to be an array) with which to multiply the pattern array after it has been created, before any output_fns are applied. This can be used to shape the pattern.\nBoundingBox of the area in which the pattern is generated.\nparam Number xdensity (allow_None=False, bounds=(0, None), constant=False, default=256, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=-1, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nDensity (number of samples per 1.0 length) in the x direction.\nparam Number y (allow_None=False, bounds=None, constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.21, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nY-coordinate location of pattern center.\nparam HookList output_fns (allow_None=False, bounds=(0, None), constant=False, default=[], instantiate=True, pickle_default_value=True, precedence=0.08, readonly=False)\nOptional function(s) to apply to the pattern array after it has been created. Can be used for normalization, thresholding, etc.\nparam Number offset (allow_None=False, bounds=None, constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.11, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nAdditive offset to input pattern, defaulting to 0.0\nOptional PatternGenerator used to construct a mask to be applied to the pattern.\nparam Composite position (allow_None=True, attribs=[‘x’, ‘y’], constant=False, default=None, instantiate=False, objtype=<class ‘imagen.patterngenerator.PatternGenerator’>, pickle_default_value=True, precedence=-1, readonly=False)\nCoordinates of location of pattern center. Provides a convenient way to set the x and y parameters together as a tuple (x,y), but shares the same actual storage as x and y (and thus only position OR x and y need to be specified).\nparam Number ydensity (allow_None=False, bounds=(0, None), constant=False, default=256, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=-1, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nDensity (number of samples per 1.0 length) in the y direction. Typically the same as the xdensity.\nparam Number aspect_ratio (allow_None=False, bounds=(0.0, None), constant=False, default=0.5, inclusive_bounds=(True, False), instantiate=False, pickle_default_value=True, precedence=None, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nRatio of the pattern’s width to height.\nparam Number size (allow_None=False, bounds=(0.0, None), constant=False, default=1.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.3, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nDetermines the overall size of the pattern.\nanim(duration, offset=0, timestep=1, label=None, unit=None, time_fn=Time(label='Time', name='Time00001', time_type=<type 'int'>, timestep=1.0, unit=None, until=Infinity()))\n\nduration: The temporal duration to animate in the units defined on the global time function.\n\noffset: The temporal offset from which the animation is generated given the supplied pattern\n\ntimestep: The time interval between successive frames. The duration must be an exact multiple of the timestep.\n\nlabel: A label string to override the label of the global time function (if not None).\n\nunit: The unit string to override the unit value of the global time function (if not None).\n\ntime_fn: The global time function object that is shared across the time-varying objects that are being sampled.\n\nNote that the offset, timestep and time_fn only affect patterns parameterized by time-dependent number generators. Otherwise, the frames are generated by successive call to the pattern which may or may not be varying (e.g to view the patterns contained within a Selector).\n\nchannels(use_cached=False, **params_to_override)\n\nChannels() adds a shared interface for single channel and multichannel structures. It will always return an ordered dict: its first element is the single channel of the pattern (if single-channel) or the channel average (if multichannel); the successive elements are the individual channels’ arrays (key: 0,1,..N-1).\n\ndebug(msg, *args, **kw)\n\nPrint msg merged with args as a debugging statement.\n\nSee Python’s logging module for details of message formatting.\n\ndefaults()\n\nReturn {parameter_name:parameter.default} for all non-constant Parameters.\n\nNote that a Parameter for which instantiate==True has its default instantiated.\n\nforce_new_dynamic_value = <functools.partial object at 0x2adfbaf6d578>\nget_param_values(onlychanged=False)\n\nReturn a list of name,value pairs for all Parameters of this object.\n\nIf onlychanged is True, will only return values that are not equal to the default value.\n\nget_value_generator = <functools.partial object at 0x2adfbaf6d788>\ninspect_value = <functools.partial object at 0x2adfbaf6d208>\nmessage(msg, *args, **kw)\n\nPrint msg merged with args as a message.\n\nSee Python’s logging module for details of message formatting.\n\nnum_channels()\n\nQuery the number of channels implemented by the PatternGenerator. In case of single-channel generators this will return 1; in case of multichannel, it will return the number of channels (eg, in the case of RGB images it would return ‘3’, Red-Green-Blue, even though the OrderedDict returned by channels() will have 4 elements – the 3 channels + their average).\n\nclassmethod params(parameter_name=None)\n\nReturn the Parameters of this class as the dictionary {name: parameter_object}\n\nIncludes Parameters from this class and its superclasses.\n\npprint(imports=None, prefix=' ', unknown_value='<?>', qualify=False, separator='')\n\n(Experimental) Pretty printed representation that may be evaluated with eval. See pprint() function for more details.\n\nclassmethod print_param_defaults()\n\nPrint the default values of all cls’s Parameters.\n\nprint_param_values()\n\nPrint the values of all this object’s Parameters.\n\nscript_repr(imports=, []prefix=' ')\n\nVariant of __repr__ designed for generating a runnable script.\n\nclassmethod set_default(param_name, value)\n\nSet the default value of param_name.\n\nEquivalent to setting param_name on the class.\n\nset_dynamic_time_fn = <functools.partial object at 0x2adfbaf6d838>\nset_matrix_dimensions(bounds, xdensity, ydensity)\n\nChange the dimensions of the matrix into which the pattern will be drawn. Users of this class should call this method rather than changing the bounds, xdensity, and ydensity parameters directly. Subclasses can override this method to update any internal data structures that may depend on the matrix dimensions.\n\nset_param = <functools.partial object at 0x2adfbaf6d260>\nstate_pop()\n\nRestore the state of the output functions saved by state_push.\n\nstate_push()\n\nSave the state of the output functions, to be restored with state_pop.\n\nverbose(msg, *args, **kw)\n\nPrint msg merged with args as a verbose message.\n\nSee Python’s logging module for details of message formatting.\n\nwarning(msg, *args, **kw)\n\nPrint msg merged with args as a warning, unless module variable warnings_as_exceptions is True, then raise an Exception containing the arguments.\n\nSee Python’s logging module for details of message formatting.\n\nclass imagen.__init__.SquareGrating(**params)[source]\n\n2D squarewave (symmetric or asymmetric) grating pattern generator.\n\nparam Number x (allow_None=False, bounds=None, constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.2, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nX-coordinate location of pattern center.\nparam Number scale (allow_None=False, bounds=None, constant=False, default=1.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.1, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nMultiplicative strength of input pattern, defaulting to 1.0\nparam String group (allow_None=False, basestring=<type ‘basestring’>, constant=False, default=Pattern, instantiate=False, pickle_default_value=True, precedence=-1, readonly=False)\nThe group name assigned to the returned HoloViews object.\nparam Number orientation (allow_None=False, bounds=None, constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.4, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nPolar angle of pattern, i.e., the orientation in the Cartesian coordinate system, with zero at 3 o’clock and increasing counterclockwise.\nparam Number phase (allow_None=False, bounds=(0.0, None), constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.51, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nPhase of the square grating.\nparam ClassSelector z (allow_None=True, constant=False, default=None, instantiate=True, is_instance=True, pickle_default_value=True, precedence=-1, readonly=False)\nThe Dimension object associated with the z-values generated by the PatternGenerator . If None, uses the default set by HoloViews.Image.\nOptional object (expected to be an array) with which to multiply the pattern array after it has been created, before any output_fns are applied. This can be used to shape the pattern.\nBoundingBox of the area in which the pattern is generated.\nparam Number xdensity (allow_None=False, bounds=(0, None), constant=False, default=256, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=-1, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nDensity (number of samples per 1.0 length) in the x direction.\nparam Number y (allow_None=False, bounds=None, constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.21, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nY-coordinate location of pattern center.\nparam HookList output_fns (allow_None=False, bounds=(0, None), constant=False, default=[], instantiate=True, pickle_default_value=True, precedence=0.08, readonly=False)\nOptional function(s) to apply to the pattern array after it has been created. Can be used for normalization, thresholding, etc.\nparam Number frequency (allow_None=False, bounds=(0.0, None), constant=False, default=2.4, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.5, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nFrequency of the square grating.\nparam Number duty_cycle (allow_None=False, bounds=(0.0, 1.0), constant=False, default=0.5, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.51, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nThe duty cycle is the ratio between the pulse duration (width of the bright bar) and the period (1/frequency). The pulse is defined as the time during which the square wave signal is 1 (high).\nparam Number offset (allow_None=False, bounds=None, constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.11, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nAdditive offset to input pattern, defaulting to 0.0\nOptional PatternGenerator used to construct a mask to be applied to the pattern.\nparam Composite position (allow_None=True, attribs=[‘x’, ‘y’], constant=False, default=None, instantiate=False, objtype=<class ‘imagen.patterngenerator.PatternGenerator’>, pickle_default_value=True, precedence=-1, readonly=False)\nCoordinates of location of pattern center. Provides a convenient way to set the x and y parameters together as a tuple (x,y), but shares the same actual storage as x and y (and thus only position OR x and y need to be specified).\nparam Number ydensity (allow_None=False, bounds=(0, None), constant=False, default=256, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=-1, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nDensity (number of samples per 1.0 length) in the y direction. Typically the same as the xdensity.\nparam Number size (allow_None=False, bounds=(0.0, None), constant=False, default=1.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.3, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nDetermines the overall size of the pattern.\nanim(duration, offset=0, timestep=1, label=None, unit=None, time_fn=Time(label='Time', name='Time00001', time_type=<type 'int'>, timestep=1.0, unit=None, until=Infinity()))\n\nduration: The temporal duration to animate in the units defined on the global time function.\n\noffset: The temporal offset from which the animation is generated given the supplied pattern\n\ntimestep: The time interval between successive frames. The duration must be an exact multiple of the timestep.\n\nlabel: A label string to override the label of the global time function (if not None).\n\nunit: The unit string to override the unit value of the global time function (if not None).\n\ntime_fn: The global time function object that is shared across the time-varying objects that are being sampled.\n\nNote that the offset, timestep and time_fn only affect patterns parameterized by time-dependent number generators. Otherwise, the frames are generated by successive call to the pattern which may or may not be varying (e.g to view the patterns contained within a Selector).\n\nchannels(use_cached=False, **params_to_override)\n\nChannels() adds a shared interface for single channel and multichannel structures. It will always return an ordered dict: its first element is the single channel of the pattern (if single-channel) or the channel average (if multichannel); the successive elements are the individual channels’ arrays (key: 0,1,..N-1).\n\ndebug(msg, *args, **kw)\n\nPrint msg merged with args as a debugging statement.\n\nSee Python’s logging module for details of message formatting.\n\ndefaults()\n\nReturn {parameter_name:parameter.default} for all non-constant Parameters.\n\nNote that a Parameter for which instantiate==True has its default instantiated.\n\nforce_new_dynamic_value = <functools.partial object at 0x2adfbaf6d890>\nfunction(p)[source]\n\nReturn a square-wave grating (alternating black and white bars).\n\nget_param_values(onlychanged=False)\n\nReturn a list of name,value pairs for all Parameters of this object.\n\nIf onlychanged is True, will only return values that are not equal to the default value.\n\nget_value_generator = <functools.partial object at 0x2adfbaf6d208>\ninspect_value = <functools.partial object at 0x2adfbaf6d158>\nmessage(msg, *args, **kw)\n\nPrint msg merged with args as a message.\n\nSee Python’s logging module for details of message formatting.\n\nnum_channels()\n\nQuery the number of channels implemented by the PatternGenerator. In case of single-channel generators this will return 1; in case of multichannel, it will return the number of channels (eg, in the case of RGB images it would return ‘3’, Red-Green-Blue, even though the OrderedDict returned by channels() will have 4 elements – the 3 channels + their average).\n\nclassmethod params(parameter_name=None)\n\nReturn the Parameters of this class as the dictionary {name: parameter_object}\n\nIncludes Parameters from this class and its superclasses.\n\npprint(imports=None, prefix=' ', unknown_value='<?>', qualify=False, separator='')\n\n(Experimental) Pretty printed representation that may be evaluated with eval. See pprint() function for more details.\n\nclassmethod print_param_defaults()\n\nPrint the default values of all cls’s Parameters.\n\nprint_param_values()\n\nPrint the values of all this object’s Parameters.\n\nscript_repr(imports=, []prefix=' ')\n\nVariant of __repr__ designed for generating a runnable script.\n\nclassmethod set_default(param_name, value)\n\nSet the default value of param_name.\n\nEquivalent to setting param_name on the class.\n\nset_dynamic_time_fn = <functools.partial object at 0x2adfbaf6d5d0>\nset_matrix_dimensions(bounds, xdensity, ydensity)\n\nChange the dimensions of the matrix into which the pattern will be drawn. Users of this class should call this method rather than changing the bounds, xdensity, and ydensity parameters directly. Subclasses can override this method to update any internal data structures that may depend on the matrix dimensions.\n\nset_param = <functools.partial object at 0x2adfbaf6d100>\nstate_pop()\n\nRestore the state of the output functions saved by state_push.\n\nstate_push()\n\nSave the state of the output functions, to be restored with state_pop.\n\nverbose(msg, *args, **kw)\n\nPrint msg merged with args as a verbose message.\n\nSee Python’s logging module for details of message formatting.\n\nwarning(msg, *args, **kw)\n\nPrint msg merged with args as a warning, unless module variable warnings_as_exceptions is True, then raise an Exception containing the arguments.\n\nSee Python’s logging module for details of message formatting.\n\nclass imagen.__init__.Gabor(**params)[source]\n\n2D Gabor pattern generator.\n\nparam Number x (allow_None=False, bounds=None, constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.2, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nX-coordinate location of pattern center.\nparam Number scale (allow_None=False, bounds=None, constant=False, default=1.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.1, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nMultiplicative strength of input pattern, defaulting to 1.0\nparam String group (allow_None=False, basestring=<type ‘basestring’>, constant=False, default=Pattern, instantiate=False, pickle_default_value=True, precedence=-1, readonly=False)\nThe group name assigned to the returned HoloViews object.\nparam Number orientation (allow_None=False, bounds=None, constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.4, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nPolar angle of pattern, i.e., the orientation in the Cartesian coordinate system, with zero at 3 o’clock and increasing counterclockwise.\nparam Number aspect_ratio (allow_None=False, bounds=(0.0, None), constant=False, default=1.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.31, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nRatio of pattern width to height. The width of the Gaussian component is size*aspect_ratio (see Gaussian).\nparam ClassSelector z (allow_None=True, constant=False, default=None, instantiate=True, is_instance=True, pickle_default_value=True, precedence=-1, readonly=False)\nThe Dimension object associated with the z-values generated by the PatternGenerator . If None, uses the default set by HoloViews.Image.\nOptional object (expected to be an array) with which to multiply the pattern array after it has been created, before any output_fns are applied. This can be used to shape the pattern.\nBoundingBox of the area in which the pattern is generated.\nparam Number xdensity (allow_None=False, bounds=(0, None), constant=False, default=256, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=-1, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nDensity (number of samples per 1.0 length) in the x direction.\nparam Number y (allow_None=False, bounds=None, constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.21, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nY-coordinate location of pattern center.\nparam HookList output_fns (allow_None=False, bounds=(0, None), constant=False, default=[], instantiate=True, pickle_default_value=True, precedence=0.08, readonly=False)\nOptional function(s) to apply to the pattern array after it has been created. Can be used for normalization, thresholding, etc.\nparam Number phase (allow_None=False, bounds=(0.0, None), constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.51, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nPhase of the sine grating component.\nparam Number offset (allow_None=False, bounds=None, constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.11, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nAdditive offset to input pattern, defaulting to 0.0\nOptional PatternGenerator used to construct a mask to be applied to the pattern.\nparam Composite position (allow_None=True, attribs=[‘x’, ‘y’], constant=False, default=None, instantiate=False, objtype=<class ‘imagen.patterngenerator.PatternGenerator’>, pickle_default_value=True, precedence=-1, readonly=False)\nCoordinates of location of pattern center. Provides a convenient way to set the x and y parameters together as a tuple (x,y), but shares the same actual storage as x and y (and thus only position OR x and y need to be specified).\nparam Number ydensity (allow_None=False, bounds=(0, None), constant=False, default=256, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=-1, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nDensity (number of samples per 1.0 length) in the y direction. Typically the same as the xdensity.\nparam Number frequency (allow_None=False, bounds=(0.0, None), constant=False, default=2.4, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.5, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nFrequency of the sine grating component.\nparam Number size (allow_None=False, bounds=(0.0, None), constant=False, default=0.25, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.3, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nDetermines the height of the Gaussian component (see Gaussian).\nanim(duration, offset=0, timestep=1, label=None, unit=None, time_fn=Time(label='Time', name='Time00001', time_type=<type 'int'>, timestep=1.0, unit=None, until=Infinity()))\n\nduration: The temporal duration to animate in the units defined on the global time function.\n\noffset: The temporal offset from which the animation is generated given the supplied pattern\n\ntimestep: The time interval between successive frames. The duration must be an exact multiple of the timestep.\n\nlabel: A label string to override the label of the global time function (if not None).\n\nunit: The unit string to override the unit value of the global time function (if not None).\n\ntime_fn: The global time function object that is shared across the time-varying objects that are being sampled.\n\nNote that the offset, timestep and time_fn only affect patterns parameterized by time-dependent number generators. Otherwise, the frames are generated by successive call to the pattern which may or may not be varying (e.g to view the patterns contained within a Selector).\n\nchannels(use_cached=False, **params_to_override)\n\nChannels() adds a shared interface for single channel and multichannel structures. It will always return an ordered dict: its first element is the single channel of the pattern (if single-channel) or the channel average (if multichannel); the successive elements are the individual channels’ arrays (key: 0,1,..N-1).\n\ndebug(msg, *args, **kw)\n\nPrint msg merged with args as a debugging statement.\n\nSee Python’s logging module for details of message formatting.\n\ndefaults()\n\nReturn {parameter_name:parameter.default} for all non-constant Parameters.\n\nNote that a Parameter for which instantiate==True has its default instantiated.\n\nforce_new_dynamic_value = <functools.partial object at 0x2adfbaf6d730>\nget_param_values(onlychanged=False)\n\nReturn a list of name,value pairs for all Parameters of this object.\n\nIf onlychanged is True, will only return values that are not equal to the default value.\n\nget_value_generator = <functools.partial object at 0x2adfbaf6d260>\ninspect_value = <functools.partial object at 0x2adfbaf6d368>\nmessage(msg, *args, **kw)\n\nPrint msg merged with args as a message.\n\nSee Python’s logging module for details of message formatting.\n\nnum_channels()\n\nQuery the number of channels implemented by the PatternGenerator. In case of single-channel generators this will return 1; in case of multichannel, it will return the number of channels (eg, in the case of RGB images it would return ‘3’, Red-Green-Blue, even though the OrderedDict returned by channels() will have 4 elements – the 3 channels + their average).\n\nclassmethod params(parameter_name=None)\n\nReturn the Parameters of this class as the dictionary {name: parameter_object}\n\nIncludes Parameters from this class and its superclasses.\n\npprint(imports=None, prefix=' ', unknown_value='<?>', qualify=False, separator='')\n\n(Experimental) Pretty printed representation that may be evaluated with eval. See pprint() function for more details.\n\nclassmethod print_param_defaults()\n\nPrint the default values of all cls’s Parameters.\n\nprint_param_values()\n\nPrint the values of all this object’s Parameters.\n\nscript_repr(imports=, []prefix=' ')\n\nVariant of __repr__ designed for generating a runnable script.\n\nclassmethod set_default(param_name, value)\n\nSet the default value of param_name.\n\nEquivalent to setting param_name on the class.\n\nset_dynamic_time_fn = <functools.partial object at 0x2adfbaf6d788>\nset_matrix_dimensions(bounds, xdensity, ydensity)\n\nChange the dimensions of the matrix into which the pattern will be drawn. Users of this class should call this method rather than changing the bounds, xdensity, and ydensity parameters directly. Subclasses can override this method to update any internal data structures that may depend on the matrix dimensions.\n\nset_param = <functools.partial object at 0x2adfbaf6d3c0>\nstate_pop()\n\nRestore the state of the output functions saved by state_push.\n\nstate_push()\n\nSave the state of the output functions, to be restored with state_pop.\n\nverbose(msg, *args, **kw)\n\nPrint msg merged with args as a verbose message.\n\nSee Python’s logging module for details of message formatting.\n\nwarning(msg, *args, **kw)\n\nPrint msg merged with args as a warning, unless module variable warnings_as_exceptions is True, then raise an Exception containing the arguments.\n\nSee Python’s logging module for details of message formatting.\n\nclass imagen.__init__.HalfPlane(**params)[source]\n\nConstant pattern on in half of the plane, and off in the rest, with optional Gaussian smoothing.\n\nparam Number x (allow_None=False, bounds=None, constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.2, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nX-coordinate location of pattern center.\nparam Number scale (allow_None=False, bounds=None, constant=False, default=1.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.1, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nMultiplicative strength of input pattern, defaulting to 1.0\nparam String group (allow_None=False, basestring=<type ‘basestring’>, constant=False, default=Pattern, instantiate=False, pickle_default_value=True, precedence=-1, readonly=False)\nThe group name assigned to the returned HoloViews object.\nparam Number orientation (allow_None=False, bounds=None, constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.4, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nPolar angle of pattern, i.e., the orientation in the Cartesian coordinate system, with zero at 3 o’clock and increasing counterclockwise.\nparam ClassSelector z (allow_None=True, constant=False, default=None, instantiate=True, is_instance=True, pickle_default_value=True, precedence=-1, readonly=False)\nThe Dimension object associated with the z-values generated by the PatternGenerator . If None, uses the default set by HoloViews.Image.\nOptional object (expected to be an array) with which to multiply the pattern array after it has been created, before any output_fns are applied. This can be used to shape the pattern.\nBoundingBox of the area in which the pattern is generated.\nparam Number smoothing (allow_None=False, bounds=(0.0, None), constant=False, default=0.02, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.61, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nWidth of the Gaussian fall-off.\nparam Number xdensity (allow_None=False, bounds=(0, None), constant=False, default=256, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=-1, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nDensity (number of samples per 1.0 length) in the x direction.\nparam Number y (allow_None=False, bounds=None, constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.21, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nY-coordinate location of pattern center.\nparam HookList output_fns (allow_None=False, bounds=(0, None), constant=False, default=[], instantiate=True, pickle_default_value=True, precedence=0.08, readonly=False)\nOptional function(s) to apply to the pattern array after it has been created. Can be used for normalization, thresholding, etc.\nparam Number offset (allow_None=False, bounds=None, constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.11, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nAdditive offset to input pattern, defaulting to 0.0\nOptional PatternGenerator used to construct a mask to be applied to the pattern.\nparam Composite position (allow_None=True, attribs=[‘x’, ‘y’], constant=False, default=None, instantiate=False, objtype=<class ‘imagen.patterngenerator.PatternGenerator’>, pickle_default_value=True, precedence=-1, readonly=False)\nCoordinates of location of pattern center. Provides a convenient way to set the x and y parameters together as a tuple (x,y), but shares the same actual storage as x and y (and thus only position OR x and y need to be specified).\nparam Number ydensity (allow_None=False, bounds=(0, None), constant=False, default=256, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=-1, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nDensity (number of samples per 1.0 length) in the y direction. Typically the same as the xdensity.\nparam Number size (allow_None=False, bounds=(0.0, None), constant=False, default=1.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.3, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nDetermines the overall size of the pattern.\nanim(duration, offset=0, timestep=1, label=None, unit=None, time_fn=Time(label='Time', name='Time00001', time_type=<type 'int'>, timestep=1.0, unit=None, until=Infinity()))\n\nduration: The temporal duration to animate in the units defined on the global time function.\n\noffset: The temporal offset from which the animation is generated given the supplied pattern\n\ntimestep: The time interval between successive frames. The duration must be an exact multiple of the timestep.\n\nlabel: A label string to override the label of the global time function (if not None).\n\nunit: The unit string to override the unit value of the global time function (if not None).\n\ntime_fn: The global time function object that is shared across the time-varying objects that are being sampled.\n\nNote that the offset, timestep and time_fn only affect patterns parameterized by time-dependent number generators. Otherwise, the frames are generated by successive call to the pattern which may or may not be varying (e.g to view the patterns contained within a Selector).\n\nchannels(use_cached=False, **params_to_override)\n\nChannels() adds a shared interface for single channel and multichannel structures. It will always return an ordered dict: its first element is the single channel of the pattern (if single-channel) or the channel average (if multichannel); the successive elements are the individual channels’ arrays (key: 0,1,..N-1).\n\ndebug(msg, *args, **kw)\n\nPrint msg merged with args as a debugging statement.\n\nSee Python’s logging module for details of message formatting.\n\ndefaults()\n\nReturn {parameter_name:parameter.default} for all non-constant Parameters.\n\nNote that a Parameter for which instantiate==True has its default instantiated.\n\nforce_new_dynamic_value = <functools.partial object at 0x2adfbaf6d208>\nget_param_values(onlychanged=False)\n\nReturn a list of name,value pairs for all Parameters of this object.\n\nIf onlychanged is True, will only return values that are not equal to the default value.\n\nget_value_generator = <functools.partial object at 0x2adfbaf6d2b8>\ninspect_value = <functools.partial object at 0x2adfbaf6d100>\nmessage(msg, *args, **kw)\n\nPrint msg merged with args as a message.\n\nSee Python’s logging module for details of message formatting.\n\nnum_channels()\n\nQuery the number of channels implemented by the PatternGenerator. In case of single-channel generators this will return 1; in case of multichannel, it will return the number of channels (eg, in the case of RGB images it would return ‘3’, Red-Green-Blue, even though the OrderedDict returned by channels() will have 4 elements – the 3 channels + their average).\n\nclassmethod params(parameter_name=None)\n\nReturn the Parameters of this class as the dictionary {name: parameter_object}\n\nIncludes Parameters from this class and its superclasses.\n\npprint(imports=None, prefix=' ', unknown_value='<?>', qualify=False, separator='')\n\n(Experimental) Pretty printed representation that may be evaluated with eval. See pprint() function for more details.\n\nclassmethod print_param_defaults()\n\nPrint the default values of all cls’s Parameters.\n\nprint_param_values()\n\nPrint the values of all this object’s Parameters.\n\nscript_repr(imports=, []prefix=' ')\n\nVariant of __repr__ designed for generating a runnable script.\n\nclassmethod set_default(param_name, value)\n\nSet the default value of param_name.\n\nEquivalent to setting param_name on the class.\n\nset_dynamic_time_fn = <functools.partial object at 0x2adfbaf6d520>\nset_matrix_dimensions(bounds, xdensity, ydensity)\n\nChange the dimensions of the matrix into which the pattern will be drawn. Users of this class should call this method rather than changing the bounds, xdensity, and ydensity parameters directly. Subclasses can override this method to update any internal data structures that may depend on the matrix dimensions.\n\nset_param = <functools.partial object at 0x2adfbaf6d158>\nstate_pop()\n\nRestore the state of the output functions saved by state_push.\n\nstate_push()\n\nSave the state of the output functions, to be restored with state_pop.\n\nverbose(msg, *args, **kw)\n\nPrint msg merged with args as a verbose message.\n\nSee Python’s logging module for details of message formatting.\n\nwarning(msg, *args, **kw)\n\nPrint msg merged with args as a warning, unless module variable warnings_as_exceptions is True, then raise an Exception containing the arguments.\n\nSee Python’s logging module for details of message formatting.\n\nclass imagen.__init__.CompositeBase(**params)\n\nPatternGenerator that combines or selects from a list of other PatternGenerators.\n\nparam Number x (allow_None=False, bounds=None, constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.2, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nX-coordinate location of pattern center.\nparam Number scale (allow_None=False, bounds=None, constant=False, default=1.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.1, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nMultiplicative strength of input pattern, defaulting to 1.0\nparam String group (allow_None=False, basestring=<type ‘basestring’>, constant=False, default=Pattern, instantiate=False, pickle_default_value=True, precedence=-1, readonly=False)\nThe group name assigned to the returned HoloViews object.\nparam Number orientation (allow_None=False, bounds=None, constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.4, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nPolar angle of pattern, i.e., the orientation in the Cartesian coordinate system, with zero at 3 o’clock and increasing counterclockwise.\nparam ClassSelector z (allow_None=True, constant=False, default=None, instantiate=True, is_instance=True, pickle_default_value=True, precedence=-1, readonly=False)\nThe Dimension object associated with the z-values generated by the PatternGenerator . If None, uses the default set by HoloViews.Image.\nOptional object (expected to be an array) with which to multiply the pattern array after it has been created, before any output_fns are applied. This can be used to shape the pattern.\nBoundingBox of the area in which the pattern is generated.\nparam Number xdensity (allow_None=False, bounds=(0, None), constant=False, default=256, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=-1, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nDensity (number of samples per 1.0 length) in the x direction.\nparam Number y (allow_None=False, bounds=None, constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.21, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nY-coordinate location of pattern center.\nparam HookList output_fns (allow_None=False, bounds=(0, None), constant=False, default=[], instantiate=True, pickle_default_value=True, precedence=0.08, readonly=False)\nOptional function(s) to apply to the pattern array after it has been created. Can be used for normalization, thresholding, etc.\nparam List generators (allow_None=False, bounds=(1, None), constant=False, default=[Constant(bounds=BoundingBox(radius=0.5), group=’Pattern’, mask=None, mask_shape=None, name=’Constant01030’, offset=0.0, orientation=0.0, output_fns=[], position=[0.0, 0.0], scale=0.0, size=1.0, x=0.0, xdensity=256, y=0.0, ydensity=256, z=None)], instantiate=True, pickle_default_value=True, precedence=0.97, readonly=False)\nList of patterns to combine or select from. The default pattern is a blank pattern, and thus should be overridden for any useful work.\nparam Number offset (allow_None=False, bounds=None, constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.11, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nAdditive offset to input pattern, defaulting to 0.0\nOptional PatternGenerator used to construct a mask to be applied to the pattern.\nparam Composite position (allow_None=True, attribs=[‘x’, ‘y’], constant=False, default=None, instantiate=False, objtype=<class ‘imagen.patterngenerator.PatternGenerator’>, pickle_default_value=True, precedence=-1, readonly=False)\nCoordinates of location of pattern center. Provides a convenient way to set the x and y parameters together as a tuple (x,y), but shares the same actual storage as x and y (and thus only position OR x and y need to be specified).\nparam Number ydensity (allow_None=False, bounds=(0, None), constant=False, default=256, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=-1, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nDensity (number of samples per 1.0 length) in the y direction. Typically the same as the xdensity.\nparam Number size (allow_None=False, bounds=(0.0, None), constant=False, default=1.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.3, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nScaling factor applied to all sub-patterns.\nanim(duration, offset=0, timestep=1, label=None, unit=None, time_fn=Time(label='Time', name='Time00001', time_type=<type 'int'>, timestep=1.0, unit=None, until=Infinity()))\n\nduration: The temporal duration to animate in the units defined on the global time function.\n\noffset: The temporal offset from which the animation is generated given the supplied pattern\n\ntimestep: The time interval between successive frames. The duration must be an exact multiple of the timestep.\n\nlabel: A label string to override the label of the global time function (if not None).\n\nunit: The unit string to override the unit value of the global time function (if not None).\n\ntime_fn: The global time function object that is shared across the time-varying objects that are being sampled.\n\nNote that the offset, timestep and time_fn only affect patterns parameterized by time-dependent number generators. Otherwise, the frames are generated by successive call to the pattern which may or may not be varying (e.g to view the patterns contained within a Selector).\n\nchannels(use_cached=False, **params_to_override)\n\nChannels() adds a shared interface for single channel and multichannel structures. It will always return an ordered dict: its first element is the single channel of the pattern (if single-channel) or the channel average (if multichannel); the successive elements are the individual channels’ arrays (key: 0,1,..N-1).\n\ndebug(msg, *args, **kw)\n\nPrint msg merged with args as a debugging statement.\n\nSee Python’s logging module for details of message formatting.\n\ndefaults()\n\nReturn {parameter_name:parameter.default} for all non-constant Parameters.\n\nNote that a Parameter for which instantiate==True has its default instantiated.\n\nforce_new_dynamic_value = <functools.partial object at 0x2adfbaf6d730>\nfunction(p)\n\nFunction to draw a pattern that will then be scaled and rotated.\n\nInstead of implementing __call__ directly, PatternGenerator subclasses will typically implement this helper function used by __call__, because that way they can let __call__ handle the scaling and rotation for them. Alternatively, __call__ itself can be reimplemented entirely by a subclass (e.g. if it does not need to do any scaling or rotation), in which case this function will be ignored.\n\nget_param_values(onlychanged=False)\n\nReturn a list of name,value pairs for all Parameters of this object.\n\nIf onlychanged is True, will only return values that are not equal to the default value.\n\nget_value_generator = <functools.partial object at 0x2adfbaf6d838>\ninspect_value = <functools.partial object at 0x2adfbaf6d368>\nmessage(msg, *args, **kw)\n\nPrint msg merged with args as a message.\n\nSee Python’s logging module for details of message formatting.\n\nnum_channels()\n\nQuery the number of channels implemented by the PatternGenerator. In case of single-channel generators this will return 1; in case of multichannel, it will return the number of channels (eg, in the case of RGB images it would return ‘3’, Red-Green-Blue, even though the OrderedDict returned by channels() will have 4 elements – the 3 channels + their average).\n\nclassmethod params(parameter_name=None)\n\nReturn the Parameters of this class as the dictionary {name: parameter_object}\n\nIncludes Parameters from this class and its superclasses.\n\npprint(imports=None, prefix=' ', unknown_value='<?>', qualify=False, separator='')\n\n(Experimental) Pretty printed representation that may be evaluated with eval. See pprint() function for more details.\n\nclassmethod print_param_defaults()\n\nPrint the default values of all cls’s Parameters.\n\nprint_param_values()\n\nPrint the values of all this object’s Parameters.\n\nscript_repr(imports=, []prefix=' ')\n\nVariant of __repr__ designed for generating a runnable script.\n\nclassmethod set_default(param_name, value)\n\nSet the default value of param_name.\n\nEquivalent to setting param_name on the class.\n\nset_dynamic_time_fn = <functools.partial object at 0x2adfbaf6d680>\nset_matrix_dimensions(bounds, xdensity, ydensity)\n\nChange the dimensions of the matrix into which the pattern will be drawn. Users of this class should call this method rather than changing the bounds, xdensity, and ydensity parameters directly. Subclasses can override this method to update any internal data structures that may depend on the matrix dimensions.\n\nset_param = <functools.partial object at 0x2adfbaf6d578>\nstate_pop()\n\nRestore the state of the output functions saved by state_push.\n\nstate_push()\n\nSave the state of the output functions, to be restored with state_pop.\n\nverbose(msg, *args, **kw)\n\nPrint msg merged with args as a verbose message.\n\nSee Python’s logging module for details of message formatting.\n\nwarning(msg, *args, **kw)\n\nPrint msg merged with args as a warning, unless module variable warnings_as_exceptions is True, then raise an Exception containing the arguments.\n\nSee Python’s logging module for details of message formatting.\n\nclass imagen.__init__.Curve(**params)[source]\n\nBases: imagen.__init__.Arc\n\n2D curve pattern generator.\n\nBased on Arc, but centered on a tangent point midway through the arc, rather than at the center of a ring, and with curvature controlled directly rather than through the overall size of the pattern.\n\nDepending on the size_type, the size parameter can control either the width of the pattern, keeping this constant regardless of curvature, or the length of the curve, keeping that constant instead (as for a long thin object being bent).\n\nSpecifically, for size_type==’constant_length’, the curvature parameter determines the ratio of height to width of the arc, with positive curvature for concave shape and negative for convex. The size parameter determines the width of the curve.\n\nFor size_type==’constant_width’, the curvature parameter determines the portion of curve radian to 2pi, and the curve radius is changed accordingly following the formula:\n\nsize=2pi*radius*curvature\n\n\nThus, the size parameter determines the total length of the curve. Positive curvature stands for concave shape, and negative for convex.\n\nSee the Disk class for a note about the Gaussian fall-off.\n\nparam Number size (allow_None=False, bounds=(0.0, None), constant=False, default=0.5, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.3, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nDetermines the overall size of the pattern.\nparam Number orientation (allow_None=False, bounds=None, constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.4, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nPolar angle of pattern, i.e., the orientation in the Cartesian coordinate system, with zero at 3 o’clock and increasing counterclockwise.\nparam Number smoothing (allow_None=False, bounds=(0.0, None), constant=False, default=0.05, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.61, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nWidth of the Gaussian fall-off inside and outside the ring.\nparam Number arc_length (allow_None=False, bounds=(0.0, None), constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=-1.0, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nLength of the arc, in radians, starting from orientation 0.0.\nparam Number scale (allow_None=False, bounds=None, constant=False, default=1.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.1, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nMultiplicative strength of input pattern, defaulting to 1.0\nparam String group (allow_None=False, basestring=<type ‘basestring’>, constant=False, default=Pattern, instantiate=False, pickle_default_value=True, precedence=-1, readonly=False)\nThe group name assigned to the returned HoloViews object.\nparam ObjectSelector size_type (allow_None=None, check_on_set=True, compute_default_fn=None, constant=False, default=constant_length, instantiate=False, objects=[‘constant_length’, ‘constant_width’], pickle_default_value=True, precedence=0.61, readonly=False)\nFor a given size, whether to draw a curve with that total length, or with that width, keeping it constant as curvature is varied.\nparam Number thickness (allow_None=False, bounds=(0.0, None), constant=False, default=0.015, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.6, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nThickness (line width) of the ring.\nparam Number xdensity (allow_None=False, bounds=(0, None), constant=False, default=256, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=-1, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nDensity (number of samples per 1.0 length) in the x direction.\nparam Number ydensity (allow_None=False, bounds=(0, None), constant=False, default=256, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=-1, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nDensity (number of samples per 1.0 length) in the y direction. Typically the same as the xdensity.\nparam Number curvature (allow_None=False, bounds=(-0.5, 0.5), constant=False, default=0.5, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.62, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nRatio of height to width of the arc, with positive value giving a concave shape and negative value giving convex.\nparam Number y (allow_None=False, bounds=None, constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.21, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nY-coordinate location of pattern center.\nparam Composite position (allow_None=True, attribs=[‘x’, ‘y’], constant=False, default=None, instantiate=False, objtype=<class ‘imagen.patterngenerator.PatternGenerator’>, pickle_default_value=True, precedence=-1, readonly=False)\nCoordinates of location of pattern center. Provides a convenient way to set the x and y parameters together as a tuple (x,y), but shares the same actual storage as x and y (and thus only position OR x and y need to be specified).\nparam Number offset (allow_None=False, bounds=None, constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.11, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nAdditive offset to input pattern, defaulting to 0.0\nOptional object (expected to be an array) with which to multiply the pattern array after it has been created, before any output_fns are applied. This can be used to shape the pattern.\nBoundingBox of the area in which the pattern is generated.\nparam HookList output_fns (allow_None=False, bounds=(0, None), constant=False, default=[], instantiate=True, pickle_default_value=True, precedence=0.08, readonly=False)\nOptional function(s) to apply to the pattern array after it has been created. Can be used for normalization, thresholding, etc.\nOptional PatternGenerator used to construct a mask to be applied to the pattern.\nparam Number aspect_ratio (allow_None=False, bounds=(0.0, None), constant=False, default=1.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=-1.0, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nRatio of width to height; size*aspect_ratio gives the overall width.\nparam Number x (allow_None=False, bounds=None, constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.2, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nX-coordinate location of pattern center.\nparam ClassSelector z (allow_None=True, constant=False, default=None, instantiate=True, is_instance=True, pickle_default_value=True, precedence=-1, readonly=False)\nThe Dimension object associated with the z-values generated by the PatternGenerator . If None, uses the default set by HoloViews.Image.\nanim(duration, offset=0, timestep=1, label=None, unit=None, time_fn=Time(label='Time', name='Time00001', time_type=<type 'int'>, timestep=1.0, unit=None, until=Infinity()))\n\nduration: The temporal duration to animate in the units defined on the global time function.\n\noffset: The temporal offset from which the animation is generated given the supplied pattern\n\ntimestep: The time interval between successive frames. The duration must be an exact multiple of the timestep.\n\nlabel: A label string to override the label of the global time function (if not None).\n\nunit: The unit string to override the unit value of the global time function (if not None).\n\ntime_fn: The global time function object that is shared across the time-varying objects that are being sampled.\n\nNote that the offset, timestep and time_fn only affect patterns parameterized by time-dependent number generators. Otherwise, the frames are generated by successive call to the pattern which may or may not be varying (e.g to view the patterns contained within a Selector).\n\nchannels(use_cached=False, **params_to_override)\n\nChannels() adds a shared interface for single channel and multichannel structures. It will always return an ordered dict: its first element is the single channel of the pattern (if single-channel) or the channel average (if multichannel); the successive elements are the individual channels’ arrays (key: 0,1,..N-1).\n\ndebug(msg, *args, **kw)\n\nPrint msg merged with args as a debugging statement.\n\nSee Python’s logging module for details of message formatting.\n\ndefaults()\n\nReturn {parameter_name:parameter.default} for all non-constant Parameters.\n\nNote that a Parameter for which instantiate==True has its default instantiated.\n\nforce_new_dynamic_value = <functools.partial object at 0x2adfbaf6d100>\nget_param_values(onlychanged=False)\n\nReturn a list of name,value pairs for all Parameters of this object.\n\nIf onlychanged is True, will only return values that are not equal to the default value.\n\nget_value_generator = <functools.partial object at 0x2adfbaf6d3c0>\ninspect_value = <functools.partial object at 0x2adfbaf6d310>\nmessage(msg, *args, **kw)\n\nPrint msg merged with args as a message.\n\nSee Python’s logging module for details of message formatting.\n\nnum_channels()\n\nQuery the number of channels implemented by the PatternGenerator. In case of single-channel generators this will return 1; in case of multichannel, it will return the number of channels (eg, in the case of RGB images it would return ‘3’, Red-Green-Blue, even though the OrderedDict returned by channels() will have 4 elements – the 3 channels + their average).\n\nclassmethod params(parameter_name=None)\n\nReturn the Parameters of this class as the dictionary {name: parameter_object}\n\nIncludes Parameters from this class and its superclasses.\n\npprint(imports=None, prefix=' ', unknown_value='<?>', qualify=False, separator='')\n\n(Experimental) Pretty printed representation that may be evaluated with eval. See pprint() function for more details.\n\nclassmethod print_param_defaults()\n\nPrint the default values of all cls’s Parameters.\n\nprint_param_values()\n\nPrint the values of all this object’s Parameters.\n\nscript_repr(imports=, []prefix=' ')\n\nVariant of __repr__ designed for generating a runnable script.\n\nclassmethod set_default(param_name, value)\n\nSet the default value of param_name.\n\nEquivalent to setting param_name on the class.\n\nset_dynamic_time_fn = <functools.partial object at 0x2adfbaf6d158>\nset_matrix_dimensions(bounds, xdensity, ydensity)\n\nChange the dimensions of the matrix into which the pattern will be drawn. Users of this class should call this method rather than changing the bounds, xdensity, and ydensity parameters directly. Subclasses can override this method to update any internal data structures that may depend on the matrix dimensions.\n\nset_param = <functools.partial object at 0x2adfbaf6d998>\nstate_pop()\n\nRestore the state of the output functions saved by state_push.\n\nstate_push()\n\nSave the state of the output functions, to be restored with state_pop.\n\nverbose(msg, *args, **kw)\n\nPrint msg merged with args as a verbose message.\n\nSee Python’s logging module for details of message formatting.\n\nwarning(msg, *args, **kw)\n\nPrint msg merged with args as a warning, unless module variable warnings_as_exceptions is True, then raise an Exception containing the arguments.\n\nSee Python’s logging module for details of message formatting.\n\nGrating pattern made from alternating smooth circular segments (pie-shapes).\n\nparam Number x (allow_None=False, bounds=None, constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.2, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nX-coordinate location of pattern center.\nparam Integer parts (allow_None=False, bounds=(1, None), constant=False, default=4, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.31, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nNumber of parts in the grating.\nparam Number scale (allow_None=False, bounds=None, constant=False, default=1.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.1, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nMultiplicative strength of input pattern, defaulting to 1.0\nparam String group (allow_None=False, basestring=<type ‘basestring’>, constant=False, default=Pattern, instantiate=False, pickle_default_value=True, precedence=-1, readonly=False)\nThe group name assigned to the returned HoloViews object.\nparam Number orientation (allow_None=False, bounds=None, constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.4, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nPolar angle of pattern, i.e., the orientation in the Cartesian coordinate system, with zero at 3 o’clock and increasing counterclockwise.\nparam ClassSelector z (allow_None=True, constant=False, default=None, instantiate=True, is_instance=True, pickle_default_value=True, precedence=-1, readonly=False)\nThe Dimension object associated with the z-values generated by the PatternGenerator . If None, uses the default set by HoloViews.Image.\nOptional object (expected to be an array) with which to multiply the pattern array after it has been created, before any output_fns are applied. This can be used to shape the pattern.\nBoundingBox of the area in which the pattern is generated.\nparam Parameter operator (allow_None=False, constant=False, default=<ufunc ‘maximum’>, instantiate=False, pickle_default_value=True, precedence=0.98, readonly=False)\nBinary Numpy function used to combine the individual patterns. Any binary Numpy array “ufunc” returning the same type of array as the operands and supporting the reduce operator is allowed here. Supported ufuncs include:: add subtract multiply divide maximum minimum remainder power The most useful ones are probably add and maximum, but there are uses for at least some of the others as well (e.g. to remove pieces of other patterns). You can also write your own operators, by making a class that has a static method named “reduce” that returns an array of the same size and type as the arrays in the list. For example:: class return_first(object): @staticmethod def reduce(x): return x\nparam Number smoothing (allow_None=False, bounds=(0.0, None), constant=False, default=0.8, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.61, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nWidth of the Gaussian fall-off outside the sector, scaled by parts.\nparam Number xdensity (allow_None=False, bounds=(0, None), constant=False, default=256, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=-1, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nDensity (number of samples per 1.0 length) in the x direction.\nparam Number y (allow_None=False, bounds=None, constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.21, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nY-coordinate location of pattern center.\nparam HookList output_fns (allow_None=False, bounds=(0, None), constant=False, default=[], instantiate=True, pickle_default_value=True, precedence=0.08, readonly=False)\nOptional function(s) to apply to the pattern array after it has been created. Can be used for normalization, thresholding, etc.\nparam List generators (allow_None=False, bounds=(1, None), constant=False, default=[Constant(bounds=BoundingBox(radius=0.5), group=’Pattern’, mask=None, mask_shape=None, name=’Constant01030’, offset=0.0, orientation=0.0, output_fns=[], position=[0.0, 0.0], scale=0.0, size=1.0, x=0.0, xdensity=256, y=0.0, ydensity=256, z=None)], instantiate=True, pickle_default_value=True, precedence=0.97, readonly=False)\nList of patterns to combine or select from. The default pattern is a blank pattern, and thus should be overridden for any useful work.\nparam Number offset (allow_None=False, bounds=None, constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.11, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nAdditive offset to input pattern, defaulting to 0.0\nOptional PatternGenerator used to construct a mask to be applied to the pattern.\nparam Composite position (allow_None=True, attribs=[‘x’, ‘y’], constant=False, default=None, instantiate=False, objtype=<class ‘imagen.patterngenerator.PatternGenerator’>, pickle_default_value=True, precedence=-1, readonly=False)\nCoordinates of location of pattern center. Provides a convenient way to set the x and y parameters together as a tuple (x,y), but shares the same actual storage as x and y (and thus only position OR x and y need to be specified).\nparam Number ydensity (allow_None=False, bounds=(0, None), constant=False, default=256, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=-1, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nDensity (number of samples per 1.0 length) in the y direction. Typically the same as the xdensity.\nparam Number size (allow_None=False, bounds=(0.0, None), constant=False, default=1.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.3, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nScaling factor applied to all sub-patterns.\nanim(duration, offset=0, timestep=1, label=None, unit=None, time_fn=Time(label='Time', name='Time00001', time_type=<type 'int'>, timestep=1.0, unit=None, until=Infinity()))\n\nduration: The temporal duration to animate in the units defined on the global time function.\n\noffset: The temporal offset from which the animation is generated given the supplied pattern\n\ntimestep: The time interval between successive frames. The duration must be an exact multiple of the timestep.\n\nlabel: A label string to override the label of the global time function (if not None).\n\nunit: The unit string to override the unit value of the global time function (if not None).\n\ntime_fn: The global time function object that is shared across the time-varying objects that are being sampled.\n\nNote that the offset, timestep and time_fn only affect patterns parameterized by time-dependent number generators. Otherwise, the frames are generated by successive call to the pattern which may or may not be varying (e.g to view the patterns contained within a Selector).\n\nchannels(use_cached=False, **params_to_override)\n\nChannels() adds a shared interface for single channel and multichannel structures. It will always return an ordered dict: its first element is the single channel of the pattern (if single-channel) or the channel average (if multichannel); the successive elements are the individual channels’ arrays (key: 0,1,..N-1).\n\ndebug(msg, *args, **kw)\n\nPrint msg merged with args as a debugging statement.\n\nSee Python’s logging module for details of message formatting.\n\ndefaults()\n\nReturn {parameter_name:parameter.default} for all non-constant Parameters.\n\nNote that a Parameter for which instantiate==True has its default instantiated.\n\nforce_new_dynamic_value = <functools.partial object at 0x2adfbaf6d838>\nget_param_values(onlychanged=False)\n\nReturn a list of name,value pairs for all Parameters of this object.\n\nIf onlychanged is True, will only return values that are not equal to the default value.\n\nget_value_generator = <functools.partial object at 0x2adfbaf6d680>\ninspect_value = <functools.partial object at 0x2adfbaf6d310>\nmessage(msg, *args, **kw)\n\nPrint msg merged with args as a message.\n\nSee Python’s logging module for details of message formatting.\n\nnum_channels()\n\nQuery the number of channels implemented by the PatternGenerator. In case of single-channel generators this will return 1; in case of multichannel, it will return the number of channels (eg, in the case of RGB images it would return ‘3’, Red-Green-Blue, even though the OrderedDict returned by channels() will have 4 elements – the 3 channels + their average).\n\noperator = <ufunc 'maximum'>\nclassmethod params(parameter_name=None)\n\nReturn the Parameters of this class as the dictionary {name: parameter_object}\n\nIncludes Parameters from this class and its superclasses.\n\npprint(imports=None, prefix=' ', unknown_value='<?>', qualify=False, separator='')\n\n(Experimental) Pretty printed representation that may be evaluated with eval. See pprint() function for more details.\n\nclassmethod print_param_defaults()\n\nPrint the default values of all cls’s Parameters.\n\nprint_param_values()\n\nPrint the values of all this object’s Parameters.\n\nscript_repr(imports=, []prefix=' ')\n\nVariant of __repr__ designed for generating a runnable script.\n\nclassmethod set_default(param_name, value)\n\nSet the default value of param_name.\n\nEquivalent to setting param_name on the class.\n\nset_dynamic_time_fn = <functools.partial object at 0x2adfbaf6d2b8>\nset_matrix_dimensions(bounds, xdensity, ydensity)\n\nChange the dimensions of the matrix into which the pattern will be drawn. Users of this class should call this method rather than changing the bounds, xdensity, and ydensity parameters directly. Subclasses can override this method to update any internal data structures that may depend on the matrix dimensions.\n\nset_param = <functools.partial object at 0x2adfbaf6d368>\nstate_pop()\n\nPop the state of all generators\n\nstate_push()\n\nPush the state of all generators\n\nverbose(msg, *args, **kw)\n\nPrint msg merged with args as a verbose message.\n\nSee Python’s logging module for details of message formatting.\n\nwarning(msg, *args, **kw)\n\nPrint msg merged with args as a warning, unless module variable warnings_as_exceptions is True, then raise an Exception containing the arguments.\n\nSee Python’s logging module for details of message formatting.\n\nclass imagen.__init__.ConcentricRings(**params)[source]\n\nConcentric rings with linearly increasing radius. Gaussian fall-off at the edges.\n\nparam Number x (allow_None=False, bounds=None, constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.2, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nX-coordinate location of pattern center.\nparam Number scale (allow_None=False, bounds=None, constant=False, default=1.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.1, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nMultiplicative strength of input pattern, defaulting to 1.0\nparam String group (allow_None=False, basestring=<type ‘basestring’>, constant=False, default=Pattern, instantiate=False, pickle_default_value=True, precedence=-1, readonly=False)\nThe group name assigned to the returned HoloViews object.\nparam Number orientation (allow_None=False, bounds=None, constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.4, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nPolar angle of pattern, i.e., the orientation in the Cartesian coordinate system, with zero at 3 o’clock and increasing counterclockwise.\nparam Number aspect_ratio (allow_None=False, bounds=(0.0, None), constant=False, default=1.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.31, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nRatio of width to height.\nparam ClassSelector z (allow_None=True, constant=False, default=None, instantiate=True, is_instance=True, pickle_default_value=True, precedence=-1, readonly=False)\nThe Dimension object associated with the z-values generated by the PatternGenerator . If None, uses the default set by HoloViews.Image.\nOptional object (expected to be an array) with which to multiply the pattern array after it has been created, before any output_fns are applied. This can be used to shape the pattern.\nBoundingBox of the area in which the pattern is generated.\nparam Number thickness (allow_None=False, bounds=(0.0, None), constant=False, default=0.04, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.6, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nThickness (line width) of the ring.\nparam Number xdensity (allow_None=False, bounds=(0, None), constant=False, default=256, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=-1, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nDensity (number of samples per 1.0 length) in the x direction.\nparam Number y (allow_None=False, bounds=None, constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.21, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nY-coordinate location of pattern center.\nparam HookList output_fns (allow_None=False, bounds=(0, None), constant=False, default=[], instantiate=True, pickle_default_value=True, precedence=0.08, readonly=False)\nOptional function(s) to apply to the pattern array after it has been created. Can be used for normalization, thresholding, etc.\nparam Number offset (allow_None=False, bounds=None, constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.11, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nAdditive offset to input pattern, defaulting to 0.0\nOptional PatternGenerator used to construct a mask to be applied to the pattern.\nparam Composite position (allow_None=True, attribs=[‘x’, ‘y’], constant=False, default=None, instantiate=False, objtype=<class ‘imagen.patterngenerator.PatternGenerator’>, pickle_default_value=True, precedence=-1, readonly=False)\nCoordinates of location of pattern center. Provides a convenient way to set the x and y parameters together as a tuple (x,y), but shares the same actual storage as x and y (and thus only position OR x and y need to be specified).\nparam Number smoothing (allow_None=False, bounds=(0.0, None), constant=False, default=0.05, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.61, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nWidth of the Gaussian fall-off inside and outside the rings.\nparam Number ydensity (allow_None=False, bounds=(0, None), constant=False, default=256, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=-1, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nDensity (number of samples per 1.0 length) in the y direction. Typically the same as the xdensity.\nparam Number size (allow_None=False, bounds=(0.01, None), constant=False, default=0.4, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.62, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nanim(duration, offset=0, timestep=1, label=None, unit=None, time_fn=Time(label='Time', name='Time00001', time_type=<type 'int'>, timestep=1.0, unit=None, until=Infinity()))\n\nduration: The temporal duration to animate in the units defined on the global time function.\n\noffset: The temporal offset from which the animation is generated given the supplied pattern\n\ntimestep: The time interval between successive frames. The duration must be an exact multiple of the timestep.\n\nlabel: A label string to override the label of the global time function (if not None).\n\nunit: The unit string to override the unit value of the global time function (if not None).\n\ntime_fn: The global time function object that is shared across the time-varying objects that are being sampled.\n\nNote that the offset, timestep and time_fn only affect patterns parameterized by time-dependent number generators. Otherwise, the frames are generated by successive call to the pattern which may or may not be varying (e.g to view the patterns contained within a Selector).\n\nchannels(use_cached=False, **params_to_override)\n\nChannels() adds a shared interface for single channel and multichannel structures. It will always return an ordered dict: its first element is the single channel of the pattern (if single-channel) or the channel average (if multichannel); the successive elements are the individual channels’ arrays (key: 0,1,..N-1).\n\ndebug(msg, *args, **kw)\n\nPrint msg merged with args as a debugging statement.\n\nSee Python’s logging module for details of message formatting.\n\ndefaults()\n\nReturn {parameter_name:parameter.default} for all non-constant Parameters.\n\nNote that a Parameter for which instantiate==True has its default instantiated.\n\nforce_new_dynamic_value = <functools.partial object at 0x2adfbaf6d5d0>\nget_param_values(onlychanged=False)\n\nReturn a list of name,value pairs for all Parameters of this object.\n\nIf onlychanged is True, will only return values that are not equal to the default value.\n\nget_value_generator = <functools.partial object at 0x2adfbaf6d310>\ninspect_value = <functools.partial object at 0x2adfbaf6d998>\nmessage(msg, *args, **kw)\n\nPrint msg merged with args as a message.\n\nSee Python’s logging module for details of message formatting.\n\nnum_channels()\n\nQuery the number of channels implemented by the PatternGenerator. In case of single-channel generators this will return 1; in case of multichannel, it will return the number of channels (eg, in the case of RGB images it would return ‘3’, Red-Green-Blue, even though the OrderedDict returned by channels() will have 4 elements – the 3 channels + their average).\n\nclassmethod params(parameter_name=None)\n\nReturn the Parameters of this class as the dictionary {name: parameter_object}\n\nIncludes Parameters from this class and its superclasses.\n\npprint(imports=None, prefix=' ', unknown_value='<?>', qualify=False, separator='')\n\n(Experimental) Pretty printed representation that may be evaluated with eval. See pprint() function for more details.\n\nclassmethod print_param_defaults()\n\nPrint the default values of all cls’s Parameters.\n\nprint_param_values()\n\nPrint the values of all this object’s Parameters.\n\nscript_repr(imports=, []prefix=' ')\n\nVariant of __repr__ designed for generating a runnable script.\n\nclassmethod set_default(param_name, value)\n\nSet the default value of param_name.\n\nEquivalent to setting param_name on the class.\n\nset_dynamic_time_fn = <functools.partial object at 0x2adfbaf6d788>\nset_matrix_dimensions(bounds, xdensity, ydensity)\n\nChange the dimensions of the matrix into which the pattern will be drawn. Users of this class should call this method rather than changing the bounds, xdensity, and ydensity parameters directly. Subclasses can override this method to update any internal data structures that may depend on the matrix dimensions.\n\nset_param = <functools.partial object at 0x2adfbaf6d3c0>\nstate_pop()\n\nRestore the state of the output functions saved by state_push.\n\nstate_push()\n\nSave the state of the output functions, to be restored with state_pop.\n\nverbose(msg, *args, **kw)\n\nPrint msg merged with args as a verbose message.\n\nSee Python’s logging module for details of message formatting.\n\nwarning(msg, *args, **kw)\n\nPrint msg merged with args as a warning, unless module variable warnings_as_exceptions is True, then raise an Exception containing the arguments.\n\nSee Python’s logging module for details of message formatting.\n\nclass imagen.__init__.RawRectangle(**params)[source]\n\n2D rectangle pattern generator with no smoothing, for use when drawing patterns pixel by pixel.\n\nparam Number x (allow_None=False, bounds=None, constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.2, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nX-coordinate location of pattern center.\nparam Number scale (allow_None=False, bounds=None, constant=False, default=1.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.1, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nMultiplicative strength of input pattern, defaulting to 1.0\nparam String group (allow_None=False, basestring=<type ‘basestring’>, constant=False, default=Pattern, instantiate=False, pickle_default_value=True, precedence=-1, readonly=False)\nThe group name assigned to the returned HoloViews object.\nparam Number orientation (allow_None=False, bounds=None, constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.4, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nPolar angle of pattern, i.e., the orientation in the Cartesian coordinate system, with zero at 3 o’clock and increasing counterclockwise.\nparam Number aspect_ratio (allow_None=False, bounds=(0.0, None), constant=False, default=1.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.31, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nRatio of width to height; size*aspect_ratio gives the width of the rectangle.\nparam ClassSelector z (allow_None=True, constant=False, default=None, instantiate=True, is_instance=True, pickle_default_value=True, precedence=-1, readonly=False)\nThe Dimension object associated with the z-values generated by the PatternGenerator . If None, uses the default set by HoloViews.Image.\nOptional object (expected to be an array) with which to multiply the pattern array after it has been created, before any output_fns are applied. This can be used to shape the pattern.\nBoundingBox of the area in which the pattern is generated.\nparam Number xdensity (allow_None=False, bounds=(0, None), constant=False, default=256, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=-1, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nDensity (number of samples per 1.0 length) in the x direction.\nparam Number y (allow_None=False, bounds=None, constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.21, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nY-coordinate location of pattern center.\nparam HookList output_fns (allow_None=False, bounds=(0, None), constant=False, default=[], instantiate=True, pickle_default_value=True, precedence=0.08, readonly=False)\nOptional function(s) to apply to the pattern array after it has been created. Can be used for normalization, thresholding, etc.\nparam Number offset (allow_None=False, bounds=None, constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.11, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nAdditive offset to input pattern, defaulting to 0.0\nOptional PatternGenerator used to construct a mask to be applied to the pattern.\nparam Composite position (allow_None=True, attribs=[‘x’, ‘y’], constant=False, default=None, instantiate=False, objtype=<class ‘imagen.patterngenerator.PatternGenerator’>, pickle_default_value=True, precedence=-1, readonly=False)\nCoordinates of location of pattern center. Provides a convenient way to set the x and y parameters together as a tuple (x,y), but shares the same actual storage as x and y (and thus only position OR x and y need to be specified).\nparam Number ydensity (allow_None=False, bounds=(0, None), constant=False, default=256, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=-1, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nDensity (number of samples per 1.0 length) in the y direction. Typically the same as the xdensity.\nparam Number size (allow_None=False, bounds=(0.0, None), constant=False, default=0.5, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.3, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nHeight of the rectangle.\nanim(duration, offset=0, timestep=1, label=None, unit=None, time_fn=Time(label='Time', name='Time00001', time_type=<type 'int'>, timestep=1.0, unit=None, until=Infinity()))\n\nduration: The temporal duration to animate in the units defined on the global time function.\n\noffset: The temporal offset from which the animation is generated given the supplied pattern\n\ntimestep: The time interval between successive frames. The duration must be an exact multiple of the timestep.\n\nlabel: A label string to override the label of the global time function (if not None).\n\nunit: The unit string to override the unit value of the global time function (if not None).\n\ntime_fn: The global time function object that is shared across the time-varying objects that are being sampled.\n\nNote that the offset, timestep and time_fn only affect patterns parameterized by time-dependent number generators. Otherwise, the frames are generated by successive call to the pattern which may or may not be varying (e.g to view the patterns contained within a Selector).\n\nchannels(use_cached=False, **params_to_override)\n\nChannels() adds a shared interface for single channel and multichannel structures. It will always return an ordered dict: its first element is the single channel of the pattern (if single-channel) or the channel average (if multichannel); the successive elements are the individual channels’ arrays (key: 0,1,..N-1).\n\ndebug(msg, *args, **kw)\n\nPrint msg merged with args as a debugging statement.\n\nSee Python’s logging module for details of message formatting.\n\ndefaults()\n\nReturn {parameter_name:parameter.default} for all non-constant Parameters.\n\nNote that a Parameter for which instantiate==True has its default instantiated.\n\nforce_new_dynamic_value = <functools.partial object at 0x2adfbaf6d5d0>\nget_param_values(onlychanged=False)\n\nReturn a list of name,value pairs for all Parameters of this object.\n\nIf onlychanged is True, will only return values that are not equal to the default value.\n\nget_value_generator = <functools.partial object at 0x2adfbaf6d2b8>\ninspect_value = <functools.partial object at 0x2adfbaf6d940>\nmessage(msg, *args, **kw)\n\nPrint msg merged with args as a message.\n\nSee Python’s logging module for details of message formatting.\n\nnum_channels()\n\nQuery the number of channels implemented by the PatternGenerator. In case of single-channel generators this will return 1; in case of multichannel, it will return the number of channels (eg, in the case of RGB images it would return ‘3’, Red-Green-Blue, even though the OrderedDict returned by channels() will have 4 elements – the 3 channels + their average).\n\nclassmethod params(parameter_name=None)\n\nReturn the Parameters of this class as the dictionary {name: parameter_object}\n\nIncludes Parameters from this class and its superclasses.\n\npprint(imports=None, prefix=' ', unknown_value='<?>', qualify=False, separator='')\n\n(Experimental) Pretty printed representation that may be evaluated with eval. See pprint() function for more details.\n\nclassmethod print_param_defaults()\n\nPrint the default values of all cls’s Parameters.\n\nprint_param_values()\n\nPrint the values of all this object’s Parameters.\n\nscript_repr(imports=, []prefix=' ')\n\nVariant of __repr__ designed for generating a runnable script.\n\nclassmethod set_default(param_name, value)\n\nSet the default value of param_name.\n\nEquivalent to setting param_name on the class.\n\nset_dynamic_time_fn = <functools.partial object at 0x2adfbaf6d520>\nset_matrix_dimensions(bounds, xdensity, ydensity)\n\nChange the dimensions of the matrix into which the pattern will be drawn. Users of this class should call this method rather than changing the bounds, xdensity, and ydensity parameters directly. Subclasses can override this method to update any internal data structures that may depend on the matrix dimensions.\n\nset_param = <functools.partial object at 0x2adfbaf6d838>\nstate_pop()\n\nRestore the state of the output functions saved by state_push.\n\nstate_push()\n\nSave the state of the output functions, to be restored with state_pop.\n\nverbose(msg, *args, **kw)\n\nPrint msg merged with args as a verbose message.\n\nSee Python’s logging module for details of message formatting.\n\nwarning(msg, *args, **kw)\n\nPrint msg merged with args as a warning, unless module variable warnings_as_exceptions is True, then raise an Exception containing the arguments.\n\nSee Python’s logging module for details of message formatting.\n\nclass imagen.__init__.Wedge(**params)[source]\n\nA sector of a circle with Gaussian fall-off, with size determining the arc length.\n\nparam Number x (allow_None=False, bounds=None, constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.2, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nX-coordinate location of pattern center.\nparam Number scale (allow_None=False, bounds=None, constant=False, default=1.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.1, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nMultiplicative strength of input pattern, defaulting to 1.0\nparam String group (allow_None=False, basestring=<type ‘basestring’>, constant=False, default=Pattern, instantiate=False, pickle_default_value=True, precedence=-1, readonly=False)\nThe group name assigned to the returned HoloViews object.\nparam Number orientation (allow_None=False, bounds=None, constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.4, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nPolar angle of pattern, i.e., the orientation in the Cartesian coordinate system, with zero at 3 o’clock and increasing counterclockwise.\nparam Number aspect_ratio (allow_None=False, bounds=(0.0, None), constant=False, default=1.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.31, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nRatio of width to height.\nparam ClassSelector z (allow_None=True, constant=False, default=None, instantiate=True, is_instance=True, pickle_default_value=True, precedence=-1, readonly=False)\nThe Dimension object associated with the z-values generated by the PatternGenerator . If None, uses the default set by HoloViews.Image.\nOptional object (expected to be an array) with which to multiply the pattern array after it has been created, before any output_fns are applied. This can be used to shape the pattern.\nBoundingBox of the area in which the pattern is generated.\nparam Number smoothing (allow_None=False, bounds=(0.0, None), constant=False, default=0.4, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.61, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nWidth of the Gaussian fall-off outside the sector.\nparam Number xdensity (allow_None=False, bounds=(0, None), constant=False, default=256, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=-1, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nDensity (number of samples per 1.0 length) in the x direction.\nparam Number y (allow_None=False, bounds=None, constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.21, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nY-coordinate location of pattern center.\nparam HookList output_fns (allow_None=False, bounds=(0, None), constant=False, default=[], instantiate=True, pickle_default_value=True, precedence=0.08, readonly=False)\nOptional function(s) to apply to the pattern array after it has been created. Can be used for normalization, thresholding, etc.\nparam Number offset (allow_None=False, bounds=None, constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.11, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nAdditive offset to input pattern, defaulting to 0.0\nOptional PatternGenerator used to construct a mask to be applied to the pattern.\nparam Composite position (allow_None=True, attribs=[‘x’, ‘y’], constant=False, default=None, instantiate=False, objtype=<class ‘imagen.patterngenerator.PatternGenerator’>, pickle_default_value=True, precedence=-1, readonly=False)\nCoordinates of location of pattern center. Provides a convenient way to set the x and y parameters together as a tuple (x,y), but shares the same actual storage as x and y (and thus only position OR x and y need to be specified).\nparam Number ydensity (allow_None=False, bounds=(0, None), constant=False, default=256, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=-1, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nDensity (number of samples per 1.0 length) in the y direction. Typically the same as the xdensity.\nparam Number size (allow_None=False, bounds=(0.0, None), constant=False, default=0.785398163397, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.6, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nAngular length of the sector, in radians.\nanim(duration, offset=0, timestep=1, label=None, unit=None, time_fn=Time(label='Time', name='Time00001', time_type=<type 'int'>, timestep=1.0, unit=None, until=Infinity()))\n\nduration: The temporal duration to animate in the units defined on the global time function.\n\noffset: The temporal offset from which the animation is generated given the supplied pattern\n\ntimestep: The time interval between successive frames. The duration must be an exact multiple of the timestep.\n\nlabel: A label string to override the label of the global time function (if not None).\n\nunit: The unit string to override the unit value of the global time function (if not None).\n\ntime_fn: The global time function object that is shared across the time-varying objects that are being sampled.\n\nNote that the offset, timestep and time_fn only affect patterns parameterized by time-dependent number generators. Otherwise, the frames are generated by successive call to the pattern which may or may not be varying (e.g to view the patterns contained within a Selector).\n\nchannels(use_cached=False, **params_to_override)\n\nChannels() adds a shared interface for single channel and multichannel structures. It will always return an ordered dict: its first element is the single channel of the pattern (if single-channel) or the channel average (if multichannel); the successive elements are the individual channels’ arrays (key: 0,1,..N-1).\n\ndebug(msg, *args, **kw)\n\nPrint msg merged with args as a debugging statement.\n\nSee Python’s logging module for details of message formatting.\n\ndefaults()\n\nReturn {parameter_name:parameter.default} for all non-constant Parameters.\n\nNote that a Parameter for which instantiate==True has its default instantiated.\n\nforce_new_dynamic_value = <functools.partial object at 0x2adfbaf6d100>\nget_param_values(onlychanged=False)\n\nReturn a list of name,value pairs for all Parameters of this object.\n\nIf onlychanged is True, will only return values that are not equal to the default value.\n\nget_value_generator = <functools.partial object at 0x2adfbaf6d158>\ninspect_value = <functools.partial object at 0x2adfbaf6d7e0>\nmessage(msg, *args, **kw)\n\nPrint msg merged with args as a message.\n\nSee Python’s logging module for details of message formatting.\n\nnum_channels()\n\nQuery the number of channels implemented by the PatternGenerator. In case of single-channel generators this will return 1; in case of multichannel, it will return the number of channels (eg, in the case of RGB images it would return ‘3’, Red-Green-Blue, even though the OrderedDict returned by channels() will have 4 elements – the 3 channels + their average).\n\nclassmethod params(parameter_name=None)\n\nReturn the Parameters of this class as the dictionary {name: parameter_object}\n\nIncludes Parameters from this class and its superclasses.\n\npprint(imports=None, prefix=' ', unknown_value='<?>', qualify=False, separator='')\n\n(Experimental) Pretty printed representation that may be evaluated with eval. See pprint() function for more details.\n\nclassmethod print_param_defaults()\n\nPrint the default values of all cls’s Parameters.\n\nprint_param_values()\n\nPrint the values of all this object’s Parameters.\n\nscript_repr(imports=, []prefix=' ')\n\nVariant of __repr__ designed for generating a runnable script.\n\nclassmethod set_default(param_name, value)\n\nSet the default value of param_name.\n\nEquivalent to setting param_name on the class.\n\nset_dynamic_time_fn = <functools.partial object at 0x2adfbaf6d998>\nset_matrix_dimensions(bounds, xdensity, ydensity)\n\nChange the dimensions of the matrix into which the pattern will be drawn. Users of this class should call this method rather than changing the bounds, xdensity, and ydensity parameters directly. Subclasses can override this method to update any internal data structures that may depend on the matrix dimensions.\n\nset_param = <functools.partial object at 0x2adfbaf6d368>\nstate_pop()\n\nRestore the state of the output functions saved by state_push.\n\nstate_push()\n\nSave the state of the output functions, to be restored with state_pop.\n\nverbose(msg, *args, **kw)\n\nPrint msg merged with args as a verbose message.\n\nSee Python’s logging module for details of message formatting.\n\nwarning(msg, *args, **kw)\n\nPrint msg merged with args as a warning, unless module variable warnings_as_exceptions is True, then raise an Exception containing the arguments.\n\nSee Python’s logging module for details of message formatting.\n\nclass imagen.__init__.Constant(**params)\n\nConstant pattern generator, i.e., a solid, uniform field of the same value.\n\nparam Number x (allow_None=False, bounds=None, constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.2, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nX-coordinate location of pattern center.\nparam Number scale (allow_None=False, bounds=None, constant=False, default=1.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.1, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nMultiplicative strength of input pattern, defaulting to 1.0\nparam String group (allow_None=False, basestring=<type ‘basestring’>, constant=False, default=Pattern, instantiate=False, pickle_default_value=True, precedence=-1, readonly=False)\nThe group name assigned to the returned HoloViews object.\nparam Number orientation (allow_None=False, bounds=None, constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=-1, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nPolar angle of pattern, i.e., the orientation in the Cartesian coordinate system, with zero at 3 o’clock and increasing counterclockwise.\nparam ClassSelector z (allow_None=True, constant=False, default=None, instantiate=True, is_instance=True, pickle_default_value=True, precedence=-1, readonly=False)\nThe Dimension object associated with the z-values generated by the PatternGenerator . If None, uses the default set by HoloViews.Image.\nOptional object (expected to be an array) with which to multiply the pattern array after it has been created, before any output_fns are applied. This can be used to shape the pattern.\nBoundingBox of the area in which the pattern is generated.\nparam Number xdensity (allow_None=False, bounds=(0, None), constant=False, default=256, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=-1, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nDensity (number of samples per 1.0 length) in the x direction.\nparam Number y (allow_None=False, bounds=None, constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.21, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nY-coordinate location of pattern center.\nparam HookList output_fns (allow_None=False, bounds=(0, None), constant=False, default=[], instantiate=True, pickle_default_value=True, precedence=0.08, readonly=False)\nOptional function(s) to apply to the pattern array after it has been created. Can be used for normalization, thresholding, etc.\nparam Number offset (allow_None=False, bounds=None, constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.11, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nAdditive offset to input pattern, defaulting to 0.0\nOptional PatternGenerator used to construct a mask to be applied to the pattern.\nparam Composite position (allow_None=True, attribs=[‘x’, ‘y’], constant=False, default=None, instantiate=False, objtype=<class ‘imagen.patterngenerator.PatternGenerator’>, pickle_default_value=True, precedence=-1, readonly=False)\nCoordinates of location of pattern center. Provides a convenient way to set the x and y parameters together as a tuple (x,y), but shares the same actual storage as x and y (and thus only position OR x and y need to be specified).\nparam Number ydensity (allow_None=False, bounds=(0, None), constant=False, default=256, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=-1, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nDensity (number of samples per 1.0 length) in the y direction. Typically the same as the xdensity.\nparam Number size (allow_None=False, bounds=(0.0, None), constant=False, default=1.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.3, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nDetermines the overall size of the pattern.\nanim(duration, offset=0, timestep=1, label=None, unit=None, time_fn=Time(label='Time', name='Time00001', time_type=<type 'int'>, timestep=1.0, unit=None, until=Infinity()))\n\nduration: The temporal duration to animate in the units defined on the global time function.\n\noffset: The temporal offset from which the animation is generated given the supplied pattern\n\ntimestep: The time interval between successive frames. The duration must be an exact multiple of the timestep.\n\nlabel: A label string to override the label of the global time function (if not None).\n\nunit: The unit string to override the unit value of the global time function (if not None).\n\ntime_fn: The global time function object that is shared across the time-varying objects that are being sampled.\n\nNote that the offset, timestep and time_fn only affect patterns parameterized by time-dependent number generators. Otherwise, the frames are generated by successive call to the pattern which may or may not be varying (e.g to view the patterns contained within a Selector).\n\nchannels(use_cached=False, **params_to_override)\n\nChannels() adds a shared interface for single channel and multichannel structures. It will always return an ordered dict: its first element is the single channel of the pattern (if single-channel) or the channel average (if multichannel); the successive elements are the individual channels’ arrays (key: 0,1,..N-1).\n\ndebug(msg, *args, **kw)\n\nPrint msg merged with args as a debugging statement.\n\nSee Python’s logging module for details of message formatting.\n\ndefaults()\n\nReturn {parameter_name:parameter.default} for all non-constant Parameters.\n\nNote that a Parameter for which instantiate==True has its default instantiated.\n\nforce_new_dynamic_value = <functools.partial object at 0x2adfbaf6d2b8>\nfunction(p)\n\nFunction to draw a pattern that will then be scaled and rotated.\n\nInstead of implementing __call__ directly, PatternGenerator subclasses will typically implement this helper function used by __call__, because that way they can let __call__ handle the scaling and rotation for them. Alternatively, __call__ itself can be reimplemented entirely by a subclass (e.g. if it does not need to do any scaling or rotation), in which case this function will be ignored.\n\nget_param_values(onlychanged=False)\n\nReturn a list of name,value pairs for all Parameters of this object.\n\nIf onlychanged is True, will only return values that are not equal to the default value.\n\nget_value_generator = <functools.partial object at 0x2adfbaf6d3c0>\ninspect_value = <functools.partial object at 0x2adfbaf6d838>\nmessage(msg, *args, **kw)\n\nPrint msg merged with args as a message.\n\nSee Python’s logging module for details of message formatting.\n\nnum_channels()\n\nQuery the number of channels implemented by the PatternGenerator. In case of single-channel generators this will return 1; in case of multichannel, it will return the number of channels (eg, in the case of RGB images it would return ‘3’, Red-Green-Blue, even though the OrderedDict returned by channels() will have 4 elements – the 3 channels + their average).\n\nclassmethod params(parameter_name=None)\n\nReturn the Parameters of this class as the dictionary {name: parameter_object}\n\nIncludes Parameters from this class and its superclasses.\n\npprint(imports=None, prefix=' ', unknown_value='<?>', qualify=False, separator='')\n\n(Experimental) Pretty printed representation that may be evaluated with eval. See pprint() function for more details.\n\nclassmethod print_param_defaults()\n\nPrint the default values of all cls’s Parameters.\n\nprint_param_values()\n\nPrint the values of all this object’s Parameters.\n\nscript_repr(imports=, []prefix=' ')\n\nVariant of __repr__ designed for generating a runnable script.\n\nclassmethod set_default(param_name, value)\n\nSet the default value of param_name.\n\nEquivalent to setting param_name on the class.\n\nset_dynamic_time_fn = <functools.partial object at 0x2adfbaf6d578>\nset_matrix_dimensions(bounds, xdensity, ydensity)\n\nChange the dimensions of the matrix into which the pattern will be drawn. Users of this class should call this method rather than changing the bounds, xdensity, and ydensity parameters directly. Subclasses can override this method to update any internal data structures that may depend on the matrix dimensions.\n\nset_param = <functools.partial object at 0x2adfbaf6d260>\nstate_pop()\n\nRestore the state of the output functions saved by state_push.\n\nstate_push()\n\nSave the state of the output functions, to be restored with state_pop.\n\nverbose(msg, *args, **kw)\n\nPrint msg merged with args as a verbose message.\n\nSee Python’s logging module for details of message formatting.\n\nwarning(msg, *args, **kw)\n\nPrint msg merged with args as a warning, unless module variable warnings_as_exceptions is True, then raise an Exception containing the arguments.\n\nSee Python’s logging module for details of message formatting.\n\nclass imagen.__init__.Sigmoid(**params)[source]\n\nTwo-dimensional sigmoid pattern, dividing the plane into positive and negative halves with a smoothly sloping transition between them.\n\nparam Number slope (allow_None=False, bounds=(None, None), constant=False, default=10.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=None, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nParameter controlling the smoothness of the transition between the two regions; high values give a sharp transition.\nparam Number x (allow_None=False, bounds=None, constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.2, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nX-coordinate location of pattern center.\nparam Number scale (allow_None=False, bounds=None, constant=False, default=1.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.1, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nMultiplicative strength of input pattern, defaulting to 1.0\nparam String group (allow_None=False, basestring=<type ‘basestring’>, constant=False, default=Pattern, instantiate=False, pickle_default_value=True, precedence=-1, readonly=False)\nThe group name assigned to the returned HoloViews object.\nparam Number orientation (allow_None=False, bounds=None, constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.4, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nPolar angle of pattern, i.e., the orientation in the Cartesian coordinate system, with zero at 3 o’clock and increasing counterclockwise.\nparam ClassSelector z (allow_None=True, constant=False, default=None, instantiate=True, is_instance=True, pickle_default_value=True, precedence=-1, readonly=False)\nThe Dimension object associated with the z-values generated by the PatternGenerator . If None, uses the default set by HoloViews.Image.\nOptional object (expected to be an array) with which to multiply the pattern array after it has been created, before any output_fns are applied. This can be used to shape the pattern.\nBoundingBox of the area in which the pattern is generated.\nparam Number xdensity (allow_None=False, bounds=(0, None), constant=False, default=256, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=-1, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nDensity (number of samples per 1.0 length) in the x direction.\nparam Number y (allow_None=False, bounds=None, constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.21, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nY-coordinate location of pattern center.\nparam HookList output_fns (allow_None=False, bounds=(0, None), constant=False, default=[], instantiate=True, pickle_default_value=True, precedence=0.08, readonly=False)\nOptional function(s) to apply to the pattern array after it has been created. Can be used for normalization, thresholding, etc.\nparam Number offset (allow_None=False, bounds=None, constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.11, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nAdditive offset to input pattern, defaulting to 0.0\nOptional PatternGenerator used to construct a mask to be applied to the pattern.\nparam Composite position (allow_None=True, attribs=[‘x’, ‘y’], constant=False, default=None, instantiate=False, objtype=<class ‘imagen.patterngenerator.PatternGenerator’>, pickle_default_value=True, precedence=-1, readonly=False)\nCoordinates of location of pattern center. Provides a convenient way to set the x and y parameters together as a tuple (x,y), but shares the same actual storage as x and y (and thus only position OR x and y need to be specified).\nparam Number ydensity (allow_None=False, bounds=(0, None), constant=False, default=256, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=-1, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nDensity (number of samples per 1.0 length) in the y direction. Typically the same as the xdensity.\nparam Number size (allow_None=False, bounds=(0.0, None), constant=False, default=1.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.3, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nDetermines the overall size of the pattern.\nanim(duration, offset=0, timestep=1, label=None, unit=None, time_fn=Time(label='Time', name='Time00001', time_type=<type 'int'>, timestep=1.0, unit=None, until=Infinity()))\n\nduration: The temporal duration to animate in the units defined on the global time function.\n\noffset: The temporal offset from which the animation is generated given the supplied pattern\n\ntimestep: The time interval between successive frames. The duration must be an exact multiple of the timestep.\n\nlabel: A label string to override the label of the global time function (if not None).\n\nunit: The unit string to override the unit value of the global time function (if not None).\n\ntime_fn: The global time function object that is shared across the time-varying objects that are being sampled.\n\nNote that the offset, timestep and time_fn only affect patterns parameterized by time-dependent number generators. Otherwise, the frames are generated by successive call to the pattern which may or may not be varying (e.g to view the patterns contained within a Selector).\n\nchannels(use_cached=False, **params_to_override)\n\nChannels() adds a shared interface for single channel and multichannel structures. It will always return an ordered dict: its first element is the single channel of the pattern (if single-channel) or the channel average (if multichannel); the successive elements are the individual channels’ arrays (key: 0,1,..N-1).\n\ndebug(msg, *args, **kw)\n\nPrint msg merged with args as a debugging statement.\n\nSee Python’s logging module for details of message formatting.\n\ndefaults()\n\nReturn {parameter_name:parameter.default} for all non-constant Parameters.\n\nNote that a Parameter for which instantiate==True has its default instantiated.\n\nforce_new_dynamic_value = <functools.partial object at 0x2adfbaf6d158>\nget_param_values(onlychanged=False)\n\nReturn a list of name,value pairs for all Parameters of this object.\n\nIf onlychanged is True, will only return values that are not equal to the default value.\n\nget_value_generator = <functools.partial object at 0x2adfbaf6d100>\ninspect_value = <functools.partial object at 0x2adfbaf6d7e0>\nmessage(msg, *args, **kw)\n\nPrint msg merged with args as a message.\n\nSee Python’s logging module for details of message formatting.\n\nnum_channels()\n\nQuery the number of channels implemented by the PatternGenerator. In case of single-channel generators this will return 1; in case of multichannel, it will return the number of channels (eg, in the case of RGB images it would return ‘3’, Red-Green-Blue, even though the OrderedDict returned by channels() will have 4 elements – the 3 channels + their average).\n\nclassmethod params(parameter_name=None)\n\nReturn the Parameters of this class as the dictionary {name: parameter_object}\n\nIncludes Parameters from this class and its superclasses.\n\npprint(imports=None, prefix=' ', unknown_value='<?>', qualify=False, separator='')\n\n(Experimental) Pretty printed representation that may be evaluated with eval. See pprint() function for more details.\n\nclassmethod print_param_defaults()\n\nPrint the default values of all cls’s Parameters.\n\nprint_param_values()\n\nPrint the values of all this object’s Parameters.\n\nscript_repr(imports=, []prefix=' ')\n\nVariant of __repr__ designed for generating a runnable script.\n\nclassmethod set_default(param_name, value)\n\nSet the default value of param_name.\n\nEquivalent to setting param_name on the class.\n\nset_dynamic_time_fn = <functools.partial object at 0x2adfbaf6d788>\nset_matrix_dimensions(bounds, xdensity, ydensity)\n\nChange the dimensions of the matrix into which the pattern will be drawn. Users of this class should call this method rather than changing the bounds, xdensity, and ydensity parameters directly. Subclasses can override this method to update any internal data structures that may depend on the matrix dimensions.\n\nset_param = <functools.partial object at 0x2adfbaf6d520>\nstate_pop()\n\nRestore the state of the output functions saved by state_push.\n\nstate_push()\n\nSave the state of the output functions, to be restored with state_pop.\n\nverbose(msg, *args, **kw)\n\nPrint msg merged with args as a verbose message.\n\nSee Python’s logging module for details of message formatting.\n\nwarning(msg, *args, **kw)\n\nPrint msg merged with args as a warning, unless module variable warnings_as_exceptions is True, then raise an Exception containing the arguments.\n\nSee Python’s logging module for details of message formatting.\n\nclass imagen.__init__.SigmoidedDoG(**params)[source]\n\nSigmoid multiplicatively combined with a difference of Gaussians, such that one part of the plane can be the mirror image of the other.\n\nparam Number positive_size (allow_None=False, bounds=(0.0, None), constant=False, default=0.15, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=1, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nSize of the positive Gaussian pattern.\nparam Number orientation (allow_None=False, bounds=None, constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.4, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nPolar angle of pattern, i.e., the orientation in the Cartesian coordinate system, with zero at 3 o’clock and increasing counterclockwise.\nparam Number sigmoid_position (allow_None=False, bounds=(None, None), constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=6, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nX position of the transition between the two regions.\nparam Number ydensity (allow_None=False, bounds=(0, None), constant=False, default=256, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=-1, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nDensity (number of samples per 1.0 length) in the y direction. Typically the same as the xdensity.\nparam Number scale (allow_None=False, bounds=None, constant=False, default=1.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.1, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nMultiplicative strength of input pattern, defaulting to 1.0\nparam String group (allow_None=False, basestring=<type ‘basestring’>, constant=False, default=Pattern, instantiate=False, pickle_default_value=True, precedence=-1, readonly=False)\nThe group name assigned to the returned HoloViews object.\nparam Composite position (allow_None=True, attribs=[‘x’, ‘y’], constant=False, default=None, instantiate=False, objtype=<class ‘imagen.patterngenerator.PatternGenerator’>, pickle_default_value=True, precedence=-1, readonly=False)\nCoordinates of location of pattern center. Provides a convenient way to set the x and y parameters together as a tuple (x,y), but shares the same actual storage as x and y (and thus only position OR x and y need to be specified).\nparam Number positive_aspect_ratio (allow_None=False, bounds=(0.0, None), constant=False, default=2.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=2, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nRatio of width to height for the positive Gaussian pattern.\nparam Number xdensity (allow_None=False, bounds=(0, None), constant=False, default=256, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=-1, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nDensity (number of samples per 1.0 length) in the x direction.\nparam Number negative_aspect_ratio (allow_None=False, bounds=(0.0, None), constant=False, default=1.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=4, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nRatio of width to height for the negative Gaussian pattern.\nparam Number size (allow_None=False, bounds=(0.0, None), constant=False, default=0.5, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.3, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nDetermines the overall size of the pattern.\nparam Number negative_size (allow_None=False, bounds=(0.0, None), constant=False, default=0.25, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=3, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nSize of the negative Gaussian pattern.\nOptional PatternGenerator used to construct a mask to be applied to the pattern.\nparam Number offset (allow_None=False, bounds=None, constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.11, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nAdditive offset to input pattern, defaulting to 0.0\nparam Number sigmoid_slope (allow_None=False, bounds=(None, None), constant=False, default=10.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=5, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nParameter controlling the smoothness of the transition between the two regions; high values give a sharp transition.\nOptional object (expected to be an array) with which to multiply the pattern array after it has been created, before any output_fns are applied. This can be used to shape the pattern.\nBoundingBox of the area in which the pattern is generated.\nparam HookList output_fns (allow_None=False, bounds=(0, None), constant=False, default=[], instantiate=True, pickle_default_value=True, precedence=0.08, readonly=False)\nOptional function(s) to apply to the pattern array after it has been created. Can be used for normalization, thresholding, etc.\nparam Number y (allow_None=False, bounds=None, constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.21, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nY-coordinate location of pattern center.\nparam Number x (allow_None=False, bounds=None, constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.2, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nX-coordinate location of pattern center.\nparam ClassSelector z (allow_None=True, constant=False, default=None, instantiate=True, is_instance=True, pickle_default_value=True, precedence=-1, readonly=False)\nThe Dimension object associated with the z-values generated by the PatternGenerator . If None, uses the default set by HoloViews.Image.\nanim(duration, offset=0, timestep=1, label=None, unit=None, time_fn=Time(label='Time', name='Time00001', time_type=<type 'int'>, timestep=1.0, unit=None, until=Infinity()))\n\nduration: The temporal duration to animate in the units defined on the global time function.\n\noffset: The temporal offset from which the animation is generated given the supplied pattern\n\ntimestep: The time interval between successive frames. The duration must be an exact multiple of the timestep.\n\nlabel: A label string to override the label of the global time function (if not None).\n\nunit: The unit string to override the unit value of the global time function (if not None).\n\ntime_fn: The global time function object that is shared across the time-varying objects that are being sampled.\n\nNote that the offset, timestep and time_fn only affect patterns parameterized by time-dependent number generators. Otherwise, the frames are generated by successive call to the pattern which may or may not be varying (e.g to view the patterns contained within a Selector).\n\nchannels(use_cached=False, **params_to_override)\n\nChannels() adds a shared interface for single channel and multichannel structures. It will always return an ordered dict: its first element is the single channel of the pattern (if single-channel) or the channel average (if multichannel); the successive elements are the individual channels’ arrays (key: 0,1,..N-1).\n\ndebug(msg, *args, **kw)\n\nPrint msg merged with args as a debugging statement.\n\nSee Python’s logging module for details of message formatting.\n\ndefaults()\n\nReturn {parameter_name:parameter.default} for all non-constant Parameters.\n\nNote that a Parameter for which instantiate==True has its default instantiated.\n\nforce_new_dynamic_value = <functools.partial object at 0x2adfbaf6d940>\nget_param_values(onlychanged=False)\n\nReturn a list of name,value pairs for all Parameters of this object.\n\nIf onlychanged is True, will only return values that are not equal to the default value.\n\nget_value_generator = <functools.partial object at 0x2adfbaf6d578>\ninspect_value = <functools.partial object at 0x2adfbaf6d680>\nmessage(msg, *args, **kw)\n\nPrint msg merged with args as a message.\n\nSee Python’s logging module for details of message formatting.\n\nnum_channels()\n\nQuery the number of channels implemented by the PatternGenerator. In case of single-channel generators this will return 1; in case of multichannel, it will return the number of channels (eg, in the case of RGB images it would return ‘3’, Red-Green-Blue, even though the OrderedDict returned by channels() will have 4 elements – the 3 channels + their average).\n\nclassmethod params(parameter_name=None)\n\nReturn the Parameters of this class as the dictionary {name: parameter_object}\n\nIncludes Parameters from this class and its superclasses.\n\npprint(imports=None, prefix=' ', unknown_value='<?>', qualify=False, separator='')\n\n(Experimental) Pretty printed representation that may be evaluated with eval. See pprint() function for more details.\n\nclassmethod print_param_defaults()\n\nPrint the default values of all cls’s Parameters.\n\nprint_param_values()\n\nPrint the values of all this object’s Parameters.\n\nscript_repr(imports=, []prefix=' ')\n\nVariant of __repr__ designed for generating a runnable script.\n\nclassmethod set_default(param_name, value)\n\nSet the default value of param_name.\n\nEquivalent to setting param_name on the class.\n\nset_dynamic_time_fn = <functools.partial object at 0x2adfbaf6d520>\nset_matrix_dimensions(bounds, xdensity, ydensity)\n\nChange the dimensions of the matrix into which the pattern will be drawn. Users of this class should call this method rather than changing the bounds, xdensity, and ydensity parameters directly. Subclasses can override this method to update any internal data structures that may depend on the matrix dimensions.\n\nset_param = <functools.partial object at 0x2adfbaf6d2b8>\nstate_pop()\n\nRestore the state of the output functions saved by state_push.\n\nstate_push()\n\nSave the state of the output functions, to be restored with state_pop.\n\nverbose(msg, *args, **kw)\n\nPrint msg merged with args as a verbose message.\n\nSee Python’s logging module for details of message formatting.\n\nwarning(msg, *args, **kw)\n\nPrint msg merged with args as a warning, unless module variable warnings_as_exceptions is True, then raise an Exception containing the arguments.\n\nSee Python’s logging module for details of message formatting.\n\nclass imagen.__init__.Gaussian(**params)[source]\n\n2D Gaussian pattern generator.\n\nThe sigmas of the Gaussian are calculated from the size and aspect_ratio parameters:\n\nysigma=size/2 xsigma=ysigma*aspect_ratio\n\nThe Gaussian is then computed for the given (x,y) values as:\n\nexp(-x^2/(2*xsigma^2) - y^2/(2*ysigma^2)\n\nparam Number x (allow_None=False, bounds=None, constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.2, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nX-coordinate location of pattern center.\nparam Number scale (allow_None=False, bounds=None, constant=False, default=1.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.1, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nMultiplicative strength of input pattern, defaulting to 1.0\nparam String group (allow_None=False, basestring=<type ‘basestring’>, constant=False, default=Pattern, instantiate=False, pickle_default_value=True, precedence=-1, readonly=False)\nThe group name assigned to the returned HoloViews object.\nparam Number orientation (allow_None=False, bounds=None, constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.4, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nPolar angle of pattern, i.e., the orientation in the Cartesian coordinate system, with zero at 3 o’clock and increasing counterclockwise.\nparam Number aspect_ratio (allow_None=False, bounds=(0.0, None), constant=False, default=3.22580645161, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.31, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nRatio of the width to the height. Specifically, xsigma=ysigma*aspect_ratio (see size).\nparam ClassSelector z (allow_None=True, constant=False, default=None, instantiate=True, is_instance=True, pickle_default_value=True, precedence=-1, readonly=False)\nThe Dimension object associated with the z-values generated by the PatternGenerator . If None, uses the default set by HoloViews.Image.\nOptional object (expected to be an array) with which to multiply the pattern array after it has been created, before any output_fns are applied. This can be used to shape the pattern.\nBoundingBox of the area in which the pattern is generated.\nparam Number xdensity (allow_None=False, bounds=(0, None), constant=False, default=256, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=-1, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nDensity (number of samples per 1.0 length) in the x direction.\nparam Number y (allow_None=False, bounds=None, constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.21, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nY-coordinate location of pattern center.\nparam HookList output_fns (allow_None=False, bounds=(0, None), constant=False, default=[], instantiate=True, pickle_default_value=True, precedence=0.08, readonly=False)\nOptional function(s) to apply to the pattern array after it has been created. Can be used for normalization, thresholding, etc.\nparam Number offset (allow_None=False, bounds=None, constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.11, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nAdditive offset to input pattern, defaulting to 0.0\nOptional PatternGenerator used to construct a mask to be applied to the pattern.\nparam Composite position (allow_None=True, attribs=[‘x’, ‘y’], constant=False, default=None, instantiate=False, objtype=<class ‘imagen.patterngenerator.PatternGenerator’>, pickle_default_value=True, precedence=-1, readonly=False)\nCoordinates of location of pattern center. Provides a convenient way to set the x and y parameters together as a tuple (x,y), but shares the same actual storage as x and y (and thus only position OR x and y need to be specified).\nparam Number ydensity (allow_None=False, bounds=(0, None), constant=False, default=256, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=-1, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nDensity (number of samples per 1.0 length) in the y direction. Typically the same as the xdensity.\nparam Number size (allow_None=False, bounds=(0.0, None), constant=False, default=0.155, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.3, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nOverall size of the Gaussian, defined by: exp(-x^2/(2*xsigma^2) - y^2/(2*ysigma^2) where ysigma=size/2 and xsigma=size/2*aspect_ratio.\nanim(duration, offset=0, timestep=1, label=None, unit=None, time_fn=Time(label='Time', name='Time00001', time_type=<type 'int'>, timestep=1.0, unit=None, until=Infinity()))\n\nduration: The temporal duration to animate in the units defined on the global time function.\n\noffset: The temporal offset from which the animation is generated given the supplied pattern\n\ntimestep: The time interval between successive frames. The duration must be an exact multiple of the timestep.\n\nlabel: A label string to override the label of the global time function (if not None).\n\nunit: The unit string to override the unit value of the global time function (if not None).\n\ntime_fn: The global time function object that is shared across the time-varying objects that are being sampled.\n\nNote that the offset, timestep and time_fn only affect patterns parameterized by time-dependent number generators. Otherwise, the frames are generated by successive call to the pattern which may or may not be varying (e.g to view the patterns contained within a Selector).\n\nchannels(use_cached=False, **params_to_override)\n\nChannels() adds a shared interface for single channel and multichannel structures. It will always return an ordered dict: its first element is the single channel of the pattern (if single-channel) or the channel average (if multichannel); the successive elements are the individual channels’ arrays (key: 0,1,..N-1).\n\ndebug(msg, *args, **kw)\n\nPrint msg merged with args as a debugging statement.\n\nSee Python’s logging module for details of message formatting.\n\ndefaults()\n\nReturn {parameter_name:parameter.default} for all non-constant Parameters.\n\nNote that a Parameter for which instantiate==True has its default instantiated.\n\nforce_new_dynamic_value = <functools.partial object at 0x2adfbaf6d260>\nget_param_values(onlychanged=False)\n\nReturn a list of name,value pairs for all Parameters of this object.\n\nIf onlychanged is True, will only return values that are not equal to the default value.\n\nget_value_generator = <functools.partial object at 0x2adfbaf6d788>\ninspect_value = <functools.partial object at 0x2adfbaf6d158>\nmessage(msg, *args, **kw)\n\nPrint msg merged with args as a message.\n\nSee Python’s logging module for details of message formatting.\n\nnum_channels()\n\nQuery the number of channels implemented by the PatternGenerator. In case of single-channel generators this will return 1; in case of multichannel, it will return the number of channels (eg, in the case of RGB images it would return ‘3’, Red-Green-Blue, even though the OrderedDict returned by channels() will have 4 elements – the 3 channels + their average).\n\nclassmethod params(parameter_name=None)\n\nReturn the Parameters of this class as the dictionary {name: parameter_object}\n\nIncludes Parameters from this class and its superclasses.\n\npprint(imports=None, prefix=' ', unknown_value='<?>', qualify=False, separator='')\n\n(Experimental) Pretty printed representation that may be evaluated with eval. See pprint() function for more details.\n\nclassmethod print_param_defaults()\n\nPrint the default values of all cls’s Parameters.\n\nprint_param_values()\n\nPrint the values of all this object’s Parameters.\n\nscript_repr(imports=, []prefix=' ')\n\nVariant of __repr__ designed for generating a runnable script.\n\nclassmethod set_default(param_name, value)\n\nSet the default value of param_name.\n\nEquivalent to setting param_name on the class.\n\nset_dynamic_time_fn = <functools.partial object at 0x2adfbaf6d7e0>\nset_matrix_dimensions(bounds, xdensity, ydensity)\n\nChange the dimensions of the matrix into which the pattern will be drawn. Users of this class should call this method rather than changing the bounds, xdensity, and ydensity parameters directly. Subclasses can override this method to update any internal data structures that may depend on the matrix dimensions.\n\nset_param = <functools.partial object at 0x2adfbaf6d100>\nstate_pop()\n\nRestore the state of the output functions saved by state_push.\n\nstate_push()\n\nSave the state of the output functions, to be restored with state_pop.\n\nverbose(msg, *args, **kw)\n\nPrint msg merged with args as a verbose message.\n\nSee Python’s logging module for details of message formatting.\n\nwarning(msg, *args, **kw)\n\nPrint msg merged with args as a warning, unless module variable warnings_as_exceptions is True, then raise an Exception containing the arguments.\n\nSee Python’s logging module for details of message formatting.\n\nclass imagen.__init__.SineGrating(**params)[source]\n\n2D sine grating pattern generator.\n\nparam Number x (allow_None=False, bounds=None, constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.2, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nX-coordinate location of pattern center.\nparam Number scale (allow_None=False, bounds=None, constant=False, default=1.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.1, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nMultiplicative strength of input pattern, defaulting to 1.0\nparam String group (allow_None=False, basestring=<type ‘basestring’>, constant=False, default=Pattern, instantiate=False, pickle_default_value=True, precedence=-1, readonly=False)\nThe group name assigned to the returned HoloViews object.\nparam Number orientation (allow_None=False, bounds=None, constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.4, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nPolar angle of pattern, i.e., the orientation in the Cartesian coordinate system, with zero at 3 o’clock and increasing counterclockwise.\nparam Number phase (allow_None=False, bounds=(0.0, None), constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.51, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nPhase of the sine grating.\nparam ClassSelector z (allow_None=True, constant=False, default=None, instantiate=True, is_instance=True, pickle_default_value=True, precedence=-1, readonly=False)\nThe Dimension object associated with the z-values generated by the PatternGenerator . If None, uses the default set by HoloViews.Image.\nOptional object (expected to be an array) with which to multiply the pattern array after it has been created, before any output_fns are applied. This can be used to shape the pattern.\nBoundingBox of the area in which the pattern is generated.\nparam Number xdensity (allow_None=False, bounds=(0, None), constant=False, default=256, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=-1, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nDensity (number of samples per 1.0 length) in the x direction.\nparam Number y (allow_None=False, bounds=None, constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.21, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nY-coordinate location of pattern center.\nparam HookList output_fns (allow_None=False, bounds=(0, None), constant=False, default=[], instantiate=True, pickle_default_value=True, precedence=0.08, readonly=False)\nOptional function(s) to apply to the pattern array after it has been created. Can be used for normalization, thresholding, etc.\nparam Number frequency (allow_None=False, bounds=(0.0, None), constant=False, default=2.4, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.5, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nFrequency of the sine grating.\nparam Number offset (allow_None=False, bounds=None, constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.11, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nAdditive offset to input pattern, defaulting to 0.0\nOptional PatternGenerator used to construct a mask to be applied to the pattern.\nparam Composite position (allow_None=True, attribs=[‘x’, ‘y’], constant=False, default=None, instantiate=False, objtype=<class ‘imagen.patterngenerator.PatternGenerator’>, pickle_default_value=True, precedence=-1, readonly=False)\nCoordinates of location of pattern center. Provides a convenient way to set the x and y parameters together as a tuple (x,y), but shares the same actual storage as x and y (and thus only position OR x and y need to be specified).\nparam Number ydensity (allow_None=False, bounds=(0, None), constant=False, default=256, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=-1, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nDensity (number of samples per 1.0 length) in the y direction. Typically the same as the xdensity.\nparam Number size (allow_None=False, bounds=(0.0, None), constant=False, default=1.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.3, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nDetermines the overall size of the pattern.\nanim(duration, offset=0, timestep=1, label=None, unit=None, time_fn=Time(label='Time', name='Time00001', time_type=<type 'int'>, timestep=1.0, unit=None, until=Infinity()))\n\nduration: The temporal duration to animate in the units defined on the global time function.\n\noffset: The temporal offset from which the animation is generated given the supplied pattern\n\ntimestep: The time interval between successive frames. The duration must be an exact multiple of the timestep.\n\nlabel: A label string to override the label of the global time function (if not None).\n\nunit: The unit string to override the unit value of the global time function (if not None).\n\ntime_fn: The global time function object that is shared across the time-varying objects that are being sampled.\n\nNote that the offset, timestep and time_fn only affect patterns parameterized by time-dependent number generators. Otherwise, the frames are generated by successive call to the pattern which may or may not be varying (e.g to view the patterns contained within a Selector).\n\nchannels(use_cached=False, **params_to_override)\n\nChannels() adds a shared interface for single channel and multichannel structures. It will always return an ordered dict: its first element is the single channel of the pattern (if single-channel) or the channel average (if multichannel); the successive elements are the individual channels’ arrays (key: 0,1,..N-1).\n\ndebug(msg, *args, **kw)\n\nPrint msg merged with args as a debugging statement.\n\nSee Python’s logging module for details of message formatting.\n\ndefaults()\n\nReturn {parameter_name:parameter.default} for all non-constant Parameters.\n\nNote that a Parameter for which instantiate==True has its default instantiated.\n\nforce_new_dynamic_value = <functools.partial object at 0x2adfbaf6d8e8>\nfunction(p)[source]\n\nReturn a sine grating pattern (two-dimensional sine wave).\n\nget_param_values(onlychanged=False)\n\nReturn a list of name,value pairs for all Parameters of this object.\n\nIf onlychanged is True, will only return values that are not equal to the default value.\n\nget_value_generator = <functools.partial object at 0x2adfbaf6d520>\ninspect_value = <functools.partial object at 0x2adfbaf6d3c0>\nmessage(msg, *args, **kw)\n\nPrint msg merged with args as a message.\n\nSee Python’s logging module for details of message formatting.\n\nnum_channels()\n\nQuery the number of channels implemented by the PatternGenerator. In case of single-channel generators this will return 1; in case of multichannel, it will return the number of channels (eg, in the case of RGB images it would return ‘3’, Red-Green-Blue, even though the OrderedDict returned by channels() will have 4 elements – the 3 channels + their average).\n\nclassmethod params(parameter_name=None)\n\nReturn the Parameters of this class as the dictionary {name: parameter_object}\n\nIncludes Parameters from this class and its superclasses.\n\npprint(imports=None, prefix=' ', unknown_value='<?>', qualify=False, separator='')\n\n(Experimental) Pretty printed representation that may be evaluated with eval. See pprint() function for more details.\n\nclassmethod print_param_defaults()\n\nPrint the default values of all cls’s Parameters.\n\nprint_param_values()\n\nPrint the values of all this object’s Parameters.\n\nscript_repr(imports=, []prefix=' ')\n\nVariant of __repr__ designed for generating a runnable script.\n\nclassmethod set_default(param_name, value)\n\nSet the default value of param_name.\n\nEquivalent to setting param_name on the class.\n\nset_dynamic_time_fn = <functools.partial object at 0x2adfbaf6d578>\nset_matrix_dimensions(bounds, xdensity, ydensity)\n\nChange the dimensions of the matrix into which the pattern will be drawn. Users of this class should call this method rather than changing the bounds, xdensity, and ydensity parameters directly. Subclasses can override this method to update any internal data structures that may depend on the matrix dimensions.\n\nset_param = <functools.partial object at 0x2adfbaf6d368>\nstate_pop()\n\nRestore the state of the output functions saved by state_push.\n\nstate_push()\n\nSave the state of the output functions, to be restored with state_pop.\n\nverbose(msg, *args, **kw)\n\nPrint msg merged with args as a verbose message.\n\nSee Python’s logging module for details of message formatting.\n\nwarning(msg, *args, **kw)\n\nPrint msg merged with args as a warning, unless module variable warnings_as_exceptions is True, then raise an Exception containing the arguments.\n\nSee Python’s logging module for details of message formatting.\n\nclass imagen.__init__.Arc(**params)[source]\n\n2D arc pattern generator.\n\nDraws an arc (partial ring) of the specified size (radius*2), starting at radian 0.0 and ending at arc_length. The orientation can be changed to choose other start locations. The pattern is centered at the center of the ring.\n\nSee the Disk class for a note about the Gaussian fall-off.\n\nparam Number x (allow_None=False, bounds=None, constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.2, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nX-coordinate location of pattern center.\nparam Number scale (allow_None=False, bounds=None, constant=False, default=1.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.1, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nMultiplicative strength of input pattern, defaulting to 1.0\nparam String group (allow_None=False, basestring=<type ‘basestring’>, constant=False, default=Pattern, instantiate=False, pickle_default_value=True, precedence=-1, readonly=False)\nThe group name assigned to the returned HoloViews object.\nparam Number orientation (allow_None=False, bounds=None, constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.4, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nPolar angle of pattern, i.e., the orientation in the Cartesian coordinate system, with zero at 3 o’clock and increasing counterclockwise.\nparam Number aspect_ratio (allow_None=False, bounds=(0.0, None), constant=False, default=1.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.31, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nRatio of width to height; size*aspect_ratio gives the overall width.\nparam ClassSelector z (allow_None=True, constant=False, default=None, instantiate=True, is_instance=True, pickle_default_value=True, precedence=-1, readonly=False)\nThe Dimension object associated with the z-values generated by the PatternGenerator . If None, uses the default set by HoloViews.Image.\nOptional object (expected to be an array) with which to multiply the pattern array after it has been created, before any output_fns are applied. This can be used to shape the pattern.\nBoundingBox of the area in which the pattern is generated.\nparam Number thickness (allow_None=False, bounds=(0.0, None), constant=False, default=0.015, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.6, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nThickness (line width) of the ring.\nparam Number smoothing (allow_None=False, bounds=(0.0, None), constant=False, default=0.05, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.61, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nWidth of the Gaussian fall-off inside and outside the ring.\nparam Number xdensity (allow_None=False, bounds=(0, None), constant=False, default=256, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=-1, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nDensity (number of samples per 1.0 length) in the x direction.\nparam Number y (allow_None=False, bounds=None, constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.21, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nY-coordinate location of pattern center.\nparam HookList output_fns (allow_None=False, bounds=(0, None), constant=False, default=[], instantiate=True, pickle_default_value=True, precedence=0.08, readonly=False)\nOptional function(s) to apply to the pattern array after it has been created. Can be used for normalization, thresholding, etc.\nparam Number arc_length (allow_None=False, bounds=(0.0, None), constant=False, default=3.14159265359, inclusive_bounds=(True, False), instantiate=False, pickle_default_value=True, precedence=0.62, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nLength of the arc, in radians, starting from orientation 0.0.\nparam Number offset (allow_None=False, bounds=None, constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.11, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nAdditive offset to input pattern, defaulting to 0.0\nOptional PatternGenerator used to construct a mask to be applied to the pattern.\nparam Composite position (allow_None=True, attribs=[‘x’, ‘y’], constant=False, default=None, instantiate=False, objtype=<class ‘imagen.patterngenerator.PatternGenerator’>, pickle_default_value=True, precedence=-1, readonly=False)\nCoordinates of location of pattern center. Provides a convenient way to set the x and y parameters together as a tuple (x,y), but shares the same actual storage as x and y (and thus only position OR x and y need to be specified).\nparam Number ydensity (allow_None=False, bounds=(0, None), constant=False, default=256, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=-1, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nDensity (number of samples per 1.0 length) in the y direction. Typically the same as the xdensity.\nparam Number size (allow_None=False, bounds=(0.0, None), constant=False, default=0.5, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.3, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nDetermines the overall size of the pattern.\nanim(duration, offset=0, timestep=1, label=None, unit=None, time_fn=Time(label='Time', name='Time00001', time_type=<type 'int'>, timestep=1.0, unit=None, until=Infinity()))\n\nduration: The temporal duration to animate in the units defined on the global time function.\n\noffset: The temporal offset from which the animation is generated given the supplied pattern\n\ntimestep: The time interval between successive frames. The duration must be an exact multiple of the timestep.\n\nlabel: A label string to override the label of the global time function (if not None).\n\nunit: The unit string to override the unit value of the global time function (if not None).\n\ntime_fn: The global time function object that is shared across the time-varying objects that are being sampled.\n\nNote that the offset, timestep and time_fn only affect patterns parameterized by time-dependent number generators. Otherwise, the frames are generated by successive call to the pattern which may or may not be varying (e.g to view the patterns contained within a Selector).\n\nchannels(use_cached=False, **params_to_override)\n\nChannels() adds a shared interface for single channel and multichannel structures. It will always return an ordered dict: its first element is the single channel of the pattern (if single-channel) or the channel average (if multichannel); the successive elements are the individual channels’ arrays (key: 0,1,..N-1).\n\ndebug(msg, *args, **kw)\n\nPrint msg merged with args as a debugging statement.\n\nSee Python’s logging module for details of message formatting.\n\ndefaults()\n\nReturn {parameter_name:parameter.default} for all non-constant Parameters.\n\nNote that a Parameter for which instantiate==True has its default instantiated.\n\nforce_new_dynamic_value = <functools.partial object at 0x2adfbaf6d260>\nget_param_values(onlychanged=False)\n\nReturn a list of name,value pairs for all Parameters of this object.\n\nIf onlychanged is True, will only return values that are not equal to the default value.\n\nget_value_generator = <functools.partial object at 0x2adfbaf6d310>\ninspect_value = <functools.partial object at 0x2adfbaf6d7e0>\nmessage(msg, *args, **kw)\n\nPrint msg merged with args as a message.\n\nSee Python’s logging module for details of message formatting.\n\nnum_channels()\n\nQuery the number of channels implemented by the PatternGenerator. In case of single-channel generators this will return 1; in case of multichannel, it will return the number of channels (eg, in the case of RGB images it would return ‘3’, Red-Green-Blue, even though the OrderedDict returned by channels() will have 4 elements – the 3 channels + their average).\n\nclassmethod params(parameter_name=None)\n\nReturn the Parameters of this class as the dictionary {name: parameter_object}\n\nIncludes Parameters from this class and its superclasses.\n\npprint(imports=None, prefix=' ', unknown_value='<?>', qualify=False, separator='')\n\n(Experimental) Pretty printed representation that may be evaluated with eval. See pprint() function for more details.\n\nclassmethod print_param_defaults()\n\nPrint the default values of all cls’s Parameters.\n\nprint_param_values()\n\nPrint the values of all this object’s Parameters.\n\nscript_repr(imports=, []prefix=' ')\n\nVariant of __repr__ designed for generating a runnable script.\n\nclassmethod set_default(param_name, value)\n\nSet the default value of param_name.\n\nEquivalent to setting param_name on the class.\n\nset_dynamic_time_fn = <functools.partial object at 0x2adfbaf6d368>\nset_matrix_dimensions(bounds, xdensity, ydensity)\n\nChange the dimensions of the matrix into which the pattern will be drawn. Users of this class should call this method rather than changing the bounds, xdensity, and ydensity parameters directly. Subclasses can override this method to update any internal data structures that may depend on the matrix dimensions.\n\nset_param = <functools.partial object at 0x2adfbaf6d3c0>\nstate_pop()\n\nRestore the state of the output functions saved by state_push.\n\nstate_push()\n\nSave the state of the output functions, to be restored with state_pop.\n\nverbose(msg, *args, **kw)\n\nPrint msg merged with args as a verbose message.\n\nSee Python’s logging module for details of message formatting.\n\nwarning(msg, *args, **kw)\n\nPrint msg merged with args as a warning, unless module variable warnings_as_exceptions is True, then raise an Exception containing the arguments.\n\nSee Python’s logging module for details of message formatting.\n\nclass imagen.__init__.PowerSpectrum(**params)[source]\n\nOutputs the spectral density of a rolling interval of the input signal each time it is called. Over time, the results could be arranged into a spectrogram, e.g. for an audio signal.\n\nparam Number x (allow_None=False, bounds=None, constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=-1, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nX-coordinate location of pattern center.\nparam Number scale (allow_None=False, bounds=(0, None), constant=False, default=0.01, inclusive_bounds=(False, False), instantiate=False, pickle_default_value=True, precedence=0.1, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nThe amount by which to scale amplitudes by. This is useful if we want to rescale to say a range [0:1]. Note: Constant scaling is preferable to dynamic scaling so as not to artificially ramp down loud sounds while ramping up hiss and other background interference.\nparam String group (allow_None=False, basestring=<type ‘basestring’>, constant=False, default=Pattern, instantiate=False, pickle_default_value=True, precedence=-1, readonly=False)\nThe group name assigned to the returned HoloViews object.\nparam Number orientation (allow_None=False, bounds=None, constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=-1, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nPolar angle of pattern, i.e., the orientation in the Cartesian coordinate system, with zero at 3 o’clock and increasing counterclockwise.\nparam Integer min_frequency (allow_None=False, bounds=(0, None), constant=False, default=0, inclusive_bounds=(True, False), instantiate=False, pickle_default_value=True, precedence=None, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nSmallest frequency for which to return an amplitude.\nparam ClassSelector z (allow_None=True, constant=False, default=None, instantiate=True, is_instance=True, pickle_default_value=True, precedence=-1, readonly=False)\nThe Dimension object associated with the z-values generated by the PatternGenerator . If None, uses the default set by HoloViews.Image.\nOptional object (expected to be an array) with which to multiply the pattern array after it has been created, before any output_fns are applied. This can be used to shape the pattern.\nBoundingBox of the area in which the pattern is generated.\nparam Parameter windowing_function (allow_None=True, constant=False, default=None, instantiate=False, pickle_default_value=True, precedence=None, readonly=False)\nThis function is multiplied with the current interval, i.e. the most recent portion of the waveform interval of a signal, before performing the Fourier transform. It thus shapes the interval, which is otherwise always rectangular. The function chosen here dictates the tradeoff between resolving comparable signal strengths with similar frequencies, and resolving disparate signal strengths with dissimilar frequencies. numpy provides a number of options, e.g. bartlett, blackman, hamming, hanning, kaiser; see http://docs.scipy.org/doc/numpy/reference/routines.window.html You may also supply your own.\nparam Number xdensity (allow_None=False, bounds=(0, None), constant=False, default=256, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=-1, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nDensity (number of samples per 1.0 length) in the x direction.\nparam Number y (allow_None=False, bounds=None, constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=-1, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nY-coordinate location of pattern center.\nparam HookList output_fns (allow_None=False, bounds=(0, None), constant=False, default=[], instantiate=True, pickle_default_value=True, precedence=0.08, readonly=False)\nOptional function(s) to apply to the pattern array after it has been created. Can be used for normalization, thresholding, etc.\nparam Integer max_frequency (allow_None=False, bounds=(0, None), constant=False, default=9999, inclusive_bounds=(False, False), instantiate=False, pickle_default_value=True, precedence=None, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nLargest frequency for which to return an amplitude.\nparam Number offset (allow_None=False, bounds=None, constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.11, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nAdditive offset to input pattern, defaulting to 0.0\nOptional PatternGenerator used to construct a mask to be applied to the pattern.\nparam Composite position (allow_None=True, attribs=[‘x’, ‘y’], constant=False, default=None, instantiate=False, objtype=<class ‘imagen.patterngenerator.PatternGenerator’>, pickle_default_value=True, precedence=-1, readonly=False)\nCoordinates of location of pattern center. Provides a convenient way to set the x and y parameters together as a tuple (x,y), but shares the same actual storage as x and y (and thus only position OR x and y need to be specified).\nparam Number ydensity (allow_None=False, bounds=(0, None), constant=False, default=256, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=-1, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nDensity (number of samples per 1.0 length) in the y direction. Typically the same as the xdensity.\nparam TimeSeriesParam signal (allow_None=False, constant=False, default=<TimeSeries TimeSeries01037>, instantiate=True, is_instance=True, pickle_default_value=True, precedence=None, readonly=False)\nA TimeSeries object on which to perfom the Fourier Transform.\nparam Number size (allow_None=False, bounds=(0.0, None), constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=-1, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nDetermines the overall size of the pattern.\nanim(duration, offset=0, timestep=1, label=None, unit=None, time_fn=Time(label='Time', name='Time00001', time_type=<type 'int'>, timestep=1.0, unit=None, until=Infinity()))\n\nduration: The temporal duration to animate in the units defined on the global time function.\n\noffset: The temporal offset from which the animation is generated given the supplied pattern\n\ntimestep: The time interval between successive frames. The duration must be an exact multiple of the timestep.\n\nlabel: A label string to override the label of the global time function (if not None).\n\nunit: The unit string to override the unit value of the global time function (if not None).\n\ntime_fn: The global time function object that is shared across the time-varying objects that are being sampled.\n\nNote that the offset, timestep and time_fn only affect patterns parameterized by time-dependent number generators. Otherwise, the frames are generated by successive call to the pattern which may or may not be varying (e.g to view the patterns contained within a Selector).\n\nchannels(use_cached=False, **params_to_override)\n\nChannels() adds a shared interface for single channel and multichannel structures. It will always return an ordered dict: its first element is the single channel of the pattern (if single-channel) or the channel average (if multichannel); the successive elements are the individual channels’ arrays (key: 0,1,..N-1).\n\ndebug(msg, *args, **kw)\n\nPrint msg merged with args as a debugging statement.\n\nSee Python’s logging module for details of message formatting.\n\ndefaults()\n\nReturn {parameter_name:parameter.default} for all non-constant Parameters.\n\nNote that a Parameter for which instantiate==True has its default instantiated.\n\nforce_new_dynamic_value = <functools.partial object at 0x2adfbaf6d7e0>\nfunction(p)\n\nFunction to draw a pattern that will then be scaled and rotated.\n\nInstead of implementing __call__ directly, PatternGenerator subclasses will typically implement this helper function used by __call__, because that way they can let __call__ handle the scaling and rotation for them. Alternatively, __call__ itself can be reimplemented entirely by a subclass (e.g. if it does not need to do any scaling or rotation), in which case this function will be ignored.\n\nget_param_values(onlychanged=False)\n\nReturn a list of name,value pairs for all Parameters of this object.\n\nIf onlychanged is True, will only return values that are not equal to the default value.\n\nget_value_generator = <functools.partial object at 0x2adfbaf6d158>\ninspect_value = <functools.partial object at 0x2adfbaf6d8e8>\nmessage(msg, *args, **kw)\n\nPrint msg merged with args as a message.\n\nSee Python’s logging module for details of message formatting.\n\nnum_channels()\n\nQuery the number of channels implemented by the PatternGenerator. In case of single-channel generators this will return 1; in case of multichannel, it will return the number of channels (eg, in the case of RGB images it would return ‘3’, Red-Green-Blue, even though the OrderedDict returned by channels() will have 4 elements – the 3 channels + their average).\n\nclassmethod params(parameter_name=None)\n\nReturn the Parameters of this class as the dictionary {name: parameter_object}\n\nIncludes Parameters from this class and its superclasses.\n\npprint(imports=None, prefix=' ', unknown_value='<?>', qualify=False, separator='')\n\n(Experimental) Pretty printed representation that may be evaluated with eval. See pprint() function for more details.\n\nclassmethod print_param_defaults()\n\nPrint the default values of all cls’s Parameters.\n\nprint_param_values()\n\nPrint the values of all this object’s Parameters.\n\nscript_repr(imports=, []prefix=' ')\n\nVariant of __repr__ designed for generating a runnable script.\n\nclassmethod set_default(param_name, value)\n\nSet the default value of param_name.\n\nEquivalent to setting param_name on the class.\n\nset_dynamic_time_fn = <functools.partial object at 0x2adfbaf6d680>\nset_param = <functools.partial object at 0x2adfbaf6d838>\nstate_pop()\n\nRestore the state of the output functions saved by state_push.\n\nstate_push()\n\nSave the state of the output functions, to be restored with state_pop.\n\nverbose(msg, *args, **kw)\n\nPrint msg merged with args as a verbose message.\n\nSee Python’s logging module for details of message formatting.\n\nwarning(msg, *args, **kw)\n\nPrint msg merged with args as a warning, unless module variable warnings_as_exceptions is True, then raise an Exception containing the arguments.\n\nSee Python’s logging module for details of message formatting.\n\nclass imagen.__init__.Ring(**params)[source]\n\n2D ring pattern generator.\n\nSee the Disk class for a note about the Gaussian fall-off.\n\nparam Number x (allow_None=False, bounds=None, constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.2, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nX-coordinate location of pattern center.\nparam Number scale (allow_None=False, bounds=None, constant=False, default=1.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.1, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nMultiplicative strength of input pattern, defaulting to 1.0\nparam String group (allow_None=False, basestring=<type ‘basestring’>, constant=False, default=Pattern, instantiate=False, pickle_default_value=True, precedence=-1, readonly=False)\nThe group name assigned to the returned HoloViews object.\nparam Number orientation (allow_None=False, bounds=None, constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.4, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nPolar angle of pattern, i.e., the orientation in the Cartesian coordinate system, with zero at 3 o’clock and increasing counterclockwise.\nparam Number aspect_ratio (allow_None=False, bounds=(0.0, None), constant=False, default=1.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.31, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nRatio of width to height; size*aspect_ratio gives the overall width.\nparam ClassSelector z (allow_None=True, constant=False, default=None, instantiate=True, is_instance=True, pickle_default_value=True, precedence=-1, readonly=False)\nThe Dimension object associated with the z-values generated by the PatternGenerator . If None, uses the default set by HoloViews.Image.\nOptional object (expected to be an array) with which to multiply the pattern array after it has been created, before any output_fns are applied. This can be used to shape the pattern.\nBoundingBox of the area in which the pattern is generated.\nparam Number thickness (allow_None=False, bounds=(0.0, None), constant=False, default=0.015, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.6, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nThickness (line width) of the ring.\nparam Number xdensity (allow_None=False, bounds=(0, None), constant=False, default=256, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=-1, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nDensity (number of samples per 1.0 length) in the x direction.\nparam Number y (allow_None=False, bounds=None, constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.21, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nY-coordinate location of pattern center.\nparam HookList output_fns (allow_None=False, bounds=(0, None), constant=False, default=[], instantiate=True, pickle_default_value=True, precedence=0.08, readonly=False)\nOptional function(s) to apply to the pattern array after it has been created. Can be used for normalization, thresholding, etc.\nparam Number offset (allow_None=False, bounds=None, constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.11, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nAdditive offset to input pattern, defaulting to 0.0\nOptional PatternGenerator used to construct a mask to be applied to the pattern.\nparam Composite position (allow_None=True, attribs=[‘x’, ‘y’], constant=False, default=None, instantiate=False, objtype=<class ‘imagen.patterngenerator.PatternGenerator’>, pickle_default_value=True, precedence=-1, readonly=False)\nCoordinates of location of pattern center. Provides a convenient way to set the x and y parameters together as a tuple (x,y), but shares the same actual storage as x and y (and thus only position OR x and y need to be specified).\nparam Number smoothing (allow_None=False, bounds=(0.0, None), constant=False, default=0.1, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.61, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nWidth of the Gaussian fall-off inside and outside the ring.\nparam Number ydensity (allow_None=False, bounds=(0, None), constant=False, default=256, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=-1, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nDensity (number of samples per 1.0 length) in the y direction. Typically the same as the xdensity.\nparam Number size (allow_None=False, bounds=(0.0, None), constant=False, default=0.5, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.3, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nDetermines the overall size of the pattern.\nanim(duration, offset=0, timestep=1, label=None, unit=None, time_fn=Time(label='Time', name='Time00001', time_type=<type 'int'>, timestep=1.0, unit=None, until=Infinity()))\n\nduration: The temporal duration to animate in the units defined on the global time function.\n\noffset: The temporal offset from which the animation is generated given the supplied pattern\n\ntimestep: The time interval between successive frames. The duration must be an exact multiple of the timestep.\n\nlabel: A label string to override the label of the global time function (if not None).\n\nunit: The unit string to override the unit value of the global time function (if not None).\n\ntime_fn: The global time function object that is shared across the time-varying objects that are being sampled.\n\nNote that the offset, timestep and time_fn only affect patterns parameterized by time-dependent number generators. Otherwise, the frames are generated by successive call to the pattern which may or may not be varying (e.g to view the patterns contained within a Selector).\n\nchannels(use_cached=False, **params_to_override)\n\nChannels() adds a shared interface for single channel and multichannel structures. It will always return an ordered dict: its first element is the single channel of the pattern (if single-channel) or the channel average (if multichannel); the successive elements are the individual channels’ arrays (key: 0,1,..N-1).\n\ndebug(msg, *args, **kw)\n\nPrint msg merged with args as a debugging statement.\n\nSee Python’s logging module for details of message formatting.\n\ndefaults()\n\nReturn {parameter_name:parameter.default} for all non-constant Parameters.\n\nNote that a Parameter for which instantiate==True has its default instantiated.\n\nforce_new_dynamic_value = <functools.partial object at 0x2adfbaf6d520>\nget_param_values(onlychanged=False)\n\nReturn a list of name,value pairs for all Parameters of this object.\n\nIf onlychanged is True, will only return values that are not equal to the default value.\n\nget_value_generator = <functools.partial object at 0x2adfbaf6d100>\ninspect_value = <functools.partial object at 0x2adfbaf6d940>\nmessage(msg, *args, **kw)\n\nPrint msg merged with args as a message.\n\nSee Python’s logging module for details of message formatting.\n\nnum_channels()\n\nQuery the number of channels implemented by the PatternGenerator. In case of single-channel generators this will return 1; in case of multichannel, it will return the number of channels (eg, in the case of RGB images it would return ‘3’, Red-Green-Blue, even though the OrderedDict returned by channels() will have 4 elements – the 3 channels + their average).\n\nclassmethod params(parameter_name=None)\n\nReturn the Parameters of this class as the dictionary {name: parameter_object}\n\nIncludes Parameters from this class and its superclasses.\n\npprint(imports=None, prefix=' ', unknown_value='<?>', qualify=False, separator='')\n\n(Experimental) Pretty printed representation that may be evaluated with eval. See pprint() function for more details.\n\nclassmethod print_param_defaults()\n\nPrint the default values of all cls’s Parameters.\n\nprint_param_values()\n\nPrint the values of all this object’s Parameters.\n\nscript_repr(imports=, []prefix=' ')\n\nVariant of __repr__ designed for generating a runnable script.\n\nclassmethod set_default(param_name, value)\n\nSet the default value of param_name.\n\nEquivalent to setting param_name on the class.\n\nset_dynamic_time_fn = <functools.partial object at 0x2adfbaf6d310>\nset_matrix_dimensions(bounds, xdensity, ydensity)\n\nChange the dimensions of the matrix into which the pattern will be drawn. Users of this class should call this method rather than changing the bounds, xdensity, and ydensity parameters directly. Subclasses can override this method to update any internal data structures that may depend on the matrix dimensions.\n\nset_param = <functools.partial object at 0x2adfbaf6d578>\nstate_pop()\n\nRestore the state of the output functions saved by state_push.\n\nstate_push()\n\nSave the state of the output functions, to be restored with state_pop.\n\nverbose(msg, *args, **kw)\n\nPrint msg merged with args as a verbose message.\n\nSee Python’s logging module for details of message formatting.\n\nwarning(msg, *args, **kw)\n\nPrint msg merged with args as a warning, unless module variable warnings_as_exceptions is True, then raise an Exception containing the arguments.\n\nSee Python’s logging module for details of message formatting.\n\nclass imagen.__init__.Disk(**params)[source]\n\n2D disk pattern generator.\n\nAn elliptical disk can be obtained by adjusting the aspect_ratio of a circular disk; this transforms a circle into an ellipse by stretching the circle in the y (vertical) direction.\n\nThe Gaussian fall-off at a point P is an approximation for non-circular disks, since the point on the ellipse closest to P is taken to be the same point as the point on the circle before stretching that was closest to P.\n\nparam Number x (allow_None=False, bounds=None, constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.2, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nX-coordinate location of pattern center.\nparam Number scale (allow_None=False, bounds=None, constant=False, default=1.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.1, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nMultiplicative strength of input pattern, defaulting to 1.0\nparam String group (allow_None=False, basestring=<type ‘basestring’>, constant=False, default=Pattern, instantiate=False, pickle_default_value=True, precedence=-1, readonly=False)\nThe group name assigned to the returned HoloViews object.\nparam Number orientation (allow_None=False, bounds=None, constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.4, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nPolar angle of pattern, i.e., the orientation in the Cartesian coordinate system, with zero at 3 o’clock and increasing counterclockwise.\nparam Number aspect_ratio (allow_None=False, bounds=(0.0, None), constant=False, default=1.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.31, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nRatio of width to height; size*aspect_ratio gives the width of the disk.\nparam ClassSelector z (allow_None=True, constant=False, default=None, instantiate=True, is_instance=True, pickle_default_value=True, precedence=-1, readonly=False)\nThe Dimension object associated with the z-values generated by the PatternGenerator . If None, uses the default set by HoloViews.Image.\nOptional object (expected to be an array) with which to multiply the pattern array after it has been created, before any output_fns are applied. This can be used to shape the pattern.\nBoundingBox of the area in which the pattern is generated.\nparam Number smoothing (allow_None=False, bounds=(0.0, None), constant=False, default=0.1, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.61, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nWidth of the Gaussian fall-off\nparam Number xdensity (allow_None=False, bounds=(0, None), constant=False, default=256, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=-1, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nDensity (number of samples per 1.0 length) in the x direction.\nparam Number y (allow_None=False, bounds=None, constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.21, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nY-coordinate location of pattern center.\nparam HookList output_fns (allow_None=False, bounds=(0, None), constant=False, default=[], instantiate=True, pickle_default_value=True, precedence=0.08, readonly=False)\nOptional function(s) to apply to the pattern array after it has been created. Can be used for normalization, thresholding, etc.\nparam Number offset (allow_None=False, bounds=None, constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.11, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nAdditive offset to input pattern, defaulting to 0.0\nOptional PatternGenerator used to construct a mask to be applied to the pattern.\nparam Composite position (allow_None=True, attribs=[‘x’, ‘y’], constant=False, default=None, instantiate=False, objtype=<class ‘imagen.patterngenerator.PatternGenerator’>, pickle_default_value=True, precedence=-1, readonly=False)\nCoordinates of location of pattern center. Provides a convenient way to set the x and y parameters together as a tuple (x,y), but shares the same actual storage as x and y (and thus only position OR x and y need to be specified).\nparam Number ydensity (allow_None=False, bounds=(0, None), constant=False, default=256, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=-1, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nDensity (number of samples per 1.0 length) in the y direction. Typically the same as the xdensity.\nparam Number size (allow_None=False, bounds=(0.0, None), constant=False, default=0.5, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.3, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nTop to bottom height of the disk\nanim(duration, offset=0, timestep=1, label=None, unit=None, time_fn=Time(label='Time', name='Time00001', time_type=<type 'int'>, timestep=1.0, unit=None, until=Infinity()))\n\nduration: The temporal duration to animate in the units defined on the global time function.\n\noffset: The temporal offset from which the animation is generated given the supplied pattern\n\ntimestep: The time interval between successive frames. The duration must be an exact multiple of the timestep.\n\nlabel: A label string to override the label of the global time function (if not None).\n\nunit: The unit string to override the unit value of the global time function (if not None).\n\ntime_fn: The global time function object that is shared across the time-varying objects that are being sampled.\n\nNote that the offset, timestep and time_fn only affect patterns parameterized by time-dependent number generators. Otherwise, the frames are generated by successive call to the pattern which may or may not be varying (e.g to view the patterns contained within a Selector).\n\nchannels(use_cached=False, **params_to_override)\n\nChannels() adds a shared interface for single channel and multichannel structures. It will always return an ordered dict: its first element is the single channel of the pattern (if single-channel) or the channel average (if multichannel); the successive elements are the individual channels’ arrays (key: 0,1,..N-1).\n\ndebug(msg, *args, **kw)\n\nPrint msg merged with args as a debugging statement.\n\nSee Python’s logging module for details of message formatting.\n\ndefaults()\n\nReturn {parameter_name:parameter.default} for all non-constant Parameters.\n\nNote that a Parameter for which instantiate==True has its default instantiated.\n\nforce_new_dynamic_value = <functools.partial object at 0x2adfbaf6d838>\nget_param_values(onlychanged=False)\n\nReturn a list of name,value pairs for all Parameters of this object.\n\nIf onlychanged is True, will only return values that are not equal to the default value.\n\nget_value_generator = <functools.partial object at 0x2adfbaf6d788>\ninspect_value = <functools.partial object at 0x2adfbaf6d8e8>\nmessage(msg, *args, **kw)\n\nPrint msg merged with args as a message.\n\nSee Python’s logging module for details of message formatting.\n\nnum_channels()\n\nQuery the number of channels implemented by the PatternGenerator. In case of single-channel generators this will return 1; in case of multichannel, it will return the number of channels (eg, in the case of RGB images it would return ‘3’, Red-Green-Blue, even though the OrderedDict returned by channels() will have 4 elements – the 3 channels + their average).\n\nclassmethod params(parameter_name=None)\n\nReturn the Parameters of this class as the dictionary {name: parameter_object}\n\nIncludes Parameters from this class and its superclasses.\n\npprint(imports=None, prefix=' ', unknown_value='<?>', qualify=False, separator='')\n\n(Experimental) Pretty printed representation that may be evaluated with eval. See pprint() function for more details.\n\nclassmethod print_param_defaults()\n\nPrint the default values of all cls’s Parameters.\n\nprint_param_values()\n\nPrint the values of all this object’s Parameters.\n\nscript_repr(imports=, []prefix=' ')\n\nVariant of __repr__ designed for generating a runnable script.\n\nclassmethod set_default(param_name, value)\n\nSet the default value of param_name.\n\nEquivalent to setting param_name on the class.\n\nset_dynamic_time_fn = <functools.partial object at 0x2adfbaf6d158>\nset_matrix_dimensions(bounds, xdensity, ydensity)\n\nChange the dimensions of the matrix into which the pattern will be drawn. Users of this class should call this method rather than changing the bounds, xdensity, and ydensity parameters directly. Subclasses can override this method to update any internal data structures that may depend on the matrix dimensions.\n\nset_param = <functools.partial object at 0x2adfbaf6d100>\nstate_pop()\n\nRestore the state of the output functions saved by state_push.\n\nstate_push()\n\nSave the state of the output functions, to be restored with state_pop.\n\nverbose(msg, *args, **kw)\n\nPrint msg merged with args as a verbose message.\n\nSee Python’s logging module for details of message formatting.\n\nwarning(msg, *args, **kw)\n\nPrint msg merged with args as a warning, unless module variable warnings_as_exceptions is True, then raise an Exception containing the arguments.\n\nSee Python’s logging module for details of message formatting.\n\n## audio Module¶", null, "Pattern generators for audio signals.\n\nclass imagen.audio.AudioFile(**params)[source]\n\nBases: imagen.TimeSeries\n\nRequires an audio file in any format accepted by audiolab (wav, aiff, flac).\n\nparam Array time_series (allow_None=True, constant=False, default=[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1], instantiate=True, is_instance=True, pickle_default_value=True, precedence=-1, readonly=False)\nAn array of numbers that form a series.\nparam Boolean repeat (allow_None=False, bounds=(0, 1), constant=False, default=True, instantiate=False, pickle_default_value=True, precedence=None, readonly=False)\nWhether the signal loops or terminates once it reaches its end.\nparam Parameter precision (allow_None=False, constant=False, default=<type ‘numpy.float64’>, instantiate=False, pickle_default_value=True, precedence=None, readonly=False)\nThe float precision to use for loaded audio files.\nparam Filename filename (allow_None=False, constant=False, default=sounds/complex/daisy.wav, instantiate=False, pickle_default_value=True, precedence=None, readonly=False, search_paths=[])\nFile path (can be relative to Param’s base path) to an audio file. The audio can be in any format accepted by audiolab, e.g. WAV, AIFF, or FLAC.\nparam Number sample_rate (allow_None=False, bounds=(0, None), constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=-1, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nThe number of samples taken per second to form the series.\nparam Number seconds_per_iteration (allow_None=False, bounds=(0.0, None), constant=False, default=0.1, inclusive_bounds=(False, False), instantiate=False, pickle_default_value=True, precedence=None, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nNumber of seconds advanced along the time series on each iteration.\nparam Number interval_length (allow_None=False, bounds=(0.0, None), constant=False, default=0.1, inclusive_bounds=(False, False), instantiate=False, pickle_default_value=True, precedence=None, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nThe length of time in seconds to be returned on each iteration.\ndebug(msg, *args, **kw)\n\nPrint msg merged with args as a debugging statement.\n\nSee Python’s logging module for details of message formatting.\n\ndefaults()\n\nReturn {parameter_name:parameter.default} for all non-constant Parameters.\n\nNote that a Parameter for which instantiate==True has its default instantiated.\n\nextract_specific_interval(interval_start, interval_end)\n\nOverload if special behaviour is required when a series ends.\n\nforce_new_dynamic_value = <functools.partial object at 0x2adfbc49f788>\nget_param_values(onlychanged=False)\n\nReturn a list of name,value pairs for all Parameters of this object.\n\nIf onlychanged is True, will only return values that are not equal to the default value.\n\nget_value_generator = <functools.partial object at 0x2adfbc49f730>\ninspect_value = <functools.partial object at 0x2adfbc49f838>\nmessage(msg, *args, **kw)\n\nPrint msg merged with args as a message.\n\nSee Python’s logging module for details of message formatting.\n\nclassmethod params(parameter_name=None)\n\nReturn the Parameters of this class as the dictionary {name: parameter_object}\n\nIncludes Parameters from this class and its superclasses.\n\npprint(imports=None, prefix=' ', unknown_value='<?>', qualify=False, separator='')\n\n(Experimental) Pretty printed representation that may be evaluated with eval. See pprint() function for more details.\n\nprecision\n\nalias of float64\n\nclassmethod print_param_defaults()\n\nPrint the default values of all cls’s Parameters.\n\nprint_param_values()\n\nPrint the values of all this object’s Parameters.\n\nscript_repr(imports=, []prefix=' ')\n\nVariant of __repr__ designed for generating a runnable script.\n\nclassmethod set_default(param_name, value)\n\nSet the default value of param_name.\n\nEquivalent to setting param_name on the class.\n\nset_dynamic_time_fn = <functools.partial object at 0x2adfbc49f7e0>\nset_param = <functools.partial object at 0x2adfbc49f8e8>\nstate_pop()\n\nRestore the most recently saved state.\n\nSee state_push() for more details.\n\nstate_push()\n\nSave this instance’s state.\n\nFor Parameterized instances, this includes the state of dynamically generated values.\n\nSubclasses that maintain short-term state should additionally save and restore that state using state_push() and state_pop().\n\nGenerally, this method is used by operations that need to test something without permanently altering the objects’ state.\n\nverbose(msg, *args, **kw)\n\nPrint msg merged with args as a verbose message.\n\nSee Python’s logging module for details of message formatting.\n\nwarning(msg, *args, **kw)\n\nPrint msg merged with args as a warning, unless module variable warnings_as_exceptions is True, then raise an Exception containing the arguments.\n\nSee Python’s logging module for details of message formatting.\n\nclass imagen.audio.AudioFolder(**params)[source]\n\nBases: imagen.audio.AudioFile\n\nReturns a rolling spectrogram, i.e. the spectral density over time of a rolling window of the input audio signal, for all files in the specified folder.\n\nparam Array time_series (allow_None=True, constant=False, default=[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1], instantiate=True, is_instance=True, pickle_default_value=True, precedence=-1, readonly=False)\nAn array of numbers that form a series.\nparam Boolean repeat (allow_None=False, bounds=(0, 1), constant=False, default=True, instantiate=False, pickle_default_value=True, precedence=None, readonly=False)\nWhether the signal loops or terminates once it reaches its end.\nparam Number gap_between_sounds (allow_None=False, bounds=(0.0, None), constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=None, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nThe gap in seconds to insert between consecutive soundfiles.\nparam Parameter precision (allow_None=False, constant=False, default=<type ‘numpy.float64’>, instantiate=False, pickle_default_value=True, precedence=None, readonly=False)\nThe float precision to use for loaded audio files.\nparam Filename filename (allow_None=True, constant=False, default=sounds/complex/daisy.wav, instantiate=False, pickle_default_value=True, precedence=-1, readonly=False, search_paths=[])\nFile path (can be relative to Param’s base path) to an audio file. The audio can be in any format accepted by audiolab, e.g. WAV, AIFF, or FLAC.\nparam Number sample_rate (allow_None=False, bounds=(0, None), constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=-1, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nThe number of samples taken per second to form the series.\nparam Number seconds_per_iteration (allow_None=False, bounds=(0.0, None), constant=False, default=0.1, inclusive_bounds=(False, False), instantiate=False, pickle_default_value=True, precedence=None, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nNumber of seconds advanced along the time series on each iteration.\nparam Foldername folderpath (allow_None=False, constant=False, default=sounds/sine_waves/normalized, instantiate=False, pickle_default_value=True, precedence=None, readonly=False, search_paths=[])\nFolder path (can be relative to Param’s base path) to a folder containing audio files. The audio can be in any format accepted by audiolab, i.e. WAV, AIFF, or FLAC.\nparam Number interval_length (allow_None=False, bounds=(0.0, None), constant=False, default=0.1, inclusive_bounds=(False, False), instantiate=False, pickle_default_value=True, precedence=None, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nThe length of time in seconds to be returned on each iteration.\ndebug(msg, *args, **kw)\n\nPrint msg merged with args as a debugging statement.\n\nSee Python’s logging module for details of message formatting.\n\ndefaults()\n\nReturn {parameter_name:parameter.default} for all non-constant Parameters.\n\nNote that a Parameter for which instantiate==True has its default instantiated.\n\nextract_specific_interval(interval_start, interval_end)[source]\n\nOverload if special behaviour is required when a series ends.\n\nforce_new_dynamic_value = <functools.partial object at 0x2adfbc49f730>\nget_param_values(onlychanged=False)\n\nReturn a list of name,value pairs for all Parameters of this object.\n\nIf onlychanged is True, will only return values that are not equal to the default value.\n\nget_value_generator = <functools.partial object at 0x2adfbc49f470>\ninspect_value = <functools.partial object at 0x2adfbc49f680>\nmessage(msg, *args, **kw)\n\nPrint msg merged with args as a message.\n\nSee Python’s logging module for details of message formatting.\n\nclassmethod params(parameter_name=None)\n\nReturn the Parameters of this class as the dictionary {name: parameter_object}\n\nIncludes Parameters from this class and its superclasses.\n\npprint(imports=None, prefix=' ', unknown_value='<?>', qualify=False, separator='')\n\n(Experimental) Pretty printed representation that may be evaluated with eval. See pprint() function for more details.\n\nprecision\n\nalias of float64\n\nclassmethod print_param_defaults()\n\nPrint the default values of all cls’s Parameters.\n\nprint_param_values()\n\nPrint the values of all this object’s Parameters.\n\nscript_repr(imports=, []prefix=' ')\n\nVariant of __repr__ designed for generating a runnable script.\n\nclassmethod set_default(param_name, value)\n\nSet the default value of param_name.\n\nEquivalent to setting param_name on the class.\n\nset_dynamic_time_fn = <functools.partial object at 0x2adfbc49f4c8>\nset_param = <functools.partial object at 0x2adfbc49f3c0>\nstate_pop()\n\nRestore the most recently saved state.\n\nSee state_push() for more details.\n\nstate_push()\n\nSave this instance’s state.\n\nFor Parameterized instances, this includes the state of dynamically generated values.\n\nSubclasses that maintain short-term state should additionally save and restore that state using state_push() and state_pop().\n\nGenerally, this method is used by operations that need to test something without permanently altering the objects’ state.\n\nverbose(msg, *args, **kw)\n\nPrint msg merged with args as a verbose message.\n\nSee Python’s logging module for details of message formatting.\n\nwarning(msg, *args, **kw)\n\nPrint msg merged with args as a warning, unless module variable warnings_as_exceptions is True, then raise an Exception containing the arguments.\n\nSee Python’s logging module for details of message formatting.\n\nclass imagen.audio.LogSpectrogram(**params)[source]\n\nBases: imagen.Spectrogram\n\nExtends Spectrogram to provide a response over an octave scale.\n\nparam Number orientation (allow_None=False, bounds=None, constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=-1, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nPolar angle of pattern, i.e., the orientation in the Cartesian coordinate system, with zero at 3 o’clock and increasing counterclockwise.\nparam Integer min_latency (allow_None=False, bounds=(0, None), constant=False, default=0, inclusive_bounds=(True, False), instantiate=False, pickle_default_value=True, precedence=1, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nSmallest latency (in milliseconds) for which to return amplitudes.\nparam Integer max_frequency (allow_None=False, bounds=(0, None), constant=False, default=9999, inclusive_bounds=(False, False), instantiate=False, pickle_default_value=True, precedence=None, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nLargest frequency for which to return an amplitude.\nparam Number ydensity (allow_None=False, bounds=(0, None), constant=False, default=256, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=-1, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nDensity (number of samples per 1.0 length) in the y direction. Typically the same as the xdensity.\nparam Number scale (allow_None=False, bounds=(0, None), constant=False, default=0.01, inclusive_bounds=(False, False), instantiate=False, pickle_default_value=True, precedence=0.1, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nThe amount by which to scale amplitudes by. This is useful if we want to rescale to say a range [0:1]. Note: Constant scaling is preferable to dynamic scaling so as not to artificially ramp down loud sounds while ramping up hiss and other background interference.\nparam String group (allow_None=False, basestring=<type ‘basestring’>, constant=False, default=Pattern, instantiate=False, pickle_default_value=True, precedence=-1, readonly=False)\nThe group name assigned to the returned HoloViews object.\nparam Composite position (allow_None=True, attribs=[‘x’, ‘y’], constant=False, default=None, instantiate=False, objtype=<class ‘imagen.patterngenerator.PatternGenerator’>, pickle_default_value=True, precedence=-1, readonly=False)\nCoordinates of location of pattern center. Provides a convenient way to set the x and y parameters together as a tuple (x,y), but shares the same actual storage as x and y (and thus only position OR x and y need to be specified).\nparam Number xdensity (allow_None=False, bounds=(0, None), constant=False, default=256, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=-1, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nDensity (number of samples per 1.0 length) in the x direction.\nparam Number size (allow_None=False, bounds=(0.0, None), constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=-1, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nDetermines the overall size of the pattern.\nparam Integer min_frequency (allow_None=False, bounds=(0, None), constant=False, default=0, inclusive_bounds=(True, False), instantiate=False, pickle_default_value=True, precedence=None, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nSmallest frequency for which to return an amplitude.\nparam Parameter windowing_function (allow_None=True, constant=False, default=None, instantiate=False, pickle_default_value=True, precedence=None, readonly=False)\nThis function is multiplied with the current interval, i.e. the most recent portion of the waveform interval of a signal, before performing the Fourier transform. It thus shapes the interval, which is otherwise always rectangular. The function chosen here dictates the tradeoff between resolving comparable signal strengths with similar frequencies, and resolving disparate signal strengths with dissimilar frequencies. numpy provides a number of options, e.g. bartlett, blackman, hamming, hanning, kaiser; see http://docs.scipy.org/doc/numpy/reference/routines.window.html You may also supply your own.\nOptional PatternGenerator used to construct a mask to be applied to the pattern.\nparam Number offset (allow_None=False, bounds=None, constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.11, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nAdditive offset to input pattern, defaulting to 0.0\nparam Integer max_latency (allow_None=False, bounds=(0, None), constant=False, default=500, inclusive_bounds=(False, False), instantiate=False, pickle_default_value=True, precedence=2, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nLargest latency (in milliseconds) for which to return amplitudes.\nparam Integer log_base (allow_None=False, bounds=(0.0, None), constant=False, default=2, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=None, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nThe base of the logarithm used to generate logarithmic frequency spacing.\nparam TimeSeriesParam signal (allow_None=False, constant=False, default=<TimeSeries TimeSeries01034>, instantiate=True, is_instance=True, pickle_default_value=True, precedence=None, readonly=False)\nA TimeSeries object on which to perfom the Fourier Transform.\nOptional object (expected to be an array) with which to multiply the pattern array after it has been created, before any output_fns are applied. This can be used to shape the pattern.\nBoundingBox of the area in which the pattern is generated.\nparam HookList output_fns (allow_None=False, bounds=(0, None), constant=False, default=[], instantiate=True, pickle_default_value=True, precedence=0.08, readonly=False)\nOptional function(s) to apply to the pattern array after it has been created. Can be used for normalization, thresholding, etc.\nparam Number y (allow_None=False, bounds=None, constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=-1, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nY-coordinate location of pattern center.\nparam Number x (allow_None=False, bounds=None, constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=-1, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nX-coordinate location of pattern center.\nparam ClassSelector z (allow_None=True, constant=False, default=None, instantiate=True, is_instance=True, pickle_default_value=True, precedence=-1, readonly=False)\nThe Dimension object associated with the z-values generated by the PatternGenerator . If None, uses the default set by HoloViews.Image.\nanim(duration, offset=0, timestep=1, label=None, unit=None, time_fn=Time(label='Time', name='Time00001', time_type=<type 'int'>, timestep=1.0, unit=None, until=Infinity()))\n\nduration: The temporal duration to animate in the units defined on the global time function.\n\noffset: The temporal offset from which the animation is generated given the supplied pattern\n\ntimestep: The time interval between successive frames. The duration must be an exact multiple of the timestep.\n\nlabel: A label string to override the label of the global time function (if not None).\n\nunit: The unit string to override the unit value of the global time function (if not None).\n\ntime_fn: The global time function object that is shared across the time-varying objects that are being sampled.\n\nNote that the offset, timestep and time_fn only affect patterns parameterized by time-dependent number generators. Otherwise, the frames are generated by successive call to the pattern which may or may not be varying (e.g to view the patterns contained within a Selector).\n\nchannels(use_cached=False, **params_to_override)\n\nChannels() adds a shared interface for single channel and multichannel structures. It will always return an ordered dict: its first element is the single channel of the pattern (if single-channel) or the channel average (if multichannel); the successive elements are the individual channels’ arrays (key: 0,1,..N-1).\n\ndebug(msg, *args, **kw)\n\nPrint msg merged with args as a debugging statement.\n\nSee Python’s logging module for details of message formatting.\n\ndefaults()\n\nReturn {parameter_name:parameter.default} for all non-constant Parameters.\n\nNote that a Parameter for which instantiate==True has its default instantiated.\n\nforce_new_dynamic_value = <functools.partial object at 0x2adfbc49f8e8>\nfunction(p)\n\nFunction to draw a pattern that will then be scaled and rotated.\n\nInstead of implementing __call__ directly, PatternGenerator subclasses will typically implement this helper function used by __call__, because that way they can let __call__ handle the scaling and rotation for them. Alternatively, __call__ itself can be reimplemented entirely by a subclass (e.g. if it does not need to do any scaling or rotation), in which case this function will be ignored.\n\nget_param_values(onlychanged=False)\n\nReturn a list of name,value pairs for all Parameters of this object.\n\nIf onlychanged is True, will only return values that are not equal to the default value.\n\nget_value_generator = <functools.partial object at 0x2adfbc49f7e0>\ninspect_value = <functools.partial object at 0x2adfbc49f6d8>\nmessage(msg, *args, **kw)\n\nPrint msg merged with args as a message.\n\nSee Python’s logging module for details of message formatting.\n\nnum_channels()\n\nQuery the number of channels implemented by the PatternGenerator. In case of single-channel generators this will return 1; in case of multichannel, it will return the number of channels (eg, in the case of RGB images it would return ‘3’, Red-Green-Blue, even though the OrderedDict returned by channels() will have 4 elements – the 3 channels + their average).\n\nclassmethod params(parameter_name=None)\n\nReturn the Parameters of this class as the dictionary {name: parameter_object}\n\nIncludes Parameters from this class and its superclasses.\n\npprint(imports=None, prefix=' ', unknown_value='<?>', qualify=False, separator='')\n\n(Experimental) Pretty printed representation that may be evaluated with eval. See pprint() function for more details.\n\nclassmethod print_param_defaults()\n\nPrint the default values of all cls’s Parameters.\n\nprint_param_values()\n\nPrint the values of all this object’s Parameters.\n\nscript_repr(imports=, []prefix=' ')\n\nVariant of __repr__ designed for generating a runnable script.\n\nclassmethod set_default(param_name, value)\n\nSet the default value of param_name.\n\nEquivalent to setting param_name on the class.\n\nset_dynamic_time_fn = <functools.partial object at 0x2adfbc49f418>\nset_param = <functools.partial object at 0x2adfbc49f998>\nstate_pop()\n\nRestore the state of the output functions saved by state_push.\n\nstate_push()\n\nSave the state of the output functions, to be restored with state_pop.\n\nverbose(msg, *args, **kw)\n\nPrint msg merged with args as a verbose message.\n\nSee Python’s logging module for details of message formatting.\n\nwarning(msg, *args, **kw)\n\nPrint msg merged with args as a warning, unless module variable warnings_as_exceptions is True, then raise an Exception containing the arguments.\n\nSee Python’s logging module for details of message formatting.\n\nclass imagen.audio.LyonsCochlearModel(**params)[source]\n\nBases: imagen.PowerSpectrum\n\nOutputs a cochlear decomposition as a set of frequency responses of linear band-pass filters. Employs Lyons Cochlear Model to do so.\n\nR. F. Lyon, “A computational model of filtering, detection and compression in the cochlea.” in Proc. of the IEEE Int. Conf. Acoust., Speech, Signal Processing, Paris, France, May 1982.\n\nSpecific implementation details can be found in:\n\nMalcolm Slaney, “Lyon’s Cochlear Model, in Advanced Technology Group, Apple Technical Report #13”, 1988.\n\nparam Number orientation (allow_None=False, bounds=None, constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=-1, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nPolar angle of pattern, i.e., the orientation in the Cartesian coordinate system, with zero at 3 o’clock and increasing counterclockwise.\nparam Integer max_frequency (allow_None=False, bounds=(0, None), constant=False, default=9999, inclusive_bounds=(False, False), instantiate=False, pickle_default_value=True, precedence=None, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nLargest frequency for which to return an amplitude.\nparam Number ydensity (allow_None=False, bounds=(0, None), constant=False, default=256, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=-1, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nDensity (number of samples per 1.0 length) in the y direction. Typically the same as the xdensity.\nparam Number scale (allow_None=False, bounds=(0, None), constant=False, default=0.01, inclusive_bounds=(False, False), instantiate=False, pickle_default_value=True, precedence=0.1, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nThe amount by which to scale amplitudes by. This is useful if we want to rescale to say a range [0:1]. Note: Constant scaling is preferable to dynamic scaling so as not to artificially ramp down loud sounds while ramping up hiss and other background interference.\nparam String group (allow_None=False, basestring=<type ‘basestring’>, constant=False, default=Pattern, instantiate=False, pickle_default_value=True, precedence=-1, readonly=False)\nThe group name assigned to the returned HoloViews object.\nparam Composite position (allow_None=True, attribs=[‘x’, ‘y’], constant=False, default=None, instantiate=False, objtype=<class ‘imagen.patterngenerator.PatternGenerator’>, pickle_default_value=True, precedence=-1, readonly=False)\nCoordinates of location of pattern center. Provides a convenient way to set the x and y parameters together as a tuple (x,y), but shares the same actual storage as x and y (and thus only position OR x and y need to be specified).\nparam Number xdensity (allow_None=False, bounds=(0, None), constant=False, default=256, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=-1, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nDensity (number of samples per 1.0 length) in the x direction.\nparam Number stage_overlap_factor (allow_None=False, bounds=None, constant=False, default=4.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=None, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nThe degree of overlap between filters. Successive filter stages are overlapped by a fraction of their bandwidth. The number is arbitrary but smaller numbers lead to more computations. We currently overlap 4 stages within the bandpass region of any one filter.\nparam Number size (allow_None=False, bounds=(0.0, None), constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=-1, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nDetermines the overall size of the pattern.\nparam Number quality_factor (allow_None=False, bounds=None, constant=False, default=8.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=None, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nQuality factor controls the bandwidth of each cochlear filter. The bandwidth of each cochlear filter is a function of its center frequency. At high frequencies the bandwidth is approximately equal to the center frequency divided by a quality constant (quality_factor). At lower frequncies the bandwidth approaches a constant given by: 1000/quality_factor.\nparam Integer min_frequency (allow_None=False, bounds=(0, None), constant=False, default=0, inclusive_bounds=(True, False), instantiate=False, pickle_default_value=True, precedence=None, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nSmallest frequency for which to return an amplitude.\nparam Parameter windowing_function (allow_None=True, constant=False, default=None, instantiate=False, pickle_default_value=True, precedence=None, readonly=False)\nThis function is multiplied with the current interval, i.e. the most recent portion of the waveform interval of a signal, before performing the Fourier transform. It thus shapes the interval, which is otherwise always rectangular. The function chosen here dictates the tradeoff between resolving comparable signal strengths with similar frequencies, and resolving disparate signal strengths with dissimilar frequencies. numpy provides a number of options, e.g. bartlett, blackman, hamming, hanning, kaiser; see http://docs.scipy.org/doc/numpy/reference/routines.window.html You may also supply your own.\nparam Parameter precision (allow_None=False, constant=False, default=<type ‘numpy.float64’>, instantiate=False, pickle_default_value=True, precedence=None, readonly=False)\nThe float precision to use when calculating ear stage filters.\nOptional PatternGenerator used to construct a mask to be applied to the pattern.\nparam Number offset (allow_None=False, bounds=None, constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.11, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nAdditive offset to input pattern, defaulting to 0.0\nparam Parameter signal (allow_None=True, constant=False, default=<TimeSeries TimeSeries01034>, instantiate=True, pickle_default_value=True, precedence=None, readonly=False)\nA TimeSeries object to be fed to the model. This can be any kind of signal, be it from audio files or live from a mic, as long as the values conform to a TimeSeries.\nOptional object (expected to be an array) with which to multiply the pattern array after it has been created, before any output_fns are applied. This can be used to shape the pattern.\nBoundingBox of the area in which the pattern is generated.\nparam HookList output_fns (allow_None=False, bounds=(0, None), constant=False, default=[], instantiate=True, pickle_default_value=True, precedence=0.08, readonly=False)\nOptional function(s) to apply to the pattern array after it has been created. Can be used for normalization, thresholding, etc.\nparam Number y (allow_None=False, bounds=None, constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=-1, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nY-coordinate location of pattern center.\nparam Number x (allow_None=False, bounds=None, constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=-1, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nX-coordinate location of pattern center.\nparam ClassSelector z (allow_None=True, constant=False, default=None, instantiate=True, is_instance=True, pickle_default_value=True, precedence=-1, readonly=False)\nThe Dimension object associated with the z-values generated by the PatternGenerator . If None, uses the default set by HoloViews.Image.\nanim(duration, offset=0, timestep=1, label=None, unit=None, time_fn=Time(label='Time', name='Time00001', time_type=<type 'int'>, timestep=1.0, unit=None, until=Infinity()))\n\nduration: The temporal duration to animate in the units defined on the global time function.\n\noffset: The temporal offset from which the animation is generated given the supplied pattern\n\ntimestep: The time interval between successive frames. The duration must be an exact multiple of the timestep.\n\nlabel: A label string to override the label of the global time function (if not None).\n\nunit: The unit string to override the unit value of the global time function (if not None).\n\ntime_fn: The global time function object that is shared across the time-varying objects that are being sampled.\n\nNote that the offset, timestep and time_fn only affect patterns parameterized by time-dependent number generators. Otherwise, the frames are generated by successive call to the pattern which may or may not be varying (e.g to view the patterns contained within a Selector).\n\nchannels(use_cached=False, **params_to_override)\n\nChannels() adds a shared interface for single channel and multichannel structures. It will always return an ordered dict: its first element is the single channel of the pattern (if single-channel) or the channel average (if multichannel); the successive elements are the individual channels’ arrays (key: 0,1,..N-1).\n\ndebug(msg, *args, **kw)\n\nPrint msg merged with args as a debugging statement.\n\nSee Python’s logging module for details of message formatting.\n\ndefaults()\n\nReturn {parameter_name:parameter.default} for all non-constant Parameters.\n\nNote that a Parameter for which instantiate==True has its default instantiated.\n\nforce_new_dynamic_value = <functools.partial object at 0x2adfbc49f3c0>\nfunction(p)\n\nFunction to draw a pattern that will then be scaled and rotated.\n\nInstead of implementing __call__ directly, PatternGenerator subclasses will typically implement this helper function used by __call__, because that way they can let __call__ handle the scaling and rotation for them. Alternatively, __call__ itself can be reimplemented entirely by a subclass (e.g. if it does not need to do any scaling or rotation), in which case this function will be ignored.\n\nget_param_values(onlychanged=False)\n\nReturn a list of name,value pairs for all Parameters of this object.\n\nIf onlychanged is True, will only return values that are not equal to the default value.\n\nget_value_generator = <functools.partial object at 0x2adfbc49f470>\ninspect_value = <functools.partial object at 0x2adfbc49f680>\nmessage(msg, *args, **kw)\n\nPrint msg merged with args as a message.\n\nSee Python’s logging module for details of message formatting.\n\nnum_channels()\n\nQuery the number of channels implemented by the PatternGenerator. In case of single-channel generators this will return 1; in case of multichannel, it will return the number of channels (eg, in the case of RGB images it would return ‘3’, Red-Green-Blue, even though the OrderedDict returned by channels() will have 4 elements – the 3 channels + their average).\n\nclassmethod params(parameter_name=None)\n\nReturn the Parameters of this class as the dictionary {name: parameter_object}\n\nIncludes Parameters from this class and its superclasses.\n\npprint(imports=None, prefix=' ', unknown_value='<?>', qualify=False, separator='')\n\n(Experimental) Pretty printed representation that may be evaluated with eval. See pprint() function for more details.\n\nprecision\n\nalias of float64\n\nclassmethod print_param_defaults()\n\nPrint the default values of all cls’s Parameters.\n\nprint_param_values()\n\nPrint the values of all this object’s Parameters.\n\nscript_repr(imports=, []prefix=' ')\n\nVariant of __repr__ designed for generating a runnable script.\n\nclassmethod set_default(param_name, value)\n\nSet the default value of param_name.\n\nEquivalent to setting param_name on the class.\n\nset_dynamic_time_fn = <functools.partial object at 0x2adfbc49f940>\nset_param = <functools.partial object at 0x2adfbc49f6d8>\nstate_pop()\n\nRestore the state of the output functions saved by state_push.\n\nstate_push()\n\nSave the state of the output functions, to be restored with state_pop.\n\nverbose(msg, *args, **kw)\n\nPrint msg merged with args as a verbose message.\n\nSee Python’s logging module for details of message formatting.\n\nwarning(msg, *args, **kw)\n\nPrint msg merged with args as a warning, unless module variable warnings_as_exceptions is True, then raise an Exception containing the arguments.\n\nSee Python’s logging module for details of message formatting.\n\nclass imagen.audio.LyonsCochleogram(**params)[source]\n\nEmploys Lyons Cochlear Model to return a Cochleoogram, i.e. the response over time along the cochlea.\n\nparam Number orientation (allow_None=False, bounds=None, constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=-1, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nPolar angle of pattern, i.e., the orientation in the Cartesian coordinate system, with zero at 3 o’clock and increasing counterclockwise.\nparam Integer max_frequency (allow_None=False, bounds=(0, None), constant=False, default=9999, inclusive_bounds=(False, False), instantiate=False, pickle_default_value=True, precedence=None, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nLargest frequency for which to return an amplitude.\nparam Number ydensity (allow_None=False, bounds=(0, None), constant=False, default=256, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=-1, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nDensity (number of samples per 1.0 length) in the y direction. Typically the same as the xdensity.\nparam Number scale (allow_None=False, bounds=(0, None), constant=False, default=0.01, inclusive_bounds=(False, False), instantiate=False, pickle_default_value=True, precedence=0.1, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nThe amount by which to scale amplitudes by. This is useful if we want to rescale to say a range [0:1]. Note: Constant scaling is preferable to dynamic scaling so as not to artificially ramp down loud sounds while ramping up hiss and other background interference.\nparam String group (allow_None=False, basestring=<type ‘basestring’>, constant=False, default=Pattern, instantiate=False, pickle_default_value=True, precedence=-1, readonly=False)\nThe group name assigned to the returned HoloViews object.\nparam Composite position (allow_None=True, attribs=[‘x’, ‘y’], constant=False, default=None, instantiate=False, objtype=<class ‘imagen.patterngenerator.PatternGenerator’>, pickle_default_value=True, precedence=-1, readonly=False)\nCoordinates of location of pattern center. Provides a convenient way to set the x and y parameters together as a tuple (x,y), but shares the same actual storage as x and y (and thus only position OR x and y need to be specified).\nparam Number xdensity (allow_None=False, bounds=(0, None), constant=False, default=256, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=-1, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nDensity (number of samples per 1.0 length) in the x direction.\nparam Number stage_overlap_factor (allow_None=False, bounds=None, constant=False, default=4.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=None, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nThe degree of overlap between filters. Successive filter stages are overlapped by a fraction of their bandwidth. The number is arbitrary but smaller numbers lead to more computations. We currently overlap 4 stages within the bandpass region of any one filter.\nparam Number size (allow_None=False, bounds=(0.0, None), constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=-1, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nDetermines the overall size of the pattern.\nparam Number quality_factor (allow_None=False, bounds=None, constant=False, default=8.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=None, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nQuality factor controls the bandwidth of each cochlear filter. The bandwidth of each cochlear filter is a function of its center frequency. At high frequencies the bandwidth is approximately equal to the center frequency divided by a quality constant (quality_factor). At lower frequncies the bandwidth approaches a constant given by: 1000/quality_factor.\nparam Integer min_frequency (allow_None=False, bounds=(0, None), constant=False, default=0, inclusive_bounds=(True, False), instantiate=False, pickle_default_value=True, precedence=None, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nSmallest frequency for which to return an amplitude.\nparam Parameter windowing_function (allow_None=True, constant=False, default=None, instantiate=False, pickle_default_value=True, precedence=None, readonly=False)\nThis function is multiplied with the current interval, i.e. the most recent portion of the waveform interval of a signal, before performing the Fourier transform. It thus shapes the interval, which is otherwise always rectangular. The function chosen here dictates the tradeoff between resolving comparable signal strengths with similar frequencies, and resolving disparate signal strengths with dissimilar frequencies. numpy provides a number of options, e.g. bartlett, blackman, hamming, hanning, kaiser; see http://docs.scipy.org/doc/numpy/reference/routines.window.html You may also supply your own.\nparam Parameter precision (allow_None=False, constant=False, default=<type ‘numpy.float64’>, instantiate=False, pickle_default_value=True, precedence=None, readonly=False)\nThe float precision to use when calculating ear stage filters.\nOptional PatternGenerator used to construct a mask to be applied to the pattern.\nparam Number offset (allow_None=False, bounds=None, constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.11, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nAdditive offset to input pattern, defaulting to 0.0\nparam Parameter signal (allow_None=True, constant=False, default=<TimeSeries TimeSeries01034>, instantiate=True, pickle_default_value=True, precedence=None, readonly=False)\nA TimeSeries object to be fed to the model. This can be any kind of signal, be it from audio files or live from a mic, as long as the values conform to a TimeSeries.\nOptional object (expected to be an array) with which to multiply the pattern array after it has been created, before any output_fns are applied. This can be used to shape the pattern.\nBoundingBox of the area in which the pattern is generated.\nparam HookList output_fns (allow_None=False, bounds=(0, None), constant=False, default=[], instantiate=True, pickle_default_value=True, precedence=0.08, readonly=False)\nOptional function(s) to apply to the pattern array after it has been created. Can be used for normalization, thresholding, etc.\nparam Number y (allow_None=False, bounds=None, constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=-1, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nY-coordinate location of pattern center.\nparam Number x (allow_None=False, bounds=None, constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=-1, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nX-coordinate location of pattern center.\nparam ClassSelector z (allow_None=True, constant=False, default=None, instantiate=True, is_instance=True, pickle_default_value=True, precedence=-1, readonly=False)\nThe Dimension object associated with the z-values generated by the PatternGenerator . If None, uses the default set by HoloViews.Image.\nanim(duration, offset=0, timestep=1, label=None, unit=None, time_fn=Time(label='Time', name='Time00001', time_type=<type 'int'>, timestep=1.0, unit=None, until=Infinity()))\n\nduration: The temporal duration to animate in the units defined on the global time function.\n\noffset: The temporal offset from which the animation is generated given the supplied pattern\n\ntimestep: The time interval between successive frames. The duration must be an exact multiple of the timestep.\n\nlabel: A label string to override the label of the global time function (if not None).\n\nunit: The unit string to override the unit value of the global time function (if not None).\n\ntime_fn: The global time function object that is shared across the time-varying objects that are being sampled.\n\nNote that the offset, timestep and time_fn only affect patterns parameterized by time-dependent number generators. Otherwise, the frames are generated by successive call to the pattern which may or may not be varying (e.g to view the patterns contained within a Selector).\n\nchannels(use_cached=False, **params_to_override)\n\nChannels() adds a shared interface for single channel and multichannel structures. It will always return an ordered dict: its first element is the single channel of the pattern (if single-channel) or the channel average (if multichannel); the successive elements are the individual channels’ arrays (key: 0,1,..N-1).\n\ndebug(msg, *args, **kw)\n\nPrint msg merged with args as a debugging statement.\n\nSee Python’s logging module for details of message formatting.\n\ndefaults()\n\nReturn {parameter_name:parameter.default} for all non-constant Parameters.\n\nNote that a Parameter for which instantiate==True has its default instantiated.\n\nforce_new_dynamic_value = <functools.partial object at 0x2adfbc49f998>\nfunction(p)\n\nFunction to draw a pattern that will then be scaled and rotated.\n\nInstead of implementing __call__ directly, PatternGenerator subclasses will typically implement this helper function used by __call__, because that way they can let __call__ handle the scaling and rotation for them. Alternatively, __call__ itself can be reimplemented entirely by a subclass (e.g. if it does not need to do any scaling or rotation), in which case this function will be ignored.\n\nget_param_values(onlychanged=False)\n\nReturn a list of name,value pairs for all Parameters of this object.\n\nIf onlychanged is True, will only return values that are not equal to the default value.\n\nget_value_generator = <functools.partial object at 0x2adfbc49f890>\ninspect_value = <functools.partial object at 0x2adfbc49fa48>\nmessage(msg, *args, **kw)\n\nPrint msg merged with args as a message.\n\nSee Python’s logging module for details of message formatting.\n\nnum_channels()\n\nQuery the number of channels implemented by the PatternGenerator. In case of single-channel generators this will return 1; in case of multichannel, it will return the number of channels (eg, in the case of RGB images it would return ‘3’, Red-Green-Blue, even though the OrderedDict returned by channels() will have 4 elements – the 3 channels + their average).\n\nclassmethod params(parameter_name=None)\n\nReturn the Parameters of this class as the dictionary {name: parameter_object}\n\nIncludes Parameters from this class and its superclasses.\n\npprint(imports=None, prefix=' ', unknown_value='<?>', qualify=False, separator='')\n\n(Experimental) Pretty printed representation that may be evaluated with eval. See pprint() function for more details.\n\nprecision\n\nalias of float64\n\nclassmethod print_param_defaults()\n\nPrint the default values of all cls’s Parameters.\n\nprint_param_values()\n\nPrint the values of all this object’s Parameters.\n\nscript_repr(imports=, []prefix=' ')\n\nVariant of __repr__ designed for generating a runnable script.\n\nclassmethod set_default(param_name, value)\n\nSet the default value of param_name.\n\nEquivalent to setting param_name on the class.\n\nset_dynamic_time_fn = <functools.partial object at 0x2adfbc49f730>\nset_param = <functools.partial object at 0x2adfbc49f7e0>\nstate_pop()\n\nRestore the state of the output functions saved by state_push.\n\nstate_push()\n\nSave the state of the output functions, to be restored with state_pop.\n\nverbose(msg, *args, **kw)\n\nPrint msg merged with args as a verbose message.\n\nSee Python’s logging module for details of message formatting.\n\nwarning(msg, *args, **kw)\n\nPrint msg merged with args as a warning, unless module variable warnings_as_exceptions is True, then raise an Exception containing the arguments.\n\nSee Python’s logging module for details of message formatting.\n\nclass imagen.audio.ModulatedLogSpectrogram(**params)[source]\n\nExtends OctaveSpectrogram with a simple model of outer ear amplification. One can set both the range to amplify and the amount.\n\nparam Number orientation (allow_None=False, bounds=None, constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=-1, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nPolar angle of pattern, i.e., the orientation in the Cartesian coordinate system, with zero at 3 o’clock and increasing counterclockwise.\nparam Integer min_latency (allow_None=False, bounds=(0, None), constant=False, default=0, inclusive_bounds=(True, False), instantiate=False, pickle_default_value=True, precedence=1, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nSmallest latency (in milliseconds) for which to return amplitudes.\nparam Integer max_frequency (allow_None=False, bounds=(0, None), constant=False, default=9999, inclusive_bounds=(False, False), instantiate=False, pickle_default_value=True, precedence=None, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nLargest frequency for which to return an amplitude.\nparam Number ydensity (allow_None=False, bounds=(0, None), constant=False, default=256, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=-1, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nDensity (number of samples per 1.0 length) in the y direction. Typically the same as the xdensity.\nparam Number scale (allow_None=False, bounds=(0, None), constant=False, default=0.01, inclusive_bounds=(False, False), instantiate=False, pickle_default_value=True, precedence=0.1, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nThe amount by which to scale amplitudes by. This is useful if we want to rescale to say a range [0:1]. Note: Constant scaling is preferable to dynamic scaling so as not to artificially ramp down loud sounds while ramping up hiss and other background interference.\nparam String group (allow_None=False, basestring=<type ‘basestring’>, constant=False, default=Pattern, instantiate=False, pickle_default_value=True, precedence=-1, readonly=False)\nThe group name assigned to the returned HoloViews object.\nparam Composite position (allow_None=True, attribs=[‘x’, ‘y’], constant=False, default=None, instantiate=False, objtype=<class ‘imagen.patterngenerator.PatternGenerator’>, pickle_default_value=True, precedence=-1, readonly=False)\nCoordinates of location of pattern center. Provides a convenient way to set the x and y parameters together as a tuple (x,y), but shares the same actual storage as x and y (and thus only position OR x and y need to be specified).\nparam Number xdensity (allow_None=False, bounds=(0, None), constant=False, default=256, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=-1, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nDensity (number of samples per 1.0 length) in the x direction.\nparam Number size (allow_None=False, bounds=(0.0, None), constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=-1, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nDetermines the overall size of the pattern.\nparam Integer min_frequency (allow_None=False, bounds=(0, None), constant=False, default=0, inclusive_bounds=(True, False), instantiate=False, pickle_default_value=True, precedence=None, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nSmallest frequency for which to return an amplitude.\nparam Parameter windowing_function (allow_None=True, constant=False, default=None, instantiate=False, pickle_default_value=True, precedence=None, readonly=False)\nThis function is multiplied with the current interval, i.e. the most recent portion of the waveform interval of a signal, before performing the Fourier transform. It thus shapes the interval, which is otherwise always rectangular. The function chosen here dictates the tradeoff between resolving comparable signal strengths with similar frequencies, and resolving disparate signal strengths with dissimilar frequencies. numpy provides a number of options, e.g. bartlett, blackman, hamming, hanning, kaiser; see http://docs.scipy.org/doc/numpy/reference/routines.window.html You may also supply your own.\nOptional PatternGenerator used to construct a mask to be applied to the pattern.\nparam Number upper_freq_bound (allow_None=False, bounds=(0.0, None), constant=False, default=7000.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=None, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nThe upper bound of the frequency range to be modulated.\nparam Number offset (allow_None=False, bounds=None, constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.11, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nAdditive offset to input pattern, defaulting to 0.0\nparam Integer max_latency (allow_None=False, bounds=(0, None), constant=False, default=500, inclusive_bounds=(False, False), instantiate=False, pickle_default_value=True, precedence=2, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nLargest latency (in milliseconds) for which to return amplitudes.\nparam Integer log_base (allow_None=False, bounds=(0.0, None), constant=False, default=2, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=None, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nThe base of the logarithm used to generate logarithmic frequency spacing.\nparam TimeSeriesParam signal (allow_None=False, constant=False, default=<TimeSeries TimeSeries01034>, instantiate=True, is_instance=True, pickle_default_value=True, precedence=None, readonly=False)\nA TimeSeries object on which to perfom the Fourier Transform.\nOptional object (expected to be an array) with which to multiply the pattern array after it has been created, before any output_fns are applied. This can be used to shape the pattern.\nBoundingBox of the area in which the pattern is generated.\nparam Number lower_freq_bound (allow_None=False, bounds=(0.0, None), constant=False, default=1000.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=None, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nThe lower bound of the frequency range to be modulated.\nparam HookList output_fns (allow_None=False, bounds=(0, None), constant=False, default=[], instantiate=True, pickle_default_value=True, precedence=0.08, readonly=False)\nOptional function(s) to apply to the pattern array after it has been created. Can be used for normalization, thresholding, etc.\nparam Number y (allow_None=False, bounds=None, constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=-1, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nY-coordinate location of pattern center.\nparam Number x (allow_None=False, bounds=None, constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=-1, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nX-coordinate location of pattern center.\nparam Parameter modulation_function (allow_None=False, constant=False, instantiate=False, pickle_default_value=True, precedence=None, readonly=False)\nThe function by which to modulate the signal between the specified frequency range. The default (hanning) multiplies a section of the signal by a hanning window.\nparam ClassSelector z (allow_None=True, constant=False, default=None, instantiate=True, is_instance=True, pickle_default_value=True, precedence=-1, readonly=False)\nThe Dimension object associated with the z-values generated by the PatternGenerator . If None, uses the default set by HoloViews.Image.\nanim(duration, offset=0, timestep=1, label=None, unit=None, time_fn=Time(label='Time', name='Time00001', time_type=<type 'int'>, timestep=1.0, unit=None, until=Infinity()))\n\nduration: The temporal duration to animate in the units defined on the global time function.\n\noffset: The temporal offset from which the animation is generated given the supplied pattern\n\ntimestep: The time interval between successive frames. The duration must be an exact multiple of the timestep.\n\nlabel: A label string to override the label of the global time function (if not None).\n\nunit: The unit string to override the unit value of the global time function (if not None).\n\ntime_fn: The global time function object that is shared across the time-varying objects that are being sampled.\n\nNote that the offset, timestep and time_fn only affect patterns parameterized by time-dependent number generators. Otherwise, the frames are generated by successive call to the pattern which may or may not be varying (e.g to view the patterns contained within a Selector).\n\nchannels(use_cached=False, **params_to_override)\n\nChannels() adds a shared interface for single channel and multichannel structures. It will always return an ordered dict: its first element is the single channel of the pattern (if single-channel) or the channel average (if multichannel); the successive elements are the individual channels’ arrays (key: 0,1,..N-1).\n\ndebug(msg, *args, **kw)\n\nPrint msg merged with args as a debugging statement.\n\nSee Python’s logging module for details of message formatting.\n\ndefaults()\n\nReturn {parameter_name:parameter.default} for all non-constant Parameters.\n\nNote that a Parameter for which instantiate==True has its default instantiated.\n\nforce_new_dynamic_value = <functools.partial object at 0x2adfbc49f9f0>\nfunction(p)\n\nFunction to draw a pattern that will then be scaled and rotated.\n\nInstead of implementing __call__ directly, PatternGenerator subclasses will typically implement this helper function used by __call__, because that way they can let __call__ handle the scaling and rotation for them. Alternatively, __call__ itself can be reimplemented entirely by a subclass (e.g. if it does not need to do any scaling or rotation), in which case this function will be ignored.\n\nget_param_values(onlychanged=False)\n\nReturn a list of name,value pairs for all Parameters of this object.\n\nIf onlychanged is True, will only return values that are not equal to the default value.\n\nget_value_generator = <functools.partial object at 0x2adfbc49f418>\ninspect_value = <functools.partial object at 0x2adfbc49f8e8>\nmessage(msg, *args, **kw)\n\nPrint msg merged with args as a message.\n\nSee Python’s logging module for details of message formatting.\n\nstatic modulation_function(M)\n\nReturn the Hanning window.\n\nThe Hanning window is a taper formed by using a weighted cosine.\n\nM : int\nNumber of points in the output window. If zero or less, an empty array is returned.\nout : ndarray, shape(M,)\nThe window, with the maximum value normalized to one (the value one appears only if M is odd).\n\nbartlett, blackman, hamming, kaiser\n\nThe Hanning window is defined as\n\n$w(n) = 0.5 - 0.5cos\\left(\\frac{2\\pi{n}}{M-1}\\right) \\qquad 0 \\leq n \\leq M-1$\n\nThe Hanning was named for Julius van Hann, an Austrian meteorologist. It is also known as the Cosine Bell. Some authors prefer that it be called a Hann window, to help avoid confusion with the very similar Hamming window.\n\nMost references to the Hanning window come from the signal processing literature, where it is used as one of many windowing functions for smoothing values. It is also known as an apodization (which means “removing the foot”, i.e. smoothing discontinuities at the beginning and end of the sampled signal) or tapering function.\n\n Blackman, R.B. and Tukey, J.W., (1958) The measurement of power spectra, Dover Publications, New York.\n E.R. Kanasewich, “Time Sequence Analysis in Geophysics”, The University of Alberta Press, 1975, pp. 106-108.\n Wikipedia, “Window function”, http://en.wikipedia.org/wiki/Window_function\n W.H. Press, B.P. Flannery, S.A. Teukolsky, and W.T. Vetterling, “Numerical Recipes”, Cambridge University Press, 1986, page 425.\n>>> np.hanning(12)\narray([ 0. , 0.07937323, 0.29229249, 0.57115742, 0.82743037,\n0.97974649, 0.97974649, 0.82743037, 0.57115742, 0.29229249,\n0.07937323, 0. ])\n\n\nPlot the window and its frequency response:\n\n>>> from numpy.fft import fft, fftshift\n>>> window = np.hanning(51)\n>>> plt.plot(window)\n[<matplotlib.lines.Line2D object at 0x...>]\n>>> plt.title(\"Hann window\")\n<matplotlib.text.Text object at 0x...>\n>>> plt.ylabel(\"Amplitude\")\n<matplotlib.text.Text object at 0x...>\n>>> plt.xlabel(\"Sample\")\n<matplotlib.text.Text object at 0x...>\n>>> plt.show()\n\n>>> plt.figure()\n<matplotlib.figure.Figure object at 0x...>\n>>> A = fft(window, 2048) / 25.5\n>>> mag = np.abs(fftshift(A))\n>>> freq = np.linspace(-0.5, 0.5, len(A))\n>>> response = 20 * np.log10(mag)\n>>> response = np.clip(response, -100, 100)\n>>> plt.plot(freq, response)\n[<matplotlib.lines.Line2D object at 0x...>]\n>>> plt.title(\"Frequency response of the Hann window\")\n<matplotlib.text.Text object at 0x...>\n>>> plt.ylabel(\"Magnitude [dB]\")\n<matplotlib.text.Text object at 0x...>\n>>> plt.xlabel(\"Normalized frequency [cycles per sample]\")\n<matplotlib.text.Text object at 0x...>\n>>> plt.axis('tight')\n(-0.5, 0.5, -100.0, ...)\n>>> plt.show()\n\nnum_channels()\n\nQuery the number of channels implemented by the PatternGenerator. In case of single-channel generators this will return 1; in case of multichannel, it will return the number of channels (eg, in the case of RGB images it would return ‘3’, Red-Green-Blue, even though the OrderedDict returned by channels() will have 4 elements – the 3 channels + their average).\n\nclassmethod params(parameter_name=None)\n\nReturn the Parameters of this class as the dictionary {name: parameter_object}\n\nIncludes Parameters from this class and its superclasses.\n\npprint(imports=None, prefix=' ', unknown_value='<?>', qualify=False, separator='')\n\n(Experimental) Pretty printed representation that may be evaluated with eval. See pprint() function for more details.\n\nclassmethod print_param_defaults()\n\nPrint the default values of all cls’s Parameters.\n\nprint_param_values()\n\nPrint the values of all this object’s Parameters.\n\nscript_repr(imports=, []prefix=' ')\n\nVariant of __repr__ designed for generating a runnable script.\n\nclassmethod set_default(param_name, value)\n\nSet the default value of param_name.\n\nEquivalent to setting param_name on the class.\n\nset_dynamic_time_fn = <functools.partial object at 0x2adfbc49faa0>\nset_param = <functools.partial object at 0x2adfbc49fba8>\nstate_pop()\n\nRestore the state of the output functions saved by state_push.\n\nstate_push()\n\nSave the state of the output functions, to be restored with state_pop.\n\nverbose(msg, *args, **kw)\n\nPrint msg merged with args as a verbose message.\n\nSee Python’s logging module for details of message formatting.\n\nwarning(msg, *args, **kw)\n\nPrint msg merged with args as a warning, unless module variable warnings_as_exceptions is True, then raise an Exception containing the arguments.\n\nSee Python’s logging module for details of message formatting.\n\n## colorspaces Module¶", null, "Utilities for converting images between various color spaces, such as:\n\n• RGB (for display on computer monitor red, green, and blue channels)\n• HSV (allowing manipulation of the hue, saturation, and value),\n• LMS (estimates of human long, medium, and short cone responses),\n• LCH (CIE perceptually uniform luminance, chroma (saturation), and hue)\n• LAB (CIE opponent black/white, red/green, blue/yellow axes)\n• XYZ (CIE interchange format)\n\nSee http://en.wikipedia.org/wiki/Color_space for more detailed descriptions.\n\nTo use these utilities, users should instantiate one of these two classes:\n\nColorSpace\nProvides a convert(from, to, what) method to perform conversion between colorspaces, e.g. convert(\"rgb\", \"hsv\", X), where X is assumed to be a numpy.dstack() object with three matching arrays.\nFeatureColorConverter\n\nDeclare a set of color spaces to allow external code to work the same for any combination of color spaces. Specifically, declares:\n\n• image color space (the space in which a dataset of images has been stored),\n\n• working color space (to which the images will be converted),\n\ne.g. to transform images to a different working dataset, and\n\n• analysis color space (space in which analyses will be performed)\n\nThese values can be set using:\n\ncolor_conversion.image_space=\"XYZ\" # e.g. RGB, XYZ, LMS\ncolor_conversion.working_space=\"RGB\" # e.g. RGB, LMS\ncolor_conversion.analysis_space=\"HSV\" # e.g. HSV, LCH\n\n\nThe other code in this file is primarily implementation for these two classes, and will rarely need to be used directly.\n\nclass imagen.colorspaces.ColorSpace(**params)[source]\n\nLow-level color conversion. The ‘convert’ method handles color conversion to and from (and through) XYZ, and supports RGB, LCH, LMS and HSV.\n\nparam Parameter dtype (allow_None=False, constant=False, default=<type ‘numpy.float32’>, instantiate=False, pickle_default_value=True, precedence=None, readonly=False)\nDatatype to use for result.\nparam NumericTuple output_limits (allow_None=False, constant=False, default=(0.0, 1.0), instantiate=False, length=2, pickle_default_value=True, precedence=None, readonly=False)\nUpper and lower bounds to enforce on output values.\nparam Dict transforms (allow_None=False, constant=False, default={‘D65’: {‘rgb_from_xyz’: array([[ 3.241 , -1.5374, -0.4986], [-0.9692, 1.876 , 0.0416], [ 0.0556, -0.204 , 1.057 ]]), ‘xyz_from_lms’: array([[ 1.87616336e+00, -1.37368291e+00, 3.40220544e-01], [ 6.37205799e-01, 3.92411765e-01, 5.61517442e-05], [ 0.00000000e+00, 0.00000000e+00, 1.60642570e+00]]), ‘xyz_from_rgb’: array([[ 0.41238088, 0.35757284, 0.1804523 ], [ 0.21261986, 0.71513879, 0.07214994], [ 0.0193435 , 0.11921217, 0.95050657]]), ‘lms_from_xyz’: array([[ 0.2435, 0.8524, -0.0516], [-0.3954, 1.1642, 0.0837], [ 0. , 0. , 0.6225]])}}, instantiate=True, is_instance=True, pickle_default_value=True, precedence=None, readonly=False)\nStructure containing the transformation matrices used by this Class. See transforms in this file.\nparam String whitepoint (allow_None=False, basestring=<type ‘basestring’>, constant=False, default=D65, instantiate=False, pickle_default_value=True, precedence=None, readonly=False)\nName of whitepoint in lookup table.\nparam ObjectSelector output_clip (allow_None=None, check_on_set=True, compute_default_fn=None, constant=False, default=silent, instantiate=False, objects=[‘silent’, ‘warn’, ‘error’, ‘none’], pickle_default_value=True, precedence=None, readonly=False)\nAction to take when the output value will be clipped.\nparam NumericTuple input_limits (allow_None=False, constant=False, default=(0.0, 1.0), instantiate=False, length=2, pickle_default_value=True, precedence=None, readonly=False)\nUpper and lower bounds to verify on input values.\nconvert(from_, to, what)[source]\n\nConvert image or color “what” from “from_” colorpace to “to” colorspace. E.g.: convert(\"rgb\", \"hsv\", X), where X is a numpy dstack or a color tuple.\n\ndebug(msg, *args, **kw)\n\nPrint msg merged with args as a debugging statement.\n\nSee Python’s logging module for details of message formatting.\n\ndefaults()\n\nReturn {parameter_name:parameter.default} for all non-constant Parameters.\n\nNote that a Parameter for which instantiate==True has its default instantiated.\n\ndtype\n\nalias of float32\n\nforce_new_dynamic_value = <functools.partial object at 0x2adfbcb3d7e0>\nget_param_values(onlychanged=False)\n\nReturn a list of name,value pairs for all Parameters of this object.\n\nIf onlychanged is True, will only return values that are not equal to the default value.\n\nget_value_generator = <functools.partial object at 0x2adfbcb3d838>\nhsv_to_gammargb(HSV)[source]\n\nhsv is already specifying gamma corrected rgb\n\nhsv_to_rgb(HSV)[source]\n\nhsv to linear rgb\n\ninspect_value = <functools.partial object at 0x2adfbcb3d788>\nmessage(msg, *args, **kw)\n\nPrint msg merged with args as a message.\n\nSee Python’s logging module for details of message formatting.\n\nclassmethod params(parameter_name=None)\n\nReturn the Parameters of this class as the dictionary {name: parameter_object}\n\nIncludes Parameters from this class and its superclasses.\n\npprint(imports=None, prefix=' ', unknown_value='<?>', qualify=False, separator='')\n\n(Experimental) Pretty printed representation that may be evaluated with eval. See pprint() function for more details.\n\nclassmethod print_param_defaults()\n\nPrint the default values of all cls’s Parameters.\n\nprint_param_values()\n\nPrint the values of all this object’s Parameters.\n\nrgb_to_hsv(RGB)[source]\n\nlinear rgb to hsv\n\nscript_repr(imports=, []prefix=' ')\n\nVariant of __repr__ designed for generating a runnable script.\n\nclassmethod set_default(param_name, value)\n\nSet the default value of param_name.\n\nEquivalent to setting param_name on the class.\n\nset_dynamic_time_fn = <functools.partial object at 0x2adfbcb3d628>\nset_param = <functools.partial object at 0x2adfbcb3d8e8>\nstate_pop()\n\nRestore the most recently saved state.\n\nSee state_push() for more details.\n\nstate_push()\n\nSave this instance’s state.\n\nFor Parameterized instances, this includes the state of dynamically generated values.\n\nSubclasses that maintain short-term state should additionally save and restore that state using state_push() and state_pop().\n\nGenerally, this method is used by operations that need to test something without permanently altering the objects’ state.\n\nverbose(msg, *args, **kw)\n\nPrint msg merged with args as a verbose message.\n\nSee Python’s logging module for details of message formatting.\n\nwarning(msg, *args, **kw)\n\nPrint msg merged with args as a warning, unless module variable warnings_as_exceptions is True, then raise an Exception containing the arguments.\n\nSee Python’s logging module for details of message formatting.\n\nclass imagen.colorspaces.ColorConverter(**params)[source]\n\nHigh-level color conversion class designed to support color space transformations along a pipeline common in color vision modelling: image (dataset colorspace) -> working (working colorspace) -> [higher stages] -> analysis\n\nparam ObjectSelector analysis_space (allow_None=None, check_on_set=True, compute_default_fn=None, constant=False, default=HSV, instantiate=False, objects=[‘HSV’, ‘LCH’], pickle_default_value=True, precedence=None, readonly=False)\nColor space in which analysis is performed.\nparam Parameter colorspace (allow_None=False, constant=False, default=<ColorSpace ColorSpace01042>, instantiate=False, pickle_default_value=True, precedence=None, readonly=False)\nObject to use for converting between color spaces.\nparam ObjectSelector working_space (allow_None=None, check_on_set=True, compute_default_fn=None, constant=False, default=RGB, instantiate=False, objects=[‘RGB’, ‘LMS’], pickle_default_value=True, precedence=None, readonly=False)\nColor space to which images will be transformed to provide working space to later stages of processing.\nparam ObjectSelector image_space (allow_None=None, check_on_set=True, compute_default_fn=None, constant=False, default=XYZ, instantiate=False, objects=[‘XYZ’, ‘LMS’, ‘RGB’], pickle_default_value=True, precedence=None, readonly=False)\nColor space in which images are encoded.\nanalysis2display(a)[source]\n\nUtility conversion function that transforms data from the analysis color space to the display space (currently hard-set to RGB) for visualization.\n\nanalysis2working(a)[source]\n\nConvert back from the analysis color space to the working space.\n\ndebug(msg, *args, **kw)\n\nPrint msg merged with args as a debugging statement.\n\nSee Python’s logging module for details of message formatting.\n\ndefaults()\n\nReturn {parameter_name:parameter.default} for all non-constant Parameters.\n\nNote that a Parameter for which instantiate==True has its default instantiated.\n\nforce_new_dynamic_value = <functools.partial object at 0x2adfbcb3d680>\nget_param_values(onlychanged=False)\n\nReturn a list of name,value pairs for all Parameters of this object.\n\nIf onlychanged is True, will only return values that are not equal to the default value.\n\nget_value_generator = <functools.partial object at 0x2adfbcb3d7e0>\nimage2working(i)[source]\n\nTransform images i provided into the specified working color space.\n\ninspect_value = <functools.partial object at 0x2adfbcb3d6d8>\njitter_hue(a, amount)[source]\n\nRotate the hue component of a by the given amount.\n\nmessage(msg, *args, **kw)\n\nPrint msg merged with args as a message.\n\nSee Python’s logging module for details of message formatting.\n\nmultiply_sat(a, factor)[source]\n\nScale the saturation of a by the given amount.\n\nclassmethod params(parameter_name=None)\n\nReturn the Parameters of this class as the dictionary {name: parameter_object}\n\nIncludes Parameters from this class and its superclasses.\n\npprint(imports=None, prefix=' ', unknown_value='<?>', qualify=False, separator='')\n\n(Experimental) Pretty printed representation that may be evaluated with eval. See pprint() function for more details.\n\nclassmethod print_param_defaults()\n\nPrint the default values of all cls’s Parameters.\n\nprint_param_values()\n\nPrint the values of all this object’s Parameters.\n\nscript_repr(imports=, []prefix=' ')\n\nVariant of __repr__ designed for generating a runnable script.\n\nclassmethod set_default(param_name, value)\n\nSet the default value of param_name.\n\nEquivalent to setting param_name on the class.\n\nset_dynamic_time_fn = <functools.partial object at 0x2adfbcb3d5d0>\nset_param = <functools.partial object at 0x2adfbcb3d998>\nstate_pop()\n\nRestore the most recently saved state.\n\nSee state_push() for more details.\n\nstate_push()\n\nSave this instance’s state.\n\nFor Parameterized instances, this includes the state of dynamically generated values.\n\nSubclasses that maintain short-term state should additionally save and restore that state using state_push() and state_pop().\n\nGenerally, this method is used by operations that need to test something without permanently altering the objects’ state.\n\nverbose(msg, *args, **kw)\n\nPrint msg merged with args as a verbose message.\n\nSee Python’s logging module for details of message formatting.\n\nwarning(msg, *args, **kw)\n\nPrint msg merged with args as a warning, unless module variable warnings_as_exceptions is True, then raise an Exception containing the arguments.\n\nSee Python’s logging module for details of message formatting.\n\nworking2analysis(r)[source]\n\nTransform working space inputs to the analysis color space.\n\n## deprecated Module¶", null, "Old patterns not intended for new code.\n\nThese patterns are expected to be deleted eventually.\n\nclass imagen.deprecated.FileImage(**params)\n\n2D Image generator that reads the image from a file.\n\nGrayscale versions of the image are always available, converted from the color version if necessary. For color images, three-channel color values are available through the channels() method. See Image’s Image class for details of supported image file formats.\n\nparam Number x (allow_None=False, bounds=None, constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.2, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nX-coordinate location of pattern center.\nparam Number scale (allow_None=False, bounds=None, constant=False, default=1.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.1, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nMultiplicative strength of input pattern, defaulting to 1.0\nparam String group (allow_None=False, basestring=<type ‘basestring’>, constant=False, default=Pattern, instantiate=False, pickle_default_value=True, precedence=-1, readonly=False)\nThe group name assigned to the returned HoloViews object.\nparam ClassSelector pattern_sampler (allow_None=False, constant=False, default=<PatternSampler PatternSampler01045>, instantiate=True, is_instance=True, pickle_default_value=True, precedence=None, readonly=False)\nThe PatternSampler to use to resample/resize the image.\nparam Boolean cache_image (allow_None=False, bounds=(0, 1), constant=False, default=False, instantiate=False, pickle_default_value=True, precedence=None, readonly=False)\nIf False, discards the image and pattern_sampler after drawing the pattern each time, to make it possible to use very large databases of images without running out of memory.\nparam Number orientation (allow_None=False, bounds=None, constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.4, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nPolar angle of pattern, i.e., the orientation in the Cartesian coordinate system, with zero at 3 o’clock and increasing counterclockwise.\nparam HookList channel_transforms (allow_None=False, bounds=(0, None), constant=False, default=[], instantiate=True, pickle_default_value=True, precedence=None, readonly=False)\nOptional functions to apply post processing to the set of channels.\nparam ClassSelector z (allow_None=True, constant=False, default=None, instantiate=True, is_instance=True, pickle_default_value=True, precedence=-1, readonly=False)\nThe Dimension object associated with the z-values generated by the PatternGenerator . If None, uses the default set by HoloViews.Image.\nOptional object (expected to be an array) with which to multiply the pattern array after it has been created, before any output_fns are applied. This can be used to shape the pattern.\nBoundingBox of the area in which the pattern is generated.\nparam Filename filename (allow_None=False, constant=False, default=images/ellen_arthur.pgm, instantiate=False, pickle_default_value=True, precedence=0.9, readonly=False, search_paths=[])\nFile path (can be relative to Param’s base path) to a bitmap image. The image can be in any format accepted by PIL, e.g. PNG, JPG, TIFF, or PGM as well or numpy save files (.npy or .npz) containing 2D or 3D arrays (where the third dimension is used for each channel).\nparam Number xdensity (allow_None=False, bounds=(0, None), constant=False, default=256, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=-1, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nDensity (number of samples per 1.0 length) in the x direction.\nparam Number y (allow_None=False, bounds=None, constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.21, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nY-coordinate location of pattern center.\nparam HookList output_fns (allow_None=False, bounds=(0, None), constant=False, default=[], instantiate=True, pickle_default_value=True, precedence=0.08, readonly=False)\nOptional function(s) to apply to the pattern array after it has been created. Can be used for normalization, thresholding, etc.\nparam Number offset (allow_None=False, bounds=None, constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.11, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nAdditive offset to input pattern, defaulting to 0.0\nOptional PatternGenerator used to construct a mask to be applied to the pattern.\nparam Composite position (allow_None=True, attribs=[‘x’, ‘y’], constant=False, default=None, instantiate=False, objtype=<class ‘imagen.patterngenerator.PatternGenerator’>, pickle_default_value=True, precedence=-1, readonly=False)\nCoordinates of location of pattern center. Provides a convenient way to set the x and y parameters together as a tuple (x,y), but shares the same actual storage as x and y (and thus only position OR x and y need to be specified).\nparam Number ydensity (allow_None=False, bounds=(0, None), constant=False, default=256, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=-1, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nDensity (number of samples per 1.0 length) in the y direction. Typically the same as the xdensity.\nparam Number aspect_ratio (allow_None=False, bounds=(0.0, None), constant=False, default=1.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.31, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nRatio of width to height; size*aspect_ratio gives the width.\nparam Number size (allow_None=False, bounds=(0.0, None), constant=False, default=1.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.3, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nHeight of the image.\nanim(duration, offset=0, timestep=1, label=None, unit=None, time_fn=Time(label='Time', name='Time00001', time_type=<type 'int'>, timestep=1.0, unit=None, until=Infinity()))\n\nduration: The temporal duration to animate in the units defined on the global time function.\n\noffset: The temporal offset from which the animation is generated given the supplied pattern\n\ntimestep: The time interval between successive frames. The duration must be an exact multiple of the timestep.\n\nlabel: A label string to override the label of the global time function (if not None).\n\nunit: The unit string to override the unit value of the global time function (if not None).\n\ntime_fn: The global time function object that is shared across the time-varying objects that are being sampled.\n\nNote that the offset, timestep and time_fn only affect patterns parameterized by time-dependent number generators. Otherwise, the frames are generated by successive call to the pattern which may or may not be varying (e.g to view the patterns contained within a Selector).\n\ndebug(msg, *args, **kw)\n\nPrint msg merged with args as a debugging statement.\n\nSee Python’s logging module for details of message formatting.\n\ndefaults()\n\nReturn {parameter_name:parameter.default} for all non-constant Parameters.\n\nNote that a Parameter for which instantiate==True has its default instantiated.\n\nforce_new_dynamic_value = <functools.partial object at 0x2adfbc4c5368>\nget_param_values(onlychanged=False)\n\nReturn a list of name,value pairs for all Parameters of this object.\n\nIf onlychanged is True, will only return values that are not equal to the default value.\n\nget_value_generator = <functools.partial object at 0x2adfbc4c53c0>\ninspect_value = <functools.partial object at 0x2adfbc4c5418>\nmessage(msg, *args, **kw)\n\nPrint msg merged with args as a message.\n\nSee Python’s logging module for details of message formatting.\n\nclassmethod params(parameter_name=None)\n\nReturn the Parameters of this class as the dictionary {name: parameter_object}\n\nIncludes Parameters from this class and its superclasses.\n\npprint(imports=None, prefix=' ', unknown_value='<?>', qualify=False, separator='')\n\n(Experimental) Pretty printed representation that may be evaluated with eval. See pprint() function for more details.\n\nclassmethod print_param_defaults()\n\nPrint the default values of all cls’s Parameters.\n\nprint_param_values()\n\nPrint the values of all this object’s Parameters.\n\nscript_repr(imports=, []prefix=' ')\n\nVariant of __repr__ designed for generating a runnable script.\n\nclassmethod set_default(param_name, value)\n\nSet the default value of param_name.\n\nEquivalent to setting param_name on the class.\n\nset_dynamic_time_fn = <functools.partial object at 0x2adfbc4c5260>\nset_matrix_dimensions(*args)\n\nSubclassed to delete the cached image when matrix dimensions are changed.\n\nset_param = <functools.partial object at 0x2adfbc4c5310>\nstate_pop()\n\nRestore the state of the output functions saved by state_push.\n\nstate_push()\n\nSave the state of the output functions, to be restored with state_pop.\n\nverbose(msg, *args, **kw)\n\nPrint msg merged with args as a verbose message.\n\nSee Python’s logging module for details of message formatting.\n\nwarning(msg, *args, **kw)\n\nPrint msg merged with args as a warning, unless module variable warnings_as_exceptions is True, then raise an Exception containing the arguments.\n\nSee Python’s logging module for details of message formatting.\n\nclass imagen.deprecated.Constant(**params)\n\nConstant pattern generator, i.e., a solid, uniform field of the same value.\n\nparam Number x (allow_None=False, bounds=None, constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.2, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nX-coordinate location of pattern center.\nparam Number scale (allow_None=False, bounds=None, constant=False, default=1.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.1, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nMultiplicative strength of input pattern, defaulting to 1.0\nparam String group (allow_None=False, basestring=<type ‘basestring’>, constant=False, default=Pattern, instantiate=False, pickle_default_value=True, precedence=-1, readonly=False)\nThe group name assigned to the returned HoloViews object.\nparam Number orientation (allow_None=False, bounds=None, constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=-1, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nPolar angle of pattern, i.e., the orientation in the Cartesian coordinate system, with zero at 3 o’clock and increasing counterclockwise.\nparam ClassSelector z (allow_None=True, constant=False, default=None, instantiate=True, is_instance=True, pickle_default_value=True, precedence=-1, readonly=False)\nThe Dimension object associated with the z-values generated by the PatternGenerator . If None, uses the default set by HoloViews.Image.\nOptional object (expected to be an array) with which to multiply the pattern array after it has been created, before any output_fns are applied. This can be used to shape the pattern.\nBoundingBox of the area in which the pattern is generated.\nparam Number xdensity (allow_None=False, bounds=(0, None), constant=False, default=256, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=-1, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nDensity (number of samples per 1.0 length) in the x direction.\nparam Number y (allow_None=False, bounds=None, constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.21, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nY-coordinate location of pattern center.\nparam HookList output_fns (allow_None=False, bounds=(0, None), constant=False, default=[], instantiate=True, pickle_default_value=True, precedence=0.08, readonly=False)\nOptional function(s) to apply to the pattern array after it has been created. Can be used for normalization, thresholding, etc.\nparam Number offset (allow_None=False, bounds=None, constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.11, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nAdditive offset to input pattern, defaulting to 0.0\nOptional PatternGenerator used to construct a mask to be applied to the pattern.\nparam Composite position (allow_None=True, attribs=[‘x’, ‘y’], constant=False, default=None, instantiate=False, objtype=<class ‘imagen.patterngenerator.PatternGenerator’>, pickle_default_value=True, precedence=-1, readonly=False)\nCoordinates of location of pattern center. Provides a convenient way to set the x and y parameters together as a tuple (x,y), but shares the same actual storage as x and y (and thus only position OR x and y need to be specified).\nparam Number ydensity (allow_None=False, bounds=(0, None), constant=False, default=256, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=-1, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nDensity (number of samples per 1.0 length) in the y direction. Typically the same as the xdensity.\nparam Number size (allow_None=False, bounds=(0.0, None), constant=False, default=1.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.3, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nDetermines the overall size of the pattern.\nanim(duration, offset=0, timestep=1, label=None, unit=None, time_fn=Time(label='Time', name='Time00001', time_type=<type 'int'>, timestep=1.0, unit=None, until=Infinity()))\n\nduration: The temporal duration to animate in the units defined on the global time function.\n\noffset: The temporal offset from which the animation is generated given the supplied pattern\n\ntimestep: The time interval between successive frames. The duration must be an exact multiple of the timestep.\n\nlabel: A label string to override the label of the global time function (if not None).\n\nunit: The unit string to override the unit value of the global time function (if not None).\n\ntime_fn: The global time function object that is shared across the time-varying objects that are being sampled.\n\nNote that the offset, timestep and time_fn only affect patterns parameterized by time-dependent number generators. Otherwise, the frames are generated by successive call to the pattern which may or may not be varying (e.g to view the patterns contained within a Selector).\n\nchannels(use_cached=False, **params_to_override)\n\nChannels() adds a shared interface for single channel and multichannel structures. It will always return an ordered dict: its first element is the single channel of the pattern (if single-channel) or the channel average (if multichannel); the successive elements are the individual channels’ arrays (key: 0,1,..N-1).\n\ndebug(msg, *args, **kw)\n\nPrint msg merged with args as a debugging statement.\n\nSee Python’s logging module for details of message formatting.\n\ndefaults()\n\nReturn {parameter_name:parameter.default} for all non-constant Parameters.\n\nNote that a Parameter for which instantiate==True has its default instantiated.\n\nforce_new_dynamic_value = <functools.partial object at 0x2adfbc4c51b0>\nfunction(p)\n\nFunction to draw a pattern that will then be scaled and rotated.\n\nInstead of implementing __call__ directly, PatternGenerator subclasses will typically implement this helper function used by __call__, because that way they can let __call__ handle the scaling and rotation for them. Alternatively, __call__ itself can be reimplemented entirely by a subclass (e.g. if it does not need to do any scaling or rotation), in which case this function will be ignored.\n\nget_param_values(onlychanged=False)\n\nReturn a list of name,value pairs for all Parameters of this object.\n\nIf onlychanged is True, will only return values that are not equal to the default value.\n\nget_value_generator = <functools.partial object at 0x2adfbc4c5158>\ninspect_value = <functools.partial object at 0x2adfbc4c50a8>\nmessage(msg, *args, **kw)\n\nPrint msg merged with args as a message.\n\nSee Python’s logging module for details of message formatting.\n\nnum_channels()\n\nQuery the number of channels implemented by the PatternGenerator. In case of single-channel generators this will return 1; in case of multichannel, it will return the number of channels (eg, in the case of RGB images it would return ‘3’, Red-Green-Blue, even though the OrderedDict returned by channels() will have 4 elements – the 3 channels + their average).\n\nclassmethod params(parameter_name=None)\n\nReturn the Parameters of this class as the dictionary {name: parameter_object}\n\nIncludes Parameters from this class and its superclasses.\n\npprint(imports=None, prefix=' ', unknown_value='<?>', qualify=False, separator='')\n\n(Experimental) Pretty printed representation that may be evaluated with eval. See pprint() function for more details.\n\nclassmethod print_param_defaults()\n\nPrint the default values of all cls’s Parameters.\n\nprint_param_values()\n\nPrint the values of all this object’s Parameters.\n\nscript_repr(imports=, []prefix=' ')\n\nVariant of __repr__ designed for generating a runnable script.\n\nclassmethod set_default(param_name, value)\n\nSet the default value of param_name.\n\nEquivalent to setting param_name on the class.\n\nset_dynamic_time_fn = <functools.partial object at 0x2adfbc4c54c8>\nset_matrix_dimensions(bounds, xdensity, ydensity)\n\nChange the dimensions of the matrix into which the pattern will be drawn. Users of this class should call this method rather than changing the bounds, xdensity, and ydensity parameters directly. Subclasses can override this method to update any internal data structures that may depend on the matrix dimensions.\n\nset_param = <functools.partial object at 0x2adfbc4c5208>\nstate_pop()\n\nRestore the state of the output functions saved by state_push.\n\nstate_push()\n\nSave the state of the output functions, to be restored with state_pop.\n\nverbose(msg, *args, **kw)\n\nPrint msg merged with args as a verbose message.\n\nSee Python’s logging module for details of message formatting.\n\nwarning(msg, *args, **kw)\n\nPrint msg merged with args as a warning, unless module variable warnings_as_exceptions is True, then raise an Exception containing the arguments.\n\nSee Python’s logging module for details of message formatting.\n\nclass imagen.deprecated.TwoRectangles(**params)[source]\n\nTwo 2D rectangle pattern generator.\n\nparam Number y2 (allow_None=False, bounds=(-1.0, 1.0), constant=False, default=0.15, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=None, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nY center of rectangle 2.\nparam Number x (allow_None=False, bounds=None, constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.2, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nX-coordinate location of pattern center.\nparam Number scale (allow_None=False, bounds=None, constant=False, default=1.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.1, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nMultiplicative strength of input pattern, defaulting to 1.0\nparam String group (allow_None=False, basestring=<type ‘basestring’>, constant=False, default=Pattern, instantiate=False, pickle_default_value=True, precedence=-1, readonly=False)\nThe group name assigned to the returned HoloViews object.\nparam Number y1 (allow_None=False, bounds=(-1.0, 1.0), constant=False, default=-0.15, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=None, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nY center of rectangle 1.\nparam Number orientation (allow_None=False, bounds=None, constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.4, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nPolar angle of pattern, i.e., the orientation in the Cartesian coordinate system, with zero at 3 o’clock and increasing counterclockwise.\nparam Number aspect_ratio (allow_None=False, bounds=(0.0, None), constant=False, default=1.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.31, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nRatio of width to height; size*aspect_ratio gives the width of the rectangle.\nparam Number x1 (allow_None=False, bounds=(-1.0, 1.0), constant=False, default=-0.15, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=None, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nX center of rectangle 1.\nparam ClassSelector z (allow_None=True, constant=False, default=None, instantiate=True, is_instance=True, pickle_default_value=True, precedence=-1, readonly=False)\nThe Dimension object associated with the z-values generated by the PatternGenerator . If None, uses the default set by HoloViews.Image.\nOptional object (expected to be an array) with which to multiply the pattern array after it has been created, before any output_fns are applied. This can be used to shape the pattern.\nBoundingBox of the area in which the pattern is generated.\nparam Number x2 (allow_None=False, bounds=(-1.0, 1.0), constant=False, default=0.15, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=None, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nX center of rectangle 2.\nparam Number xdensity (allow_None=False, bounds=(0, None), constant=False, default=256, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=-1, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nDensity (number of samples per 1.0 length) in the x direction.\nparam Number y (allow_None=False, bounds=None, constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.21, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nY-coordinate location of pattern center.\nparam HookList output_fns (allow_None=False, bounds=(0, None), constant=False, default=[], instantiate=True, pickle_default_value=True, precedence=0.08, readonly=False)\nOptional function(s) to apply to the pattern array after it has been created. Can be used for normalization, thresholding, etc.\nparam Number offset (allow_None=False, bounds=None, constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.11, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nAdditive offset to input pattern, defaulting to 0.0\nOptional PatternGenerator used to construct a mask to be applied to the pattern.\nparam Composite position (allow_None=True, attribs=[‘x’, ‘y’], constant=False, default=None, instantiate=False, objtype=<class ‘imagen.patterngenerator.PatternGenerator’>, pickle_default_value=True, precedence=-1, readonly=False)\nCoordinates of location of pattern center. Provides a convenient way to set the x and y parameters together as a tuple (x,y), but shares the same actual storage as x and y (and thus only position OR x and y need to be specified).\nparam Number ydensity (allow_None=False, bounds=(0, None), constant=False, default=256, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=-1, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nDensity (number of samples per 1.0 length) in the y direction. Typically the same as the xdensity.\nparam Number size (allow_None=False, bounds=(0.0, None), constant=False, default=0.5, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.3, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nDetermines the overall size of the pattern.\nanim(duration, offset=0, timestep=1, label=None, unit=None, time_fn=Time(label='Time', name='Time00001', time_type=<type 'int'>, timestep=1.0, unit=None, until=Infinity()))\n\nduration: The temporal duration to animate in the units defined on the global time function.\n\noffset: The temporal offset from which the animation is generated given the supplied pattern\n\ntimestep: The time interval between successive frames. The duration must be an exact multiple of the timestep.\n\nlabel: A label string to override the label of the global time function (if not None).\n\nunit: The unit string to override the unit value of the global time function (if not None).\n\ntime_fn: The global time function object that is shared across the time-varying objects that are being sampled.\n\nNote that the offset, timestep and time_fn only affect patterns parameterized by time-dependent number generators. Otherwise, the frames are generated by successive call to the pattern which may or may not be varying (e.g to view the patterns contained within a Selector).\n\nchannels(use_cached=False, **params_to_override)\n\nChannels() adds a shared interface for single channel and multichannel structures. It will always return an ordered dict: its first element is the single channel of the pattern (if single-channel) or the channel average (if multichannel); the successive elements are the individual channels’ arrays (key: 0,1,..N-1).\n\ndebug(msg, *args, **kw)\n\nPrint msg merged with args as a debugging statement.\n\nSee Python’s logging module for details of message formatting.\n\ndefaults()\n\nReturn {parameter_name:parameter.default} for all non-constant Parameters.\n\nNote that a Parameter for which instantiate==True has its default instantiated.\n\nforce_new_dynamic_value = <functools.partial object at 0x2adfbc4c5470>\nget_param_values(onlychanged=False)\n\nReturn a list of name,value pairs for all Parameters of this object.\n\nIf onlychanged is True, will only return values that are not equal to the default value.\n\nget_value_generator = <functools.partial object at 0x2adfbc4c5260>\ninspect_value = <functools.partial object at 0x2adfbc4c5050>\nmessage(msg, *args, **kw)\n\nPrint msg merged with args as a message.\n\nSee Python’s logging module for details of message formatting.\n\nnum_channels()\n\nQuery the number of channels implemented by the PatternGenerator. In case of single-channel generators this will return 1; in case of multichannel, it will return the number of channels (eg, in the case of RGB images it would return ‘3’, Red-Green-Blue, even though the OrderedDict returned by channels() will have 4 elements – the 3 channels + their average).\n\nclassmethod params(parameter_name=None)\n\nReturn the Parameters of this class as the dictionary {name: parameter_object}\n\nIncludes Parameters from this class and its superclasses.\n\npprint(imports=None, prefix=' ', unknown_value='<?>', qualify=False, separator='')\n\n(Experimental) Pretty printed representation that may be evaluated with eval. See pprint() function for more details.\n\nclassmethod print_param_defaults()\n\nPrint the default values of all cls’s Parameters.\n\nprint_param_values()\n\nPrint the values of all this object’s Parameters.\n\nscript_repr(imports=, []prefix=' ')\n\nVariant of __repr__ designed for generating a runnable script.\n\nclassmethod set_default(param_name, value)\n\nSet the default value of param_name.\n\nEquivalent to setting param_name on the class.\n\nset_dynamic_time_fn = <functools.partial object at 0x2adfbc4c5418>\nset_matrix_dimensions(bounds, xdensity, ydensity)\n\nChange the dimensions of the matrix into which the pattern will be drawn. Users of this class should call this method rather than changing the bounds, xdensity, and ydensity parameters directly. Subclasses can override this method to update any internal data structures that may depend on the matrix dimensions.\n\nset_param = <functools.partial object at 0x2adfbc4c53c0>\nstate_pop()\n\nRestore the state of the output functions saved by state_push.\n\nstate_push()\n\nSave the state of the output functions, to be restored with state_pop.\n\nverbose(msg, *args, **kw)\n\nPrint msg merged with args as a verbose message.\n\nSee Python’s logging module for details of message formatting.\n\nwarning(msg, *args, **kw)\n\nPrint msg merged with args as a warning, unless module variable warnings_as_exceptions is True, then raise an Exception containing the arguments.\n\nSee Python’s logging module for details of message formatting.\n\nclass imagen.deprecated.Composite(**params)\n\nPatternGenerator that accepts a list of other PatternGenerators. To create a new pattern, asks each of the PatternGenerators in the list to create a pattern, then it combines the patterns to create a single pattern that it returns.\n\nparam Number x (allow_None=False, bounds=None, constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.2, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nX-coordinate location of pattern center.\nparam Number scale (allow_None=False, bounds=None, constant=False, default=1.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.1, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nMultiplicative strength of input pattern, defaulting to 1.0\nparam String group (allow_None=False, basestring=<type ‘basestring’>, constant=False, default=Pattern, instantiate=False, pickle_default_value=True, precedence=-1, readonly=False)\nThe group name assigned to the returned HoloViews object.\nparam Number orientation (allow_None=False, bounds=None, constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.4, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nPolar angle of pattern, i.e., the orientation in the Cartesian coordinate system, with zero at 3 o’clock and increasing counterclockwise.\nparam ClassSelector z (allow_None=True, constant=False, default=None, instantiate=True, is_instance=True, pickle_default_value=True, precedence=-1, readonly=False)\nThe Dimension object associated with the z-values generated by the PatternGenerator . If None, uses the default set by HoloViews.Image.\nOptional object (expected to be an array) with which to multiply the pattern array after it has been created, before any output_fns are applied. This can be used to shape the pattern.\nBoundingBox of the area in which the pattern is generated.\nparam Parameter operator (allow_None=False, constant=False, default=<ufunc ‘maximum’>, instantiate=False, pickle_default_value=True, precedence=0.98, readonly=False)\nBinary Numpy function used to combine the individual patterns. Any binary Numpy array “ufunc” returning the same type of array as the operands and supporting the reduce operator is allowed here. Supported ufuncs include:: add subtract multiply divide maximum minimum remainder power The most useful ones are probably add and maximum, but there are uses for at least some of the others as well (e.g. to remove pieces of other patterns). You can also write your own operators, by making a class that has a static method named “reduce” that returns an array of the same size and type as the arrays in the list. For example:: class return_first(object): @staticmethod def reduce(x): return x\nparam Number xdensity (allow_None=False, bounds=(0, None), constant=False, default=256, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=-1, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nDensity (number of samples per 1.0 length) in the x direction.\nparam Number y (allow_None=False, bounds=None, constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.21, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nY-coordinate location of pattern center.\nparam HookList output_fns (allow_None=False, bounds=(0, None), constant=False, default=[], instantiate=True, pickle_default_value=True, precedence=0.08, readonly=False)\nOptional function(s) to apply to the pattern array after it has been created. Can be used for normalization, thresholding, etc.\nparam List generators (allow_None=False, bounds=(1, None), constant=False, default=[Constant(bounds=BoundingBox(radius=0.5), group=’Pattern’, mask=None, mask_shape=None, name=’Constant01030’, offset=0.0, orientation=0.0, output_fns=[], position=[0.0, 0.0], scale=0.0, size=1.0, x=0.0, xdensity=256, y=0.0, ydensity=256, z=None)], instantiate=True, pickle_default_value=True, precedence=0.97, readonly=False)\nList of patterns to combine or select from. The default pattern is a blank pattern, and thus should be overridden for any useful work.\nparam Number offset (allow_None=False, bounds=None, constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.11, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nAdditive offset to input pattern, defaulting to 0.0\nOptional PatternGenerator used to construct a mask to be applied to the pattern.\nparam Composite position (allow_None=True, attribs=[‘x’, ‘y’], constant=False, default=None, instantiate=False, objtype=<class ‘imagen.patterngenerator.PatternGenerator’>, pickle_default_value=True, precedence=-1, readonly=False)\nCoordinates of location of pattern center. Provides a convenient way to set the x and y parameters together as a tuple (x,y), but shares the same actual storage as x and y (and thus only position OR x and y need to be specified).\nparam Number ydensity (allow_None=False, bounds=(0, None), constant=False, default=256, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=-1, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nDensity (number of samples per 1.0 length) in the y direction. Typically the same as the xdensity.\nparam Number size (allow_None=False, bounds=(0.0, None), constant=False, default=1.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.3, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nScaling factor applied to all sub-patterns.\nanim(duration, offset=0, timestep=1, label=None, unit=None, time_fn=Time(label='Time', name='Time00001', time_type=<type 'int'>, timestep=1.0, unit=None, until=Infinity()))\n\nduration: The temporal duration to animate in the units defined on the global time function.\n\noffset: The temporal offset from which the animation is generated given the supplied pattern\n\ntimestep: The time interval between successive frames. The duration must be an exact multiple of the timestep.\n\nlabel: A label string to override the label of the global time function (if not None).\n\nunit: The unit string to override the unit value of the global time function (if not None).\n\ntime_fn: The global time function object that is shared across the time-varying objects that are being sampled.\n\nNote that the offset, timestep and time_fn only affect patterns parameterized by time-dependent number generators. Otherwise, the frames are generated by successive call to the pattern which may or may not be varying (e.g to view the patterns contained within a Selector).\n\nchannels(use_cached=False, **params_to_override)\n\nChannels() adds a shared interface for single channel and multichannel structures. It will always return an ordered dict: its first element is the single channel of the pattern (if single-channel) or the channel average (if multichannel); the successive elements are the individual channels’ arrays (key: 0,1,..N-1).\n\ndebug(msg, *args, **kw)\n\nPrint msg merged with args as a debugging statement.\n\nSee Python’s logging module for details of message formatting.\n\ndefaults()\n\nReturn {parameter_name:parameter.default} for all non-constant Parameters.\n\nNote that a Parameter for which instantiate==True has its default instantiated.\n\nforce_new_dynamic_value = <functools.partial object at 0x2adfbc4c54c8>\nfunction(p)\n\nConstructs combined pattern out of the individual ones.\n\nget_param_values(onlychanged=False)\n\nReturn a list of name,value pairs for all Parameters of this object.\n\nIf onlychanged is True, will only return values that are not equal to the default value.\n\nget_value_generator = <functools.partial object at 0x2adfbc4c5100>\ninspect_value = <functools.partial object at 0x2adfbc4c50a8>\nmessage(msg, *args, **kw)\n\nPrint msg merged with args as a message.\n\nSee Python’s logging module for details of message formatting.\n\nnum_channels()\n\nQuery the number of channels implemented by the PatternGenerator. In case of single-channel generators this will return 1; in case of multichannel, it will return the number of channels (eg, in the case of RGB images it would return ‘3’, Red-Green-Blue, even though the OrderedDict returned by channels() will have 4 elements – the 3 channels + their average).\n\noperator = <ufunc 'maximum'>\nclassmethod params(parameter_name=None)\n\nReturn the Parameters of this class as the dictionary {name: parameter_object}\n\nIncludes Parameters from this class and its superclasses.\n\npprint(imports=None, prefix=' ', unknown_value='<?>', qualify=False, separator='')\n\n(Experimental) Pretty printed representation that may be evaluated with eval. See pprint() function for more details.\n\nclassmethod print_param_defaults()\n\nPrint the default values of all cls’s Parameters.\n\nprint_param_values()\n\nPrint the values of all this object’s Parameters.\n\nscript_repr(imports=, []prefix=' ')\n\nVariant of __repr__ designed for generating a runnable script.\n\nclassmethod set_default(param_name, value)\n\nSet the default value of param_name.\n\nEquivalent to setting param_name on the class.\n\nset_dynamic_time_fn = <functools.partial object at 0x2adfbc4c53c0>\nset_matrix_dimensions(bounds, xdensity, ydensity)\n\nChange the dimensions of the matrix into which the pattern will be drawn. Users of this class should call this method rather than changing the bounds, xdensity, and ydensity parameters directly. Subclasses can override this method to update any internal data structures that may depend on the matrix dimensions.\n\nset_param = <functools.partial object at 0x2adfbc4c5208>\nstate_pop()\n\nPop the state of all generators\n\nstate_push()\n\nPush the state of all generators\n\nverbose(msg, *args, **kw)\n\nPrint msg merged with args as a verbose message.\n\nSee Python’s logging module for details of message formatting.\n\nwarning(msg, *args, **kw)\n\nPrint msg merged with args as a warning, unless module variable warnings_as_exceptions is True, then raise an Exception containing the arguments.\n\nSee Python’s logging module for details of message formatting.\n\nclass imagen.deprecated.OldSweeper(**params)[source]\n\nPatternGenerator that sweeps a supplied PatternGenerator in a direction perpendicular to its orientation.\n\nparam Number x (allow_None=False, bounds=None, constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.2, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nX-coordinate location of pattern center.\nparam Number scale (allow_None=False, bounds=None, constant=False, default=1.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.1, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nMultiplicative strength of input pattern, defaulting to 1.0\nparam String group (allow_None=False, basestring=<type ‘basestring’>, constant=False, default=Pattern, instantiate=False, pickle_default_value=True, precedence=-1, readonly=False)\nThe group name assigned to the returned HoloViews object.\nparam Parameter generator (allow_None=False, constant=False, default=<Gaussian Gaussian01049>, instantiate=False, pickle_default_value=True, precedence=0.97, readonly=False)\nPattern to sweep.\nparam Number orientation (allow_None=False, bounds=None, constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.4, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nPolar angle of pattern, i.e., the orientation in the Cartesian coordinate system, with zero at 3 o’clock and increasing counterclockwise.\nparam ClassSelector z (allow_None=True, constant=False, default=None, instantiate=True, is_instance=True, pickle_default_value=True, precedence=-1, readonly=False)\nThe Dimension object associated with the z-values generated by the PatternGenerator . If None, uses the default set by HoloViews.Image.\nOptional object (expected to be an array) with which to multiply the pattern array after it has been created, before any output_fns are applied. This can be used to shape the pattern.\nBoundingBox of the area in which the pattern is generated.\nparam Number xdensity (allow_None=False, bounds=(0, None), constant=False, default=256, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=-1, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nDensity (number of samples per 1.0 length) in the x direction.\nparam Number y (allow_None=False, bounds=None, constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.21, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nY-coordinate location of pattern center.\nparam Number step (allow_None=False, bounds=None, constant=False, default=1, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=None, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nNumber of steps at the given speed to move in the sweep direction. The distance moved is speed*step.\nparam HookList output_fns (allow_None=False, bounds=(0, None), constant=False, default=[], instantiate=True, pickle_default_value=True, precedence=0.08, readonly=False)\nOptional function(s) to apply to the pattern array after it has been created. Can be used for normalization, thresholding, etc.\nparam Number offset (allow_None=False, bounds=None, constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.11, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nAdditive offset to input pattern, defaulting to 0.0\nOptional PatternGenerator used to construct a mask to be applied to the pattern.\nparam Composite position (allow_None=True, attribs=[‘x’, ‘y’], constant=False, default=None, instantiate=False, objtype=<class ‘imagen.patterngenerator.PatternGenerator’>, pickle_default_value=True, precedence=-1, readonly=False)\nCoordinates of location of pattern center. Provides a convenient way to set the x and y parameters together as a tuple (x,y), but shares the same actual storage as x and y (and thus only position OR x and y need to be specified).\nparam Number ydensity (allow_None=False, bounds=(0, None), constant=False, default=256, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=-1, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nDensity (number of samples per 1.0 length) in the y direction. Typically the same as the xdensity.\nparam Number speed (allow_None=False, bounds=(0.0, None), constant=False, default=0.25, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=None, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nSweep speed: number of sheet coordinate units per unit time.\nparam Number size (allow_None=False, bounds=(0.0, None), constant=False, default=1.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.3, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nDetermines the overall size of the pattern.\nanim(duration, offset=0, timestep=1, label=None, unit=None, time_fn=Time(label='Time', name='Time00001', time_type=<type 'int'>, timestep=1.0, unit=None, until=Infinity()))\n\nduration: The temporal duration to animate in the units defined on the global time function.\n\noffset: The temporal offset from which the animation is generated given the supplied pattern\n\ntimestep: The time interval between successive frames. The duration must be an exact multiple of the timestep.\n\nlabel: A label string to override the label of the global time function (if not None).\n\nunit: The unit string to override the unit value of the global time function (if not None).\n\ntime_fn: The global time function object that is shared across the time-varying objects that are being sampled.\n\nNote that the offset, timestep and time_fn only affect patterns parameterized by time-dependent number generators. Otherwise, the frames are generated by successive call to the pattern which may or may not be varying (e.g to view the patterns contained within a Selector).\n\nchannels(use_cached=False, **params_to_override)\n\nChannels() adds a shared interface for single channel and multichannel structures. It will always return an ordered dict: its first element is the single channel of the pattern (if single-channel) or the channel average (if multichannel); the successive elements are the individual channels’ arrays (key: 0,1,..N-1).\n\ndebug(msg, *args, **kw)\n\nPrint msg merged with args as a debugging statement.\n\nSee Python’s logging module for details of message formatting.\n\ndefaults()\n\nReturn {parameter_name:parameter.default} for all non-constant Parameters.\n\nNote that a Parameter for which instantiate==True has its default instantiated.\n\nforce_new_dynamic_value = <functools.partial object at 0x2adfbc4c52b8>\nfunction(p)[source]\n\nSelects and returns one of the patterns in the list.\n\nget_param_values(onlychanged=False)\n\nReturn a list of name,value pairs for all Parameters of this object.\n\nIf onlychanged is True, will only return values that are not equal to the default value.\n\nget_value_generator = <functools.partial object at 0x2adfbc4c5418>\ninspect_value = <functools.partial object at 0x2adfbc4c5158>\nmessage(msg, *args, **kw)\n\nPrint msg merged with args as a message.\n\nSee Python’s logging module for details of message formatting.\n\nnum_channels()\n\nQuery the number of channels implemented by the PatternGenerator. In case of single-channel generators this will return 1; in case of multichannel, it will return the number of channels (eg, in the case of RGB images it would return ‘3’, Red-Green-Blue, even though the OrderedDict returned by channels() will have 4 elements – the 3 channels + their average).\n\nclassmethod params(parameter_name=None)\n\nReturn the Parameters of this class as the dictionary {name: parameter_object}\n\nIncludes Parameters from this class and its superclasses.\n\npprint(imports=None, prefix=' ', unknown_value='<?>', qualify=False, separator='')\n\n(Experimental) Pretty printed representation that may be evaluated with eval. See pprint() function for more details.\n\nclassmethod print_param_defaults()\n\nPrint the default values of all cls’s Parameters.\n\nprint_param_values()\n\nPrint the values of all this object’s Parameters.\n\nscript_repr(imports=, []prefix=' ')\n\nVariant of __repr__ designed for generating a runnable script.\n\nclassmethod set_default(param_name, value)\n\nSet the default value of param_name.\n\nEquivalent to setting param_name on the class.\n\nset_dynamic_time_fn = <functools.partial object at 0x2adfbc4c5260>\nset_matrix_dimensions(bounds, xdensity, ydensity)\n\nChange the dimensions of the matrix into which the pattern will be drawn. Users of this class should call this method rather than changing the bounds, xdensity, and ydensity parameters directly. Subclasses can override this method to update any internal data structures that may depend on the matrix dimensions.\n\nset_param = <functools.partial object at 0x2adfbc4c5310>\nstate_pop()\n\nRestore the state of the output functions saved by state_push.\n\nstate_push()\n\nSave the state of the output functions, to be restored with state_pop.\n\nverbose(msg, *args, **kw)\n\nPrint msg merged with args as a verbose message.\n\nSee Python’s logging module for details of message formatting.\n\nwarning(msg, *args, **kw)\n\nPrint msg merged with args as a warning, unless module variable warnings_as_exceptions is True, then raise an Exception containing the arguments.\n\nSee Python’s logging module for details of message formatting.\n\nclass imagen.deprecated.GaussiansCorner(**params)[source]\n\nTwo Gaussian pattern generators with a variable intersection point, appearing as a corner or cross.\n\nparam Number x (allow_None=False, bounds=(-1.0, 1.0), constant=False, default=-0.15, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.2, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nX center of the corner\nparam Number scale (allow_None=False, bounds=None, constant=False, default=1.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.1, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nMultiplicative strength of input pattern, defaulting to 1.0\nparam String group (allow_None=False, basestring=<type ‘basestring’>, constant=False, default=Pattern, instantiate=False, pickle_default_value=True, precedence=-1, readonly=False)\nThe group name assigned to the returned HoloViews object.\nparam Number angle (allow_None=False, bounds=(0, 3.141592653589793), constant=False, default=1.57079632679, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=None, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nThe angle of the corner\nparam Number orientation (allow_None=False, bounds=None, constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.4, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nPolar angle of pattern, i.e., the orientation in the Cartesian coordinate system, with zero at 3 o’clock and increasing counterclockwise.\nparam Number aspect_ratio (allow_None=False, bounds=(0, None), constant=False, default=3.22580645161, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=None, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nRatio of the width to the height for both Gaussians\nparam ClassSelector z (allow_None=True, constant=False, default=None, instantiate=True, is_instance=True, pickle_default_value=True, precedence=-1, readonly=False)\nThe Dimension object associated with the z-values generated by the PatternGenerator . If None, uses the default set by HoloViews.Image.\nOptional object (expected to be an array) with which to multiply the pattern array after it has been created, before any output_fns are applied. This can be used to shape the pattern.\nBoundingBox of the area in which the pattern is generated.\nparam Number cross (allow_None=False, bounds=(0, 1), constant=False, default=0.4, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=None, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nWhere the two Gaussians cross, as a fraction of their half length\nparam Number xdensity (allow_None=False, bounds=(0, None), constant=False, default=256, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=-1, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nDensity (number of samples per 1.0 length) in the x direction.\nparam Number y (allow_None=False, bounds=(-1.0, 1.0), constant=False, default=-0.15, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.21, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nY center of the corner\nparam HookList output_fns (allow_None=False, bounds=(0, None), constant=False, default=[], instantiate=True, pickle_default_value=True, precedence=0.08, readonly=False)\nOptional function(s) to apply to the pattern array after it has been created. Can be used for normalization, thresholding, etc.\nparam Number offset (allow_None=False, bounds=None, constant=False, default=0.0, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.11, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nAdditive offset to input pattern, defaulting to 0.0\nOptional PatternGenerator used to construct a mask to be applied to the pattern.\nparam Composite position (allow_None=True, attribs=[‘x’, ‘y’], constant=False, default=None, instantiate=False, objtype=<class ‘imagen.patterngenerator.PatternGenerator’>, pickle_default_value=True, precedence=-1, readonly=False)\nCoordinates of location of pattern center. Provides a convenient way to set the x and y parameters together as a tuple (x,y), but shares the same actual storage as x and y (and thus only position OR x and y need to be specified).\nparam Number ydensity (allow_None=False, bounds=(0, None), constant=False, default=256, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=-1, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nDensity (number of samples per 1.0 length) in the y direction. Typically the same as the xdensity.\nparam Number size (allow_None=False, bounds=(0, None), constant=False, default=0.5, inclusive_bounds=(True, True), instantiate=False, pickle_default_value=True, precedence=0.3, readonly=False, time_dependent=False, time_fn=<Time Time00001>)\nThe size of the corner\nanim(duration, offset=0, timestep=1, label=None, unit=None, time_fn=Time(label='Time', name='Time00001', time_type=<type 'int'>, timestep=1.0, unit=None, until=Infinity()))\n\nduration: The temporal duration to animate in the units defined on the global time function.\n\noffset: The temporal offset from which the animation is generated given the supplied pattern\n\ntimestep: The time interval between successive frames. The duration must be an exact multiple of the timestep.\n\nlabel: A label string to override the label of the global time function (if not None).\n\nunit: The unit string to override the unit value of the global time function (if not None).\n\ntime_fn: The global time function object that is shared across the time-varying objects that are being sampled.\n\nNote that the offset, timestep and time_fn only affect patterns parameterized by time-dependent number generators. Otherwise, the frames are generated by successive call to the pattern which may or may not be varying (e.g to view the patterns contained within a Selector).\n\nchannels(use_cached=False, **params_to_override)\n\nChannels() adds a shared interface for single channel and multichannel structures. It will always return an ordered dict: its first element is the single channel of the pattern (if single-channel) or the channel average (if multichannel); the successive elements are the individual channels’ arrays (key: 0,1,..N-1).\n\ndebug(msg, *args, **kw)\n\nPrint msg merged with args as a debugging statement.\n\nSee Python’s logging module for details of message formatting.\n\ndefaults()\n\nReturn {parameter_name:parameter.default} for all non-constant Parameters.\n\nNote that a Parameter for which instantiate==True has its default instantiated.\n\nforce_new_dynamic_value = <functools.partial object at 0x2adfbc4c50a8>\nfunction(p)\n\nFunction to draw a pattern that will then be scaled and rotated.\n\nInstead of implementing __call__ directly, PatternGenerator subclasses will typically implement this helper function used by __call__, because that way they can let __call__ handle the scaling and rotation for them. Alternatively, __call__ itself can be reimplemented entirely by a subclass (e.g. if it does not need to do any scaling or rotation), in which case this function will be ignored.\n\nget_param_values(onlychanged=False)\n\nReturn a list of name,value pairs for all Parameters of this object.\n\nIf onlychanged is True, will only return values that are not equal to the default value.\n\nget_value_generator = <functools.partial object at 0x2adfbc4c5100>\ninspect_value = <functools.partial object at 0x2adfbc4c5578>\nmessage(msg, *args, **kw)\n\nPrint msg merged with args as a message.\n\nSee Python’s logging module for details of message formatting.\n\nnum_channels()\n\nQuery the number of channels implemented by the PatternGenerator. In case of single-channel generators this will return 1; in case of multichannel, it will return the number of channels (eg, in the case of RGB images it would return ‘3’, Red-Green-Blue, even though the OrderedDict returned by channels() will have 4 elements – the 3 channels + their average).\n\nclassmethod params(parameter_name=None)\n\nReturn the Parameters of this class as the dictionary {name: parameter_object}\n\nIncludes Parameters from this class and its superclasses.\n\npprint(imports=None, prefix=' ', unknown_value='<?>', qualify=False, separator='')\n\n(Experimental) Pretty printed representation that may be evaluated with eval. See pprint() function for more details.\n\nclassmethod print_param_defaults()\n\nPrint the default values of all cls’s Parameters.\n\nprint_param_values()\n\nPrint the values of all this object’s Parameters.\n\nscript_repr(imports=, []prefix=' ')\n\nVariant of __repr__ designed for generating a runnable script.\n\nclassmethod set_default(param_name, value)\n\nSet the default value of param_name.\n\nEquivalent to setting param_name on the class.</" ]
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https://ww2.mathworks.cn/help/finance/portfolio-optimization-theory-mv.html
[ "## 投资组合优化理论\n\n• 最小化风险代理。\n\n• 匹配或超过收益代理。\n\n• 满足基本的可行性要求。\n\n### 投资组合问题设定\n\n• 投资组合收益代理 (μ)\n\n• 投资组合风险代理 (σ)\n\n• 可行投资组合的集合 (X)，称为投资组合集\n\nFinancial Toolbox™ 用三个对象来解决特定类型的投资组合优化问题：\n\n• `Portfolio` 对象支持均值-方差投资组合优化（请参阅Portfolio Optimization中的 Markowitz 、）。此对象将投资组合总收益或净收益数据（作为收益代理），将投资组合收益的方差数据（作为风险代理），以及由指定约束的任意组合构成的投资组合集。\n\n• `PortfolioCVaR` 对象实现所谓的条件风险值投资组合优化（请参阅Portfolio Optimization中的 Rockafellar 和 Uryasev 、），称为 CVaR 投资组合优化。CVaR 投资组合优化与均值-方差投资组合优化使用相同的收益代理和投资组合集，但它使用投资组合收益的条件风险值作为风险代理。\n\n• `PortfolioMAD` 对象实现所谓的均值-绝对偏差投资组合优化（请参阅Portfolio Optimization中的 Konno 和 Yamazaki ），称为 MAD 投资组合优化。MAD 投资组合优化与均值-方差投资组合优化使用相同的收益代理和投资组合集，但它使用均值-绝对偏差投资组合收益作为风险代理。\n\n### 收益代理\n\n`$m=\\frac{1}{S}\\sum _{s=1}^{S}{y}_{s},$`\n\n`$C=\\frac{1}{S-1}\\sum _{s=1}^{S}\\left({y}_{s}-m\\right){\\left({y}_{s}-m\\right)}^{T}.$`\n\n#### 投资组合总收益\n\n$x\\in X$ 的投资组合总收益为\n\n`$\\mu \\left(x\\right)={r}_{0}+{\\left(m-{r}_{0}1\\right)}^{T}x,$`\n\nr0 是无风险利率（标量）。\n\nm 是资产收益的均值（长度为 n 的向量）。\n\n• `RiskFreeRate` 为 r0\n\n• `AssetMean` 为 m\n\n#### 净投资组合收益\n\n$x\\in X$ 投资组合的净收益为\n\n`$\\mu \\left(x\\right)={r}_{0}+{\\left(m-{r}_{0}1\\right)}^{T}x-{b}^{T}\\mathrm{max}\\left\\{0,x-{x}_{0}\\right\\}-{s}^{T}\\mathrm{max}\\left\\{0,{x}_{0}-x\\right\\},$`\n\nr0 是无风险利率（标量）。\n\nm 是资产收益的均值（长度为 n 的向量）。\n\nb 是购买资产的比例成本（长度为 n 的向量）。\n\ns 是出售资产的比例成本（长度为 n 的向量）。\n\n• `RiskFreeRate` 为 r0\n\n• `AssetMean` 为 m\n\n• `InitPort` 为 x0\n\n• `BuyCost` 为 b\n\n• `SellCost` 为 s\n\n### 风险代理\n\n#### 方差\n\n`$Variance\\left(x\\right)={x}^{T}Cx$`\n\n，其中 C 是资产收益（`n` × `n` 正半定矩阵）的协方差。\n\n`Portfolio` 对象中指定投资组合收益方差的属性为对应于 C 的 `AssetCovar`\n\n#### 条件风险值\n\n`$CVa{R}_{\\alpha }\\left(x\\right)=\\frac{1}{1-\\alpha }\\underset{f\\left(x,y\\right)\\ge Va{R}_{\\alpha }\\left(x\\right)}{\\int }f\\left(x,y\\right)p\\left(y\\right)dy,$`\n\n，其中：\n\nα 是概率水平，满足 `0` < α < `1`\n\nf(x,y) 是投资组合 x 和资产收益 y 的损失函数。\n\np(y) 是资产收益 y 的概率密度函数。\n\nVaRα 是投资组合 x 在概率水平 α 处的风险值。\n\n`$Va{R}_{\\alpha }\\left(x\\right)=\\mathrm{min}\\left\\{\\gamma :\\mathrm{Pr}\\left[f\\left(x,Y\\right)\\le \\gamma \\right]\\ge \\alpha \\right\\}.$`\n\nCVaR 的另一种形式是：\n\n`$CVa{R}_{\\alpha }\\left(x\\right)=Va{R}_{\\alpha }\\left(x\\right)+\\frac{1}{1-\\alpha }\\underset{{R}^{n}}{\\int }\\mathrm{max}\\left\\{0,\\left(f\\left(x,y\\right)-Va{R}_{\\alpha }\\left(x\\right)\\right)\\right\\}p\\left(y\\right)dy$`\n\n`$CVa{R}_{\\alpha }\\left(x\\right)=Va{R}_{\\alpha }\\left(x\\right)+\\frac{1}{\\left(1-\\alpha \\right)S}\\sum _{s=1}^{S}\\mathrm{max}\\left\\{0,-{y}_{s}^{T}x-Va{R}_{\\alpha }\\left(x\\right)\\right\\}$`\n\n#### 均值绝对偏差\n\n$x\\in X$ 投资组合的均值绝对偏差 (MAD) 定义为\n\n`$MAD\\left(x\\right)=\\frac{1}{S}\\sum _{s=1}^{S}|{\\left({y}_{s}-m\\right)}^{T}x|$`\n\n，其中：\n\nys 是情景 s = 1,...S 的资产收益（包含 S 个长度为 n 的向量的集合）。\n\nf(x,y) 是投资组合 x 和资产收益 y 的损失函数。\n\nm 是资产收益的均值（长度为 n 的向量）。\n\n`$m=\\frac{1}{S}\\sum _{s=1}^{S}{y}_{s}$`" ]
[ null ]
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https://www.studyadda.com/sample-papers/mathematics-sample-paper-4_q13/1240/399419
[ "• # question_answer Find the shortest distance between lines $\\frac{x-3}{1}=\\frac{y-5}{-\\,2}=\\frac{z-7}{1}$ and       $\\frac{x+1}{7}=\\frac{y+1}{-\\,6}=\\frac{z+1}{1}.$\n\nGiven equations of lines are                         $\\frac{x-3}{1}=\\frac{y-5}{-\\,2}=\\frac{z-7}{1}$              ?(i)             and       $\\frac{x+1}{7}=\\frac{y+1}{-\\,6}=\\frac{z+1}{1}$                    ?(ii) On comparing above equations with one point form of equation of line which is             $\\frac{x-{{x}_{1}}}{a}=\\frac{y-{{y}_{1}}}{b}=\\frac{z-{{z}_{1}}}{c},$ we get ${{a}_{1}}=1,$ ${{b}_{1}}=-\\,2,$ ${{c}_{1}}=1,$ ${{x}_{1}}=3,$             ${{y}_{1}}=5,$ ${{z}_{1}}=7$ and       ${{a}_{2}}=7,$ ${{b}_{2}}=-\\,6,$             ${{c}_{2}}=1,$ ${{x}_{2}}=-\\,1,$             ${{y}_{2}}=-\\,1,$ ${{z}_{2}}=-\\,1$ We know that the shortest distance between two lines is given by", null, "$\\therefore$", null, "", null, "$=\\left| \\frac{-\\,4(-2\\,+6)+6(1-7)-8(-\\,6+14)}{\\sqrt{{{(4)}^{2}}+{{(6)}^{2}}+{{(8)}^{2}}}} \\right|$ $=\\left| \\frac{-\\,4(4)+6(-6)-8(8)}{\\sqrt{16+36+64}} \\right|$ $=\\left| \\frac{-\\,16-36-64}{\\sqrt{116}} \\right|$ $=\\left| \\frac{-\\,116}{\\sqrt{116}} \\right|=\\frac{116}{\\sqrt{116}}$ $=\\frac{{{(\\sqrt{116})}^{2}}}{\\sqrt{116}}=\\sqrt{116}$ Hence, the required shortest distance is $\\sqrt{116}$units.\nYou will be redirected in 3 sec", null, "" ]
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http://mizar.uwb.edu.pl/version/current/html/proofs/waybel35/29
[ "let L be non empty antisymmetric lower-bounded RelStr ; :: thesis: for R being auxiliary(iv) Relation of L\nfor C being strict_chain of R st C is maximal holds\nBottom L in C\n\nlet R be auxiliary(iv) Relation of L; :: thesis: for C being strict_chain of R st C is maximal holds\nBottom L in C\n\nlet C be strict_chain of R; :: thesis: ( C is maximal implies Bottom L in C )\nassume A1: for D being strict_chain of R st C c= D holds\nC = D ; :: according to WAYBEL35:def 4 :: thesis: Bottom L in C\nC \\/ {()} is strict_chain of R by Th5;\nthen A2: C \\/ {()} = C by ;\nassume not Bottom L in C ; :: thesis: contradiction\nthen not Bottom L in {()} by ;\nhence contradiction by TARSKI:def 1; :: thesis: verum" ]
[ null ]
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https://scikit-survival.readthedocs.io/en/latest/generated/sksurv.meta.Stacking.html
[ "# sksurv.meta.Stacking¶\n\nclass sksurv.meta.Stacking(meta_estimator, base_estimators, probabilities=True)\n\nMeta estimator that combines multiple base learners.\n\nBy default, base estimators’ output corresponds to the array returned by predict_proba. If predict_proba is not available or probabilities = False, the output of predict is used.\n\nParameters: meta_estimator (instance of estimator) – The estimator that is used to combine the output of different base estimators. base_estimators (list) – List of (name, estimator) tuples (implementing fit/predict) that are part of the ensemble. probabilities (bool, optional, default: True) – Whether to allow using predict_proba method of base learners, if available.\n__init__(meta_estimator, base_estimators, probabilities=True)\n\nInitialize self. See help(type(self)) for accurate signature.\n\nMethods\n\n __init__(meta_estimator, base_estimators[, …]) Initialize self. fit(X[, y]) Fit base estimators. get_params([deep])\n\nAttributes\n\n predict mock imports predict_log_proba mock imports predict_proba mock imports\nfit(X, y=None, **fit_params)\n\nFit base estimators.\n\nParameters: X (array-like, shape = (n_samples, n_features)) – Training data. y (array-like, optional) – Target data if base estimators are supervised. self" ]
[ null ]
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https://codegolf.stackexchange.com/questions/175090/repeat-this-gcd-operation/175101
[ "# Repeat this GCD operation\n\nProblem A3 from the 2008 Putnam competition says:\n\nStart with a finite sequence $$\\a_1, a_2, \\dots, a_n\\$$ of positive integers. If possible, choose two indices $$\\j < k\\$$ such that $$\\a_j\\$$ does not divide $$\\a_k\\$$, and replace $$\\a_j\\$$ and $$\\a_k\\$$ by $$\\\\gcd(a_j, a_k)\\$$ and $$\\\\text{lcm}(a_j, a_k)\\$$, respectively. Prove that if this process is repeated, it must eventually stop and the final sequence does not depend on the choices made.\n\nYour goal in this challenge is to take a finite sequence of positive integers as input, and output the result of repeating this process until no further progress is possible. (That is, until every number in the resulting sequence divides all the numbers that come after it.) You don't need to solve the Putnam problem.\n\nThis is : the shortest solution in every programming language wins.\n\n## Test cases\n\n[1, 2, 4, 8, 16, 32] => [1, 2, 4, 8, 16, 32]\n[120, 24, 6, 2, 1, 1] => [1, 1, 2, 6, 24, 120]\n[97, 41, 48, 12, 98, 68] => [1, 1, 2, 4, 12, 159016368]\n[225, 36, 30, 1125, 36, 18, 180] => [3, 9, 18, 90, 180, 900, 4500]\n[17, 17, 17, 17] => [17, 17, 17, 17]\n[1, 2, 3, 4, 5, 6, 7, 8, 9, 10] => [1, 1, 1, 1, 1, 2, 2, 6, 60, 2520]\n\n• What a neat problem! Write each integer $a_i$ as $\\displaystyle 2^{\\alpha_i} 3^{\\beta_i} 5^{\\gamma_i} \\cdots$ and note that the process simply bubble-sorts the lists $\\alpha, \\beta, \\gamma, \\dots$ in parallel :) – Lynn Nov 2 '18 at 2:57\n\n# Jelly, 9 bytes\n\nÆEz0Ṣ€ZÆẸ\n\n\nTry it online!\n\n### How it works\n\nÆEz0Ṣ€ZÆẸ Main link. Argument: A (array)\n\nÆE For each n in A, compute the exponents of n's prime factorization.\nE.g., 2000000 = 2⁷3⁰5⁶ gets mapped to [7, 0, 6].\nz0 Zip 0; append 0's to shorter exponent arrays to pad them to the same\nlength, then read the resulting matrix by columns.\nṢ€ Sort the resulting arrays (exponents that correspond to the same prime).\nZ Zip; read the resulting matrix by columns, re-grouping the exponents by\nthe integers they represent.\nÆẸ Unexponents; map the exponent arrays back to integers.\n\n\n# Pari/GP, 33 bytes\n\nCalculate the elementary divisors of the diagonal matrix.\n\na->Vecrev(matsnf(matdiagonal(a)))\n\n\nTry it online!\n\n# J, 17 bytes\n\n/:~\"1&.|:&.(_&q:)\n\n\nTry it online!\n\nProbably the first J answer on PPCG to use &. twice. After this and that, I'm starting to feel like a weird J hacker.\n\nBasically a translation from Dennis' Jelly answer.\n\n### How it works\n\n/:~\"1&.|:&.(_&q:) Single monadic verb.\n(_&q:) Convert each number to prime exponents\n(automatically zero-filled to the right)\n|:&. Transpose\n/:~\"1&. Sort each row in increasing order\n|:&. Transpose again (inverse of transpose == transpose)\n(_&q:) Apply inverse of prime exponents; convert back to integers\n\n• An earlier one is here – FrownyFrog Nov 2 '18 at 9:47\n\n# Wolfram Language (Mathematica), 44 bytes\n\nTable[GCD@@LCM@@@#~Subsets~{i},{i,Tr[1^#]}]&\n\n\nThe $$\\k\\$$-th element of the result is the GCD of the LCM's of the subsets with $$\\k\\$$ elements.\n\n$$\\b_k = \\gcd(\\{\\operatorname{lcm}(a_{i_1}, \\cdots, a_{i_k}) | 1 \\le i_1 < \\cdots < i_k \\le n\\})\\$$\n\nTry it online!\n\n• Very nice! You're two for two on weird approaches I didn't see coming :) – Misha Lavrov Nov 2 '18 at 5:14\n\n# Python 3, 103 bytes\n\nimport math\ndef f(a,i=0,j=-1):d=math.gcd(a[i],a[j]);a[j]*=a[i]//d;a[i]=d;a[i:j]and f(a,i,j-1)==f(a,i+1)\n\n\nTry it online!\n\n### Explanation\n\nThis problem is essentially a parallel sort on the prime factors, and (gcd(a,b), lcm(a,b)) is analogous to (min(a,b), max(a,b)). So let's talk in terms of sorting.\n\nWe will prove by induction that after f(i,j), a[i] becomes the smallest value in (the old value of) L, where L is the range between a[i] and a[j], including both ends. And if j = -1, f(i,j) will sort the range L.\n\nThe case when L contains one element is trivial. For the first claim, notice that the smallest of L can't stay in a[j] after the swap, so f(i,j-1) will put it in a[i], and f(i+1,-1) will not affect it.\n\nFor the second claim, note that a[i] is the smallest value, and f(i+1,-1) will sort the remaining values, so L becomes sorted after f(i,j).\n\n# Retina, 65 bytes\n\n\\d+\n*\n+\\b((_+)(\\2)+)\\b(.*)\\b(?!\\1+\\b)(\\2+)\\b\n$2$4$5$#3*$5 _+$.&\n\n\nTry it online! Link includes the faster test cases. Explanation:\n\n\\d+\n*\n\n\nConvert to unary.\n\n+\\b((_+)(\\2)+)\\b(.*)\\b(?!\\1+\\b)(\\2+)\\b\n\n\nRepeatedly match: any number with a factor, then a later number that is not divisible by the first number but is divisible by the factor.\n\n$2$4$5$#3*$5 $1 is the first number. $2 is the factor. Because regex is greedy this is the largest factor i.e the gcd. $4 is the part of the match between the original numbers. $5 is the second number. $#3 (in decimal rather than unary) is one less than $1 divided by $2, since it doesn't include the original $2. This means that to calculate the lcm we need to multiply $5 by one more than $#3 which is most succintly written as the sum of $5 and the product of $#3 and $5.\n\n_+\n$.& Convert to decimal. • Unary is allowed by default for Retina, so you can count this as 52 bytes. – Dennis Nov 2 '18 at 0:53 • @Dennis Only three of my Retina answers take input in unary; I've got used to doing I/O in decimal. – Neil Nov 2 '18 at 9:40 # 05AB1E, 10 bytes Credit for the approach goes to alephalpha. εIæN>ù€.¿¿ Try it online! εIæN>ù€.¿¿ Full program. Takes a list from STDIN, outputs another one to STDOUT. ε Execute for each element of the input, with N as the index variable. Iæ Powerset of the input. N>ù Only keep the elements of length N+1. €.¿ LCM each. ¿ Take the GCD of LCMs. # Perl 6, 53 bytes {map {[gcd] map {[lcm]$_},.combinations: $^i},1..$_}\n\n\nTry it online!\n\n# JavaScript (SpiderMonkey), 69 bytes\n\na=>a.map((q,i)=>a.map(l=(p,j)=>a[j]=j>i&&(t=p%q)?p/t*l(q,j,q=t):p)|q)\n\n\nTry it online!\n\n• Function l assign lcm(p,q) to a[j], and assign gcd(p, q) to q if j > i, otherwise keeps everything unchanged.\n• lcm(p,q) = if p%q=0 then p else p*lcm(q,p%q)/(p%q)\n\n# JavaScript (SpiderMonkey), 73 bytes\n\na=>a.map((u,i)=>a.map((v,j)=>i<j?a[j]*=u/(g=p=>p%u?g(u,u=p%u):u)(v):0)|u)\n\n\nTry it online!\n\n• Function g calculate gcd(u, v) and assign return value to u.\n\n# 05AB1E, 1514 13 bytes\n\nÓ¾ζ€{øεgÅpymP\n\n\nPort of @Dennis♦' Jelly answer, but unfortunately 05AB1E doesn't have an Unexponents-builtin, so that takes more than halve the program.. :(\n-1 byte thanks to @Mr.Xcoder.\n-1 byte thanks to @Enigma.\n\nExplanation:\n\nÓ # Prime exponents of the (implicit) input-list\n¾ζ # Zip, swapping rows and columns, with integer 0 as filler\n€{ # Sort each inner list\nø # Zip, swapping rows and columns again\nε # Map each inner list:\ngÅp # Get the first l primes, where l is the size of the inner list\nym # Take the power of the prime-list and inner list\nP # And then take the product of that result\n# (And output implicitly)\n\n• Oh, I hadn't seen your answer prior to posting my own, lol. 14 bytes by using ¾ and removing 0ï, +1. (I've tried this before because I tried to port Dennis' answer as well lol) – Mr. Xcoder Nov 2 '18 at 8:18\n• Using εgÅpymP would save another byte over the one Mr. Xcoder metioned – Emigna Nov 2 '18 at 8:28\n• @Mr.Xcoder Oh, didn't knew there was a difference between the filler with 0 and ¾. Need to remember that! In fact, I will add it to my small 05AB1E tips right now. :) – Kevin Cruijssen Nov 2 '18 at 10:00" ]
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https://www.hindawi.com/journals/ace/2020/9198356/
[ "/ / Article\n\nResearch Article | Open Access\n\nVolume 2020 |Article ID 9198356 | https://doi.org/10.1155/2020/9198356\n\nBaohua Guo, Chenlin Wang, Long Wang, Yan Chen, Tan Cheng, \"A Modified Cubic Law for Rough-Walled Marble Fracture by Embedding Peak Density\", Advances in Civil Engineering, vol. 2020, Article ID 9198356, 10 pages, 2020. https://doi.org/10.1155/2020/9198356\n\n# A Modified Cubic Law for Rough-Walled Marble Fracture by Embedding Peak Density\n\nRevised04 Sep 2019\nAccepted01 Nov 2019\nPublished03 Jan 2020\n\n#### Abstract\n\nThe property of water flow through a single rock fracture is the base of describing the seepage characteristics of jointed rock mass. Five artificial tensile fractures of coarse-grained cylinder marble samples were made at about the midpoint of the long axis by using a self-made splitting mold. The upper and lower surfaces of the tensile fractures were scanned by a 3D laser scanner (OKIO) to obtain their 3D coordinates. Then, the Geomagic Studio Software and rock surface topography scan test software were used to obtain peak density values of each single fracture surface. To study the seepage characteristics of open fracture, 4 rectangular plastic spacers with the size of about 3 mm × 2 mm × 0.2 mm were put into the fracture when water flowed through the single rough fracture tests were conducted under different normal stresses using the self-developed radial flow system. According to the testing data, the relationships between the seepage characteristics of single rough rock fracture and the peak density of fracture surface were studied. It is discovered that the 3D fracture morphology had great influences on the seepage characteristics of the single rock fracture. A modified cubic law was put forward to present the relationship between the seepage characteristics of a rough rock fracture and peak density of two fracture surfaces. Comparison between the modified cubic law and the experimental data showed a relatively good agreement.\n\n#### 1. Introduction\n\nGroundwater flow through jointed rock mass affects the stability of many engineering structures in civil engineering, mining engineering, hydropower engineering, petroleum engineering, and environmental engineering . The water flow through a single rock fracture is usually the base of describing the seepage characteristics of jointed rock mass, which is why the water flow through a single rock fracture has been tested extensively in laboratory by a number of researchers.\n\nIn the early research on the seepage model for water flow through a single fracture, Lomize , De Marsily and Romm [1, 3], and Louis firstly carried out the water flow test through two parallel plates and developed the so-called cubic law, which stated that the flow rate through the parallel plates had a cubic relation with the aperture of the plates. Thus, tiny change of the aperture may lead to major variation of the seepage flow rate. However, the surface of natural fractures is usually rough and undulant instead of smooth. If the aperture is large enough, the effect of rough and undulant fracture surface on the seepage characteristics of rock fractures may be slight or negligibly low . Singh et al. found that water flowing through a single rough fracture in granite still obeyed the well-known “cubic law” even if the fractures were under the combination conditions of high bp (maximum inlet water pressure, 25 MPa) and σ3 (maximum confining pressure, 40 MPa). However, Konzuk and Kueper summarized the research progress achieved on the seepage properties of rough rock joints and modified cubic law and suggested that the applicability of the local cubic law should be studied under the condition of different fracture surface three-dimensional morphology or/and abrupt aperture changes. Moreover, Raven and Gale found the deviation of the relationship between the joint flow rate and the joint deformation from behaviour predicted by the parallel plate model increased with the sample size and the number of loading cycles increasing. Therefore, the validity of the cubic law is suspicious [10, 11], and the cubic law has a certain limitation in practical application.\n\nCorrespondingly, in order to still apply the cubic law in analyzing seepage properties of rough rock fracture, various researchers have tried to modify the cubic law by incorporating some fracture roughness parameters. JRC (joint roughness coefficient) is usually used to describe rock joint roughness in rock engineering since the morphology of the actual rock joint is usually very complex and it is difficult to completely describe the profile feature of the rock joint according to the 10 standard section lines . Jaeger et al. [6, 10, 11] studied the effect of rock joint roughness on the seepage properties of the joint from different point of views and modified the cubic law by using JRC to quantify the rock joint roughness so that the modified cubic law could be applied in analyzing the seepage characteristics of the rough rock joint. Neuzil and Park and Hahn imported a function of aperture density distribution to analyze the effect of joint surface roughness on the joint seepage properties. Iwai conducted the seepage experiment and concluded that the way of the joint roughness affecting on the water flow through a single joint was related to the contact ratio of the rock joint surfaces. Subsequently, Zhou and Xiong put forward a modified cubic law by incorporating a joint contact ratio. Zhao proposed a new parameter, i.e., JMC (joint matching coefficient), to describe the effect of the contact state on the seepage characteristics of the rock joint qualitatively. Tsang and Tsang proposed a channel model to describe the seepage property of the rock joint based on the integrated laboratory test and theoretical analysis. Luis et al. studied the channel flow phenomenon of seepage and solute transport in a single joint using the discrete element method. Brown et al. studied the effect of joint roughness on the joint seepage properties using the Reynolds equation and the fractal model of joint surface morphology. A friction factor was introduced in reference as a function of two-independent variables, Reynolds number and relative roughness, and was then formulated to describe the influence of friction drag of the wall and local aperture changes on pressure head distribution.\n\nSince the fracture surface is rough, the cubic law with the use of average aperture may not be able to describe the true seepage characteristics of the rough rock fracture. Moreover, as reviewed above, most of the modified cubic laws have used either JRC or the fracture aperture distribution function to characterize the influence of the fracture roughness on the fracture seepage properties although neither JRC nor the aperture distribution function are easy to obtain. Therefore, the objective of this paper is to put forward a modified cubic law to present the relationships between the seepage characteristics and a 3D fracture morphology parameter of a rough fracture by conducting water flow tests through a single rough fracture.\n\n#### 2. Materials and Methods\n\n##### 2.1. Sample Preparation\n\nFive cylindrical samples with a diameter of 50 mm and a height of 100 mm were firstly manufactured from white coarse-grained marble, then a blind hole with a length of 60 mm and a diameter of 6 mm was drilled from one end along the axis of each cylindrical sample; finally, a self-designed splitting mold, as shown in Figure 1(a), was used to divide each cylinder sample into two halves at about the midpoint of the long axis. The splitting mold consists of two identical parts, each of which consists of an iron plate with a cylindrical groove and a wire with a triangular cross section. The iron plate has a slot at the midpoint of the long axis perpendicular to the axis and the wire is fixed in the slot to split the sample with an edge. Marble fracture surfaces of sample M1 and 5 single-fractured samples are shown in Figure 1(b).\n\n##### 2.2. 3D Morphology Parameters of Rock Fracture Surface\n\nThe upper and lower surfaces of the tensile fractures in a coarse-grained marble were firstly scanned by a Tianyuan OKIO-typed 3D laser scanner with CCD camera resolution of 1.44 × 106 pixel and with measurement accuracy of up to 10 μm, as shown in Figure 1(c), and the distance between adjacent points was about 16 μm. Marking points (black rings on the surface of the sample, as shown in Figure 1(b)) are used to control the stitching of scanning data because one time of scan is incomplete to obtain all the morphological data of a fracture surface. The coordinates of the scanned surface will be written in ASCII or binary files in the X, Y, and Z format, in which X, Y, and Z coordinates represent the width, length, and height of the fracture surface, respectively. Subsequently, the ASCII or binary files were imported to the Geomagic Studio Software to complete the encapsulation of the sample surface and were saved as OBJ files, and encapsulated fracture surfaces of the sample M1 were illustrated in Figures 1(d) and 1(e), respectively. Finally, the OBJ files were imported to Rock Surface Topography Scan Test Software (RSTST) by which 3D fracture morphology parameters could be calculated. In the scanned point cloud grid network, the point on the fracture surface is selected as a peak if its height is higher than its adjacent eight points. Peak density Spd is the peak number in the unit area, and it can be obtained by the number of all the peak points being divided by the projected area of fracture surface, as shown in Table 1.\n\n M1 M2 M3 M4 M5 Upper fracture 0.64 0.32 0.40 0.07 0.32 Lower fracture 0.06 0.33 0.26 0.51 0.38 Maximum 0.64 0.33 0.40 0.51 0.38 Average 0.35 0.32 0.33 0.29 0.35 Minimum 0.06 0.32 0.26 0.07 0.32\n##### 2.3. Flowing Test Device\n\nFigure 2(a) depicts the test system for studying the seepage characteristics of the splitting fracture, which includes three parts, i.e., the water supplying system, the loading-seepage-measurement system, and the water collecting system. The inlet water head is controlled by the height of the water tank relative to the position of the rock fracture. The loading-seepage-measurement system includes normal loading system, normal deformation measurement system, and water switch. The water collecting system mainly includes heat-shrink tubing (collecting water outflow from the rock fracture), discharging tube, beaker, and balance. The upper and lower parts of heat-shrink tubing were tightened by the pipe clamp after their shrinkage by heating, and the middle part of the heat-shrinkable tubing near the fracture plane outlet had no pressure on the sample side. Vaseline was filled between the heat-shrinkable tube and the side surface of the sample within the specified range of the two pipe clamps to prevent water from flowing out through the upper or lower part of the heat-shrinkable tube.\n\nThe normal load is applied on the sample through a self-developed creep testing device UCT-2, which includes upper pressure head, lower pressure head, and feed water plate, as shown in Figure 2(a). The normal stress can then be calculated according to the pump pressure and the cross-sectional area of the rock sample. The normal displacement is measured by three equidistant dial indicators attached to the rods which are fixed to the upper plate. The measuring heads of the three dial indicators touch the ring plate which is fixed to the sample. Thus, the reading variation of the three dial indicators can reflect the normal displacement between the upper plate and the ring plate, the average of which is taken as the normal deformation of the rock fracture approximately under lower normal stress levels.\n\n##### 2.4. Test Procedure\n\nThe single-fractured specimen in the radial flow test is shown in Figure 2(b). Four rectangular plastic spacers with the size of about 3 mm × 2 mm × 0.2 mm were placed in the fracture to make sure the fracture remains open and their size was very small compared with that of the fracture so that the four rectangular plastic spacers had little effect on the water seepage through the fracture. During the radial flow test, the water was supplied from the inlet hole and then flowed along the blind hole reaching the rock fracture. After that the water seeped radially from the centre of the specimen through the rock fracture and finally left the fracture flowing into the breaker through the discharging tube. During the radial flow test, a constant normal stress was applied on the rock fracture, which was set as 1∼6 MPa, respectively. Under each normal stress, the inflow water head were all set as 22 m. The readings of three dial indicators are recorded once normal stress or water head changed.\n\n#### 3. Results and Discussion\n\n##### 3.1. The Flow State of Fluid through a Rock Fracture\n\nReynolds number Re can describe the flow state of fluid and reflect the influence of parameters such as flow velocity, viscous coefficient of fluid, and shape of seepage passage. By calculating Reynolds number, the flow state of water through a rock fracture can be judged. The calculation formula is as follows:where Re is Reynolds number; υ is characteristic velocity, m/s; μ is dynamic viscous coefficient of water; the temperature of water is about 10°C;  = 1.31 × 10−3 kpa·s; L is characteristic length, and for fracture flow, its value is twice the equivalent hydraulic aperture .\n\nIn the test, the seepage flow starts from the inner hole boundary of the sample and flows radially along the fracture surface to the outer circumference. The flow velocity and Reynolds number are different at the inner and outer boundary of the fracture surface. According to the test scheme, when the initial normal stress is 2 MPa and the head difference is 22 m, the flowrate and Reynolds number calculated are the largest. The inner Reynolds number Rei and the outer Reynolds number Reo are calculated as shown in Table 2. From Table 2, it can be seen that under initial normal stress of 2 MPa, the inner Reynolds number Rei is greater than the outer Reynolds number Reo and its maximum value is 9.54, which is far less than the critical Reynolds number 500. Therefore, the flow state of water through the rock fracture can be considered as laminar flow. In addition, the permeability of intact rock is generally very small and its permeability coefficient is generally less than 10−7 cm/s. The minimum rock fracture permeability coefficient in this paper is 5.38 × 10−3 cm/s, which is about 4 orders higher than that of intact rock; thus, the influence of rock permeability on rock fracture seepage test results can be neglected.\n\n Sample M1 M2 M3 M4 M5 R ei 4.16 8.43 9.71 9.16 9.54 R eo 0.5 1.01 1.17 1.1 1.14\n##### 3.2. The Basic Theory of Radial Flow in a Single Fracture\n\nThe cubic law was derived from the Navier–Stocks equation based on the smooth parallel plates model as follows:where μ is flow velocity, K is hydraulic conductivity, J is hydraulic gradient, ν is kinematic viscosity coefficient, is acceleration of gravity, and b is mechanical aperture.  = 1.31 × 10−6 kpa·s at room temperature of 10°C and  = 9.8 × 103 kg/m3.\n\nBased on the seepage theory for groundwater flow, the radial flow rate can be calculated using the following equation:where Q is flow rate, r is radius, and H is water head.\n\nEquation (4) can be integrated to become where R is the outer boundary radius, r0 is the internal boundary radius, and ΔH is head difference.\n\nCombining equation (3), equation (5) is written as\n\nEquation (6) can be simplified as follows:where\n\nEquation (7) is used to describe the radial flow through smooth parallel plates. Since natural fractures are usually rough, equivalent hydraulic aperture be can be used to replace the aperture b in equation (7), that is,\n\n##### 3.3. The Relations between Equivalent Hydraulic Aperture and Fracture Closure\n\nFracture aperture directly affects the seepage flow, but it is difficult to measure the fracture aperture directly. On the other hand, the fracture closure can be easily measured. The fracture closure reaches the maximum value when the equivalent hydraulic aperture be calculated by equation (9) is zero theoretically. Figure 3 shows the relationship between the equivalent hydraulic aperture be and fracture closure ∆b obtained from the water radial seepage through the fractures of 5 specimens under six normal stresses described in Section 2.\n\nIt can be seen from Figure 3 that the equivalent hydraulic aperture be decreases linearly with the fracture closure ∆b increasing as a whole. That is, the equivalent hydraulic aperture be has a negative linear correlation with the fracture closure ∆b. Thus, when the equivalent hydraulic aperture be decreases and reaches zero, the maximum mechanical aperture (bm)max which is defined as the maximum normal closure ∆b of the rock fracture can be obtained. Therefore, the mechanical aperture bm under different normal stresses can be calculated by subtracting normal closure ∆b from maximum mechanical aperture (bm)max. The relationship between the equivalent hydraulic aperture and the fracture closure iswhere p1 and p2 are fitting parameters.\n\n##### 3.4. The Relationship between the Flow Rate Per Head and Mechanical Aperture\n\nFigure 4 depicts the relationship between the flow rate per head and the mechanical aperture obtained from the water radial seepage through the fractures of 5 specimens tests under different normal stresses. As can be seen from Figure 4, the flow rate per head increases with the mechanical aperture increasing, which can be well fitted by the power function in the following equation:where p3 is a fitting parameter and n is the exponent.\n\nThe values of p3 and n and correlation coefficient R2 are listed in Table 3 for the five fractures tested in the radial seepage tests. The correlation coefficients R2 for all five fractures are above 0.94. The range of the exponent n is 2.94∼3.17, i.e., close to 3, which is consistent with the general cubic relationship between the flow rate per head and the mechanical aperture. As the mechanical aperture increases, the increasing rate of the flow rate per head increases gradually. It is because the contact area between the fracture surfaces becomes larger and larger as the normal closure increases, which results in fewer flow paths and smaller flow rates. The fitting parameter p3 in equation (11) reveals the influence of the fracture roughness on the flow rate, which is unequal to the coefficient C in equation (9) derived according to the smooth parallel plate model. Correspondingly, a correction coefficient ξ (Table 3) is introduced to modify equation (9), which becomes\n\n No. (be)max (mm) Equation (10) Equation (11) Equation (12) Equation (14) P 1 P 2 R 2 P 3 n R 2 ξ R 2 P 4 P 5 R 2 M1 0.45 −0.13 0.06 0.94 5.53 3.17 0.95 2.29 0.91 −0.05 0.45 0.99 M2 0.71 −0.09 0.06 0.98 1.34 2.98 0.97 0.72 0.99 −0.06 0.77 1.00 M3 0.58 −0.12 0.07 1.00 3.11 3.04 1.00 1.57 1.00 −0.06 0.63 0.99 M4 1.63 −0.04 0.07 0.95 0.13 2.94 0.94 0.07 0.95 −0.08 1.70 0.99 M5 0.59 −0.11 0.07 0.98 2.50 2.95 0.98 1.39 1.00 −0.05 0.63 1.00\n\nAfter that, the relationships between the flow rate per head and the mechanical aperture are fitted again using equation (12) with the regression parameter ξ and correlation coefficients R2 are listed in Table 3. As can be seen from Table 3, the correlation coefficients R2 are all above 0.91.\n\nFurther, the relationship between the regression parameter ξ and the average peak density is shown in Figure 5. As can be seen from Figure 5, there is a power relationship between ξ and the average peak density (Spd)ave (which is one of the 3D morphology parameters), and the correlation coefficient is 0.91.\n\nIf the fitting equation between ξ and the average peak density (Spd)ave illustrated in Figure 5 is substituted into equation (12), the following equation can be obtained:\n\nEquation (13) indicates that the relationship between the flow rate per head and the mechanical aperture is a modified cubic law containing the 3D morphology parameter Spd. It should be pointed out that whether the proposed modified cubic law here can be used for a different rock fracture size needs a further study.\n\n##### 3.5. The Relationship between Mechanical Aperture and Normal Stress\n\nHowever, as mentioned before, the mechanical aperture is a parameter which cannot be easily obtained, but it is easy to obtain the normal stress during the fracture seepage test. Therefore, it is rather useful to build a relationship between the flow rate and the normal stress from the practical point of view.\n\nFigure 6 depicts the relationship between the mechanical aperture and the normal stress obtained from the fracture seepage tests. As shown in Figure 6, the mechanical aperture decreases linearly with the increase of the normal stress and the decreasing rates are rather similar for all five specimens. Thus, the linear relationship between the mechanical aperture and the normal stress σ can be denoted using the following equation:where p4 and p5 are linear regression parameters.\n\nThe regression parameters p4 and p5 and the correlation coefficient R2 for each specimen are shown in Table 3. Theoretically, the 3D morphology parameters affect the relationship between the mechanical aperture and the normal stress. Thus, the 3D morphology parameters should have effect on the fitting parameters p4 and p5 in equation (14) too. The relationship between the fitting parameter p4 and the average peak density (Spd)ave and that between the parameter p5 and (Spd)ave are illustrated in Figure 7, respectively. It can be seen from Figure 7 that both p4 and p5 are exponentially related to (Spd)ave with the correlation coefficients R2 of 0.97 and 0.98, respectively, and p4 increases with the increase of (Spd)ave while p5 decreases with the increase of (Spd)ave. Correspondingly, the average peak density (Spd)ave of the fracture surfaces influences the size of the mechanical aperture directly. The greater the average peak density is, the smaller the mechanical aperture is under the same normal stress.\n\nSubstituting the relationship between p4 and (Spd)ave and that between p5 and (Spd)ave in Figure 8 into equation (14), the following equation can be obtained:\n\nIf equation (15) is substituted into equation (13), the following equation is obtained:\n\nIn equation (16), (Spd)ave can be obtained by adopting 3D laser scanner and Rock Joint Morphology Test Software and all other parameters can be obtained easily, too, during the fracture seepage test. Thus, equation (16) provides an important new relationship between the flow rate and the normal stress taking the influence of the fracture roughness into account through incorporating the 3D morphology parameter Spd.\n\n##### 3.6. The Amendment of Equation (16)\n\nFigure 8 depicts the relationships between the flow rate per head and the normal stress obtained both experimentally from the fracture seepage tests and theoretically according to equation (16). There exists obvious deviation between the theoretical prediction using equation (16) and the experimental data from the fracture seepage tests. Specially, the theoretical prediction using equation (16) is larger than the experimental data for specimens M1 and M4 and is lower than the experimental data for other specimens, which may be because equation (16) contains total errors of equations (10)∼(16). From Table 1, we can see that (Spd)max of specimens M1 and M4 are also larger than other specimens so that the deviation between the theoretical prediction using equation (16) and the experimental data may has some relation with (Spd)max. Thus, an amendment coefficient k is introduced, which is the average ratio between the flow rates per head obtained experimentally from the fracture seepage test and theoretically using equation (16). The relationship between k and the maximum peak density of the fracture surface (Spd)max for the five specimens is shown in Figure 9. It can be seen from Figure 9 that the amendment coefficient k has an exponential relationship with (Spd)max, and the fitting correlation coefficient R2 is more than 0.99.\n\nAfter introducing the amendment coefficient, equation (16) becomes\n\nThe relationships between the flow rate per head and the normal stress obtained theoretically according to equation (17) are also illustrated in Figure 8. It can be seen from Figure 8 that after including a 3D morphology parameter, i.e., the peak density, the cubic model in equation (17) predicts the relationship between the flow rate per head and the normal stress in the rock fracture seepage test well. Therefore, equation (17) may be used in numerical simulation or theoretical prediction on the flow rate per head in the rock fracture seepage test under different normal stresses with the peak density taken into account.\n\n#### 4. Conclusions\n\n(1)There is a linear relationship between the equivalent hydraulic aperture and the fracture closure during the rough rock fracture seepage tests under various normal stresses. The equivalent hydraulic aperture decreases with the increase of the fracture closure. The total normal closure can be set as the maximum mechanical aperture, and then the mechanical aperture under different normal stresses can be calculated by subtracting the normal closure from the maximum mechanical aperture.(2)There is a power relationship between the flow rate per head and the mechanical aperture, and the index n is close to 3. Thus, the relationship between the flow rate per head and the mechanical aperture meets approximately the cubic model. Since the mechanical aperture cannot be measured easily from the rock fracture seepage test, a correction coefficient ξ is introduced to relate the mechanical aperture to the average peak density (Spd)ave, which is a 3D morphology parameter to be measured easily.(3)The mechanical aperture has a linear relationship with the normal stress during the rough rock fracture seepage tests, and the mechanical aperture decreases with the increase of the normal stress.(4)Equation (13) is a modified cubic law containing the 3D morphology parameter (Spd)ave of rock fracture, which can describe the influence of rock fracture roughness on the cubic relationship between the flow rate per head and the mechanical aperture. Equation (17) is suitable to predict the relationship between the flow rate per head and the normal stress of rock fracture after including a 3D morphology parameter (Spd)max.\n\n#### Data Availability\n\nThe research data used to support the findings of this study are included within the article. Request for more details should be made to the corresponding author.\n\n#### Conflicts of Interest\n\nThe authors declare no conflicts of interest.\n\n#### Acknowledgments\n\nThis research was funded by the China National Natural Science Foundation (grant no. 51109076).\n\n1. G. De Marsily, Quantitative Hydrogeology: Groundwater Hydrology for engineers, Academic Press, Orlando, FL, USA, 1986.\n2. G. M. Lomize, Flow in Fractured Rocks, Gosenergoizdat, Moscow, Russia, 1951, in Russian.\n3. E. S. Romm, Flow Characteristics of Fractured Rocks, Nedra, Moscow, Russia, 1966.\n4. C. A. Louis, “Study of groundwater flow in jointed rock and its influence on the stability of rock mass,” Tech. Rep., Imperial College of Science and Technology, London, UK, 1969, Imperial College Rock Mechanics Report 10. View at: Google Scholar\n5. D. Elsworth and T. W. Doe, “Application of non-linear flow laws in determining rock fissure geometry from single borehole pumping tests,” International Journal of Rock Mechanics & Mining Science & Geomechanics Abstracts, vol. 23, no. 3, pp. 245–254, 1986. View at: Publisher Site | Google Scholar\n6. J. C. Jaeger and N. Cook, Fundamentals of Rock Mechanics, Publication of Chapman & Hall, London, UK, 2nd edition, 1976.\n7. K. K. Singh, D. N. Singh, and P. G. Ranjith, “Laboratory simulation of flow through single fractured granite,” Rock Mechanics and Rock Engineering, vol. 48, no. 3, pp. 987–1000, 2015. View at: Publisher Site | Google Scholar\n8. J. S. Konzuk and B. H. Kueper, “Evaluation of cubic law based models describing single-phase flow through a rough-walled fracture,” Water Resources Research, vol. 40, no. 2, pp. 389–391, 2004. View at: Publisher Site | Google Scholar\n9. K. G. Raven and J. E. Gale, “Water flow in a natural rock fracture as a function of stress and sample size,” International Journal of Rock Mechanics & Mining Sciences & Geomechanics Abstracts, vol. 22, no. 85, pp. 251–261, 1985. View at: Publisher Site | Google Scholar\n10. P. A. Witherspoon, J. S. Y. Wang, K. Iwai, and J. E. Gale, “Validity of Cubic Law for fluid flow in a deformable rock fracture,” Water Resources Research, vol. 16, no. 6, pp. 1016–1024, 1980. View at: Publisher Site | Google Scholar\n11. P. A. Witherspoon, “Effect of size on fluid movement in rock fractures,” Geophysical Research Letters, vol. 8, no. 7, pp. 659–661, 1981. View at: Publisher Site | Google Scholar\n12. N. Barton and V. Choubey, “The shear strength of rock joints in theory and practice,” Rock Mechanics Felsmechanik Mecanique des Roches, vol. 10, no. 1-2, pp. 1–54, 1977. View at: Publisher Site | Google Scholar\n13. C. E. Neuzil, “Groundwater flow in low-permeability environments,” Water Resources Research, vol. 22, no. 8, pp. 1163–1195, 1986. View at: Publisher Site | Google Scholar\n14. C. K. Park and P. S. Hahn, “Effects of aperture density distribution on the flow through a rock fracture with line-source and line-collection,” Nuclear Engineering & Technology, vol. 30, pp. 485–495, 1998. View at: Google Scholar\n15. K. Iwai, Fundamental Studies of Fluid Flow through a Single fracture, University of California, Oakland, CA, USA, 1976.\n16. C. Zhou and W. A. Xiong, “Generalized cubic law for percolation in rock joints,” Rock and Soil Mechanics, vol. 17, no. 4, pp. 1–7, 1996. View at: Google Scholar\n17. J. Zhao, “Joint surface matching and shear strength part B: JRC-JMC shear strength criterion,” International Journal of Rock Mechanics and Mining Sciences, vol. 34, no. 2, pp. 179–185, 1997. View at: Publisher Site | Google Scholar\n18. Y. W. Tsang and C. F. Tsang, “Channel model of flow through fractured media,” Water Resources Research, vol. 23, no. 3, pp. 467–479, 1987. View at: Publisher Site | Google Scholar\n19. M. Luis, G. Björn, and N. Ivars, “Solute transport in fractured media—the important mechanisms for performance assessment,” Journal of Contaminant Hydrology, vol. 25, no. 3-4, pp. 283–298, 1997. View at: Publisher Site | Google Scholar\n20. S. R. Brown, H. W. Stockman, and S. J. Reeves, “Applicability of the Reynolds equation for modeling fluid flow between rough surfaces,” Geophysical Research Letters, vol. 22, no. 18, pp. 2537–2540, 1995. View at: Publisher Site | Google Scholar\n21. Z. Zhang and J. Nemcik, “Friction factor of water flow through rough rock fractures,” Rock Mechanics and Rock Engineering, vol. 46, no. 5, pp. 1125–1134, 2013. View at: Publisher Site | Google Scholar\n22. R. W. Fox, A. T. Mcdonald, and P. J. Pritchard, Introduction to Fluid Mechanics, John Wiley & Sons, Hoboken, NJ, USA, 6th edition, 2004.\n\n#### More related articles\n\nArticle of the Year Award: Outstanding research contributions of 2020, as selected by our Chief Editors. Read the winning articles." ]
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https://www.tutorialspoint.com/in-an-equilateral-triangle-prove-that-three-times-the-square-of-one-side-is-equal-to-four-times-the-square-of-one-of-its-altitudes
[ "# In an equilateral triangle, prove that three times the square of one side is equal to four times the square of one of its altitudes.\n\nTo do:\n\nWe have to prove that three times the square of one side of an equilateral triangle is equal to four times the square of one of its altitudes.\n\nSolution:\n\nLet in a $\\triangle \\mathrm{ABC}$,\n\n$\\mathrm{AB}=\\mathrm{BC}=\\mathrm{AC}$\n\n$\\mathrm{AD} \\perp \\mathrm{BC}$", null, "In $\\triangle \\mathrm{ADB}$,\n\n$\\mathrm{AB}^{2}=\\mathrm{AD}^{2}+\\mathrm{BD}^{2}$\n\n$\\mathrm{AD}^{2}=\\mathrm{AB}^{2}-\\mathrm{BD}^{2}$\n\n$=\\mathrm{AB}^{2}-(\\frac{1}{2} \\mathrm{BC})^{2}$\n\n$=\\mathrm{AB}^{2}-\\frac{1}{4} \\mathrm{BC}^{2}$\n\n$4 \\mathrm{AD}^{2}=4 \\mathrm{AB}^{2}-\\mathrm{BC}^{2}$\n\n$=4 \\mathrm{AB}^{2}-\\mathrm{AB}^{2}$            (Since $BC=AB$)\n\n$4 \\mathrm{AD}^{2} =3 \\mathrm{AB}^{2}$\n\nHence proved." ]
[ null, "https://www.tutorialspoint.com/assets/questions/media/153848-60013-1647102749.png", null ]
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http://www.tescera.com/mer-part-ii-the-one-ring/
[ "# Mer: Part II – the one ring\n\nPrevious page Mer part I – the Hieroglyph\n\nNext I placed the Mer hieroglyph and attached figure into a circle and found that the longer straight piece started a square in that circle. To orient the image correctly I rotated it 33°, and noticed that the baseline was then a further 33° from the circle centre. A mirrored line would then make 66° angle. (Where the baseline intersects the circle is precisely on the horizontal midpoint.)\n\nFor each corner of the square\n\nThis line will bounce around the circle 60 times, making a 60 pointed star. Obviously each point is 66°, and as measured from the circle centre, each point is 6° from its neighbour.\n\nOne might imagine that the initial 33° has a correspondence with Freemasonry, equally I imagine these 3 numbers; 66, 6 and 60 as a reference to Satanism. I think these are the numbers behind the usual 666.\n\nWhen depicted as in the above triangle, one can read the 6, then the 66, and then as an equilateral triangle each 6 also reads as 60.\n\nNext page Mer part III – 12 Pentagrams" ]
[ null ]
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https://stat.ethz.ch/pipermail/r-sig-mixed-models/2017q3/026064.html
[ "# [R-sig-ME] How to specify user-defined matrix Z?\n\nZhengyang Zhou Zhengyang.Zhou at UTSouthwestern.edu\nThu Sep 28 22:15:21 CEST 2017\n\n```?Hi all,\n\nIn genetic studies, we sometimes include the genetic relatedness matrix as a variance component, so we have this following model:\nY~Xbeta+Zb+error,\n\nwhere beta are the fixed effects, b~N(0,sigma^2*I) are the random effects, error are the random error, Z is the cholesky decomposition of the known genetic relatedness matrix. So how to use lme4 to fit this model if we know X and Z beforehand? I can use the package \"nlme\" to do it using the code like\n\nlme(y~-1+X, random=list(group=pdIdent(~-1+Z))),\nbut how to do it using lme4?\n\n(It's my first time to submit a post, and please let me know if I made anything wrong/inproper.)\n\nThank you.\nZhengyang\n\n________________________________\n\nUT Southwestern\n\nMedical Center\n\nThe future of medicine, today.\n\n[[alternative HTML version deleted]]\n\n```" ]
[ null ]
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https://www.coursehero.com/file/p6hb17e/Solve-the-equations-a-2-7-11-x-x-b-4-1-5-2-x-c-2-2-5-x-x-Math-012-60-Practice/
[ "Solve the equations a 2 7 11 x x b 4 1 5 2 x c 2 2 5 x x Math 012 60 Practice\n\n# Solve the equations a 2 7 11 x x b 4 1 5 2 x c 2 2 5\n\n• Notes\n• 11\n• 100% (2) 2 out of 2 people found this document helpful\n\nThis preview shows page 8 - 11 out of 11 pages.\n\n47) Solve the equations: +=-\nMath 012 60 Practice Problems for the Final Exam 948) Solve the equations: a) 2430xx+-b) ()2316x-c) 2261yy-d) 23270xx--49) Simplify the following: a) 4612849x yzb) 3341627343-c) 15612d) 36250) ====+-+51) If()321fxxx=-+, find each of the following values: a) ( )2f\nMath 012 60 Practice Problems for the Final Exam 10b) ()2fc) 12f   52) In 1995 there were 35 computers in a certain elementary school. In 2000 there were 52 computers in the same school and by 2005 there were 157 computers in the school. In 2008, there were 125 computers in the school. a) What was the percent increase in number of computers in the school from 1995 to 2000? b) What was the percent increase in number of computers in the school from 1995 to 2005? c) What was the percent decrease in number of computers in the school from 2005 to 2008? 53) Monica can mow the lawn in 4 hours using a riding mower. Her daughter can mow the same lawn in 12 hours using a push mower. How long would it take them to mow the lawn if they are working together? 54) The perimeter of a rectangle is 360 feet. The length of the rectangle is 60 feet less than twice the width of the rectangle. What are the dimensions of the rectangle? 55) According to the World Health Organization, in 2002 the annual cigarette consumption per person in Japan was 3023. If the population in Japan in 2002 was 127,096,000, how many cigarettes were consumed in Japan in 2002? Write your answer using scientific notation rounded to three decimal places. -56) Simplify the expression: () ()()40323243258xx yx y.\nMath 012 60 Practice Problems for the Final Exam 1158) Draw a graph of the following: 21yx=-+. 60) For what values of x is the following expression undefined? 32\n•", null, "•", null, "•", null, "" ]
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https://www.thestudentroom.co.uk/showthread.php?t=4399760
[ "# Vectors\n\nWatch\nAnnouncements\n#1\nYyjvyj\n0\n3 years ago\n#2\n(Original post by Deeboss)\nSuppose a 2D line passes through two points P0(10, 15) and P1(200, 20). Answer Questions 7 *- 10 regarding this line.\n\nQuestion 7) Which of the following vectors parallel to the line?\n\n(180, *10)\n\n(190, 5)\n\n(*380, *10)\n\n(*180, 10)\n\nI AM NOT WANTING AN ANSWER. I am hoping someone can take some time to explain to me how to work this out. I have searched online around this topic, and havent seemed to find much unless I am searching the wrong thing. I know this is about placement lines in vectors. So far what I think is I am meant to draw a 200x200cm grid, plot all the answers and see what is parallel to the two points P0(10, 15) and P1(200, 20)?\n\nAll explanations and help is much appreciated.\nYou don't need to draw a 200x200 grid.... Just find what the vector from", null, "to", null, "is and take the answer which is a multiple of it.\n0\n#3\nWait how do i find the vector of p0, and p 1? Could you like give me a worked example.\n0\n#4\n(Original post by Mr Moon Man)\nIt's (190,5)\nThe equation of the line is r=(10,15) +lambda(190,5)\nHow did you find the equation of the line? Can you give me a worked example please?\n0\n3 years ago\n#5\n(Original post by Deeboss)\nWait how do i find the vector of p0, and p 1? Could you like give me a worked example.\nBy doing", null, "which a basic vector property which you should know\n0\n3 years ago\n#6\n0\n#7\nSo if I want to work out the vector that is perpendicular to the line would I have to do 20-15 = 5\n200-10 = 190\n\n(5,190)?\n0\n3 years ago\n#8\n(Original post by Deeboss)\nSo if I want to work out the vector that is perpendicular to the line would I have to do 20-15 = 5\n200-10 = 190\n\n(5,190)?\nNo.\n\nA perpendicular vector would one named", null, "such that", null, "where", null, "is your parallel vector.\n\nFor a vector", null, "you would have perpendicular vector", null, "for some x,y.\n0\n3 years ago\n#9\nWhat level are you at, GCSE or A level? If so what module are you doing it in?\n0\n#10\n(Original post by B_9710)\nWhat level are you at, GCSE or A level? If so what module are you doing it in?\nI only did up to GCSE maths, and got a C.\n\nThe uni module I am doing is Quantitative method for computing.\n\nFYI: Im not so great at maths, but I putting in MAX effort on my coursework.\n0\nX\n\nnew posts", null, "Back\nto top\nLatest\nMy Feed\n\n### Oops, nobody has postedin the last few hours.\n\nWhy not re-start the conversation?\n\nsee more\n\n### See more of what you like onThe Student Room\n\nYou can personalise what you see on TSR. Tell us a little about yourself to get started.\n\n### Poll\n\nJoin the discussion\n\n#### Current uni students - are you thinking of dropping out of university?\n\nYes, I'm seriously considering dropping out (56)\n15.77%\nI'm not sure (9)\n2.54%\nNo, I'm going to stick it out for now (122)\n34.37%\nI have already dropped out (6)\n1.69%\nI'm not a current university student (162)\n45.63%" ]
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https://de.mathworks.com/matlabcentral/answers/1437894-how-to-keep-both-readability-and-calculation-speed-when-using-anonymous-functions
[ "# How to keep both readability and calculation speed when using anonymous functions?\n\n2 views (last 30 days)\nDaiki on 21 Aug 2021\nEdited: Stephen on 21 Aug 2021\nThere are some time when I use anonymous functions which include product of other anonymous functions. For example, as two anonymous functions\nh_exp1 = @(x)exp(1i.*x);\nh_exp2 = @(x)exp(1i.*sqrt(x.^2+A^2));\nand their product\nh_prod = @(x)(h_exp1(x) .* h_exp2(x));\nThis expression is inefficient in that the product h_prod call exp function twice and it is slower than\nh_prod2 = @(x)exp(1i.*(x+sqrt(x.^2+A^2)));\nwhich call exp function once. There are cases where this consumption of time become dominant if h_prod is called millions of times or more.\nOf course, its enough to use h_prod2 where the respective constituents are simple, but it seems to become less readable and less extendable when the formulation is basically not simple.\nAre there any methods to cope with this? Please forgive my inexperience of program development.\nThank you.\nStephen on 21 Aug 2021\n\nAlan Stevens on 21 Aug 2021\nhexp = @(x,y) exp(1i*(x+y));\nx = ..; % set to whatever is required\ny = sqrt(x.^2 + A^2);\nh1 = hexp(x,0);\nh2 = hexp(0,y);\nh3 = hexp(x,y);\n\nR2021a\n\n### Community Treasure Hunt\n\nFind the treasures in MATLAB Central and discover how the community can help you!\n\nStart Hunting!" ]
[ null ]
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https://stats.stackexchange.com/questions/314030/modelling-using-the-binomial-distribution-formula
[ "# Modelling using the Binomial Distribution Formula\n\nSo I'm in my first semester at University studying Actuarial Science and one of my classes is Probability. Needless to say, I have fallen in love with the whole topic and given my passion, I constantly try to solve problems on my own. Except that this time, I really am puzzled.\n\nI first started with a typical American Roulette game at the casino (zero and double zero are possible outcomes). I was interested in finding how many times would the casino need to spin the wheel before being almost sure of turning a profit; assuming there is only 1 bet per spin, the player always bets on red and the bet amount is always \\$100. Well, this problem is not too difficult to solve. Intuitively we know that because the casino has an edge (expected value of 5,26 dollars for \\$100 spin), it will beat the player over the long haul and turn a profit. But knowing the player could get lucky, and delay the inevitable (going bankrupt), how long could the \"long haul\" be? Would it be 10 spins? 50 spins? 100 spins?\n\nAs it turns out, I did the model for this projection and noticed that after 10 spins, the casino will only turn a profit 44.32% of the time. After 100 spins, it becomes 66.57% and after 1000 spins it is 94.89%. Conclusion, our intuition was confirmed. Over time, chances are the casino will crush the player.\n\nI was able to do this using the Binomial Distribution Formula below:", null, "Now, what if instead, my new game at the casino was to roll a fixed die. Possible outcomes would include (1,2,3,4,5,6) and their corresponding probabilities would be (10%,15%,20%,15%,10%,30%). Each number has the following profits for the casino (-\\$200,-\\$100,-\\$50,-\\$100,-\\$200,\\$500).\n\nAs you can see, the casino only makes money when a 6 is rolled (30% of the time), and although it doesn't win as often as with the Roulette game, its expected value is even higher (\\$70 per roll). How would I find out how many events it would take for the casino to be profitable in this game? Intuitively I'm puzzled because the lower chance of winning tells me it would take much longer than the Roulette game but it's expected value being much higher tells me it would take fewer events. Can I use a Binomial Distribution once again? For instance, after 5 rolls, the results could have been (5,4,6,3,1) and in that case, the casino would have lost 50 dollars (-\\$200,-\\$100,\\$500,-\\$50,-\\$200).\n\nIt's confusing because unlike the roulette game, the casino has 4 distinct outcomes (-\\$200,-\\$100,-\\$50,\\$500). Should I run my model with the binomial formula based on winning 150 dollars, 30 percent of the time and losing 80 dollars, 70 percent of the time? Those figures represent the sum of the expected values. I'm not sure how to solve this.\n\nI will generalise your particular problem to show how to deal with this type of problem. Suppose you have a series of bets, each with $$m$$ possible outcomes. The probability vector for the outcomes, and the profit to the casino for each outcome, are given respectively by the vectors:\n\n$$\\mathbf{p} = (p_1,...,p_m) \\quad \\quad \\quad \\mathbf{\\pi} = (\\pi_1,...,\\pi_m).$$\n\nAfter $$n$$ rounds of play, the counts of outcomes follow a multinomial distribution. The profit to the casino after $$n$$ rounds of play is a random variable given by:\n\n$$\\Pi_n = \\sum_{i=1}^m N_i \\pi_i \\quad \\quad \\quad \\mathbf{N} = (N_1, ..., N_m) \\sim \\text{Multinomial}(n, \\mathbf{p}).$$\n\nThe expected value and variance of the profit to the casino after $$n$$ rounds is:\n\n\\begin{equation} \\begin{aligned} \\mu_n \\equiv \\mathbb{E}(\\Pi_n) &= n \\sum_{i=1}^m p_i \\pi_i, \\\\[6pt] \\sigma_n^2 \\equiv \\mathbb{V}(\\Pi_n) &= n \\sum_{i=1}^m p_i (1-p_i) \\pi_i^2. \\\\[6pt] \\end{aligned} \\end{equation}\n\nProbability of profit: The exact probability that the casino has profited after $$n$$ rounds is:\n\n$$\\mathbb{P}(\\Pi_n > 0) = \\sum_{\\mathbf{n} \\in \\mathcal{S}_n(\\mathbf{\\pi})} \\text{Multinomial}(\\mathbf{n}|n, \\mathbf{p}),$$\n\nwhere $$\\mathcal{S}_n(\\mathbf{\\pi}) \\equiv \\{ \\mathbf{n} | \\sum_i n_i \\pi_i > 0, \\sum_i n_i = n \\}$$ is the set of count vectors that yield profit under the vector $$\\mathbf{\\pi}$$. For large $$n$$ it is computationally expensive to find this set, so it would be usual to approximate the multinomial distribution by the normal distribution to yield the approximation $$\\Pi_n \\sim \\text{N}(\\mu_n, \\sigma_n^2)$$, which then gives an approximate probability of profit:\n\n$$\\mathbb{P}(\\Pi_n > 0) \\approx 1 - \\Phi \\Big( - \\frac{\\mu_n}{\\sigma_n} \\Big) = 1 - \\Phi \\Big( - \\frac{\\mu_1}{\\sigma_1} \\cdot \\sqrt{n} \\Big).$$\n\nThis can easily be calculated for any $$n$$ using the standard normal CDF $$\\Phi$$. For large $$n$$ it will give a good approximation to the exact probability of profit.\n\n\\begin{equation} \\begin{aligned} \\mathbf{p} &= (0.10, 0.15, 0.20, 0.15, 0.10, 0.30), \\\\[6pt] \\mathbf{\\pi} &= (-200, -100, -50, -100, -200, 500). \\\\[6pt] \\end{aligned} \\end{equation}\n\nThis gives moments $$\\mu_n = 70 n$$ and $$\\sigma_n^2 = 62650 n$$. Hence, the approximate probability of profit after $$n$$ rounds is:\n\n\\begin{equation} \\begin{aligned} \\mathbb{P}(\\Pi_n > 0) &\\approx 1 - \\Phi \\Big( - \\frac{70n}{\\sqrt{62650n}} \\Big) \\\\[6pt] &= 1 - \\Phi \\Big( - \\frac{14}{\\sqrt{2506}} \\cdot \\sqrt{n} \\Big) \\\\[6pt] &= 1 - \\Phi ( - 0.2796646 \\cdot \\sqrt{n} ). \\\\[6pt] \\end{aligned} \\end{equation}\n\nCoding this in R: You can code this in R to show how the probability of profit changes as we increase $$n$$. Note that the approximation is poor for small values of $$n$$ and so the early part of the curve is not an accurate representation of the true probability of profit.\n\n#Generate function for approximate probability of profit\nPROB <- function(p, pi, N) { R <- sum(p*pi)/sqrt(sum(p*(1-p)*pi^2));\nPPP <- rep(0,N);\nfor (n in 1:N) { PPP[n] <- pnorm(-R*sqrt(n),\nlower.tail = FALSE); }\nPPP; }\n\n#Generate example\np <- c(0.10, 0.15, 0.20, 0.15, 0.10, 0.30);\npi <- c(-200, -100, -50, -100, -200, 500);\n\n#Plot probability of profit for n = 1,...,100\nlibrary(ggplot2);\nDATA <- data.frame(n = 1:100, PROB = PROB(p, pi, 100));\nFIGURE <- ggplot(data = DATA, aes(x = n , y = PROB)) +\ngeom_line(size = 1, colour = 'blue') +\nexpand_limits(y = c(0,1)) +\ntheme(plot.title = element_text(hjust = 0.5, size = 14, face = 'bold'),\nplot.subtitle = element_text(hjust = 0.5, size = 10, face = 'bold')) +\nggtitle('Probability of Profit') +\nlabs(subtitle = '(Using normal approximation to the multinomial distribution)') +\nxlab('Number of bets') +\nylab('Probability of profit');\nFIGURE;", null, "N.B. My undergraduate degree was also in actuarial studies, and that is how I came to fall in love with probability and statistics. (So much so that I abandoned actuarial mathematics and became a statistician!) Good luck with your program.\n\nIf you're assuming that each outcome of the game is independent of the previous outcomes, you can just use the linearity property of the expectation (where $c$ is a constant): $$\\mathbb E[c \\cdot X] = c \\cdot \\mathbb E[X]$$\n\nYou just set up the equation as $x \\cdot \\mathbb E[X] = P$, where P is the profit you're interested in, and solving for $x$ will tell you how many games need to be played for casino to win $P$ in expectation.\n\n• Hi @Martn thank you! I think that would tell you how many trials to meet the expectation you're shooting for, but doesn't address the question of how many trials are needed before being profitable. I'm looking to see how to do this in R. Maybe even C#. Otherwise, it gets pretty ugly. Nov 27, 2017 at 2:52" ]
[ null, "https://www.s-cool.co.uk/gifs/a-mat-sdisc-dia08.gif", null, "https://i.stack.imgur.com/A6aig.jpg", null ]
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https://www.cliffsnotes.com/study-guides/algebra/algebra-ii/radicals-and-complex-numbers/complex-numbers
[ "## Complex Numbers\n\nThe expression", null, "has no real answer. The symbol i is created to represent", null, "and is called an imaginary value. Since", null, ", i 2 = –1. Any expression that is a product of a real number with i is called a pure imaginary number.\n\nExample 1\n\nSimplify each of the following.\n\n1.", null, "2.", null, "3. (6 i)(4 i)\n\n4.", null, "1.", null, "2.", null, "3. This last expression is commonly written as", null, "so that the i is not mistakenly written under the radical.\n\n4. (6 i)(4 i) = 24 i 2 = 24(–1) = –24\n\n5.", null, "For this last example, all imaginary values had to be put into their “ i‐form” before any simplifying could be done. Note that", null, "That is, the product rule for radicals does not hold (in general) with imaginary numbers.\n\nWhen i is raised to powers, it has a repeating pattern.", null, "When i is raised to any whole number power, the result is always 1, i, –1 or – i. If the exponent on i is divided by 4, the remainder indicates which of the four values is the result.\n\nExample 2\n\nSimplify each of the following.\n\n1. i 34\n\n2. i 95\n\n3. i 108\n\n4. i 53\n\n1. i 34\n\nSince 34 divided by 4 has a remainder of 2, i 34 = i 2 = –1. Think of it as", null, ", so", null, "2. i 95\n\nSince 95 divided by 4 has a remainder of 3, i 95 = i 3 = – i.\n\n3. i 108\n\nSince 108 divided by 4 has a zero remainder, i 108 = i 0 = 1.\n\n4. i 53\n\nSince 53 divided by 4 has a remainder of 1, i 53 = i 1 = i.\n\nComplex numbers and complex conjugates. A complex number is any expression that is a sum of a pure imaginary number and a real number. A complex number usually is expressed in a form called the a + bi form, or standard form, where a and b are real numbers. The expressions a + bi and abi are called complex conjugates. Complex conjugates are used to simplify the denominator when dividing with complex numbers. It is equivalent to rationalizing the denominator when dealing with fractions. The objective is to not end up with a complex number in the quotient's denominator.\n\nArithmetic with complex numbers is done in a similar manner as arithmetic with polynomials. The following are definitions for arithmetic with two complex numbers called ( a + bi) an d ( c + di).\n\nCombining like terms and factoring out the i,", null, "Using the distributive property,", null, "Simplifying the denominator,", null, "Example 3\n\nFind the sum, difference, product, and quotient of (4 + 3 i) and (5 – 4 i).", null, "Quotient: Rationalize the denominator.", null, "Example 4\n\nSimplify", null, ".\n\nSince 6 i is 0 + 6 i, its complex conjugate is 0 – 6 i. Therefore,", null, "" ]
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https://www.kopykitab.com/blog/vtu-previous-year-question-papers-be-ec-4th-semester-microcontrollers-december-2010/
[ "# Micro controllers December 2010\n\nNote:!. Answer any FIVE full questions, selecting at least TWO questions from Part A and Part – B.\n\n2. Missing data may be assumed suitably.\n\nPART – A\n\n1 a. Bring out the architectural difference between Von ~ Neumann and Harvard architecture.\n\nb.  With a neat diagram, write the programming model of 8051 with addresses of SFRs and ports. Also give the 128 bytes RAM allocation.\n\nc.   Explain the oscillator circuit and timing of a 8051 micro controller.    (04 Marks)\n\n2 a. Write a program to set the carry flag to 1, if the number in reg A is even and reset the carry flag to 0, if the number in reg A is odd. Use the assembly language of 8051.\n\nb.  Explain the following instructions of 8051 with examples :\n\ni) XCHD A, @ Ri ii) MOV CA, @A + PC iii) SWAP A iv) RL A v) MUL AB vi) DA A.\n\nc.   Explain the different addressing modes of 8051. Give an example for each of them and state the advantages and disadvantages of each.\n\n3      a. Explain the different types of conditional and unconditional jump instructions of 8051. Specify the different ranges associated with jump instructions.\n\nb.  Find the address of first two internal RAM locations between 20H and 40H, which contains consecutive numbers. If so, set the carry flag to 1, else clear the carry flag.\n\nc.   What does the following program do? What is the final result in accumulator? Give the result in terms of functionality.\n\nSTART : MOV A, R3 RLA\n\nANL A, # OAAh PUSH ACC MOV A, R3 RRA\n\nANL A, # 55h MOV R3, A POP ACC ORL 03h, A STMPS\n\nEND\n\n4 a. Explain C data types for 8051 with their data size in bits and data range.\n\nb.  Write a 8051 C – program to read the PI.0 and PI.1 bits of 8051 and issue an ASCII character to port 0 according to the following table. Use ease statement only.\n\nc.   Write a 8051 C program to convert packed BCD number 0 * 29 to ASCII and display the result on port 1 and port 2.\n\nPART-B\n\n5    a. Explain the different modes of operation of timer / counter of 8051 with relevant block diagram and steps to program the modes.\n\nb.  With a neat diagram, explain the TMOD and TCON registers of 8051.\n\nc.   Write a 8051 C program to toggle all the bits of port PI continuously with some delay in between. Use timer 0,16 bit mode to generate the delay and calculate the delay in msec.\n\n6  a.Explain the serial port of 8051. In detail, explain the SCON register with the diagram. State asynchronous serial communication and data framing. Explain with diagram RS232 pinout.\n\nb. Write a program in assembly language for 8051 to transfer the message “XES” serially at 9600 band, 8 bit data, 1 stop bit. Do this continuously.\n\n7 a. Explain the six interrupts of 8051, with the priority and interrupt vector table.\n\nb.  Explain with a diagram, IP and IE registers of 8051. What is their significance?\n\nc.   Write an ALP for 8051 to generate a square wave of 50Hz frequency on PI.2, using an interrupt for timer <j). Assume that XTAL ~ 11.0592 MHz.\n\n8 a. Explain with a diagram, the interfacing of DAC 0808 to 8051 chip. Write the program to generate a sine wave on the CRO. Show the relevant calculation and look up table.\n\nb.  Show the interfacing circuit and functional pins of LCD.\n\nc.   With a neat diagram, show how a stepper motor is interfaced’ to 8051. Write a program to rotate, it continuously." ]
[ null ]
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https://www.trccompsci.online/mediawiki/index.php?title=C%2B%2B_Creating_%26_Drawing_a_Map&diff=7057&oldid=7046
[ "# Tileset & Map\n\nYou will need to declare a texture and use it to load in a tile sheet.\n\nThen you can create a list of integers to identify the tile to display for each tile position.\n\n sf::Texture tileset;\n//this tile set is 14 x 14 tiles\n//each tile is 32 x 32\n\n// this is a list, it is not a 2d structure\n// this is 10 x 10, 100 in total, each is a tile number\nvector<int> map{\n0, 16, 16, 0, 0, 0, 0, 0, 0, 0,\n0, 0, 0, 0, 0, 0, 0, 0, 0, 0,\n0, 0, 0, 0, 0, 0, 0, 0, 0, 0,\n0, 0, 0, 0, 0, 0, 37, 37, 0, 0,\n0, 0, 0, 0, 0, 0, 0, 0, 0, 0,\n0, 0, 0, 0, 0, 0, 0, 0, 0, 0,\n0, 0, 21, 21, 21, 0, 0, 0, 0, 0,\n0, 0, 0, 0, 0, 0, 0, 0, 0, 0,\n0, 0, 0, 0, 0, 0, 0, 0, 0, 0,\n1, 1, 1, 1, 1, 1, 1, 1, 1, 1,\n};\n\n\nThis tile set is 14 tiles by 14 tiles, so tile 16 will not be on the first row. This will be on the second row in position 3.\n\n# Drawing the map\n\nWe will need to know the size of the map declared above, and also the pixel dimensions of a single tile. Remember the 'map' structure is not 2d so we need a 'count' to cycle through each element.\n\nSo in between 'window.clear()' and 'window.display()' you need the following code:\n\n\t\twindow.clear();\nint count = 0; // used to access the list\nfor (int y = 0; y < 10; y++)\n{\nfor (int x = 0; x < 10; x++)\n{\nif (map[count] != 0) // 0 in the map represents no tile\n{\nint tx = map[count] % 14; // remainder should be the tilesheet column\nint ty = map[count] / 14; // integer division would give tilesheet row\nsf::Sprite tile{ tileset }; // create a tile\ntile.setTextureRect({ tx * 32, ty *32, 32, 32 }); // set the tile rectangle\ntile.setPosition({ x*32.f,y*32.f }); // set the tile position\nwindow.draw(tile); // draw the tile\n}\ncount++;\n}\n}\n\nwindow.display();\n\n\nThis could be improved by also declaring:\n\nint map_rows = 10;\nint map_cols = 10;\nint tile_rows = 14;\nint tile_width = 32;\nint tile_height = 32;\n\n\nYou can now change the code to use these new variables:\n\n\t\twindow.clear();\nint count = 0; // used to access the list\nfor (int y = 0; y < map_rows; y++)\n{\nfor (int x = 0; x < map_cols; x++)\n{\nif (map[count] != 0) // 0 in the map represents no tile\n{\nint tx = map[count] % tile_rows; // remainder should be the tilesheet column\nint ty = map[count] / tile_rows; // integer division would give tilesheet row\nsf::Sprite tile{ tileset }; // create a tile\ntile.setTextureRect({ tx * tile_width, ty *tile_height, tile_width, tile_height }); // set the tile rectangle\ntile.setPosition({(float)( x*tile_width),(float)(y*tile_height) }); //needs casting to float\nwindow.draw(tile); // draw the tile\n}\ncount++;\n}\n}\n\nwindow.display();" ]
[ null ]
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https://www.wired.com/story/physics-tank-shell-polar-coordinates/
[ "# Track a Tank Shell With a Mirror and Polar Coordinates\n\nUltimately you get a differential equation that you can solve with a bit of code I wrote for you.\n\nIf the internet was your online physics textbook, the Slow Mo Guys would be writing a good number of those homework questions. Of course the Slow Mo Guys are Gavin and Dan, and they use a super-high-speed camera and look at stuff around us. OK—in this case, they aren't looking at normal things. They are looking at the motion of a high-speed shell fired from a tank.\n\nBut how do you see this tank shell if it is traveling around 2,000 feet per second (609 m/s)? You could just put the camera far enough away that the path of the projectile would be in the frame. However, in that case you would barely see the fast-moving object. It would be too small in the video. OK, what about getting close to the path so that the shell looks larger? Yes, you would see it, but just for a tiny fraction of the total path.\n\nThe solution to this problem is to use both methods. Get the camera close to the path and then rotate the view as the projectile passes. The Slow Mo Guys are going to put the camera 82 feet from the path, which means it would have to rotate at around 3,000 degrees per second—which is pretty much impossible. But instead of rotating a camera, they will just use a rotating mirror. The camera looks at the mirror and from that it can see the tank shell. Then the camera can stay in place while the mirror rotates. Perfect.\n\nHere is the real question. How do you determine the angular position of a mirror so that it can track the projectile? The answer: polar coordinates. Yes, you thought they were just joking when they made you do stuff with polar coordinates in math class. Surprise. You actually need this sometimes.\n\nLet's do this. How about a review of two different coordinate systems: Cartesian and polar coordinates. Also, how do you use polar coordinates to track a super fast projectile?\n\nCartesian Coordinates\n\nThis is the one you are likely familiar with. In two dimensions, there is an x-axis and a y-axis. They are perpendicular to each other. Once you pick the origin, you can describe the location of an object with x and y coordinates.\n\nThere's really not too much to say about this coordinate system, since you've probably seen it before. Let me just make some comments. Don't forget about units. It's not just x and y numbers. These numbers have to have units to make a connection to the real world.\n\nNow let's say that the projectile is moving in the negative x-direction with a velocity of 600 m/s. In that case, I can write the following kinematic equations for the position of the projectile.\n\nIn these expressions, x1 is the starting x-position and x2 is the position after some time Δt. Notice that the y-position doesn't change since it's only moving in the x-direction.\n\nBut just because it's easy to find the position doesn't mean you would know where to point your camera mirror. OK, I get it. It's possible to use the position to calculate the angle to aim the mirror—but that's not as much fun as using polar coordinates.\n\nOh, I should also point out that if you move the origin of the Cartesian coordinate system it's not a big deal. Sure, you will have different starting positions, but the velocity equations mostly look the same.\n\nPolar Coordinates\n\nIf you are still dealing with motion on a flat plane (ignoring the vertical motion of the tank shell), you will need two coordinates to describe the location of the object relative to the origin. Instead of using two perpendicular distances (x and y), polar coordinates uses an angle and a distance. Here is the same object from before using polar coordinates.\n\nInstead of x and y, we use r (the distance from the original) and θ the angle from the x-axis. Yes, if you draw the polar coordinates on top of the Cartesian coordinates it's possible to see the connection between the two systems. If you want to find the r and θ values you can use a right triangle. The hypotenuse of this triangle would be r and the angle would be θ. This gives the following conversion.\n\nEverything looks great. But there is a problem. How do you express the velocity of an object in polar coordinates? It's not a simple problem. If a projectile is moving in the x-direction, its velocity is just in the x-direction in the Cartesian coordinate system. However, for polar coordinates both its angular value and its r value will change. You can see this if I show the coordinates of the object at two different times.\n\nDescribing the velocity in polar coordinates isn't just in one dimension and those values aren't constant. Why would anyone use polar coordinates? Because with polar coordinates, you get the angular position of the object. This is exactly what you need to aim the mirror. Oh, notice that if I move the origin for the polar coordinate system the values can change quite a bit.\n\nOK, let's just do this. Let's get an expression for the velocity in polar coordinates. Since it involves a lot of math, I'm just going to share this video of my derivation instead of writing it out. Actually, I wrote it out too—here you go.\n\nBut in the end, you don't get something nice and simple like you do in Cartesian coordinates. You get an r and θ expression that changes with time and depends on second derivatives with respect to time. Yes, you get a differential equation. But wait! All is not lost. I know you don't want to solve a differential equation—and you don't have to. We can create a solution to this problem by breaking it into tiny steps and solving each step. This is the key idea in a numerical calculation. It's easiest to do something like this with a small bit of computer code.\n\nIn order to create a numerical calculation, I need the following (in polar coordinates).\n\n• The starting position of the object. The video states that the camera is 82 feet away (25 meters), so I will use that as my starting r value. The initial angle will be 90 degrees.\n• What about the starting velocity? Since I have two dimensions (r and θ) I need the velocity in these two directions. Here is the weird thing about the velocity in polar coordinates. As the object moves, the r-direction and θ-direction change. In Cartesian coordinates, the x and y-direction stay constant. So let's give this thing an initial velocity in the θ direction with a magnitude of 600 m/s.\n\nThat should be enough. With these values, I can use the differential equations to find the polar velocity and position after some short time interval. Then I just keep doing that until I want to stop or my computer explodes. Here is the code with a plot of the angular value of the position as a function of time. Feel free to edit it and rerun it. You can't break anything.\n\nFrom the plot of angle vs. time, you can see it's not such a simple problem. You can't just turn the camera mirror at a particular angular speed to follow the projectile. The closer the tank shell gets to the camera, the faster you have to rotate the mirror for it to stay in view.\n\nOK, now for some questions for you (or for me in the future).\n\nHomework\n• Use the code above. Create a plot of r vs. time.\n• In the code, use the values of r and theta during each time step to calculate the x-position of the object. Plot the position vs. time to show that it is indeed a constant x-velocity.\n• Modify the starting position (r) in the code. What happens if the starting position is closer to the tank shell? What if it is farther away?\n• What is the maximum angular velocity (in radians per second) for the mirror?\n• Suppose you put a camera that has a length of 10 cm and rotates about the center. Calculate the centripetal acceleration for the end of this camera if it were to follow to projectile. Suppose the end of the camera has a mass of 50 grams. Calculate the force needed to keep it together.\n• Estimate the power (in watts) needed for a camera to rotate to track the tank shell.\n\nMore Great WIRED Stories" ]
[ null ]
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http://tephra.smith.edu/classwiki/index.php/MTH301_Math_Research
[ "# MTH301 Math Research\n\nWelcome to the MTH301 Math Research Page\n\nHow to edit Wiki pages: See the Wikipedia editing cheat sheet.\n\nParticipants:\n\nLink to Moodle pages for MTH301. However, I think we will use this wiki instead of Moodle. In line with that thought, I will duplicate the two links from Moodle below.\n\n## Resources\n\n• My initial beamer presentation is here.\n• The Dumitrescu-Jiang paper is here.\n\n## Hypotheses and Theorems and Lemmas\n\n### 28 Jan 2010\n\n#### For Arbitrary Shapes\n\nHypotheses:\n\n• The best sweep can always be achieved by two sweeps: three or more are never needed to achieve the minimum sweep cost.\n• The best sweep can be found by surrounding the shape with the minimum perimeter parallelogram, and then slant-sweeping twice, with cost half the perimeter.\n\n#### Hairpins\n\nDefine a hairpin as two segments of unit length joined at an endpoint of each.\n\n• The best sweep of a hairpin depends on the angle theta between them.\n• For θ ≥ 73 deg = 2 arccos[4/5], it is best to sweep each pin separately, for a cost of 2.\n• for θ < this angle, it is best to sweep down the bisector, and then sweep the resulting line segment, for a cost of cos(θ/2) + 2sin(θ/2).\n\nWe believe that this description is consistent with the parallelogram Hypothesis above.\n\n### 4 Feb 2010\n\n#### Proved\n\n• Lemma 1: 1 sweep (either orthogonal or slanted) will suffice if and only if all points are collinear.\n\nProof: First we assume that one sweep will suffice. If it is not the case that all points in a shape lie on the same line, then there exist three non-collinear points. A sweep encountering these points will move all three along parallel lines. To reach one point, these three lines must coincide. This of course is a contradiction since we have assumed that the three points do not lie on the same line. Thus, if one sweep will suffice then all points must be collinear. Now, we assume instead that all points are collinear. So there exists some line on which all points in the shape are located. Clearly, sweeping along this line will move all points to the single point located at the end of the sweep. Therefore, one sweep suffices if and only if all points are collinear\n\n• Corollary 1: If 1 sweep suffices then the cost of the (optimal) sweep will equal the length of the line segment connecting the two points furthest from each other.\n• Lemma 2: If limited to 2 sweeps, the minimal cost will be half the perimeter of the minimal parallelogram.\n\nProof. (Sketch?). We know the first sweep must sweep the entire shape into a line, by Lemma 1 above. Let the cost of the first sweep be d1, and the cost of the second d2. We know from Corollary 1 that d2 is the length of the line into which the first sweep compresses the shape. And the total cost of both sweeps is d1+d2. We want to minimize d1+d2. The two sweeps determine a parallelogram, whose side lengths constitute d1+d2.\n\n#### Investigated\n\n• How might cost be decreased if we are allowed three (or more) sweeps?\n• Can Dumitrescu/Jiang's proof of Theorem 2 (constrained variants, discrete points along perimeter of triangle) be applied to a continuous distribution?\n\n#### Minimum Perimeter Parallelogram\n\nI (JOR) got interested in computing the minimum perimeter enclosing parallelogram (MPEP). It will likely be useful to have an implementation to test out hypotheses, if for no other reason. I wrote a brute-force search program in Mathematica. Essentially it tries all possible pairs of directions, specified by two angles α and β. Eventually I will link to the code from here, but for now I just want to record the fact that an implementation exists, albeit in a crude form. Here is a typical output, showing the best parallelogram enclosing six random points.\n\n• Question: Is it true that the MPEP for a triangle always has one side flush with a triangle side?\n\n### 11 Feb 2010\n\n#### Two Sweeps Not Always Best\n\n• Found examples where 3 and 5 sweeps are better than 2. (Rectangle with a line--or thin rectangle--coming out diagonally from one corner)\n• New question: Is 3 (or less) sweeps always best?\n\n#### MPEP for Triangle: One Side Always Flush?\n\n• Asked: Can we always rotate an enclosing parallelogram so that the triangle has one side flush with a triangle side? No. The diagonal of a parallelogram is longer than the length. If we have a triangle along the diagonal that is very thin (triangle height approaching the length of the diagonal) we are unable to rotate the parallelogram so that one side is flush with a triangle side.\n• Right triangle: Examples suggest that the MPEP is always flush against the two shorter sides of the triangle.\n\n#### Mathematica Code for MPEP\n\nThe Mathematica code comes in three notebooks:\n\nInstructions for how to use them is in the latter file, in a comment at the top. If you right-click on these links and save the files on a machine that has Mathematica, then you will be able to launch and run them.\n\n### 18 Feb 2010\n\n#### Experiment for θ=120\n\nHere is the experiment I (JOR) promised in today's meeting. I started with an isosceles triangle/hairpin. I chose the angle θ=120 deg, which, because greater than 73 deg, implies that the best parallelogram includes the two edges meeting at the θ angle. Then I gradually increased the horizontal leg of the triangle, making it increasingly non-isosceles. You can see that the brute-force searching program concludes that, independent of the mismatch in the length of the two edges of the hairpin, the MPEP still is flush with the two edges meeting at the θ angle. (Obviously the figures below are not to the same scale!)\n\n#### Experiment for θ=30\n\nThe situation is different if we start with an angle smaller than our critical 73 deg. Here I started with 30 deg. For all x > 1.2, there are two edges flush. Not sure what to make of this...\n\n#### Proof that 2 sweeps don't suffice for all figures\n\nConsider a 1x1 square with a diagonal of length √2 jutting out from one corner. By the 1-flush lemma, there are two ways of enclosing this shape in a parallelogram, namely (a) within a 2x2 square or (b) within a parallelogram formed by connecting the vertex of the diagonal with the two adjacent vertices of the square (this makes two sides of the figure, then reflect those sides to complete.) (a) has cost 4, and (b) cost 2√5=4.47 which are each greater than the cost of sweeping the diagonal and then the square (2+√2=3.41), requiring at least 3 sweeps.\n\n### 25 Feb 2010\n\n#### Flush Function Mathematica Notebook\n\nHere is the Mathematica calculations we did today.\n\nToday's favorite image!\n\nHere is the result of using ContourPlot[ FlushFunction[] ]:\n\nI solved the equation for b in terms of a. Here it is in raw form. Did not try to simplify or reorganize.\n\n#### Beamer Skeleton Files\n\nHere is a .zip file containing everything needed to run off the beamer skeleton we created today:\n\nYou need to download this file, and unzip it, usually by double-clicking on it (depends if Windows/MacOS/Linux). Once unzipped, you can edit MarchPresentation.tex in any text editor, save, and then LaTeX. On my Mac I use TeXShop. On Linux I use pdflatex. Exactly how to do this varies with the context.\n\nHere is the .pdf file it produces when LaTeX'ed. This file is in the .zip file, but if you want to see it on its own, here it is:\n\n##### 4Mar10\n\nThe links above to MarchPresentation.zip (and to MarchPresentation.pdf) have been updated to reflect our work today. I just replaced the files they point to.\n\n### 13 Mar 2010: Observations\n\nI have two observations.\n\n• First, this minor variant of our square-with-diagonal-antenna seems also to require three sweeps, in fact the same three sweeps. I've just filled out the antenna into the pink parallelogram.", null, "Another example that seems to need three sweeps\n• This example (which is nonconvex) makes me realize that there is a hypothesis close to our very first falsified hypothesis that we haven't yet killed:\n• Hypothesis: The optimal sweeping of any convex polygon uses only two sweeps.\n\n### 23 Mar 2010\n\nThis image needs an explanation!\n\n• Light colors: 1 side flush\n• Dark colors: 2 sides flush\n\nNow determined that the above image is misleading in several ways.\n\n### 26 Mar 2010\n\nThe new computation, correcting the 1-flush cost from (h+1), used above, to (h+x), where x is the length of the base plus whatever extra (if any) is need to reach the foot of the altitude. For the 1-flush rectangle has dimensions h by x, not h by 1. I also corrected an unrelated renormalizing error, just a mental bug on my part.", null, "Triangle (1,a,b), 1-flush against a-side, 1-flush against b-side, 2-flush against a & b.\n• Color scheme same as above:\n• Light colors: 1 side flush\n• Dark colors: 2 sides flush\n• Circle is centered on (0,0), radius 1.\n\nThis is quite a surprise to me! It seems to be saying that many of the cases that we thought were 2-flush are actually 1-flush. Let me give one example that I worked out by hand as a check.\n\n(1,a,b)=(1,3/4,3/4). Isosceles triangle, with an angle > 83 at apex, larger than our critical hairpin angle of 73 deg. So we thought this was a 2-flush case, well under our cube-root curve, well within the dark green. I compute the 2-flush cost is a+b=3/2=1.50. But I get a competing value of 1.49 for 1-flush against either the a or b edge. (And this case doesn't even involve the new base computation, because the altitude projects inside the triangle.) That cube-root curve we had is the correct transition between 1- and 2-flush, just green vs. light green, but when the others (all six options) are all included (correctly!), 2-flush loses.\n\nSo, there are two questions:\n\n1. Does this new image make sense??\n2. The digital boundary between the 2-flush and the 1-flush regions is almost perfectly fit by a circle. Why???\n\n## Theorem.\n\nNormalize triangle so that the longest edge=1. Let θ be the ab-apex. If θ ≥ 90, the min cost sweep is determined by the parallelogram 2-flush against a and b. If θ ≤ 90, the min cost sweep is determined by the rectangle 1-flush against the shortest side (which must be a or b by the normalization).\n\nProof.\n\n1. 2-flush for obtuse angles. Let b<a. Construct side l=b+x so that x,h,a form a right triangle. Want to show h+l>a+b. Since h+x>a by triangle inequality, we are done.\n2. 1-flush for acute angles. Compare h+a to a+b, b+1, a+1. We have a,b<1 and h<b, so h+a<a+b<a+1<b+1, where a is the shortest side.\n3. I seem to have two proofs of this same thing written down, and I think they both need to be changed to proofs by contradiction, because as they are, they just end in a true conclusion. I'll put them both up though, maybe someone can let me know why they're different and can change them to better proofs:\n1-flush against 1 is worse than 1-flush against the shortest side (a). A=.5bh'<.5ab, since h'<a by the triangle inequality. So h<ab. We have a+b ≤ h+1<ab+1. So a+b<ab+1 and a(1-b)<1-b. Since a<1, we are done.\n1-flush against 1 is worse than 1-flush against the shortest side (a). A=h=h'a. h+1>h'+b, so h'(1-b)<1-b, which is true since h'<1.\n\nWhat are we missing? (Also, my apologies for not adding the diagrams. I can draw them in Illustrator, but I'm not sure how to upload them here.)\n\nI think we were trying to do the two different angle cases (obtuse and acute between shorter sides), but I am confused too looking at my notes.\n\nThe 2nd of your last proofs (1-flush against short side beats 1-flush against 1) seems right to me. h+1>h'+b is what we are trying to show, not something we know already. We start our proof with the fact that we know h'<1 (we have constructed a right triangle with hypotenuse 1 and one of the short sides h'). From there we have h'(1-b)<1-b. Distributing and rearranging: h'+b<1+h'b. From the equation for area we know h=h'b. So substitution gives us: h'+b<1+h, which is what we wanted. I have this labeled as the \"acute\" case.\n\nI am confused on what I have as the \"obtuse\" case in my notes. Using the same method I described above, we seemed to have proved a+b<1+ab. Remind me why we were trying to prove this? What does this show?\n\nSo we have proofs: Obtuse, 2-flush against shorter sides is better than 1-flush against shortest side. Acute, 1-flush against shortest side is better than 2-flush against two shorter sides is better than 2-flush against longest and shortest side is better than 2-flush against longest and mid-length side. And then (also in the acute case), 1-flush against shortest side is better than 1-flush against longest side.\n\nSo it seems that in the acute case we need only show that 1-flush against the shortest side is better than 1-flush against the mid-length side (which seems pretty clear, right?)\n\nIn the obtuse case we still need to show that 2-flush against shorter sides is better than 1-flush against the longest side. I think we did this during our last meeting but I don't understand what I have written. [Just to be thorough, I guess we also should include in our proof that 2-flush against shorter sides is better than 2-flush against the longest and shortest and 2-flush against longest and mid-length (though both of these statements are obvious). But we could make a general note of this at the beginning of our proofs since it does not depend on the acute/obtuse angle.]\n\n## Three Figures\n\nI drew these figures for possible use in the poster... --JOR", null, "Acute Triangle, Six Cases: 1-flush against shortest side b\n\n# Poster Draft\n\nHere is a rough draft of the poster, as a crude image. I put in all the figures we agreed upon, extending the first sweeping figure to show that two sweeps and four sweeps both result in the same cost. The only text with which I was careful was the title, and the proof. I've put all the various pieces in boxes which are 'grouped' in Illustrator, which means they move as a unit. (You can ungroup them by selecting and choosing ungroup someplace [I have all the shortcuts memorized and I no longer remember how to find the options in the menus].) I had to use a .jpg image for our Mathematica plot, because the original was so huge I couldn't save the file. So we may see some rasterization in the final print.\n\nI left the background white, mainly because I couldn't think of a color that would work with everything else. I'm not the greatest judge of colors. :-/ You can make suggestions. Or if you know how to change colors, go ahead (direct selection tool, color dialog box, fill color, etc.).\n\nBut your main task is to add appropriate text, size it appropriately, and arrange all the pieces as you want. The text is all Times New Roman, except θ etc. which use font Symbol. I used italics for the variables. You can add text with the Font tool (T), and then adjust the size and font. You don't have to stick to the pt-size options they give you. There is a general scale tool that I used to make the title. If you can't accomplish something that you want to do, you can describe it to and leave it for me.\n\n[First draft image removed]\n\nBecause I am not absolutely certain which format is best, or which will work in your environment, I am providing three versions. Start with the first, and work your way down:\n\nPlease save the poster in CS3 format, because that's all I have on my workstation. There are options in the Save dialog box to save it in \"legacy\" versions. If you can't figure out how to do it, go ahead and save in CS4, and I'll downconvert myself.\n\n### Second Draft\n\nHere is the revised poster, followed by links to the PDF and the AI format.\n\n### First Draft PowerPoint\n\nPoster contents copied to PowerPoint slides.\n\n# 1-flush vs. 2-flush: Statistics\n\nI ran one trial, generating random polygons up to 10 sides. In 891 instances, 55% of the min perim paras were 1-flush, and 45% 2-flush. However, there were 7% numerically close calls among the 1-flush, which might have been 2-flush. And given that my random polygon generator has a bias toward one long edge, I would say the data is consistent with the hypothesis that the 1-flush/2-flush percentages are 50%-50% on truly random polygons, with exact computation.\n\nA later experiment, for k=10 (decagons), 400 trials, 1-flush=195, 2-flush=205, 49% vs. 51%. So it seems for larger k, the breakdown might approach 50%-50%.\n\nLink added 30Apr: Here are the 50 random quadrilaterals. I couldn't figure out how to copy them out easily, so I left them in a Mathematica Notebook. So you'll have to launch Mathematica to view them.\n\n# Paper Drafts\n\nI updated the paper in four ways [4May10]:\n\n1. I flipped the figures so that a is shortest. I also labeled the little foot x. I can adjust if you want different notation.\n2. I added the hard-case figure (but no explanation).\n3. I added a corollary (Corollary 9) that clarifies something I was thinking about. It is not important, and will likely have to be deleted to reach four pages anyway.\n4. I added the explicit equation of the cubic curve for the hard case.\n\n1. Incorporated Leona's triangles.tex (thanks!).\n2. Explained the (a,b)-graph\n3. Explained the hard case.\n4. Cited Corollary 9 as justifying the cases in the proof.\n\n# Proofs\n\n## For Both Cases\n\nLet a,b,1 be the sides of our triangle such that a<b<1.\n\nObserve that a+b<a+1<b+1.\n\nSo 2-flush against the two shorter sides always beats the other 2-flush cases.\n\n## Acute Case\n\nWe will denote the height of the parallelogram that is flush against side a (which we had previously called h_a) by a'.\n\n• 1-flush against shortest side beats 2-flush cases\n\nBecause we have a right triangle, a'<b. Thus, a+a'<a+b. So 1-flush against a beats 2-flush against a,b and hence beats all 2-flush cases.\n\n• 1-flush against shortest side beats 1-flush against longest side\n\nLet h be the height of the parallelogram flush against the longest side. Because we have a right triangle, a'<1. So, a'(1-a)<1-a a'-a'a<a-a a'+a<1+a'a. From our area equations ½(1)(h)=½(a')(a), so h=a'a. Thus, a'+a<1+h.\n\n• 1-flush against shortest side beats 1-flush against median-length side\n\nDefine b' as the height of the parallelogram flush against side b. We know that a<b, so a(1-(a'/b))<b(1-(a'/b)) a-(aa'/b)<b-(ba'/b) a-(aa'/b)<b-a' a+a'<b+(aa'/b). From our area equations ½aa'=½bb', so aa'=bb' and hence aa'/b=b'. Thus, a+a'<b+b'.\n\nSo 1-flush against the shortest side wins in all cases.\n\n## Obtuse Case\n\nDefine a',b',and h as before.\n\n• 2-flush against shortest sides beats 1-flush against shortest side.\n\nExtend side a by length x so that a perpendicular line of length a' with intersect the b,1 vertex (so we have created a right triangle with sides x,a',b). The cost of sweeping 1-flush against a will be a+x+a'. By the triangle inequality, b<a'+x. Thus, a+b<a+x+a'.\n\n• 2-flush against shortest sides beats 1-flush against median-length side.\n\nExtend side b by length y so that a perpendicular line of length b' with intersect the a,1 vertex (so we have created a right triangle with sides y,b',a). The cost of sweeping 1-flush against b will be b+y+b'. By the triangle inequality, a<b'+y. Thus, a+b<b'+y+b.\n\n• 2-flush against the shortest sides beats 1-flush against the longest side.\n\n[We realized Thursday 29Apr that this proof below is not correct. However, we know it is true simply by plotting the relationships in Mathematica.] Because we have a right triangle, we know that a'<1. Hence, a'(1-(a+x))<1-(a+x) a'-a'(a+x)<1-(a+x) a'+a+x<1+a'(a+x) From our area equations ½(1)(h)=½(a')(a+x), so h=a'(a+x). Thus, a'+a+x<1+h. By the triangle inequality, b<a'+x. So, a+b<a+(a'+x)<1+h. Hence, a+b<1+h.\n\nSince 2-flush against the shortest sides beats both other 2-flush possibilities, we are able to conclude that 2-flush against the shortest sides wins in every case." ]
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https://zbmath.org/authors/?q=ai%3Abegehr.heinrich
[ "# zbMATH — the first resource for mathematics\n\n## Begehr, Heinrich\n\nCompute Distance To:\n Author ID: begehr.heinrich", null, "Published as: Begehr, Heinrich; Begehr, H.; Begehr, Heinrich G. W.; Begehr, H. G. W.; Begehr, Heinrich G. Homepage: http://page.mi.fu-berlin.de/begehrh/ External Links: MGP · Math-Net.Ru · dblp · GND\n Documents Indexed: 217 Publications since 1968, including 32 Books Reviewing Activity: 83 Reviews Biographic References: 6 Publications\nall top 5\n\n#### Co-Authors\n\n 82 single-authored 23 Gilbert, Robert Pertsch 15 Vaitekhovich, Tatyana S. 10 Wen, Guo Chun 9 Çelebi, Ahmet Okay 9 Dai, Daoqing 7 Dzhuraev, Abduhamid 6 Kumar, Ajay 5 Harutyunyan, Gohar V. 5 Hile, Gerald N. 5 Hsiao, George C. 5 Zhang, Zhongxiang 4 Barsegian, Grigor A. 3 Akel, Mohamed S. 3 Aksoy, Ümit 3 Burgumbayeva, Saule 3 Du, Jinyuan 3 Shupeyeva, Bibinur 3 Wong, Man Wah 2 Chen, Xiuqiu 2 Dubinskiĭ, Yuliĭ Andreevich 2 Efendiev, Messoud 2 Jeffrey, Alan P. 2 Kajiwara, Joji 2 Koch, Helmut 2 Li, Xing 2 Lin, Hanxing 2 Lin, Wei 2 Schmersau, Dieter 2 Vu Thi Ngoc Ha 2 Wang, Yufeng 2 Zhao, Zhen 1 Abdel-Rady, A. S. 1 Abdymanapov, S. A. 1 Aigner, Martin 1 Akel, Mohamed S. M. 1 Chaudhary, Arun 1 Chen, Dechang 1 Costache, M.-R. 1 Dauletkulova, Aigul 1 Demidenko, Gennadiĭ Vladimirovich 1 Du, Zhihua 1 Gaertner, Evgenija 1 Ghazaryan, Hayk G. 1 Giri, Debasis 1 Kal’menov, Tynysbek Sharipovich 1 Kramer, Jürg 1 Laine, Ilpo 1 Lenz, Hanfried 1 Liu, Hua 1 Matveeva, Inessa Izotovna 1 Meziani, Abdelhamid 1 Mohammed, Alip 1 Mohapatra, Ram Narayan 1 Muldoon, Martin E. 1 Nakhushev, Adam Maremovich 1 Neressian, A. 1 Nicolosi, Francesco 1 Obaidat, Mohammad S. 1 Obolashvili, Elena Irodionovna 1 Otto, Heinz 1 Schappacher, Norbert 1 Soldatov, Aleksandr Pavlovich 1 Tappert, S. 1 Thiele, Ernst-Jochen 1 Tungatarov, Aliaskar B. 1 Tutschke, Wolfgang 1 Vanegas, Carmen Judith 1 Vanegas, Judith C. 1 Wang, Ning 1 Xu, Zhenyuan 1 Ziegler, Günter Matthias\nall top 5\n\n#### Serials\n\n 18 Complex Variables and Elliptic Equations 10 Complex Variables. Theory and Application 7 Zeitschrift für Analysis und ihre Anwendungen 6 Applicable Analysis 6 Revue Roumaine de Mathématiques Pures et Appliquées 6 Mathematische Nachrichten 6 Journal of Hebei Normal University. Natural Science Edition 4 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 4 Journal of Applied Functional Analysis 3 Acta Mathematica Vietnamica 3 Mathematische Zeitschrift 3 General Mathematics 3 Analysis (München) 3 Eurasian Mathematical Journal 2 Zeitschrift für Angewandte Mathematik und Mechanik (ZAMM) 2 Annali di Matematica Pura ed Applicata. Serie Quarta 2 Archiv der Mathematik 2 Demonstratio Mathematica 2 Journal of Differential Equations 2 Le Matematiche 2 Memoirs on Differential Equations and Mathematical Physics 2 Boletín de la Asociación Matemática Venezolana 2 Nonlinear Analysis. Theory, Methods & Applications 1 Jahresbericht der Deutschen Mathematiker-Vereinigung (DMV) 1 Mathematical Proceedings of the Cambridge Philosophical Society 1 Rocky Mountain Journal of Mathematics 1 Analele Ştiinţifice ale Universităţii Al. I. Cuza din Iaşi. (Serie Nouă.) Secţiunea Ia. Matematică-Informatică 1 Annales Academiae Scientiarum Fennicae. Series A I. Mathematica 1 Colloquium Mathematicum 1 Functiones et Approximatio. Commentarii Mathematici 1 Journal of Computational and Applied Mathematics 1 Journal für die Reine und Angewandte Mathematik 1 Mathematica Pannonica 1 Journal of Elasticity 1 Russian Academy of Sciences. Doklady. Mathematics 1 Georgian Mathematical Journal 1 Integral Transforms and Special Functions 1 Uzbekskiĭ Matematicheskiĭ Zhurnal 1 Acta Mathematica Scientia. Series B. (English Edition) 1 Journal of Analysis and Applications 1 Lecture Notes of TICMI 1 Proceedings of the Steklov Institute of Mathematics 1 NATO Science Series II: Mathematics, Physics and Chemistry 1 Communications in Computer and Information Science 1 Advances in Pure and Applied Mathematics 1 Annales Academiae Scientiarum Fennicae. Series A I\nall top 5\n\n#### Fields\n\n 139 Partial differential equations (35-XX) 121 Functions of a complex variable (30-XX) 57 Potential theory (31-XX) 26 General and overarching topics; collections (00-XX) 20 Several complex variables and analytic spaces (32-XX) 19 History and biography (01-XX) 12 Integral equations (45-XX) 8 Numerical analysis (65-XX) 7 Operator theory (47-XX) 6 Functional analysis (46-XX) 6 Fluid mechanics (76-XX) 5 Ordinary differential equations (34-XX) 5 Mechanics of deformable solids (74-XX) 4 Integral transforms, operational calculus (44-XX) 3 Calculus of variations and optimal control; optimization (49-XX) 2 Biology and other natural sciences (92-XX) 1 Real functions (26-XX) 1 Approximations and expansions (41-XX) 1 Computer science (68-XX)\n\n#### Citations contained in zbMATH Open\n\n120 Publications have been cited 948 times in 396 Documents Cited by Year\nComplex analytic methods for partial differential equations. An introductory text. Zbl 0840.35001\nBegehr, Heinrich G. W.\n1994\nA hierarchy of integral operators. Zbl 0902.30030\nBegehr, Heinrich; Hile, G. N.\n1997\nHarmonic boundary value problems in half disc and half ring. Zbl 1183.30039\nBegehr, Heinrich; Vaitekhovich, Tatyana\n2009\nA Dirichlet problem for polyharmonic functions. Zbl 1223.30016\nBegehr, Heinrich; Du, Jinyuan; Wang, Yufeng\n2008\nIterated Neumann problem for the higher order Poisson equation. Zbl 1091.31001\nBegehr, H.; Vanegas, C. J.\n2006\nThe Schwarz problem for polyanalytic functions. Zbl 1089.30040\nBegehr, H.; Schmersau, D.\n2005\nBoundary value problems in complex analysis. I. Zbl 1260.30021\nBegehr, Heinrich\n2005\nIterated integral operators in Clifford analysis. Zbl 0940.31005\nBegehr, H.\n1999\nBoundary value problems for elliptic equations and systems. Zbl 0711.35038\nWen, Guo Chun; Begehr, Heinrich G. W.\n1990\nBoundary value problems for the inhomogeneous polyanalytic equation. I. Zbl 1077.30034\nBegehr, Heinrich; Kumar, Ajay\n2005\nTransformations, transmutations, and kernel functions. Vol. 1. Zbl 0827.35001\nBegehr, Heinrich; Gilbert, Robert P.\n1992\nIntegral representations in complex, hypercomplex and Clifford analysis. Zbl 1054.30047\nBegehr, Heinrich\n2002\nSchwarz problem in lens and lune. Zbl 1284.35123\nBegehr, H.; Vaitekhovich, T.\n2014\nA Dirichlet problem for the imhomogeneous polyharmonic equation in the upper half plane. Zbl 1141.31001\nBegehr, Heinrich; Gaertner, Evgenija\n2007\nModified harmonic Robin function. Zbl 1272.31003\nBegehr, H.; Vaitekhovich, T.\n2013\nOn continuous solutions of a generalized Cauchy-Riemann system with more than one singularity. Zbl 1109.30033\nBegehr, Heinrich; Dai, Daoqing\n2004\nAn introduction to several complex variables and partial differential equations. Zbl 0894.32002\nBegehr, Heinrich G. W.; Dzhuraev, Abduhamid\n1997\nHarmonic Dirichlet problem for some equilateral triangle. Zbl 1238.31004\nBegehr, H.; Vaitekhovich, T.\n2012\nBoundary value problems in complex analysis. II. Zbl 1116.30032\nBegehr, Heinrich\n2005\nNonlinear elliptic boundary value problems and their applications. Zbl 0931.35001\nBegehr, Heinrich G. W.; Wen, Guo Chun\n1996\nHele-shaw type flows in $${\\mathbb{R}}^ n$$. Zbl 0664.76041\nBegehr, Heinrich; Gilbert, Robert P.\n1986\nSome harmonic Robin functions in the complex plane. Zbl 1195.31004\nBegehr, Heinrich; Vaitekhovich, Tatyana\n2010\nPolyharmonic Dirichlet problems. Zbl 1351.30033\nBegehr, H.; Vu, T. N. H.; Zhang, Z.-X.\n2006\nOn higher order Cauchy-Pompeiu formula in Clifford analysis and its applications. Zbl 1249.35040\nBegehr, Heinrich; Du, Jinyuan; Zhang, Zhongxiang\n2003\nHow to find harmonic Green functions in the plane. Zbl 1246.30070\nBegehr, H.; Vaitekhovich, T.\n2011\nOn Cauchy-Pompeiu formula for functions with values in a universal Clifford algebra. Zbl 1145.30314\nBegehr, Heinrich; Zhang, Zhongxiang; Du, Jinyuan\n2003\nIterations of Pompeiu operators. Zbl 0908.47048\nBegehr, Heinrich\n1997\nNonlinear boundary value problems of Riemann-Hilbert type. Zbl 0501.35070\nBegehr, Heinrich; Hsiao, George C.\n1982\nOrthogonal decompositions of the function space $$L_2(\\bar{D};\\mathbb C)$$. Zbl 0999.30031\nBegehr, H.\n2002\nBiharmonic Green function. Zbl 1135.31001\nBegehr, H.\n2006\nNon-Newtonian Hele-Shaw flows in n$$\\geq 2$$ dimensions. Zbl 0659.35040\nBegehr, Heinrich; Gilbert, Robert P.\n1987\nRandwertaufgaben ganzzahliger Charakteristik für verallgemeinerte hyperanalytische Funktionen. Zbl 0349.35033\nBegehr, Heinrich; Gilbert, Robert P.\n1977\nNonlinear Riemann boundary value problems for a nonlinear elliptic system in the plane. Zbl 0484.35074\nBegehr, Heinrich; Hile, Gerald N.\n1982\nGreen function for a hyperbolic strip and a class of related plane domains. Zbl 1307.31006\nBegehr, H.\n2014\nOn the asymptotics of meromophic solutions for nonlinear Riemann-Hilbert problems. Zbl 0949.35105\nBegehr, H.; Efendiev, M. A.\n1999\nComplex analytic methods for partial differential equations. Zbl 0888.35022\nBegehr, H.\n1996\nGeneralized integral representations in Clifford analysis. Zbl 1109.30039\nBegehr, Heinrich; Zhang, Zhongxiang; Ha, Vu Thi Ngoc\n2006\nBoundary value problems for bi-polyanalytic functions. Zbl 1105.30032\nBegehr, Heinrich; Kumar, Ajay\n2006\nGreen functions, reflections, and plane parqueting. Zbl 1218.31002\nBegehr, Heinrich; Vaitekhovich, Tatyana\n2010\nRepresentation formulas in Clifford analysis. Zbl 1058.30042\nBegehr, H.\n2002\nThe parqueting-reflection principle for constructing Green functions. Zbl 1357.35095\nBegehr, H.; Vaitekhovich, T.\n2014\nThe Hilbert boundary value problem for nonlinear elliptic systems. Zbl 0532.35061\nBegehr, Heinrich; Hsiao, George C.\n1983\nA particular polyharmonic Dirichlet problem. Zbl 1152.31002\nBegehr, H.\n2007\nSix biharmonic Dirichlet problems in complex analysis. Zbl 1157.31002\nBegehr, Heinrich\n2008\nTransformations, transmutations, and kernel functions. Vol. 2. Zbl 0827.35002\nBegehr, Heinrich; Gilbert, Robert P.\n1993\nDirichlet problems for the biharmonic equation. Zbl 1136.31001\nBegehr, Heinrich\n2005\nThe Schwarz problem for analytic functions in torus-related domains. Zbl 1108.32003\nBegehr, Heinrich; Mohammed, Alip\n2006\nPiecewise continuous solutions of pseudoparabolic equations in two space dimensions. Zbl 0395.35047\nBegehr, Heinrich; Gilbert, Robert P.\n1978\nFour boundary value problems for the Cauchy-Riemann equation in a quarter plane. Zbl 1185.30042\nAbdymanapov, S. A.; Begehr, H.; Harutyunyan, G.; Tungatarov, A. B.\n2009\nOn Riemann boundary value problems for cerrtain linear elliptic systems in the plane. Zbl 0424.35041\nBegehr, Heinrich; Gilbert, Robert P.\n1979\nA mixed-contact boundary problem in orthotropic elasticity. Zbl 0819.35038\nBegehr, H.; Lin, W.\n1992\nOn the Riemann-Hilbert-Poincaré problem for analytic functions. Zbl 1058.30030\nBegehr, Heinrich; Dai, Dao-Qing\n2002\nIntegral representation formulas in polydomains. Zbl 1035.32003\nBegehr, H.; Dai, D. -Q.; Li, X.\n2002\nRobin boundary value problem for the Cauchy-Riemann operator. Zbl 1082.30029\nBegehr, H.; Harutjunjan, G.\n2005\nRobin boundary value problem for the Poisson equation. Zbl 1110.31002\nBegehr, H.; Harutjunjan, G.\n2006\nBi-polyanalytic functions on the upper half plane. Zbl 1188.30057\nBegehr, Heinrich; Chaudhary, Arun; Kumar, Ajay\n2010\nIterated Dirichlet problem for the higher order Poisson equation. Zbl 1193.31002\nBegehr, H.; Vaitekhovich, T.\n2008\nSome boundary value problems for a Beltrami equation. Zbl 0853.30029\nBegehr, H.; Obolashvili, Elena\n1994\nBoundary value problems for the inhomogeneous polyanalytic equation. II. Zbl 1137.30010\nBegehr, Heinrich; Kumar, Ajay\n2007\nComplex boundary value problems in a quarter plane. Zbl 1114.30042\nBegehr, H.; Harutyunyan, G.\n2006\nRiemann boundary value problems for nonlinear elliptic systems. Zbl 0522.35075\nBegehr, Heinrich; Hile, Gerald N.\n1983\nNeumann problem for the Beltrami operator and for second order operators with Poisson/Bitsadze operator as main part. Zbl 1189.30077\nBegehr, Heinrich; Harutyunyan, Gohar\n2009\nDirichlet problems for inhomogeneous complex mixed partial differential equations of higher order in the unit disc: new view. Zbl 1213.30083\nBegehr, H.; Du, Zhihua; Wang, Ning\n2010\nGreen functions, reflections, and plane parqueting revisited. (Letter to the editors). Zbl 1250.31002\nBegehr, Heinrich; Vaitekhovich, Tatyana\n2011\nPseudohyperanalytic functions. Zbl 0652.30030\nBegehr, Heinrich; Gilbert, Robert P.\n1988\nRiemann-Hilbert boundary value problems in $$\\mathbb{C}^N$$. Zbl 0923.35116\nBegehr, Heinrich\n1999\nSome orthogonal decompositions of Sobolev spaces and applications. Zbl 0988.46023\nBegehr, H.; Dubinskiĭ, Yu.\n2001\nSpatial Riemann problem for analytic functions of two complex variables. Zbl 0944.30025\nBegehr, H.; Dai, D. Q.\n1999\nBoundary value problems associated with first order elliptic systems in the plane. Zbl 0493.35045\nBegehr, H.; Gilbert, R. P.\n1982\nHigher order Cauchy Pompeiu operators. Zbl 0916.35030\nBegehr, Heinrich; Hile, Gerald N.\n1998\nThe two-dimensional nonlinear orthotropic plate. Zbl 0764.73041\nBegehr, H.; Gilbert, R. P.; Lo, C. Y.\n1991\nOrthogonal decompositions of Sobolev spaces in Clifford analysis. Zbl 1102.30049\nDubinskii, Ju.; Begehr, H.\n2002\nZur Nullpunktabhängigkeit der Nevanlinnaschen Defekte. Zbl 0159.36902\nBegehr, H.\n1968\nÜber Defektbegriffe in der Theorie der meromorphen Funktionen. Zbl 0198.11002\nBegehr, H.\n1970\nRemark on Robin problem for Poisson equation. Zbl 1379.31005\nBegehr, Heinrich; Burgumbayeva, Saule; Shupeyeva, Bibinur\n2017\nEine Bemerkung zum nichtlinearen klassischen Satz von Cauchy-Kowalewski. (A remark on the nonlinear classical Cauchy-Kowalewski theorem). Zbl 0638.35004\nBegehr, Heinrich\n1987\nOn higher order Bessel potentials. Zbl 1059.31004\n2004\nÜber das Randwert-Normproblem für ein nichtlineares elliptisches System. Zbl 0346.35021\nBegehr, Heinrich; Gilbert, Robert P.\n1976\nApproximate solution of periodic Riemann boundary value problem for analytic functions. Zbl 0987.65026\nBegehr, Heinrich; Li, Xing\n2001\nZur Wertverteilung approximativ analytischer Funktionen. Zbl 0238.30029\nBegehr, Heinrich\n1972\nOn nonlinear boundary value problems for an elliptic system in the plane. Zbl 0474.35050\nBegehr, Heinrich; Hsiao, George C.\n1981\nOn asymptotics of solutions to the hypergeometric equation. Zbl 1070.34011\nBegehr, H.; Usmanov, Z. D.\n2004\nNonlinear boundary value problems for a class of elliptic systems. Zbl 0523.35086\nBegehr, Heinrich; Hsiao, George C.\n1980\nSchauder estimates and existence theory for entire solutions of linear elliptic equations. Zbl 0674.35019\nBegehr, Heinrich; Hile, G. N.\n1988\nOn nonlinear Riemann-Hilbert boundary value problems for second order elliptic systems in the plane. Zbl 0882.30028\nAkal, M.; Begehr, H.\n1996\nOn the Pompeiu operator of higher order and applications. Zbl 0882.30029\nAkal, M.; Begehr, H.\n1997\nInitial boundary value problem for nonlinear pseudoparabolic equations. Zbl 0814.35064\nBegehr, H.; Dai, D. Q.\n1992\nEine Bemerkung zum Maximumprinzip für morphe Funktionen mehrerer komplexer Veränderlichen. Zbl 0334.32007\nBegehr, Heinrich\n1975\nDifferential operators, their fundamental solutions and related integral representations in Clifford analysis. Zbl 1184.30042\nBegehr, H.; Otto, Heinz; Zhang, Zhong-Xiang\n2006\nComplex partial differential equations in a manner of I. N. Vekua. Zbl 1189.31003\nBegehr, H.; Vaitekhovich, T.\n2007\nCombined integral representations. Zbl 1093.30036\nBegehr, Heinrich\n2005\nGreen functions in complex plane domains. Zbl 1189.31002\nBegehr, Heinrich; Vaitekhovich, Tatyana\n2008\nPolyharmonic Green functions for particular plane domains. Zbl 1212.31008\nBegehr, Heinrich; Vaitekhovich, Tatyana\n2009\nRemark on Hilbert’s boundary value problem for Beltrami systems. Zbl 0562.35071\nBegehr, Heinrich\n1984\nMathematics in Berlin. Zbl 0997.00008\nBegehr, H. G. W. (ed.); Koch, Helmut (ed.); Kramer, Jürg (ed.); Schappacher, N. (ed.); Thiele, E.-J. (ed.)\n1998\nOverdeterminded systems of second order elliptic equations in several complex variables. Zbl 0916.35074\nBegehr, H.; Dzhuraev, A.\n1998\nSystems of first order partial differential equations – a hypercomplex approach. Zbl 0920.35038\nBegehr, Heinrich\n1999\nOblique derivative problems for elliptic systems of second order equations in infinite domains. Zbl 0939.35057\nBegehr, H.; Wen, G. C.\n1999\nBi-analytic functions of several variables. Zbl 0794.32005\nBegehr, Heinrich; Kumar, Ajay\n1994\nIteration of the Pompeiu integral operator and complex higher order equations. Zbl 0999.30025\nBegehr, Heinrich\n1999\nA. V. Bitsadze’s observation on bianalytic functions and the Schwarz problem. Zbl 1423.30027\nAksoy, Ümit; Begehr, Heinrich; Çelebi, A. Okay\n2019\nSchwarz problem for higher-order complex partial differential equations in the upper half plane. Zbl 1422.30060\nAksoy, Ümit; Begehr, Heinrich; Çelebi, A. Okay\n2019\nRemark on Robin problem for Poisson equation. Zbl 1379.31005\nBegehr, Heinrich; Burgumbayeva, Saule; Shupeyeva, Bibinur\n2017\nNeumann function for a hyperbolic strip and a class of related plane domains. Zbl 1366.31002\nAkel, M.; Begehr, H.\n2017\nThe parqueting-reflection principle. Zbl 1331.30028\nBegehr, Heinrich\n2015\nIntegral representations related to complex partial differential operators. Zbl 1323.31005\nBegehr, Heinrich\n2015\nSchwarz problem in lens and lune. Zbl 1284.35123\nBegehr, H.; Vaitekhovich, T.\n2014\nGreen function for a hyperbolic strip and a class of related plane domains. Zbl 1307.31006\nBegehr, H.\n2014\nThe parqueting-reflection principle for constructing Green functions. Zbl 1357.35095\nBegehr, H.; Vaitekhovich, T.\n2014\nModified harmonic Robin function. Zbl 1272.31003\nBegehr, H.; Vaitekhovich, T.\n2013\nHarmonic Dirichlet problem for some equilateral triangle. Zbl 1238.31004\nBegehr, H.; Vaitekhovich, T.\n2012\nHow to find harmonic Green functions in the plane. Zbl 1246.30070\nBegehr, H.; Vaitekhovich, T.\n2011\nGreen functions, reflections, and plane parqueting revisited. (Letter to the editors). Zbl 1250.31002\nBegehr, Heinrich; Vaitekhovich, Tatyana\n2011\nIterated polyharmonic Green functions for plane domains. Zbl 1233.31002\nBegehr, Heinrich\n2011\nSome harmonic Robin functions in the complex plane. Zbl 1195.31004\nBegehr, Heinrich; Vaitekhovich, Tatyana\n2010\nGreen functions, reflections, and plane parqueting. Zbl 1218.31002\nBegehr, Heinrich; Vaitekhovich, Tatyana\n2010\nBi-polyanalytic functions on the upper half plane. Zbl 1188.30057\nBegehr, Heinrich; Chaudhary, Arun; Kumar, Ajay\n2010\nDirichlet problems for inhomogeneous complex mixed partial differential equations of higher order in the unit disc: new view. Zbl 1213.30083\nBegehr, H.; Du, Zhihua; Wang, Ning\n2010\nHarmonic Green and Neumann representations in a triangle, quarter-disc and octo-plane. Zbl 1266.31003\nBegehr, H.; Costache, M.-R.; Tappert, S.; Vaitekhovic, T.\n2010\nHarmonic boundary value problems in half disc and half ring. Zbl 1183.30039\nBegehr, Heinrich; Vaitekhovich, Tatyana\n2009\nFour boundary value problems for the Cauchy-Riemann equation in a quarter plane. Zbl 1185.30042\nAbdymanapov, S. A.; Begehr, H.; Harutyunyan, G.; Tungatarov, A. B.\n2009\nNeumann problem for the Beltrami operator and for second order operators with Poisson/Bitsadze operator as main part. Zbl 1189.30077\nBegehr, Heinrich; Harutyunyan, Gohar\n2009\nPolyharmonic Green functions for particular plane domains. Zbl 1212.31008\nBegehr, Heinrich; Vaitekhovich, Tatyana\n2009\nA Dirichlet problem for polyharmonic functions. Zbl 1223.30016\nBegehr, Heinrich; Du, Jinyuan; Wang, Yufeng\n2008\nSix biharmonic Dirichlet problems in complex analysis. Zbl 1157.31002\nBegehr, Heinrich\n2008\nIterated Dirichlet problem for the higher order Poisson equation. Zbl 1193.31002\nBegehr, H.; Vaitekhovich, T.\n2008\nGreen functions in complex plane domains. Zbl 1189.31002\nBegehr, Heinrich; Vaitekhovich, Tatyana\n2008\nA Dirichlet problem for the imhomogeneous polyharmonic equation in the upper half plane. Zbl 1141.31001\nBegehr, Heinrich; Gaertner, Evgenija\n2007\nA particular polyharmonic Dirichlet problem. Zbl 1152.31002\nBegehr, H.\n2007\nBoundary value problems for the inhomogeneous polyanalytic equation. II. Zbl 1137.30010\nBegehr, Heinrich; Kumar, Ajay\n2007\nComplex partial differential equations in a manner of I. N. Vekua. Zbl 1189.31003\nBegehr, H.; Vaitekhovich, T.\n2007\nIterated Neumann problem for the higher order Poisson equation. Zbl 1091.31001\nBegehr, H.; Vanegas, C. J.\n2006\nPolyharmonic Dirichlet problems. Zbl 1351.30033\nBegehr, H.; Vu, T. N. H.; Zhang, Z.-X.\n2006\nBiharmonic Green function. Zbl 1135.31001\nBegehr, H.\n2006\nGeneralized integral representations in Clifford analysis. Zbl 1109.30039\nBegehr, Heinrich; Zhang, Zhongxiang; Ha, Vu Thi Ngoc\n2006\nBoundary value problems for bi-polyanalytic functions. Zbl 1105.30032\nBegehr, Heinrich; Kumar, Ajay\n2006\nThe Schwarz problem for analytic functions in torus-related domains. Zbl 1108.32003\nBegehr, Heinrich; Mohammed, Alip\n2006\nRobin boundary value problem for the Poisson equation. Zbl 1110.31002\nBegehr, H.; Harutjunjan, G.\n2006\nComplex boundary value problems in a quarter plane. Zbl 1114.30042\nBegehr, H.; Harutyunyan, G.\n2006\nDifferential operators, their fundamental solutions and related integral representations in Clifford analysis. Zbl 1184.30042\nBegehr, H.; Otto, Heinz; Zhang, Zhong-Xiang\n2006\nThe Schwarz problem for polyanalytic functions. Zbl 1089.30040\nBegehr, H.; Schmersau, D.\n2005\nBoundary value problems in complex analysis. I. Zbl 1260.30021\nBegehr, Heinrich\n2005\nBoundary value problems for the inhomogeneous polyanalytic equation. I. Zbl 1077.30034\nBegehr, Heinrich; Kumar, Ajay\n2005\nBoundary value problems in complex analysis. II. Zbl 1116.30032\nBegehr, Heinrich\n2005\nDirichlet problems for the biharmonic equation. Zbl 1136.31001\nBegehr, Heinrich\n2005\nRobin boundary value problem for the Cauchy-Riemann operator. Zbl 1082.30029\nBegehr, H.; Harutjunjan, G.\n2005\nCombined integral representations. Zbl 1093.30036\nBegehr, Heinrich\n2005\nMixed complex boundary value problems in complex analysis. Zbl 1129.30317\nBegehr, Heinrich; Kumar, Ajay; Schmersau, Dieter; Vanegas, Judith C.\n2005\nOn continuous solutions of a generalized Cauchy-Riemann system with more than one singularity. Zbl 1109.30033\nBegehr, Heinrich; Dai, Daoqing\n2004\nOn higher order Bessel potentials. Zbl 1059.31004\n2004\nOn asymptotics of solutions to the hypergeometric equation. Zbl 1070.34011\nBegehr, H.; Usmanov, Z. D.\n2004\nSome boundary value problems for bi-bianalytic functions. Zbl 1063.30035\nBegehr, Heinrich\n2004\nOn higher order Cauchy-Pompeiu formula in Clifford analysis and its applications. Zbl 1249.35040\nBegehr, Heinrich; Du, Jinyuan; Zhang, Zhongxiang\n2003\nOn Cauchy-Pompeiu formula for functions with values in a universal Clifford algebra. Zbl 1145.30314\nBegehr, Heinrich; Zhang, Zhongxiang; Du, Jinyuan\n2003\nIntegral representations in complex, hypercomplex and Clifford analysis. Zbl 1054.30047\nBegehr, Heinrich\n2002\nOrthogonal decompositions of the function space $$L_2(\\bar{D};\\mathbb C)$$. Zbl 0999.30031\nBegehr, H.\n2002\nRepresentation formulas in Clifford analysis. Zbl 1058.30042\nBegehr, H.\n2002\nOn the Riemann-Hilbert-Poincaré problem for analytic functions. Zbl 1058.30030\nBegehr, Heinrich; Dai, Dao-Qing\n2002\nIntegral representation formulas in polydomains. Zbl 1035.32003\nBegehr, H.; Dai, D. -Q.; Li, X.\n2002\nOrthogonal decompositions of Sobolev spaces in Clifford analysis. Zbl 1102.30049\nDubinskii, Ju.; Begehr, H.\n2002\nRepresentations in polydomains. Zbl 1046.35080\nBegehr, H.\n2002\nSome orthogonal decompositions of Sobolev spaces and applications. Zbl 0988.46023\nBegehr, H.; Dubinskiĭ, Yu.\n2001\nApproximate solution of periodic Riemann boundary value problem for analytic functions. Zbl 0987.65026\nBegehr, Heinrich; Li, Xing\n2001\nIterated integral operators in Clifford analysis. Zbl 0940.31005\nBegehr, H.\n1999\nOn the asymptotics of meromophic solutions for nonlinear Riemann-Hilbert problems. Zbl 0949.35105\nBegehr, H.; Efendiev, M. A.\n1999\nRiemann-Hilbert boundary value problems in $$\\mathbb{C}^N$$. Zbl 0923.35116\nBegehr, Heinrich\n1999\nSpatial Riemann problem for analytic functions of two complex variables. Zbl 0944.30025\nBegehr, H.; Dai, D. Q.\n1999\nSystems of first order partial differential equations – a hypercomplex approach. Zbl 0920.35038\nBegehr, Heinrich\n1999\nOblique derivative problems for elliptic systems of second order equations in infinite domains. Zbl 0939.35057\nBegehr, H.; Wen, G. C.\n1999\nIteration of the Pompeiu integral operator and complex higher order equations. Zbl 0999.30025\nBegehr, Heinrich\n1999\nHigher order Cauchy Pompeiu operators. Zbl 0916.35030\nBegehr, Heinrich; Hile, Gerald N.\n1998\nMathematics in Berlin. Zbl 0997.00008\nBegehr, H. G. W.; Koch, Helmut; Kramer, Jürg; Schappacher, N.; Thiele, E.-J.\n1998\nOverdeterminded systems of second order elliptic equations in several complex variables. Zbl 0916.35074\nBegehr, H.; Dzhuraev, A.\n1998\nA hierarchy of integral operators. Zbl 0902.30030\nBegehr, Heinrich; Hile, G. N.\n1997\nAn introduction to several complex variables and partial differential equations. Zbl 0894.32002\nBegehr, Heinrich G. W.; Dzhuraev, Abduhamid\n1997\nIterations of Pompeiu operators. Zbl 0908.47048\nBegehr, Heinrich\n1997\nOn the Pompeiu operator of higher order and applications. Zbl 0882.30029\nAkal, M.; Begehr, H.\n1997\nBoundary value problems in $$\\mathbb{C}$$ and $$\\mathbb{C}^n$$. Zbl 0911.32007\nBegehr, Heinrich\n1997\nNonlinear elliptic boundary value problems and their applications. Zbl 0931.35001\nBegehr, Heinrich G. W.; Wen, Guo Chun\n1996\nComplex analytic methods for partial differential equations. Zbl 0888.35022\nBegehr, H.\n1996\nOn nonlinear Riemann-Hilbert boundary value problems for second order elliptic systems in the plane. Zbl 0882.30028\nAkal, M.; Begehr, H.\n1996\nComplex analytic methods for partial differential equations. An introductory text. Zbl 0840.35001\nBegehr, Heinrich G. W.\n1994\nSome boundary value problems for a Beltrami equation. Zbl 0853.30029\nBegehr, H.; Obolashvili, Elena\n1994\nBi-analytic functions of several variables. Zbl 0794.32005\nBegehr, Heinrich; Kumar, Ajay\n1994\nOn a boundary value problem for a first order holomorphic system in $$\\mathbb{C}^ 2$$. Zbl 0874.35024\nDzhuraev, A.; Begehr, H.\n1994\nTransformations, transmutations, and kernel functions. Vol. 2. Zbl 0827.35002\nBegehr, Heinrich; Gilbert, Robert P.\n1993\nTransformations, transmutations, and kernel functions. Vol. 1. Zbl 0827.35001\nBegehr, Heinrich; Gilbert, Robert P.\n1992\nA mixed-contact boundary problem in orthotropic elasticity. Zbl 0819.35038\nBegehr, H.; Lin, W.\n1992\nInitial boundary value problem for nonlinear pseudoparabolic equations. Zbl 0814.35064\nBegehr, H.; Dai, D. Q.\n1992\nNonlinear half-Dirichlet problems for first order elliptic equations in the unit ball of $$\\mathbb{R}^ m$$ $$(m{\\geq{}}3)$$. Zbl 0776.35020\nBegehr, H.; Xu, Zhenyuan\n1992\nPartial differential equations with complex analysis. Dedicated to Robert Pertsch Gilbert on the occasion of his 60th birthday. Zbl 0771.00048\nBegehr, H.; Jeffrey, A.\n1992\nThe two-dimensional nonlinear orthotropic plate. Zbl 0764.73041\nBegehr, H.; Gilbert, R. P.; Lo, C. Y.\n1991\nBoundary value problems for elliptic equations and systems. Zbl 0711.35038\nWen, Guo Chun; Begehr, Heinrich G. W.\n1990\nA priori estimate for the discontinuous oblique derivative problem for elliptic systems. Zbl 0701.35029\nBegehr, Heinrich; Wen, Guochun\n1989\nPseudohyperanalytic functions. Zbl 0652.30030\nBegehr, Heinrich; Gilbert, Robert P.\n1988\nSchauder estimates and existence theory for entire solutions of linear elliptic equations. Zbl 0674.35019\nBegehr, Heinrich; Hile, G. N.\n1988\nThe discontinuous oblique derivative problem for nonlinear elliptic systems of first order. Zbl 0682.35033\nBegehr, H.; Wen, G. C.\n1988\nNon-Newtonian Hele-Shaw flows in n$$\\geq 2$$ dimensions. Zbl 0659.35040\nBegehr, Heinrich; Gilbert, Robert P.\n1987\nEine Bemerkung zum nichtlinearen klassischen Satz von Cauchy-Kowalewski. (A remark on the nonlinear classical Cauchy-Kowalewski theorem). Zbl 0638.35004\nBegehr, Heinrich\n1987\nA priori estimates for elliptic systems. Zbl 0647.35069\nBegehr, H.; Hsiao, G. C.\n1987\n...and 20 more Documents\nall top 5\n\n#### Cited by 353 Authors\n\n 42 Begehr, Heinrich 18 Abreu-Blaya, Ricardo 18 Bory Reyes, Juan 14 Du, Jinyuan 14 Ku, Min 12 Wang, Yufeng 12 Zhang, Zhongxiang 11 Kumar, Ajay 10 Çelebi, Ahmet Okay 10 Gilbert, Robert Pertsch 10 Kähler, Uwe 9 Wang, Ying 8 Aksoy, Ümit 8 He, Fuli 8 Kravchenko, Vladislav V. 7 Akel, Mohamed S. 7 Dai, Daoqing 7 Karachik, Valeriĭ Valentinovich 7 Rasulov, Abdurauf Babadzhanovich 6 De la Cruz-Toranzo, Lianet 6 Du, Zhihua 6 Meziani, Abdelhamid 6 Mohammed, Alip 6 Vaitekhovich, Tatyana S. 5 Černe, Miran 5 Kohr, Mirela 5 Turmetov, Batirkhan Khudaybergenovich 5 Wendland, Wolfgang L. 4 Hizliyel, Sezayi 4 Jost, Jürgen 4 Lanza de Cristoforis, Massimo 4 Moreno García, Arsenio 4 Moreno García, Tania 4 Qian, Tao 4 Reissig, Michael 4 Torba, Sergii M. 4 Vilaire, Jean-Marie 4 Wang, Jinxun 4 Wen, Guo Chun 3 Alabbad, Fatimah 3 Campañá, Carlos 3 Cerejeiras, Paula 3 Chen, Shaolin 3 Dattori da Silva, Paulo L. 3 Fedorov, Yury Sergeevich 3 Gürlebeck, Klaus 3 Herrera, Ismael 3 Hile, Gerald N. 3 Kal’menov, Tynysbek Sharipovich 3 Koca, Kerim 3 Li, Mingzhong 3 Lin, Wei 3 Mishra, Mukund Madhav 3 Mshimba, Ali Seif A. 3 Prakash, Ravi 3 Shupeyeva, Bibinur 3 Sitnik, Sergei Mihailovich 3 Soldatov, Aleksandr Pavlovich 3 Sommen, Franciscus 3 Taghizadeh, Nasir 3 Torebek, Berikbol Tillabayuly 3 Tutschke, Wolfgang 3 Vanegas, Carmen Judith 3 Vu Thi Ngoc Ha 3 Wang, Yanjin 3 Zhu, Miaomiao 2 Akbari, Mozhgan 2 Altun, Ishak 2 Ariza, Eusebio 2 Babayan, Armenak O. 2 Bernstein, Swanhild 2 Bobodzhanova, Mashkura Abdukhafizovna 2 Borovikov, I. A. 2 Çağliyan, Mehmet 2 Chaudhary, Arun 2 Chen, Qun 2 Chkadua, George 2 Di Teodoro, Antonio Nicola 2 Ding, Chao 2 Dubey, Shivani 2 Dubinskiĭ, Yuliĭ Andreevich 2 Flores, Manuel T. 2 Fu, Yingxiong 2 Goldschmidt, Bernd 2 Groşan, Teodor S. 2 Guo, Guoan 2 Gutlyanskiĭ, Vladimir Ya. 2 Han, Pengju 2 Hayrapetyan, Hrachik Mergo 2 Hsiao, George C. 2 Infante, Adrián 2 Joveini, Fatemeh 2 Koshanov, Bakytbek Danebekovich 2 Li, Peijin 2 Li, Wei 2 Li, Xing 2 Lin, Hanxing 2 Liu, Hua 2 Mohammadi, V. Soltani 2 Mohapatra, Manas Ranjan ...and 253 more Authors\nall top 5\n\n#### Cited in 115 Serials\n\n 71 Complex Variables and Elliptic Equations 26 Journal of Mathematical Analysis and Applications 20 Applicable Analysis 20 Advances in Applied Clifford Algebras 12 Journal of Mathematical Sciences (New York) 11 Mathematische Nachrichten 11 Zeitschrift für Analysis und ihre Anwendungen 9 Mathematical Methods in the Applied Sciences 9 Complex Analysis and Operator Theory 8 Nonlinear Analysis. Theory, Methods & Applications 7 Applied Mathematics and Computation 7 Journal of Differential Equations 6 Mathematische Zeitschrift 6 Acta Mathematica Sinica. English Series 5 Journal of Contemporary Mathematical Analysis. Armenian Academy of Sciences 5 Differential Equations 4 Transactions of the American Mathematical Society 4 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 4 Integral Transforms and Special Functions 4 Advances in Pure and Applied Mathematics 4 Eurasian Mathematical Journal 3 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 3 Proceedings of the American Mathematical Society 3 Acta Mathematicae Applicatae Sinica. English Series 3 Numerical Methods for Partial Differential Equations 3 Science in China. Series A 3 European Journal of Applied Mathematics 3 Computational Mathematics and Mathematical Physics 3 Wuhan University Journal of Natural Sciences (WUJNS) 3 Analysis (München) 3 Mediterranean Journal of Mathematics 3 Boundary Value Problems 2 Journal of Mathematical Physics 2 Mathematical Notes 2 Integral Equations and Operator Theory 2 Journal of Computational and Applied Mathematics 2 Mathematische Annalen 2 Memoirs of the American Mathematical Society 2 Results in Mathematics 2 The Journal of Geometric Analysis 2 SIAM Journal on Scientific Computing 2 Georgian Mathematical Journal 2 Doklady Mathematics 2 Journal of Shanghai University 2 Computational Methods and Function Theory 2 Proceedings of the Steklov Institute of Mathematics 2 Analysis and Mathematical Physics 1 Archive for Rational Mechanics and Analysis 1 Bulletin of the Australian Mathematical Society 1 Computers & Mathematics with Applications 1 Communications in Mathematical Physics 1 Journal d’Analyse Mathématique 1 Journal of Engineering Mathematics 1 Rocky Mountain Journal of Mathematics 1 Ukrainian Mathematical Journal 1 ZAMP. Zeitschrift für angewandte Mathematik und Physik 1 Journal of Geometry and Physics 1 The Mathematical Intelligencer 1 Advances in Mathematics 1 Annali di Matematica Pura ed Applicata. Serie Quarta 1 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie IV 1 Archiv der Mathematik 1 Functional Analysis and its Applications 1 International Journal of Mathematics and Mathematical Sciences 1 Journal of Approximation Theory 1 Journal für die Reine und Angewandte Mathematik 1 Journal of Soviet Mathematics 1 Meccanica 1 Michigan Mathematical Journal 1 Monatshefte für Mathematik 1 Nagoya Mathematical Journal 1 Quaestiones Mathematicae 1 Quarterly of Applied Mathematics 1 Siberian Mathematical Journal 1 Applied Mathematics and Mechanics. (English Edition) 1 Chinese Annals of Mathematics. Series B 1 Acta Applicandae Mathematicae 1 Mathematical and Computer Modelling 1 Japan Journal of Industrial and Applied Mathematics 1 Numerical Algorithms 1 Journal of Elasticity 1 Mathematical Programming. Series A. Series B 1 Potential Analysis 1 The Journal of Analysis 1 Applied Mathematics. Series B (English Edition) 1 Calculus of Variations and Partial Differential Equations 1 St. Petersburg Mathematical Journal 1 Turkish Journal of Mathematics 1 Bulletin des Sciences Mathématiques 1 Engineering Analysis with Boundary Elements 1 Boletín de la Sociedad Matemática Mexicana. Third Series 1 Matematychni Metody ta Fizyko-Mekhanichni Polya 1 Mathematical Problems in Engineering 1 Annales Academiae Scientiarum Fennicae. Mathematica 1 Journal of Inequalities and Applications 1 Revista Matemática Complutense 1 Matematicheskie Trudy 1 Journal of Mathematical Fluid Mechanics 1 Journal of the European Mathematical Society (JEMS) 1 Lobachevskii Journal of Mathematics ...and 15 more Serials\nall top 5\n\n#### Cited in 36 Fields\n\n 225 Functions of a complex variable (30-XX) 200 Partial differential equations (35-XX) 83 Potential theory (31-XX) 33 Integral equations (45-XX) 24 Fluid mechanics (76-XX) 23 Numerical analysis (65-XX) 20 Several complex variables and analytic spaces (32-XX) 18 Operator theory (47-XX) 15 Functional analysis (46-XX) 9 Ordinary differential equations (34-XX) 9 Mechanics of deformable solids (74-XX) 8 Harmonic analysis on Euclidean spaces (42-XX) 8 Global analysis, analysis on manifolds (58-XX) 7 Linear and multilinear algebra; matrix theory (15-XX) 7 Differential geometry (53-XX) 5 Integral transforms, operational calculus (44-XX) 4 Special functions (33-XX) 4 Quantum theory (81-XX) 3 History and biography (01-XX) 3 Topological groups, Lie groups (22-XX) 3 Approximations and expansions (41-XX) 3 Calculus of variations and optimal control; optimization (49-XX) 3 Classical thermodynamics, heat transfer (80-XX) 3 Systems theory; control (93-XX) 2 Algebraic geometry (14-XX) 2 Measure and integration (28-XX) 2 Dynamical systems and ergodic theory (37-XX) 2 Optics, electromagnetic theory (78-XX) 2 Relativity and gravitational theory (83-XX) 1 Number theory (11-XX) 1 Nonassociative rings and algebras (17-XX) 1 Convex and discrete geometry (52-XX) 1 Algebraic topology (55-XX) 1 Probability theory and stochastic processes (60-XX) 1 Mechanics of particles and systems (70-XX) 1 Operations research, mathematical programming (90-XX)" ]
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http://travelquaz.com/best-country-to-visit-in-september.html
[ "# Best country to visit in september\n\nOptimal control theory. A set of mathematical techniques and theorems concerned with finding optimal time-paths of particular systems. The state of the system at any point in time is completely described by the\n\nOptimal growth theory numerical values of a set of variables called state variables. The values of these variables, and so the state of the system, change over time according to some dynamic relationships which must be specified mathematically. There is a second set of variables, called the control variables, whose values at each point in time are to be chosen by the decision-taker and which then determine the time-paths of the state variables. The decision-taker will have a preference ordering over alternative time-paths of the system, and this must also be specified mathematically. Optimal control theory then studies the problem of choosing those time-paths of the control variables out of the set of paths which are feasible, which leads to the preferred time-path of the entire system.\n\nBest country to visit in september Travel" ]
[ null ]
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https://plainenglish.io/blog/analysing-powerball-numbers-with-python-84ebcb56065d
[ "", null, "# How to Analyse PowerBall Numbers with Python\n\n## Pandas can't Predict the Future. Can You?", null, "Anyone playing the lottery can be carried away with fantasies about unspeakable riches and ways of spending it unspeakably fast. From a data point of view, looking into the numbers can be a fun project to practice some of the tools you have under your belt, and can actually lead to interesting experiments.\n\nCan you predict lottery numbers? Assuming the drawings are indeed random the answer is no. Can you expect certain numbers to pop up in the future? Well, not really.\n\nGiven a large enough sample size — according to the law of large numbers — all you can expect is that the average value of the numbers drawn is going to be very close to the expected value.\n\nLooking into what happened in the past could be still fun — if you want to choose your next winning combination, well, go ahead, build a hypothesis and find your favourites.\n\nLet's play with historic PowerBall numbers!\n\n### The base data\n\nWe have a rather simple CSV file with the date and numbers drawn:", null, "The first four columns are the game name and date values (M/D/Y), the next five are the “white balls” drawn, the next is the “PowerBall”, the last is the PowerPlay value. I've used the ‘names' parameter of the read_csv method to keep the column name house in order.", null, "I would like to focus on the “white ball” numbers — this is just a decision out of convenience, the point here is to show a way to look into the data, not a comprehensive statistical analysis.\n\nNote that since the rules of the game have changed since 2015 (the number of possible white numbers drawn have increased), I am focusing on the period after the change to avoid distortion in frequency comparison.\n\n``````# Create a DateTime Series based on the Y/M/D columns\npowerball_df[\"Date\"] = pd.to_datetime(powerball_df[[\"Year\", \"Month\", \"Day\"]])\n\n# Put the \"white ball\" numbers drawn into one list\npowerball_df[\"Nums\"] = powerball_df[[\"Num1\", \"Num2\", \"Num3\", \"Num4\", \"Num5\"]].values.tolist()\n\n# Sort the numbers (for reading convenience, the order of draw has no on the prize)\npowerball_df[\"Sorted_Nums\"] = powerball_df[\"Nums\"].apply(lambda x: sorted(x))\n\n# Create 3 number combinations out of the 5 numbers drawn\npowerball_df[\"3_Num_Combos\"] = powerball_df[\"Sorted_Nums\"].apply(lambda x: [str(list(i)) for i in combinations(x, 3)])\n\nfiltered_powerball_df = powerball_df[[\"Date\", \"Num1\", \"Num2\", \"Num3\", \"Num4\", \"Num5\", \"Sorted_Nums\", \"3_Num_Combos\"]]\n\nfiltered_powerball_df = filtered_powerball_df[filtered_powerball_df[\"Date\"] > \"2015-10-07\"]\n``````", null, "I have inserted a column where all possible 3 number combinations of a single day array are listed.\n\nI want to look into the distribution of combinations as well, not just single numbers, and since 3 is the lowest number of matching white balls where you win a prize (without a PowerBall) I've chosen this option.\n\nThe combination method is coming from the itertools library, and it takes an iterable and integer as input: the combinations will be generated from the elements of the iterable, the integer is the number of elements in the combinations (this returns an iterator object thus the list conversion is needed to have the values).", null, "If you would like to keep me caffeinated for creating more content like this please consider to support me, with just a coffee.", null, "### Looking at 3 number combinations\n\nIn order to analyse the distribution of 3 number combinations, we better have them in separate columns instead of in nested lists.", null, "Now we can count the occurrences — little looping and merging can do the trick.\n\n``````# Count the frequency of the 3 number pairs across the columns\ncombos_df = pd.DataFrame()\n\nnums_fields = list(separated_combos.columns)\n# Looping through the columns\nfor col in nums_fields:\n# count the number each unique value occurs in the column\ncombo_counts = pd.DataFrame(separated_combos[col].value_counts())\n# If this is the first iteration, the first value_counts output will be\n# the starter DataFrame\nif combos_df.shape == (0, 0):\ncombos_df = combo_counts\nelse:\n# Merge the value_counts outputs along their index\ncombos_df = combos_df.merge(combo_counts, how='outer', left_index=True, right_index=True)\n\n# Sum the values in each row to get\n# the total occurrence of each 3 number combination\ncombos_df[\"3_Num_Combo_Frequency\"] = combos_df.sum(axis=1)\n``````", null, "How to Join DataFrames in Python Using Pandas Merge\n\nAfter a little more clean-up we can take a look at what we have cooked so far.", null, "Over 6 thousand combinations have been drawn since 2015. That is a lot, however not much over 1/8 of all the possible 3 number combinations:", null, "Screenshot by Author\n\nThis means that I have now a ton of undrawn combinations — how am I supposed to pick the most underperforming (whatever that might mean)? There is no other way out, we have to look at the individual numbers too.\n\n### Individual number frequency\n\nWe can actually use the logic written for the combinations — with slight alterations — to calculate the frequency.", null, "Note that here the index is the drawn number we are counting across the columns, and the values in Num1, Num2 … Num5 are the total occurrences in each column.\n\n### Combine the two frequency datasets\n\nThe logic I've followed here is the following:\n\n1. Merge all possible 3 number combo with the ones that already have occurred,\n\n2. Split the 3 number combinations into single number columns,\n\n3. Merge the single number frequency data with the individual numbers from the 3 number combinations\n\n``````# Merge all 3 number possible combinations with the actuals\nmerged_combos = all_combos_df.merge(combos_to_analyse, on='Combinations', how='outer')\n\n# Conversion to match data types for merging\nmerged_combos[\"Combinations\"] = merged_combos[\"Combinations\"].apply(lambda x: list(x[1:-1].split(', ')))\nmerged_combos[\"Combinations\"] = merged_combos[\"Combinations\"].apply(lambda x: [int(i) for i in x])\n\n# Split 3 number combinations into single number columns\nmerged_combos[\"Num_1\"] = merged_combos[\"Combinations\"].apply(lambda x: x)\nmerged_combos[\"Num_2\"] = merged_combos[\"Combinations\"].apply(lambda x: x)\nmerged_combos[\"Num_3\"] = merged_combos[\"Combinations\"].apply(lambda x: x)\n\n# Merge single number frequency to numbers\nmerged_combos = merged_combos.merge(single_nums_df[[\"Num_Frequency\"]], how='left', left_on='Num_1', right_index=True)\nmerged_combos = merged_combos.merge(single_nums_df[[\"Num_Frequency\"]], how='left', left_on='Num_2', right_index=True)\nmerged_combos = merged_combos.merge(single_nums_df[[\"Num_Frequency\"]], how='left', left_on='Num_3', right_index=True)\n\n# Rename columns to keep things nice\nmerged_combos.fillna({\"3_Num_Combo_Frequency\": 0}, inplace=True)\nmerged_combos.rename({\"Num_Frequency_x\": \"Num_1_Freq\", \"Num_Frequency_y\": \"Num_2_Freq\", \"Num_Frequency\": \"Num_3_Freq\"}, axis=1, inplace=True)\n\n# Sort DataFrame across frequency columns\nmerged_combos.sort_values([\"3_Num_Combo_Frequency\", \"Num_1_Freq\", \"Num_2_Freq\", \"Num_3_Freq\"], ascending=True)\n``````\n\nThis is the output:", null, "This way we can create a sort-of-accurate list about the combinations really underperforming in terms of being drawn.\n\nThis is of course not a laser-precision output: look at combinations [65, 68, 69] and [65, 67, 68] for instance. [65, 67, 68] is ranked lower, however, the 3rd number frequency is actually much higher than in [65, 68, 69].\n\nThis is because of the multi-column sorting: if we changed the ordering in the sort_values method the results would be slightly different. We could go and sum the individual number frequencies to use that as the sorting column. At this point I have no further preference in the ordering, I let you decide the next steps.\n\n### Plotting the data\n\nA little bit of tailoring of the single number frequency data to accommodate for this task:", null, "I used a simple Seaborn bar plot to show all the numbers and the number of times each has been drawn. The horizontal blue line marks the average number of draws.", null, "There is some noise for sure, but it looks pretty uniform if you ask me. Remember the law of large numbers I mentioned at the beginning? Even though this is not a huge sample, we can take a look at the mean of the numbers drawn:", null, "How do we calculate the expected value of the game? Just multiply each number by the probability of being drawn in a game and sum up the products!", null, "The difference of 0.265 is definitely not going to disprove the “law” here — but once again, under 7000 experiments are probably not considered a large number when examining the lottery.\n\nI hope you enjoyed this poking around the lottery numbers. I think these kinds of exercises can be a good playground to practice some of the data manipulation tools you have learned with Python.\n\nOnce again, this was not an attempt to predict the future of PowerBall games in any way, I do not think that would be possible. However if you read this article and it gave you an idea to come up with an algorithm that actually can predict the numbers, well, I accept donations if you want to thank me." ]
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https://www.elclauer.cat/color-by-number-math-worksheets-4th-grade/
[ "# Color By Number Math Worksheets 4th Grade", null, "These spring addition color by number worksheets are a perfect kindergarten, first grade or second grade math fact activity! Free math coloring worksheets 2nd grade.", null, "4th of July Color by Number Addition Kindergarten", null, "Color by number math worksheets 4th grade. Easily download and print our 4th grade math worksheets. Some of the worksheets for this concept are kindergarten basic skills, name, trace number 2 and color the, color by number math work, 1 brown 2 blue 3 red 4 yellow 5, easy color by number work, color by number, math work color by numbers volcano. This page has a collection of color by number multiplication worksheets appropriate for third grade, fourth grade or fifth grade students.\n\nThis is a suitable resource page for fourth graders, teachers and parents. Instead let’s make it fun with this division color by number christmas.this free christmas math activity is sure to make practicing dividing fun as grade 3, grade 4, grade 5, and grade 6 students solve equations and color by code to decorate the pictures in these christmas worksheets. Our grade 4 math worksheets help build mastery in computations with the 4 basic operations, delve deeper into the use of fractions and decimals and introduce the concept of factors.\n\n4th grade math worksheets multiplication color by number. Free 4th grade math worksheets for teachers, parents, and kids. Free color by code math number addition subtraction worksheets multiplication activity color by number fraction math worksheets worksheets level 2 math worksheets geometry area test free worksheets for teachers algebra 1 textbook 4th grade reading aside from helping you assess your child’s comprehension of a subject matter, printable home school worksheets also provide something for your.\n\nDivision color by number christmas. The monthly color by numbers provides students with opportunities to review skills previously learned and is aligned specifically to each grade level. Coloring squared will try to provide you with a new math coloring page often.\n\nUsing math coloring worksheets is a great way for preschoolers to get help with basic math problems. Color cuddly zoo animals, crazy race cars, and more while practicing math and reading skills. These math sheets can be printed as extra teaching material for teachers, extra math practice for kids or as homework material parents can use.\n\nHalloween math coloring pages 2nd grade christmas sheets 4th. Choose your grade 4 topic: Make you have what you search.\n\nSecond grade math worksheets, free printable color by number worksheets and 4th grade math worksheets pdf are three main things we will show you based on the post title. Take a peak at all the grade 4 math worksheets and math games to learn addition, subtraction, multiplication, division, measurement, graphs, shapes, telling time, adding money, fractions, and skip counting by 3s, 4s, 6s, 7s, 8s, 9s, 11s, 12s, and other fourth grade math. While we talk concerning basic number worksheets, below we will see various variation of images to give you more ideas.\n\nAs your child learns new words and numbers and concepts, she can use her colors to help her understand math and create great pictures and charts. Math coloring worksheets 4th grade 5; Students complete a math pr\n\nOur 4th grade math worksheets can help. Orange color by number math coloring math coloring worksheets printable numbers 4th grade math mystery pictures coloring worksheets and task cards. Spring addition color by number worksheets:\n\nFind more coloring pages online for kids and adults of color by number adults maths coloring pages to print. This christmas math set is perfect to use in centers, in small groups, or with the whole class! Math coloring worksheets 2nd grade math worksheets printable math worksheets second grade math number worksheets third grade free printables grade 2 preschool worksheets.\n\nFree math coloring worksheets 4th grade. Grade 4 math worksheets from k5 learning. The 4th grade color by number math bundle includes all 4th grade color by number printables.\n\nClick on the free 4th grade math worksheet you would like to print or download. Color 4th grade level math concepts such as rounding, factors, and angles. They are randomly generated, printable from your browser, and include the answer key.\n\nGive us some feedback on pages you have used and enjoyed. Our goal is that these 6th grade color by number worksheets images gallery can be useful for you, bring you more inspiration and most important: 3rd grade, 4th grade, 5th grade:\n\nFree fraction worksheets 3rd grade 3rd grade color by number math. Practice various 4th grade level math fraction concepts. Math is ramping up in 4th grade and it’s time to really put it to practice.\n\nInstructions 6 color by number worksheets 6 student problem worksheets 6 teacher answer. Math coloring worksheets first grade math worksheets social studies worksheets printable math worksheets 1st grade math kindergarten worksheets number worksheets free printable pronoun worksheets. Looking for worksheets to make learning math on valentine's day a bit more fun?\n\nDownload all (7) click on a worksheet in the set below to see more info or download the pdf. Some of the worksheets for this concept are name, addition color by number butter ies, addition color by number house, activities for colors, easy color by number work, patchwork giraffe, sample work from, summer reinforcement packet students entering 2nd grade. Christmas math coloring worksheets multiplication worksheets.\n\nChristmas math coloring worksheets multiplication. This is a comprehensive collection of free printable math worksheets for fourth grade, organized by topics such as addition, subtraction, mental math, place value, multiplication, division, long division, factors, measurement, fractions, and decimals. Saved by teachers pay teachers.\n\nThe 4th grade color by number math bundle includes all 4th grade color by number printables. Addition, elementary, color by number, math games, centers, early finishers. Buy the bundle and save 50%!the monthly color by numbers provide students with opportunities to review skills previously learned and is aligned specifically to each grade level.\n\nJust because the holidays are here doesn’t mean we pause learning; Continue with more related things such 6th grade math coloring worksheets, free printable math worksheets for 6th grade and doubles addition color by number. Multiplication, division, fractions and decimals are a few if the things your kids should be learning.\n\nRegroup to the hundreds with fun coloring puzzles. This page has a collection of color by number multiplication worksheets appropriate for third … Students complete a math problem, record the answer, a\n\nFree printable pdfs, including a full color preview of the completed drawing. Math worksheet ~ math worksheet free color by number worksheets coloring for kids christmas pages printable 2nd math coloring worksheets multiplication.", null, "4th Grade Coloring Pages Math coloring, Math coloring", null, "Pictures Color By Number Spring Math Worksheet Double", null, "Multiplication Color By Number Yahoo Image Search", null, "Elmo Advanced Multiplication Halloween math worksheets", null, "Autumn/Fall Color by Multiplication Worksheets (With", null, "May FunFilled Learning! Math division worksheets", null, "4th Grade Christmas Activities 4th Grade Christmas Math", null, "20 Division Coloring Worksheets in 2020 Fun math", null, "Spring Math Color by Number Differentiated Division", null, "Free Printable Math Coloring Worksheets 4th Grade di 2020", null, "Subtraction Color by Number 2nd grade math worksheets", null, "3rd Grade Go Math 1.10 Use Place Value to Subtract Color", null, "Pin su Printables for the Elementary Classroom", null, "3rd Grade Go Math 1.7 Use Place Value to Add MultiDigit", null, "Addition Worksheets Math coloring worksheets, Math", null, "Pin by G. A. on Számolós színezők 2.o Pinterest", null, "rekenen en kleuren Math pictures, Math sheets, Math", null, "Halloween Three Digit Addition Color by Number with and", null, "Autumn/Fall Color by Multiplication Worksheets (With", null, "" ]
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https://bookboon.com/it/study-notes-for-statistical-physics-ebook
[ "Categories Pricing Corporate", null, "", null, "Libro di testo gratuito\n\n# Study notes for Statistical Physics\n\n### A concise, unified overview of the subject\n\n0 Recensioni\n116\nLingua:  English\nThis is an academic textbook for a one-semester course in statistical physics at honours BSc level.\nDescrizione\nContenuto\n\nThis is an academic textbook for a one-semester course in statistical physics at honours BSc level. It is in three parts and begins with a unified treatment of equilibrium systems, based on the concept of the statistical ensemble, in which the usual combinatorial calculation only has to be worked out once. In the second part, it deals with strongly interacting systems in terms of many-body theory, including the virial expansion and critical phenomena at the level of mean-field theory. The third, and last, part of the book is concerned with time-dependence; and, it begins with a classical treatment of the paradox posed by the `arrow of time'. This is the question of why macroscopic systems are irreversible when their constituent microscopic interactions are reversible in time. It then treats the derivation of transport equations, linear response theory, and quantum dynamics. Throughout the book, the emphasis is on a clear, concise exposition, with all steps being clearly explained.\n\n1. Introduction\n1. The isolated assembly\n2. Method of the most probable distribution\n3. Ensemble of assemblies: relationship between Gibbs and Boltzmann entropies\n2. Stationary ensembles\n1. Types of ensemble\n2. Variational method for the most probable distribution\n3. Canonical ensemble\n4. Compression of a perfect gas\n5. The Grand Canonical Ensemble (GCE)\n3. Examples of stationary ensembles\n1. Assembly of distinguishable particles\n2. Assembly of nonconserved, indistinguishable particles\n3. Conserved particles: general treatment for Bose-Einstein and Fermi-Dirac statistics\n4. The Classical Limit: Boltzmann Statistics\n4. The bedrock problem: strong interactions\n1. The interaction Hamiltonian\n2. Diagonal forms of the Hamiltonian\n3. Theory of specific heats of solids\n4. Quasi-particles and renormalization\n5. Perturbation theory for low densities\n6. The Debye-Hückel theory of the electron gas\n5. Phase transitions\n1. Critical exponents\n2. The ferro-paramagnetic transition\n3. The Weiss theory of ferromagnetism\n4. Macroscopic mean field theory: the Landau model for phase transitions\n5. Theoretical models\n6. The Ising model\n7. Mean-field theory with a variational principle\n8. Mean-field critical exponents for the Ising model\n6. Classical treatment of the Hamiltonian N-body assembly\n1. Hamilton’s equations and phase space\n2. Hamilton’s equations and 6N-dimensional phase space\n3. Liouville’s theorem for N particles in a box\n4. Probability density as a fluid\n5. Liouville’s equation: operator formalism\n6. The generalised H-theorem (due to Gibbs)\n7. Reduced probability distributions\n8. Basic cells in Γ space\n7. Derivation of transport equations\n1. BBGKY hierarchy (Born, Bogoliubov, Green, Kirkwood, Yvon)\n2. Equations for the reduced distribution functions\n3. The kinetic equation\n4. The Boltzmann equation\n5. The Boltzmann H-theorem\n6. Macroscopic balance equations\n8. Dynamics of Fluctuations\n1. Brownian motion and the Langevin equation\n2. Fluctuation-dissipation relations\n3. The response (or Green) function\n4. General derivation of the fluctuation-dissipation theorem\n9. Quantum dynamics\n1. Fermi’s master equation\n2. Applications of the master equation\n10. Consequences of time-reversal symmetry\n1. Detailed balance\n2. Dynamics of fluctuations\n3. Onsager’s theorem\nhome.libro.su_autore\n\nW. David McComb" ]
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https://numberworld.info/1404
[ "# Number 1404\n\n### Properties of number 1404\n\nCross Sum:\nFactorization:\n2 * 2 * 3 * 3 * 3 * 13\nDivisors:\n1, 2, 3, 4, 6, 9, 12, 13, 18, 26, 27, 36, 39, 52, 54, 78, 108, 117, 156, 234, 351, 468, 702, 1404\nCount of divisors:\nSum of divisors:\nPrime number?\nNo\nFibonacci number?\nNo\nBell Number?\nNo\nCatalan Number?\nNo\nBase 2 (Binary):\nBase 3 (Ternary):\nBase 4 (Quaternary):\nBase 5 (Quintal):\nBase 8 (Octal):\n57c\nBase 32:\n1bs\nsin(1404)\n0.28778784246934\ncos(1404)\n-0.95769418799889\ntan(1404)\n-0.30050077161967\nln(1404)\n7.2470805845858\nlg(1404)\n3.1473671077938\nsqrt(1404)\n37.46998799039\nSquare(1404)\n\n### Number Look Up\n\nLook Up\n\n1404 which is pronounced (one thousand four hundred four) is a impressive number. The cross sum of 1404 is 9. If you factorisate the figure 1404 you will get these result 2 * 2 * 3 * 3 * 3 * 13. 1404 has 24 divisors ( 1, 2, 3, 4, 6, 9, 12, 13, 18, 26, 27, 36, 39, 52, 54, 78, 108, 117, 156, 234, 351, 468, 702, 1404 ) whith a sum of 3920. 1404 is not a prime number. 1404 is not a fibonacci number. The figure 1404 is not a Bell Number. The figure 1404 is not a Catalan Number. The convertion of 1404 to base 2 (Binary) is 10101111100. The convertion of 1404 to base 3 (Ternary) is 1221000. The convertion of 1404 to base 4 (Quaternary) is 111330. The convertion of 1404 to base 5 (Quintal) is 21104. The convertion of 1404 to base 8 (Octal) is 2574. The convertion of 1404 to base 16 (Hexadecimal) is 57c. The convertion of 1404 to base 32 is 1bs. The sine of the figure 1404 is 0.28778784246934. The cosine of 1404 is -0.95769418799889. The tangent of the figure 1404 is -0.30050077161967. The root of 1404 is 37.46998799039.\nIf you square 1404 you will get the following result 1971216. The natural logarithm of 1404 is 7.2470805845858 and the decimal logarithm is 3.1473671077938. You should now know that 1404 is amazing figure!" ]
[ null ]
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https://gamedev.stackexchange.com/questions/12429/opengl-3d-camera
[ "# OpenGL 3D Camera\n\nAnd here I am again, looking for help with my OpenGL camera once again. This is starting to get embarrassing. Anyway, here's the deal: I think my OpenGL First Person free roaming camera is starting to work correctly. I can draw objects, see them, and my coordinate system is set up as expected. Great. I solved the gimbal lock issue by fixing the UP vector to be the Y unit vector and restricted the camera's rotation to no more than PI/2 and -PI/2 up/down. All of this is used to build the modelview matrix, which I invert and set at the beginning of every frame. Sweet. It can move in all directions and seems to work just fine.\n\nThat is until I try to change the projection settings. For whatever reason, no matter what I do, my clipping plane is always around +50.0 Z, regardless of the OpenGL calls I attempt. If I move the camera around and move it into certain positions, rotating the camera causes my objects to disappear and reappear. They tend to appear on the edges of the screen, and disappear near the center. In order to facilitate a better answer, allow me to state my assumptions:\n\n• glFrustum only needs to be called ONCE. OpenGL maintains the Projection Matrix and AUTOMATICALLY multiplies the Modelview and Projection Matrices during rendering.\n• The math on the gluPerspective page and glFrustum pages is correct, despite the gluPerspective matrix listing seemingly containing 19 elements when OpenGL only uses 16 of those.\n• I'm assuming that the INVERSION of my camera's Modelview Matrix is somehow screwing with my Projection frustum. I have to bet it's something to do with how the rotation is being calculated.\n\nHas anyone seen this kind of behavior before? Where should I look to start tracking down the problem? Am I doing this completely wrong?\n\nHere is the step-by-step code:\n\n \n// -[[ When my application is ready, this code is run only once ]]-\n\nglMatrixMode(GL_PROJECTION);\n\nfieldOfVision = 60.0f;\naspect = 1.5f;\nnear = 0.1f;\nfar = 100.0f;\n\nymin = -ymax;\nxmin = ymin * aspect;\nxmax = ymax * aspect;\n\nglFrustum(xmin, xmax, ymin, ymax, near, far);\n\nglEnable(GL_DEPTH_TEST);\n\n// -[[ That should setup the viewing volume such that the field of view is 120.0 degrees, the near plane is at 0.1 and the far plane is at 100.0. For whatever reason, my clipping plane is ALWAYS around 50.0, even if I set the far plane to 1000.0. Additionally, I can move around objects using this camera and cause them to clip out by rotating the camera. Does this code snippet need to be run more than once? I was pretty sure that OpenGL takes care of storing the Projection Matrix for the pipeline. ]]-\n\n// -[[ The next chunk of code is performed at every frame. ]]-\n\nglClear(GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT | GL_STENCIL_BUFFER_BIT);\nglMatrixMode(GL_MODELVIEW);\n\n// Pos, forward, and up are 3D vectors and forward and up are normalized before the modelview matrix is processed.\n\nside = crossProduct(forward, up);\n\nGLfloat m[] =\n{\nside.x, side.y, side.z, 0,\nup.x, up.y, up.z, 0,\n-forward.x, -forward.y, -forward.z, 0\npos.x, pos.y, pos.z, 1\n};\n\nm = matrixInvert(m);\n\n// Multing onto the Modelview Identity\nglMultMatrix(m);\n\nforeach object\n{\nglPushMatrix();\nobject.translate();\nobject.rotate();\nobject.scale();\nobject.draw();\nglPopMatrix();\n}\n\nglPushMatrix();\nrenderInterface();\nglPopMatrix();\n\nGLenum err = glGetError();\nif (err != GL_NO_ERROR)\n{\nreportError();\n}\n\nglFlush();\n\n// -[[ End per-frame drawing. It looks right to me, but please let me know what I am doing wrong! Thank you very much for your time and consideration! ]]-\n</code>\n\n• There seems to be a matrix order problem. Can you describe in which orders you do your model view operations? You might be translating before rotating, which would rotate your camera around some other point in the world.\n– void\nMay 18, 2011 at 5:37\n• Translation/rotation order shouldn't be an issue if I am using a single matrix for my transform, should it? I thought matrices were used to solve that issue. Additionally, the camera seems to move and rotate correctly, except for the frustum. Is it possible that translation/rotation order doesn't effect modelview but effects the projection matrix? That seems very strange to me. I'm uncertain how to answer your comment, because the camera can be moved and/or rotated at any time and it's modelview matrix is calculated each frame. May 18, 2011 at 6:26\n• No you will still have to order things correctly, since rotating before or after a translation will have completely different results. Do you set your matrices correctly in the different matrix slots?\n– void\nMay 18, 2011 at 6:29\n• Matrix slots? As in Projection and Modelview? I think so, but obviously I've got something wrong here. My modelview matrix calculations are based on the gluLookAt page. The resulting matrix looks something like M = (s s s 0 u u u 0 -f -f -f 0 p.x p.y p.z 1) where s=side u=up and f=forward and p=position. Once that is built, it is inverted and then glMultMatrix'd onto the identity Modelview. If necessary, I can do a full psuedocode dump as an edit. May 18, 2011 at 6:54\n• Please show us the code where you calculate s, u and f. Additionally it is always helpful to dump the values for each step up to the matrix and post it here, including the final matrix passed to the glMultMatrix/glLoadMatrix func. Also post the code where you pass the result matrix to OpenGL. May 18, 2011 at 8:32\n\nDo you set the correct current matrix prior to update the projection matrix (using glMatrixMode())? Please provide a snippet of your code where you set the projection / modelview matrices.\n\nIt should look something like this:\n\n// Setup projection - needs to be done only if the projection\n// params change, but doesn't hurt to do on every frame\nglMatrixMode(GL_PROJECTION);\ngluPerspective(...);\n\n// Setup view transform matrix (the view part from model-view)\nglMatrixMode(GL_MODELVIEW);\ngluLookAt(...);\n\n// Draw scene\nfor each object:\n\n// Setup model transform matrix (the model part of model-view)\nglMatrixMode(GL_MODELVIEW);\nglPushMatrix();\n\nglTranslate(); // finally, translate object into position\nglRotate(); // then rotate object\nglScale(); // first scale object\n\n[draw object]\n\n// optionally draw sub-objects (if you have a scene graph / transform hierchy)\n\nglPopMatrix();" ]
[ null ]
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http://uyzh.adisangiorgioacremano.it/rbf-python-examples.html
[ "Options include: ‘multiquadric’, ‘inverse’, ‘gaussian’, ‘linear’, ‘cubic’, ‘quintic’, and ‘thin_plate’. After completing […]. interpolate. It can be ‘linear’, ‘poly’, ‘rbf. OutlineIntroductionCommonly Used Radial Basis Functions Training RBFN RBF ApplicationsComparison I The Gaussian and Inverse Multi-Quadric Functions arelocalizedin the sense that ˚(r) !0 as krk!1 I For all the other mentioned functions: ˚(r) !1as krk!1 I In RBFNN the hidden layer and output layer play very di erent role. array([[3, 1], [2, 2]]) w, v. choose()) # there are various options associated with SVM training; like changing kernel, gamma and C value. Protein Fold and Remote Homology Detection. Rather we can simply use Python's Scikit-Learn library that to implement and use the kernel SVM. This is obtained by simply changing the kernel parameter. For example, if the observation space is one-dimensional then a thin-plate spline can be obtained with the arguments phi = rbf. Following is the RBF kernel equation. Tuning examples include optimizing regularization or kernel parameters. The second segment shows how to perform 1-d interpolation. 20 Dec 2017. Here are the examples of the python api sklearn. With certain choices of basis functions and polynomial orders this interpolant is equivalent to a thin-plate spline. Famous python library for face recognition uses SVM for face classification. Classification report for classifier SVC (C = 1. The weights are computed using the RBF-FD method described in . Tensorflow documentation provides very nice tutorial examples. 702353 specificity 0. This is a simple example of multiple linear regression, and x has exactly two columns. By using the above data, let us create a interpolate function and draw a new interpolated graph. We will start with a simple example of 2 half-moon shapes generated by the make_moons function from scikit-learn. Submodules; GPy. Remembering relevant facts and examples is very much a part of the RBF-Like Nets for Classification Problems 199 human learning process because it facilitates compar- ison of facts and information that forms the basis for rapid learning. Provide services and support for in-house departments such as Land Development, Planning, Water Resources, Survey, Storm Water, Environmental, and Graphics. A small value of will make the model behave like a linear SVM. We'll go over other practical tools, widely used in the data science industry, below. Explore and run machine learning code with Kaggle Notebooks | Using data from Nomad2018 Predicting Transparent Conductors. After the Statsbot team published the post about time series anomaly detection, many readers asked us to tell them about the Support Vector Machines approach. We will be using iris dataset from scikit-learn − We will start by importing following packages −. pyplot as plt from sklearn import datasets data = datasets. The kernel is given by:. interpolate in python:. Note that we set this equal to zero. Python Programming tutorials from beginner to advanced on a massive variety of topics. interpolate. Support Vector Regression (SVR) is a regression algorithm, and it applies a similar technique of Support Vector Machines (SVM) for regression analysis. 0909-560-01, 0909-454-01 Fall 2004 Lab Project 3: Radial Basis Function Neural Networks. Then it extracts the feature from each pixel as face or nonface. 1), x Rn is the input, n xc R is the center, and 0 WW T is a positive-definite. Support Vector Machine Example Separating two point clouds is easy with a linear line, but what if they cannot be separated by a linear line? In that case we can use a kernel, a kernel is a function that a domain-expert provides to a machine learning algorithm (a kernel is not limited to an svm). Aug 18, 2017. 844867 positive likelihood 8. Requirements. Background. import numpy as np from scipy. Define the covariance kernel, i. We will start with a simple example of 2 half-moon shapes generated by the make_moons function from scikit-learn. , accuracy for classification) with each set of hyperparameters. 1d example¶ This example compares the usage of the Rbf and UnivariateSpline classes from the scipy. It is a model of a single neuron that can be used for two-class classification problems and provides the foundation for later developing much larger networks. Roberts Cross Edge Detector. Hence, the edges in the resulting Roberts Cross image, are rather faint. In the first example of predicting the fruit type. SVM offers very high accuracy compared to other classifiers such as logistic regression, and decision trees. This is an example plot from the tutorial which accompanies an explanation of the support vector machine GUI. In this example, we will train an SVC with RBF kernel using scikit-learn. maxVal as arbitrary numbers. use (' Agg ') import matplotlib. Tech project ‘Digit Recognition in python’ and this time I am going to discuss a kernel based learning algorithm, Support Vector Machine. Get RBF of an unknown data point x with respect to all centroids. You should refer to the official docs for exploration of this rich and rapidly growing library. For example, an RBF network could be used to predict the scores of two football teams that are scheduled to play each other, based on historical data such as each team's current winning percentage, home field advantage (-1. Now that we have understood the basics of SVM, let’s try to implement it in Python. interpolate import RBF. linspace(-1,1,100) X, Y = np. One-class SVM with non-linear kernel (RBF)¶ An example using a one-class SVM for novelty detection. To run the. We’ll use radial basis functions, tougher tools for a more civilized age. Each RBF neuron compares the input vector to its prototype, and outputs a value between 0 and 1 which is a measure of similarity. To install it just run the command: Scikit-multilearn works with Python 2 and 3 on Windows, Linux and OSX. Fundamentals 17 2. For all test examples in example_file the predicted values are written to output_file. When IPython starts a kernel, it passes it a connection file. In a sample scenario, construct a model that assigns music-listener profiles. By voting up you can indicate which examples are most useful and appropriate. For example, have a look at the sample dataset below that consists of the temperature values (each hour), for the past 2 years. griddata using 400 points chosen randomly from an interesting function. Get RBF of an unknown data point x with respect to all centroids. Python Example. The following code snippet shows an example of how to create and predict an SVM model using the libraries from scikit-learn. In this case, we have to tune two hyperparameters: C and gamma. It’s an extreme learning machine too. 801859 sensitivity 0. The weights are computed using the RBF-FD method described in . Support vector machines are an example of such a maximum margin estimator. rbf_kernel: Radial basis function kernel. Support Vector Machines (SVM) are one of the most powerful machine learning models around, and this topic has been one that students have requested ever since I started making courses. Y = dot (G, self. Refer to Packager Command Syntax for more information about invoking the packager. scatter ( X [:, 0 ], X [:, 1 ], c = y , s = 50 , cmap = 'autumn' );. rbf_kernel extracted from open source projects. Python source code: plot_oneclass. Support Vector Machine Use Cases. In this post I will demonstrate how to plot the Confusion Matrix. Toy example of 1D regression using linear, polynominial and RBF kernels. I have rewritten it yesterday to work with tensorflow 2. 1)) score: 0. the Gaussian RBF interpolant is ill-conditioned for most series in the sense that the interpolant is the small difference of terms with exponentially large coefficients. linspace (0, 10, 9) y = np. pairwise import rbf_kernel K = var * rbf_kernel(X, gamma = gamma) Run-time comparison I use 25,000 random samples of 512 dimensions for testing and perform experiments on an Intel Core i7-7700HQ (4 cores @ 2. For example you can use EV3 Explorer with WiFi and the Small Basic program can use the USB connection. cm_rbf = table (test_set[, 3], y_pred_rbf) We have evaluated our model based on the confusion matrix and we can still say that our model performed not so great compared to the model in Python. Python* Examples Deprecation Notice: With the introduction of daal4py , a package that supersedes PyDAAL, Intel is deprecating PyDAAL and will discontinue support starting with Intel® DAAL 2021 and Intel® Distribution for Python 2021. Discover Long Short-Term Memory (LSTM) networks in Python and how you can use them to make stock market predictions! In this tutorial, you will see how you can use a time-series model known as Long Short-Term Memory. rbf_func – Specifies which function to use for Rbf interpolation. 001, kernel = 'rbf', max_iter =-1, probability = False, random_state = None, shrinking = True, tol = 0. build problems for android_binary_package - Eclipse Indigo, Ubuntu 12. rbf_kernel extracted from open source projects. One of the reasons why SVMs enjoy popularity in machine learning is that they can be easily kernelized to solve nonlinear classification problems. The following is an example for creating an SVM classifier by using kernels. For example, if diffs is [[2, 0], [0, 1]], then order is set to 2. linear_kernel: Linear kernel. [email protected] For example, RBF kernel of Support Vector Machines or the L1 and L2 regularized linear models typically work better when all features have unit variance and/or zero mean. Examples In the following two examples, we demonstrate the practical use of svm() along with a comparison to classi cation and regression trees as implemented in rpart(). In this example, we will train an SVC with RBF kernel using scikit-learn. In this set of screencasts, we demonstrate methods to perform interpolation with the SciPy, the scientific computing library for Python. Higher values. Support Vector Machines (SVMs) are a family of nice supervised learning algorithms that can train classification and regression models efficiently and with very good performance in practice. Here, temperature is the dependent variable (dependent on Time). Select a Web Site. So for example, 0 is Iris-setosa. The code: The Rbf function takes as arguments the x and y axes, and a list of the values in the points. Each RBF neuron compares the input vector to its prototype, and outputs a value between 0 and 1 which is a measure of similarity. Ask Question Asked 1 year, 4 months ago. A few examples of kernels used in SVM are linear and radial basis function (RBF) kernels. RBF SVM parameters. The Python Radial Basis Function Toolbox (RBFT) is software for implementing RBF interpolation methods and RBF methods for the numerical solution of PDEs on scattered centers located in complexly shaped domains. If you're not sure which to choose, learn more about installing packages. metrics) and Matplotlib for displaying the results in a more intuitive visual format. from cdo import * cdo = Cdo() # create the CDO caller ifile = 'tsurf. SysFont ( \"Comic Sans MS\", 20) myfont2 = pygame. A low value of gamma means 'far' and high value means 'close'. The test examples in example_file are given in the same format as the training examples (possibly with 0 as class label). Intuitively, the gamma parameter defines how far the influence of a single training example reaches, with low values meaning 'far' and high values meaning 'close'. interpolate. The figure below shows an example response surface, in which we optimized the hyperparameters of an SVM with RBF kernel. So for example, 0 is Iris-setosa. The Quartus® Prime software generates this RBF by compiling the AFU design. linalg import eigh import numpy as np def rbf_kernel_pca(X, gamma, n_components. , g (x)= k X i =1 i G q. Python implementation of precomputed RBF kernel with Gram matrix? Python implementation. Here, temperature is the dependent variable (dependent on Time). To summarize, RBF nets are a special type of neural network used for regression. The PRBFT is under constant development as it is heavily used in RBF research projects. Python is an interpreted high-level programming language for general-purpose programming. As the title suggests, we’re going to use both R and Python to predict whether a dispatcher was diagnosed with a sleeping disorder. Tags; rbf (6) I saw this post here where they talk about a similar thing but I didn't find the exact way to get equivalent python code to matlab function f… machine learning - Where is it best to use svm with linear kernel?. The python library scipy has a function called RBF that does that. No matter what kind of software we write, we always need to make sure everything is working as expected. Digit Recognition in python : SVM Hello friends. The RBF kernel as a projection into infinite dimensions Recall a kernel is any function of the form: K(x;x0) = h (x); (x0)i where is a function that projections vectors x into a new vector space. Loading… 2016-07-29. Examples In the following two examples, we demonstrate the practical use of svm() along with a comparison to classi cation and regression trees as implemented in rpart(). sin (x) xi = np. Bioinformatics. x, y, z, …, d, where x, y, z, … are the coordinates of the nodes and d is the array of values at the nodes. Following is the RBF kernel equation. Results using a linear SVM in the original space, a linear SVM using the approximate mappings and using a kernelized. SysFont ( \"Comic Sans MS\", 20) myfont2 = pygame. The second segment shows how to perform 1-d interpolation. In here we learn why SVM is so powerful. The kernel. Today we’ll talk more about interpolation. The script reads the file from this path. Browse other questions tagged machine-learning python neural-network deep-learning rbf or ask your own question. 0, decision_function_shape = 'ovr', degree = 3, gamma = 0. interpolate. I discussed its concept of working, process of implementation in python, the tricks to make the model efficient by tuning its parameters, Pros and Cons, and finally a problem to solve. Support Vector Machine(SVM) code in R. 10/27/2004 3 RBF Architecture • RBF Neural Networks are 2-layer, feed-forward networks. Rbf¶ class scipy. RBFSampler taken from open source projects. I have an assignment to implement a Gaussian radial basis function-kernel principal component analysis (RBF-kernel PCA) and have some challenges here. To do so, we use the linspace method from the NumPy library. This example shows how to use stratified K-fold crossvalidation to set C and gamma in an RBF. O’Reilly members get unlimited access to live online training experiences, plus books, videos, and digital content from 200+ publishers. The second layer which is also called the hidden layer is where RBF of all input data is stored. To solve this problem, we should instead use a nonlinear SVM. The most widely used library for implementing machine learning algorithms in Python is scikit-learn. KernelScale — One strategy is to try a geometric sequence of the RBF sigma parameter scaled at the original kernel scale. So for example, 0 is Iris-setosa. Files for model training: train. py contains an example of model training and its usage for prediction. rbf_func – Specifies which function to use for Rbf interpolation. For example, to use a Gaussian RBF kernel with ˙= 1 and C= 1: # Train a nonlinear SVM svp <- ksvm(x,y,type=\"C-svc\",kernel=’rbf’,kpar=list(sigma=1),C=1) # Visualize it. We'll go over other practical tools, widely used in the data science industry, below. Let’s use the same dataset of apples and oranges. Using pyKriging. interpolate import Rbf import matplotlib matplotlib. Protein Fold and Remote Homology Detection. import numpy as np a = np. Following is the RBF kernel equation. data, columns=data. import numpy as np from scipy. Support Vector Machines in Python Wow, I didn’t think I’d be coming out with another course so soon – but here it is! RBF Networks (Radial Basis Function. So for example, 0 is Iris-setosa. We assume each data point is a 'center' and use Gaussian type RBFs. The RBF Neurons. They are from open source Python projects. But I would like to understand what kind of operations are involved, for example: What are the trnorms vectors? What are they for? What is the meaning of creating the matrices k1 and k2? Is this algorithm any different from the sklearn implementation?. One of the reasons why SVMs enjoy popularity in machine learning is that they can be easily kernelized to solve nonlinear classification problems. As a representative application, we demonstrate graph classification using the MUTAG dataset. 0) ¶ Returns the weights which map a functions values at s to an approximation of that functions derivative at x. The Python Radial Basis Function Toolbox (RBFT) is software for implementing RBF interpolation methods and RBF methods for the numerical solution of PDEs on scattered centers located in complexly shaped domains. By Sebastian Raschka, Michigan State University. pyplot as plt # setup data x = np. A small value of will make the model behave like a linear SVM. Section 4 provides an illustrative example of the framework and demonstrates the results on a small problem of a process containing a reactor and a separator. choosing a good sigma and C value is very essential for good accuracy. Scattered multidimensional interpolation is one of the most important - and hard to solve - practical problems. Satya Mallick. These NCL and Python scripts are companion examples to the excellent NCL to Python Transition Guide, written by Karin Meier-Fleischer of DKRZ (Deutsches Klimarechenzentrum). For Python training, our top recommendation is DataCamp. Cross-validating is easy with Python. RBF SVM parameters. Based on Support Vector Machines (SVM) evaluation, the One-class SVM applies a One-class classification method for novelty detection. Background. The following is an example for creating an SVM classifier by using kernels. Machine Learning with scikit-learn scikit-learn installation scikit-learn : Features and feature extraction - iris dataset scikit-learn : Machine Learning Quick Preview. The 'similarity' is computed using the radial basis function (RBF), also known as the gaussian function. We only consider the first 2 features of this dataset: Sepal length; Sepal width; This example shows how to plot the decision surface for four SVM classifiers with different kernels. In this post I will demonstrate how to plot the Confusion Matrix. You can rate examples to help us improve the quality of examples. 1), x Rn is the input, n xc R is the center, and 0 WW T is a positive-definite. The following are code examples for showing how to use scipy. We will consider the Weights and Size for 20 each. Cython code lies behind many of the big Python scientific libraries including scikit-learn and pandas. Last Updated on April 17, 2020. import numpy as np from sklearn. [email protected] Machine learning tasks that once required enormous processing power are now possible on desktop machines. Define the covariance kernel, i. Rbf¶ class scipy. This tutorial draws heavily on the code used in Sebastian Raschka's book Python Machine Learning. Continued from scikit-learn : Support Vector Machines (SVM). rbf_kernel extracted from open source projects. These are the top rated real world Python examples of sklearnpreprocessing. Support Vector Regression (SVR) using linear and non-linear kernels¶. Since Radial basis functions (RBFs) have only one hidden layer, the convergence of optimization objective is much faster, and despite having one hidden layer RBFs are proven to be universal approximators. Recommended Python Training - DataCamp. Instead of inferring a distribution over the parameters of a parametric function Gaussian processes can be used to infer a distribution over functions directly. As the max depth increases, it looks like sci kit learn gives the better results. Creating a grid from scattered data using inverse of the distance with python (gdal_grid approach) OK, I have to admit that I was so happy when I found the scipy rbf function that I went too fast writing the entry about inverse of the distance. In this tutorial we will visually explore the effects of the two parameters from the support vector classifier (SVC) when using the radial basis function kernel (RBF). python analyze_data. Choose a web site to get translated content where available and see local events and offers. Package ‘kernlab’ November 12, 2019 Version 0. rbfnnpy module is an implementation of RBF Neural Network model training, dump and prediction for Python. The Quartus® Prime software generates this RBF by compiling the AFU design. To demonstrate, let's use a data set on breast cancer cases in Wisconsin. RBF(input_dim= 1, variance = 1. In the course of the various examples you will see how you can implement JavaScript code in a totally Python environment, using the large capacity of integrative IPython Notebook. According this blogpost, since these two points 'support' the hyperplane to be in 'equilibrium' by exerting torque (mechanical analogy), these data points are called as the support vectors. Python rbf_kernel - 30 examples found. You can vote up the examples you like or vote down the ones you don't like. In this example, we will perform nonlinear regression using LS-SVM with RBF kernel using the LS-SVMlab toolbox. Below is the Octave / MATLAB code which I used in my two part tutorial on RBF Networks for classification and RBF Networks for function approximation. Technically, gamma is not a parameter of the SVM, but a parameter for the 'rbf' kernel to handle non-linear classification. The following example demonstrates the approximate SVM method on the MNIST database of handwritten digits. py It should let you know more-or-less what’s going on — printing the filtering and plotting it’s doing to the console. It is ideally suited for actual industrial problems, since it allows to handle: Computer Aided Design files (in. Support Vector regression is a type of Support vector machine that supports linear and non-linear regression. Seleting hyper-parameter C and gamma of a RBF-Kernel SVM¶ For SVMs, in particular kernelized SVMs, setting the hyperparameter is crucial but non-trivial. In this section, we will apply the RBF kernel PCA to different nonlinear sample data in order to perform dimensionality reduction. predict(x) >> ans = 0 1 1 0 the SVM easily finds the correct result. data, columns=data. Support Vector Regression (SVR) using linear and non-linear kernels¶. It can be done by using kernels. py: import numpy as np from scipy. Loading… 2016-07-29. In this case, we have to tune two hyperparameters: C and gamma. In this article a few machine learning problems from a few online courses will be described. Mlxtend (machine learning extensions) is a Python library of useful tools for the day-to-day data science tasks. It will be removed after 2020-01-01. While histogram equalization has the advantage that it requires no parameters,. For Python training, our top recommendation is DataCamp. 0 z = x * np. Instantly share code, notes, and snippets. 0, cache_size = 200, class_weight = None, coef0 = 0. Another important problem is scattered fitting with smoothing, which differs from interpolation by presence of noise in the data and need for controlled smoothing. LibSVM reports many useful statistics about LibSVM classifier (e. One of the most common errors you’ll see is this one: As far as errors go, “unable to find vcvarsall. linspace (0, 10, 101) # use fitpack2 method ius = InterpolatedUnivariateSpline (x,. I)It is appropriate to use di erent learning alg. Step 3: Create a model and fit it. Radial Basis Function network was formulated by Broomhead and Lowe in 1988. import numpy as np. python - 'bad input shape' when using scikit-learn SVM and optunity 2020腾讯云共同战“疫”，助力复工（优惠前所未有！ 4核8G,5M带宽 1684元/3年），. def toy_poisson_rbf_1d_laplace (optimize = True, plot = True): \"\"\"Run a simple demonstration of a standard Gaussian process fitting it to data sampled from an RBF covariance. psi_comp package. phs3 and order = 1. O’Reilly members get unlimited access to live online training experiences, plus books, videos, and digital content from 200+ publishers. Principal component analysis (PCA) is an unsupervised linear transformation technique that is widely used across different fields, most prominently for dimensionality reduction. I run a rbf SVM on a full dataset of about 4 - 5000 with 650 features. Calculate dot product of RBF and W and select an index of maximum value; Implementation of theory in Python. Here in the second example and plot, we show the use of the polynomial kernel instead of the RBF kernel. It can be ‘linear’, ‘poly’, ‘rbf. Ask Question Asked 1 year, 4 months ago. The target class will have many fruits like apple, mango, orange, banana, etc. These NCL and Python scripts are companion examples to the excellent NCL to Python Transition Guide, written by Karin Meier-Fleischer of DKRZ (Deutsches Klimarechenzentrum). Generalized versions may use (possibly different) Mahalanobis norms, i. This website uses cookies to ensure you get the best experience on our website. Today we’ll talk more about interpolation. Step 3: Create a model and fit it. Nice and Simple code. Download the file for your platform. Let's do this! In order to use radial basis functions on SciPy we'll use Rbf, a function within interpolate. Using pyKriging. You can see how simple the data is, and why it is useful for learning concepts. Introduction. Python source code: plot_svm_regression. In this section, we will apply the RBF kernel PCA to different nonlinear sample data in order to perform dimensionality reduction. The second segment shows how to perform 1-d interpolation. rbf_kernel: Radial basis function kernel. 844867 positive likelihood 8. If Y is also a matrix (with the same number of columns as X), the kernel function is evaluated between all data points of X and Y. 2 ) # product of kernels k_prod = k1 * k2 k_prod. Continued from scikit-learn : Support Vector Machines (SVM). Python Implementation. Each run takes about a minute. Clone via HTTPS Clone with Git or checkout with SVN using the repository’s web address. There's also many of SVM blog that i ma. Digit Recognition in python : SVM Hello friends. scikit-learn : Radial Basis Function kernel, RBF. Now if we specify a RBF kernel and run the same example again, then: gaussSvm = fitcsvm(x,y,'KernelFunction','rbf'); % RBF kernel gaussSvm. csv contains feature vector for each sample; target. interpolate is a convenient method to create a function based on fixed data points, which can be evaluated anywhere within the domain defined by the given data using linear interpolation. Consider the following example: There's no linear decision boundary for this dataset, which will separate observations of two classes. csv contains feature vector for each sample; target. However, the test accuracy stays fairly flat for both models while the Python model training accuracy increase to 1. If that succeeded you are ready for the tutorial, otherwise check your installation (see Installing Theano). 333549 , which is pretty close to the actual price of $180. When we write a. There is one line per test example in output_file containing the value of the decision function on that example. 1d example¶ This example compares the usage of the Rbf and UnivariateSpline classes from the scipy. Get project updates, sponsored content from our select partners, and more. Package ‘kernlab’ November 12, 2019 Version 0. While histogram equalization has the advantage that it requires no parameters,. The test examples in example_file are given in the same format as the training examples (possibly with 0 as class label). Tags: Science And Data Analysis, Machine Learning, Data Analysis, Financial, Scientific, Sock Trading, Stock Market. Neural Networks: MATLAB examples Neural Networks course (practical examples) © 2012 Primoz Potocnik Primoz Potocnik University of Ljubljana Faculty of Mechanical. The following code snippet shows an example of how to create and predict an SVM model using the libraries from scikit-learn. One of the most common errors you’ll see is this one: As far as errors go, “unable to find vcvarsall. Troppo codice, lo raccolgo nello script rbf1. There are forms of machine learning called \"unsupervised learning,\" where data labeling isn't used, as is the case with clustering, though this example is a form of supervised learning. In this blog post, we will go through the most basic three algorithms: grid, random, and Bayesian search. Clone via HTTPS Clone with Git or checkout with SVN using the repository's web address. gaussherm module; GPy. This tutorial draws heavily on the code used in Sebastian Raschka’s book Python Machine Learning. If Y is also a matrix (with the same number of columns as X), the kernel function is evaluated between all data points of X and Y. py does the following: Example of what EEGrunt should print to the console. (RBF) kernel. sin (x) xi = np. We talked about it …. The task is to predict the type of a glass. Using Python (and R) to calculate Linear Regressions You might also be interested in my page on doing Rank Correlations with Python and/or R. Machine learning: Choosing between models with stratified k-fold validation Michael Allen machine learning April 20, 2018 December 21, 2018 6 Minutes In previous examples we have used multiple random sampling in order to obtain a better measurement of accuracy for modes (repeating the model with different random training/test splits). Ask Question Asked 1 year, 4 months ago. It is used to separate different objects into their distinct categories. The second segment shows how to perform 1-d interpolation. Support Vector Machine Use Cases. interpolate. Python Command Line IMDB Scraper. The parameters of each of these functions is learned by incremental adjustment based on errors generated through repeated presentation of inputs. Okay, remember this slide from the presentation: The above is a simple kfold with 4 folds (as the data is divided into 4 test/train splits). With SciKit, a powerful Python-based machine learning package for model construction and evaluation, learn how to build and apply a model to simulated customer product purchase histories. 1 documentation; 他にもmatplotlibを入れておくとグラフがかけるので嬉しいです. By Sebastian Raschka, Michigan State University. Introduced a little more than 50 years ago, they have evolved over time and have also been adapted to various other problems like regression, outlier analysis, and ranking. It will result in a more complex decision boundary. A Gaussian process generalizes the multivariate normal to infinite dimension. linspace (0, 10, 9) y = np. xl_RBF and xl_RBFGrid provide Radial Basis Function interpolation. array([[3, 1], [2, 2]]) w, v. I have one question about your code which confuses me. import matplotlib. py It should let you know more-or-less what’s going on — printing the filtering and plotting it’s doing to the console. griddata using 400 points chosen randomly from an interesting function. The other half is a radial basis function network (see The Secret of The Big Guys ) based on clustering and distance measures. To install it just run the command: Scikit-multilearn works with Python 2 and 3 on Windows, Linux and OSX. Now that we have understood the basics of SVM, let's try to implement it in Python. This example illustrates the effect of the parameters gamma and C of the Radial Basis Function (RBF) kernel SVM. nc' # input: surface temperature cdo. gaussherm module; GPy. Why Support Vector Regression (SVR) Support Vector Machines (SVM) analysis is a popular machine learning tool for classification and regression, it supports linear and nonlinear regression that we can refer to as SVR. After a successful application of SVM with linear kernel, we will look at one more example of an SVM with RBF kernel to start with. I saw this post here where they talk about a similar thing but I didn't. O’Reilly members experience live online training, plus books, videos, and digital content from 200+ publishers. fit(X, y) we obtain the following: As you can see, without making any further computation, but simply changing one parameter of our model, we converted a no-linear problem. The figure below shows an example response surface, in which we optimized the hyperparameters of an SVM with RBF kernel. 001 and the radial basis function (rbf) kernel. The creation of a support vector machine in R and Python follow similar approaches, let’s take a look now at the following code: #Import Library require(e1071) #Contains the SVM Train <- read. In the article I explain how to train an RBF network classifier. In the original dataset each pixel of the image is represented by a value between 0 and 255, where 0 is black, 255 is white and anything in between is a different shade of grey. Python Implementation. SVC(kernel='rbf', C = 10. I have one question about your code which confuses me. RBF, and then form the GPy model m. In a sample scenario, construct a model that assigns music-listener profiles. It would be great if someone could point me to the right direction because I am obviously doing something wrong here. SVM - scikit learn. Note that we set this equal to zero. We will start with a simple example of 2 half-moon shapes generated by the make_moons function from scikit-learn. It certainly looks like max depth 4 and 5 in Python have overfit the data. linear_model import LogisticRegression from sklearn. linspace(-1,1,100) X, Y = np. RBF nets can learn to approximate the underlying trend using many Gaussians/bell curves. In this blog post, we will go through the most basic three algorithms: grid, random, and Bayesian search. If you are not aware of the multi-classification problem below are examples of multi-classification problems. linear_psi_comp module. Checkout this Github Repo for code examples and datasets. 9-29 Title Kernel-Based Machine Learning Lab Description Kernel-based machine learning methods for classification,. 6 (288 ratings) Created by Lazy Programmer Inc. , accuracy for classification) with each set of hyperparameters. These are the top rated real world Python examples of sklearnmetricspairwise. predict(x) >> ans = 0 1 1 0 the SVM easily finds the correct result. SVM Example. Random Features for Large-Scale Kernel Machines Ali Rahimi and Ben Recht Abstract To accelerate the training of kernel machines, we propose to map the input data to a randomized low-dimensional feature space and then apply existing fast linear methods. We began by looking at regularization approaches for RBF networks. 9 Model ELM (20,rbf (0. rbf neural network python rbf network weights rbf examples rbf test rbf network weights rbf prediction gaussian rbf network keras rbf network rbf network python rbf neural network wiki. In this section, we will apply the RBF kernel PCA to different nonlinear sample data in order to perform dimensionality reduction. Official documentation: The official documentation is clear, detailed and includes many code examples. ensemble import VotingClassifier from sklearn. Python rbf_kernel - 30 examples found. RBF instance or str, optional) – Type of RBF. Examples of RBF Kernel PCA. This is a JSON file that describes the metadata that create-gbs appends to the RBF. The RBF kernel is defined as K RBF(x;x 0) = exp h kx x k2 i where is a parameter that sets the \"spread\" of the kernel. Python rbf_kernel - 30 examples found. linalg import eigh import numpy as np def rbf_kernel_pca(X, gamma, n_components. fd (Radial Basis Function Finite Differences)¶ This module provides functions for generating RBF-FD weights. We will consider the Weights and Size for 20 each. ) Creates an EEGrunt object called EEG. metrics) and Matplotlib for displaying the results in a more intuitive visual format. Radial basis functions can be used for smoothing/interpolating scattered data in n-dimensions, but should be used with caution for extrapolation outside of the observed data range. interpolate. Satya Mallick. In this case, we have to tune two hyperparameters: C and gamma. 1310 32 bit (Intel)] numpy version: 1. Kernel principal component analysis (kPCA) is an extension a PCA analysis that conducts the calculations in a broader dimensionality defined by a kernel function. linspace(-1,1,100) y = np. m, I simulated my output network using sim. for example we can do a two layer grid search. In the context of spam or document classification, each \"feature\" is the prevalence or importance of a particular word. In our previous Machine Learning blog we have discussed about SVM (Support Vector Machine) in Machine Learning. LibSVM reports many useful statistics about LibSVM classifier (e. f1 = interp1d (x, y, kind = 'linear') f2 = interp1d (x, y, kind = 'cubic'). It is one of the examples of how we are using python for stock market and how it can be used to handle stock market-related adventures. interpolate. 1)) score: 0. interpolate in python:. Since Radial basis functions (RBFs) have only one hidden layer, the convergence of optimization objective is much faster, and despite having one hidden layer RBFs are proven to be universal approximators. I this post, I will use SVR to predict the price of TD stock (TD US Small-Cap Equity. Fitting the distribution of heights data This problem appeared as an assignment problem in the coursera course Mathematics for Machine Learning: Multivariate Calculus. Some background information on the method implemented in rbf. Checkout this Github Repo for code examples and datasets. Here's a simple example project where we used wandb with sklearn. SysFont ( \"Comic Sans MS\", 20) myfont2 = pygame. However, this is usually not ideal, since the algorithms “learns” the data instead of providing a generalizable rule. 1), x Rn is the input, n xc R is the center, and 0 WW T is a positive-definite. If you're not sure which to choose, learn more about installing packages. 7875 Model ELM (20,rbf (0. This website uses cookies to ensure you get the best experience on our website. To solve this problem, we should instead use a nonlinear SVM. After completing […]. Classification. 0, decision_function_shape = 'ovr', degree = 3, gamma = 0. Join the most influential Data and AI event in Europe. SVM is a supervised machine learning algorithm is a representation of the examples as points in space, mapped so that the examples of the separate categories are divided by a clear gap that is as wide as possible. A kernel is a set of mathematical functions. Python has very limited information and precomputed kernels examples. For example, rbf_kernel(gamma =. The documentation for Confusion Matrix is pretty good, but I struggled to find a quick way to add labels and. interpolate. The most popular machine learning library for Python is SciKit Learn. Rbf (*args) [source] ¶ A class for radial basis function interpolation of functions from n-dimensional scattered data to an m-dimensional domain. In the article I explain how to train an RBF network classifier. 0 z = x * np. Radial basis functions can be used for smoothing/interpolating scattered data in n-dimensions, but should be used with caution for extrapolation outside of the observed data range. I used the C# language for the demo. Everything we’re about to do can be done entirely in either one of the languages. For the same data, the rbf function is creating a fully occupied contour map whereas the contourf function is only plotting the data at (x,y) -> z. We talked about it …. cm_rbf = table (test_set[, 3], y_pred_rbf) We have evaluated our model based on the confusion matrix and we can still say that our model performed not so great compared to the model in Python. xl_RBF and xl_RBFGrid provide Radial Basis Function interpolation. SysFont ( \"Comic Sans MS\", 20) This comment has been minimized. A collection of examples are provided with Qt for Python to help new users to understand different use cases of the module. 2, train_fraction=0. Using pyKriging. I have this algorithm to compute the RBF kernel and it seems to work just fine. Though we implemented our own classification algorithms, actually, SVM also can do the same. We talked about it …. To run the. Intuitively, the gamma parameter defines how far the influence of a single training example reaches, with low values meaning ‘far’ and high values meaning ‘close’. 333549 , which is pretty close to the actual price of$180. A MLP consists of an input layer, several hidden layers, and an output layer. This example illustrates the effect of the parameters gamma and C of the Radial Basis Function (RBF) kernel SVM. Nevertheless you cannot start two programs at the same time. Comparison of the RBF smoothing with the median and Gaussian filtering in a one-dimensional example. Fitting the distribution of heights data This problem appeared as an assignment problem in the coursera course Mathematics for Machine Learning: Multivariate Calculus. py file) with the appropriate methods. Last Updated on April 7, 2020 It is important that beginner machine Read more. 1) In the above example, we are using the Radial Basis Fucttion expalined in our previous post with parameter gamma set to 0. Python source code: plot_oneclass. The RBF kernel as a projection into infinite dimensions Recall a kernel is any function of the form: K(x;x0) = h (x); (x0)i where is a function that projections vectors x into a new vector space. If you're not sure which to choose, learn more about installing packages. Senior GIS Analyst 01/2003 to 03/2009 RBF Consulting – Irvine, CA Responsible for data management, client communications, and mentoring of technicians. Rbf¶ class scipy. 875 Model ELM (10,sinsq) score: 0. After a successful application of SVM with linear kernel, we will look at one more example of an SVM with RBF kernel to start with. The output looks likes this:. I used the C# language for the demo. Here are some examples of MNIST digits: For convenience we pickled the dataset to make it easier to use in python. For example, if the observation space is one-dimensional then a thin-plate spline can be obtained with the arguments phi = rbf. Radial Basis Function network was formulated by Broomhead and Lowe in 1988. The most popular machine learning library for Python is SciKit Learn. Instantly share code, notes, and snippets. RBFNeuralNetwork. 1)) score: 0. This tutorial draws heavily on the code used in Sebastian Raschka’s book Python Machine Learning. For example, have a look at the sample dataset below that consists of the temperature values (each hour), for the past 2 years. The following code trains a binary classifier using as training set 4,000 examples of the digit '0' as class 1 and 4,000 examples of the digit '1' as class 2. These days, everyone seems to be talking about deep learning, but in fact there was a time when support vector machines were seen as superior to neural networks. Following are some examples of daily life applications of SVM: Face Recognition: SVM is a more accurate and reliable classifier when it comes to face recognition. Please update all the lines having / to // as python 3 does not give back Integer with normal division symbol if the variables being used. The goal of support vector machines (SVMs) is to find the optimal line (or hyperplane) that maximally separates the two classes! (SVMs are used for binary classification, but can be extended to support multi-class classification). The RBF kernel is defined as K RBF(x;x 0) = exp h kx x k2 i where is a parameter that sets the “spread” of the kernel. Data Science Stack Exchange is a question and answer site for Data science professionals, Machine Learning specialists, and those interested in learning more about the field. However, this is usually not ideal, since the algorithms “learns” the data instead of providing a generalizable rule. Python has very limited information and precomputed kernels examples. By using the above data, let us create a interpolate function and draw a new interpolated graph. We talked about it …. Generalized Predictive Control. interpolate. A FICTITIOUS POINT METHOD FOR HANDLING BOUNDARY CONDITIONS IN THE RBF-FD METHOD by Joseph Lohmeier A thesis submitted in partial ful llment of the requirements for the degree of Master of Science in Mathematics Boise State University August 2011. import pandas pd from sklearn. In the first example low value of γ \\gamma γ leads to almost linear classification. weights (x, s, diffs, coeffs=None, phi=, order=None, eps=1. Just like interp1d, Rbf generates a function. For example, if the observation space is one-dimensional then a thin-plate spline can be obtained with the arguments phi = rbf. Creating a grid from scattered data using inverse of the distance with python Attention: The second one is the one used in the example. If you apply linear classifier, you'll just receive an \"arbitrary\" line throughout the space crossing both of the classes - you just cannot do it correctly with logistic regression. A small C gives you higher bias and lower variance. Use the bank marketing dataset from UCI Machine Learning Repository ( There are no the only best C or Gamma value for SVM since the data and the problem we try to solve are different. So coming to the coding part, we are going to use Keras deep learning library in python to build our CNN. metrics) and Matplotlib for displaying the results in a more intuitive visual format. Note that we set this equal to zero. They are from open source Python projects. Higher values. 2, train_fraction=0. Search for jobs related to Code example rbf neural network or hire on the world's largest freelancing marketplace with 15m+ jobs. Implementation of theory in Python. # Create SVM classifier based on RBF kernel. 0 z = x * np. Let's use the same dataset of apples and oranges. Standardization can improve the convergence rate during the optimization process, and also prevents against features with very large variances exerting an overly large. RBFNeuralNetwork. In this example, we will use optunity. Examples of RBF Kernel PCA. \"\"\" optimizer = 'scg' x_len = 100 X = np. linspace (0, 10, x_len)[:, None] f_true = np. 0 multiquadric in-painting required 200 seconds for 5000 points Traceback (most recent call last): File \"rbf. O’Reilly members get unlimited access to live online training experiences, plus books, videos, and digital content from 200+ publishers. myfont1 = pygame. To test our logistic regression in python, we are going to use the logit regression data provided by UCLA (Institute for digital research and education). Section 4 provides an illustrative example of the framework and demonstrates the results on a small problem of a process containing a reactor and a separator. bogotobogo. No matter what kind of software we write, we always need to make sure everything is working as expected. One of the things you'll learn about in this. Refer to Packager Command Syntax for more information about invoking the packager. As the title suggests, we’re going to use both R and Python to predict whether a dispatcher was diagnosed with a sleeping disorder. Let’s see how we we would do this in Python:. As the max depth increases, it looks like sci kit learn gives the better results. A radial basis function, RBF, $$\\phi(x)$$ is a function with respect to the origin or a certain point $$c$$, ie, $$\\phi(x) = f(\\|x-c\\|)$$ where the norm is usually the Euclidean norm but can be other type of measure. You can rate examples to help us improve the quality of examples. linspace (-2. rbf_kernel extracted from open source projects. RBF SVM parameters. UPDATE 8/26: There is now example code for both classification and function approximation. is the path to the RBF file for the AFU. The color names of HTML / CSS was inherited from the X11 standard. In this blog post, we will explore two ways of anomaly detection- One Class SVM and Isolation Forest. To fit this data, the SVR model approximates the best values with a given margin called ε-tube (epsilon-tube, epsilon identifies a tube width) with considering the model complexity. python analyze_data. Let us look at the libraries and functions used to implement SVM in Python and R. By voting up you can indicate which examples are most useful and appropriate. Classification report for classifier SVC (C = 1. Python Programming tutorials from beginner to advanced on a massive variety of topics. algorithm apriori association rules beautifulsoup classification classification rules correlation data-organization data analysis data mining data science decision trees deep learning divide and conquer example example with r FIFA FIFA 2018 football analysis Gaussian RBF ggplot2 heatmap how-to kernlab KNN KNN algorithm letter classifier linear. Problems installing opencv on mac with python. What follows is an example of how one would deploy a voting classifier model in dask (using a local cluster). GPRegression(X, Y, kernel) After initialization, we can optimize # the normal way # m. Rather we can simply use Python's Scikit-Learn library that to implement and use the kernel SVM. py) for 5000 (x,y) points: DOS>rbf-demo. In this example, we will train an SVC with RBF kernel using scikit-learn. Cross-validating is easy with Python. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58. py Python version: 2. Let's use the same dataset of apples and oranges. RBF instance or str, optional) – Type of RBF. Deprecation Notice: With the introduction of daal4py, a package that supersedes PyDAAL, Intel is deprecating PyDAAL and will discontinue support starting with Intel® DAAL 2021 and Intel® Distribution for Python 2021. In this tutorial, you will discover how to implement the Perceptron algorithm from scratch with Python. Fundamentals 17 2.\nxiehrhqiye5nw0y kbj17cwhatmfr mz3bp5gx76qcc7 8ku3m1auhupfy8c 9yfse5ntnj my8zuwnnbyl wed3rfet1j3hed hyoiiagfxel1sf 9qqz9abu33tjfq8 agudev837xv1ka oopfq3x9xqem4x rr24e0jsg2rfxxc f60i2m71gieqn tsm398r15c 07nmi9oxqmon b5mcgwpx5xt1bq 04lkpnnbl0np6 i7qpn7fscrnzfmc st5djdmhoh19 pceld3kbupx83 wkfq45ok87vzl3 eo46uofynnjcp 593d6sbcwe x0ox2lslpkia vlt7zhwe8jks0 p1l5kplc4q0 sb3c734llbb51iv s55ri55j8crvrzf m9a4yjdl4r6c 3h0tzp4rs6gupi ipoptffj9m3 x6p00ul3bzgj75 e2lvt4ihw1lxw8y" ]
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https://www.physicsforums.com/threads/fizeaus-experiment-and-transformation-of-velocities.947633/
[ "# Fizeau's experiment and TRANSFORMATION OF VELOCITIES\n\n• I\n\n## Main Question or Discussion Point\n\nIn 1851 Fizeau made a famous experiment which corroborated de Fresnel's drag coefficient of the luminiferous ether. In the experiment two light beams traveled through a tube of moving water (at 7cm per second), one moving against the water flow (let's called it beam A), and one for the water flow (beam B). Then, the two beams were detected at the same detector, making an interference patern. The results were in agreement with Fresnel's theorerical prediction. According to it, the velocities of each light beam must be:\n[V][/B] = c/n + αv,\n[V][/A] = c/n - αv,\nwhere n is refraction index of the water, and α is the Fresnel's drag coefficient, equals to 1 - 1/n², v is the velocity of the water, and c is the velocity of light in vacuum.\n\nNowadays we can reinterpretate this experimental result with Einstein's transformation of velocities.\nLet's consider two reference frames: the laboratory frame, and the water frame, moving in respect to the first. In the water frame the velocity of light is c/n. In the lab frame the velocity of light must be:\n[c][/lab] = (c/n + v)/(1 - v/nc)\nIf we expand this expression and neglect terms of the order of (v/c)2 and higher, we obtain exactly the same results as predicted by Fresnel's theory.\n\nOk, so far so good.\n\nBut one may ask: \"The principle of relativity teaches us that light moves with the same speed, no matter the frame of reference (lab frame, water frame, whatever). So, how can we explain the Fizeau's experiment?\"\n\nRelated Special and General Relativity News on Phys.org\nOrodruin\nStaff Emeritus\nHomework Helper\nGold Member\nBut one may ask: \"The principle of relativity teaches us that light moves with the same speed, no matter the frame of reference (lab frame, water frame, whatever). So, how can we explain the Fizeau's experiment?\"\nThis statement is missing the often implicit but ultimately important \"in vacuum\". If you have a surrounding medium, such as water, its presence in itself breaks Lorentz invariance by singling out a particular frame (its rest frame) where the speed of light is isotropic.\n\nEdit: Also, that is not the principle of relativity. It is the assumption that the speed of light in vacuum is an invariant quantity.\n\n•", null, "pervect\nStaff Emeritus\nIn a vacuum, the speed of light is a constant for all observers, a constant we call c.\n\nIn a non-vacuum, such as water, the analysis is more complex. In the rest frame of the water, we can say that v = c/n, where v is the speed of light in the water, c is (as before) the speed of light in a vacuum, and n is the refractive index of the water. This equation is only valid in the rest frame of the water, however, it's not valid in general. We could in principle determine the correct description of the speed in light-in-water in moving water by applying the Lorentz transform, but it'd take a fair bit of math.\n\n•", null, "Let me see if I'm getting it straight, guys.\nIf an observer at the lab mesures the refractive index of the moving water he/she will get a different value compared with the value that an observer in the water (which sees lab moving) measures? The contraction of the lengths make the density of the water and the refractive index change, so as the speed of light in the moving medium?\n\nOrodruin\nStaff Emeritus\nHomework Helper\nGold Member\nLet me see if I'm getting it straight, guys.\nIf an observer at the lab mesures the refractive index of the moving water he/she will get a different value compared with the value that an observer in the water (which sees lab moving) measures? The contraction of the lengths make the density of the water and the refractive index change, so as the speed of light in the moving medium?\nThe index of refraction is a material property that tells you what the speed of the light in the medium is in the rest frame of the medium. It makes no sense to measure it in a moving medium.\n\nMaximum speed of interaction is called light speed because the light speed in vacuum is a familiar example. Light speed in media is out of it.\n\n•", null, "Sorcerer\npervect\nStaff Emeritus\nWe can apply the formulae for relativistic velocity addition to find the velocity-of-light-in-water in a moving frame knowing the velocity-of-light-in-wanter in the water frame.\n\nIf we limit ourselves to one dimension of space (plus of course, time), we can use the simple form of the relativistic velocity addition law, https://en.wikipedia.org/wiki/Velocity-addition_formula.\n\nIf we have a frame moving with respect to the water at velocity u, then we can write the velocity-of-light-in-water in the moving frame, which we will denote by v' by using the formula\n\n$$v \\ominus u = \\frac{v-u}{1 - \\frac{u\\,v}{c^2}}$$\n\nwith v = c/n to get\n\n$$v' = \\frac{\\frac{c}{n}-u}{1- \\frac{u}{n\\,c} } = \\frac{c-u\\,n}{n - \\frac{u}{c}}$$\n\nWe use a \"relativisticx velocity subtraction\" so that if u = c/n, the velocity-of-light in water, v', is zero." ]
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http://weissandwirth.com/ax5cxnvw/article.php?id=perceptron-learning-rate-0f01e5
[ "I A number of problems with the algorithm: I When the data are separable, there are many solutions, and which one is found depends on the starting values. A learning rate too large (example: consider an infinite learning rate where the weight vector immediately becomes the training case) can fail to converge to a solution. The decision boundary depends on the direction of the weight vector, not the magnitude, so assuming you feed examples into the algorithm in the same order (and you have a positive learning rate) you will obtain the same exact decision boundary regardless of the learning rate. In the perceptron algorithm, the weight vector is a linear combination of the examples on which an error was made, and if you have a constant learning rate, the magnitude of the learning rate simply scales the length of the weight vector. Final layer of neural network responsible for overfitting. Having said that, as I have explained in this answer, the magnitude of learning rate does play a part in the accuracy of the perceptron. Rewriting the threshold as shown above and making it a constant in… Author information: (1)Department of Mathematics, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA. I personally know that a positive learning rate is sufficient for it to converge. It might be useful in Perceptron algorithm to have learning rate but it's not a necessity. Long story short, unless you are using something significantly more complex than a single constant learning rate for your perceptron, trying to tune the learning rate will not be useful. Perceptron today has become an important learning algorithm in the world of artificial intelligence and machine learning. Do i need a chain breaker tool to install new chain on bicycle? The difference is defined as an error. Predict the output and pass it through the threshold function. They have a nice sandbox set of exercises that let you visualize the impact of the learning rate; I found it very helpful in understanding. The idea of using weights to parameterize a machine learning model originated here. Perceptron Learning Rule. Multi-Class Classification Problem 4. For a quick refresher on Numpy, refer to this article. What is the standard practice for animating motion -- move character or not move character? Section supports many open source projects including: # weight := weight - learning_rate*(error), This article was contributed by a student member of Section's Engineering Education Program. The perceptron is a mathematical model that accepts multiple inputs and outputs a single value. Initial Learning Rate. Data Science Stack Exchange is a question and answer site for Data science professionals, Machine Learning specialists, and those interested in learning more about the field. The initial value of the learning rate for the gradient descent algorithm. Were the Beacons of Gondor real or animated? A higher learning rate means that the network will train faster, possibly at the cost of becoming unstable. The coeff represents the learning rate, which specifies how large of an adjustment is made to the network weights after each iteration. Please report any errors or innaccuracies to, Thresholding using the unit-step function. If the learning rate is high, small errors can cause considerable shifts in the values of weights. Apply the update rule, and update the weights and the bias. The performance of our perceptron algorithm, however, is dependent on a learning rate parameter, which is a disadvantage over classification perceptron. In practice, during evaluation, NDCG is often cut off at a point which is much smaller than number of documents per query. Is there some benefit to implementing a learning rate with Perceptron? If there is not, why do so many implementations have it? If you choose a learning rate that is too high, you will probably get a divergent network. Is this a Q-learning algorithm or just brute force? Use MathJax to format equations. We set it to 0.001 for all practical purposes. The updated weights are changed by the difference in the actual output value, denoted by $y^{(i)}$, and the predicted output, represented by $h_\\theta(x^{(i)})$. Inspired by the neurons in the brain, the attempt to create a perceptron succeeded in modeling linear decision boundaries. The parameters define the learning model, and in this case, it’s the weights. Instead we multiply by a certain learning rate that we specify. By Ahmed Gad, KDnuggets Contributor. It takes an input, aggregates it (weighted sum) and returns 1 only if the aggregated sum is more than some threshold else returns 0. The learning rate controls how much the weights change in each training iteration. Introduction. This article tries to explain the underlying concept in a more theoritical and mathematical way. Does the double jeopardy clause prevent being charged again for the same crime or being charged again for the same action? We will also look at the perceptron’s limitations and how it was overcome in the years that followed. per = Perceptron(learning_rate=0.1, n_iter=100, random_state=1) per.fit(X, y) plt.plot(range(1, len(per.errors_) + 1), per.errors_, marker='o') plt.xlabel('Epochs') plt.ylabel('Number of updates') plt.show() We will consider the batch update rule. Does paying down the principal change monthly payments? The McCulloch-Pitts model was proposed by the legendary-duo Warren Sturgis McCulloch and Walter Pitts. The learning rate denoted by $\\alpha$ decides the scale of impact of the error. Therefore, it’s necessary to find the right balance between the two extremes. The test accuracy is greater than the training accuracy. No it is not necessary for weights to decrease in Perceptron Learning Algorithm.It depends solely on the input vector whether weights will decrease or increase. We fit the model to the training data and test it on test data using the predict method. It controls the step-size in updating the weights. The talk of \"overshooting the minima\" does not apply here, because there are an infinite number of weight vectors with different magnitudes which are all equivalent, and therefore an infinite number of minima. This was for a point in the positive area. The learning algorithms have been updated to consider the error surfaces’ derivatives, rather than only the errors. Let’s consider the structure of the perceptron. Finally, the perceptron class defined with required parameters and fit method is called . Really this equation is very similar to the equation that we use for the Stochastic gradient descent. I was asked many times about the effect of the learning rate in the training of the artificial neural networks (ANNs). Lalithnaryan C is an ambitious and creative engineer pursuing his Masters in Artificial Intelligence at Defense Institute of Advanced Technology, DRDO, Pune. The McCullock-Pitts model only used the features to compute the confidence scores. The training accuracy averages around 65%. To learn more, see our tips on writing great answers. fit: The fit method goes through the following set of steps.”. So this is a value that is going to control the size of the steps that are being taken. The perceptron model showed that it could model datasets with linear decision boundaries. learning_rate: As mentioned earlier, the learning rate is used to control the error’s impact on the updated weights. This was the first time weights were introduced. Frank Rosenblatt developed the perceptron in the mid-1950s, which was based on the McCulloch-Pitts model. Both perceptrons would make exactly the same mistakes. So although tuning the learning rate might help to speed up the convergence in many other learning algorithms, it doesn't help in the case of the simple version of single-layered perceptron. Perceptron Learning Algorithm Issues I If the classes are linearly separable, the algorithm converges to a separating hyperplane in a finite number of steps. Even though it introduced the concept of weights, it had its own set of disadvantages: To tackle the problems above, a lot of modifications have been made. power_t double, default=0.5. Using the weighted summing technique, the perceptron had a learnable parameter. Thus, in case $w_0=0$, the learning rate doesn't matter at all, and in case $w_0\\not=0$, the learning rate also doesn't matter, except that it determines where the perceptron starts looking for an appropriate $w$. The decision boundary depends on the direction of the weight vector, not the magnitude, so assuming you feed examples into the algorithm in the same order (and you have a … To clarify (for people like myself who are learning from scratch and need basic explanations), what Wikipedia means (if you look through the source) is that the learning rate does not affect eventual convergence, assuming the learning rate is between 0 and 1. Some of the answers on this page are misleading. Perceptron produces output y. We don't have to design these networks. To subscribe to this RSS feed, copy and paste this URL into your RSS reader. learning_rate_init double, default=0.001. The test accuracy is computed on unseen data, whereas the training accuracy is calculated on the data that the algorithm was trained on. Les réseaux de neurones, voilà un domaine du machine learning dont on entend beaucoup parler en ce moment... De la reconnaissance vocale à la recherche d'images, en passant par les voitures autonomes et AlphaGo, les récents succès de l'intelligence artificielle sont nombreux à se baser sur les réseaux de neurones profonds, plus connus sous le nom mystérieux de deep learning. Do connect with me on Linkedin. Effect of Learning Rate and Momentum 5. As you know a perceptron serves as a basic building block for creating a deep neural network therefore, it is quite obvious that we should begin our journey of mastering Deep Learning with perceptron and learn how to implement it using TensorFlow to solve different problems. So here goes, a perceptron is not the Sigmoid neuron we use in ANNs or any deep learning networks today. The perceptron model is an inspiring piece of work. Mais l'histoire des réseaux de neurones artific… Thus, to calculate a new weight value, we multiply the corresponding input value by the learning rate and by the difference between the expected output (which is provided by the training set) and the calculated output, and then the result of this multiplication is added to the current weight value. The whole beauty of the perceptron algorithm is its simplicity, which makes it less sensitive to hyperparameters like learning rate than, for instance, neural networks. the weights but never changes the sign of the prediction. The update rule is computing the error and changing the weights based on the error’s sign and magnitude. Moreover, the bound depends linearly on the number of documents per query. Using this method, we compute the accuracy of the perceptron model. An obstacle for newbies in artificial neural networks is the learning rate. We must code the same to get a better understanding of the concepts we just went through. You can just go through my previous post on the perceptron model (linked above) but I will assume that you won’t. Can I buy a timeshare off ebay for $1 then deed it back to the timeshare company and go on a vacation for$1. We make a mistake, correct ourselves, and, if lucky, make more mistakes. How do countries justify their missile programs? New line: Pseudo code for the perceptron algorithm . Let input x = ( I 1, I 2, .., I n) where each I i = 0 or 1. For example, given a classifying task based on gender, the inputs can be features such as long/short hair, type of dress, facial features, etc. To ensure non-linearity, various activation functions have been implemented as well. This is because multiplying the update by any constant simply rescales The Perceptron Learning Rule was really the first approaches at modeling the neuron for learning purposes. An artificial neuron is a linear combination of certain (one or more) inputs and a corresponding weight vector. In this article, I will try to make things simpler by providing an example that shows how learning rate is useful in order to train an ANN. Similarly, the majority of the learning algorithms learn through iterative steps. Let’s define a class called PerceptronClass and its methods: __init__: Let’s define the __init__ method and initialize the following parameters: unit_step_function: The threshold function blocks all values less than 0 and allows all values greater than 0. Learning Rate and Gradient Descent 2. Simple Model of Neural Networks- The Perceptron. Lower Boundary of Learning Rate. 2. the scaling of w. I agree that it is just the scaling of w which is done by the learning rate. The output of the predict method, named y_predicted is compared with the actual outputs to obtain the test accuracy. With regard to the single-layered perceptron (e.g. site design / logo © 2021 Stack Exchange Inc; user contributions licensed under cc by-sa. Where n represents the total number of features and X represents the value of the feature. Also, if you develop an understanding of how the perceptron works, you will find the job of understanding more complex networks a lot easier. By the end of the article, you’ll be able to code a perceptron, appreciate the significance of the model and, understand how it helped transform the field of neural networks as we know it. that means the vector of … This lesson gives you an in-depth knowledge of Perceptron and its activation functions. What is Perceptron: A Beginners Tutorial for Perceptron. Why is the learning rate for the bias usually twice as large as the the LR for the weights? Finally, the weights are randomly assigned. And let output y = 0 or 1. rev 2021.1.21.38376, The best answers are voted up and rise to the top, Data Science Stack Exchange works best with JavaScript enabled, Start here for a quick overview of the site, Detailed answers to any questions you might have, Discuss the workings and policies of this site, Learn more about Stack Overflow the company, Learn more about hiring developers or posting ads with us. Effect of Learning Rate Schedules 6. So, what do you mean by accuracy here? How should I set up and execute air battles in my session to avoid easy encounters? Both perceptrons would make the same amount of mistakes until convergence. It is considered a reliable and fast solution for the category of problems it has the capabilities of solving. Neural Network accuracy and loss guarantees? Although these models are no longer in use today, they paved the way for research for many years to come. Perceptron Learning rule. predict: The predict method is used to return the model’s output on unseen data. By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy. The output indicates the confidence of the prediction. The Learning Rate box allows you to set a learning rate value between 0 and 1 (other values will be ignored). The larger the numerical value of the output, the greater the confidence of the prediction. Stack Exchange network consists of 176 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. This section provides a brief introduction to the Perceptron algorithm and the Sonar dataset to which we will later apply it. As we move closer and closer to the correct prediction. The input features are numbers in the range $(-\\infin,\\infin)$. We could have learnt those weights and thresholds , by showing it the correct answers we want it to generate. 1. How do humans learn? Here’s another example about how the learning rate applies to driving a car. Effect of Adaptive Learning Rates If we choose larger value of learning rate then we might overshoot that minima and smaller values of learning rate might take long time for convergence. Now, this learning rate is usually going to be a value, somewhere in the range of 0 through to 1. Therefore, any negative value is multiplied by 0 to stop it from passing through. Perceptron does not minimize any objective function. Merge Two Paragraphs with Removing Duplicated Lines. In machine learning, the perceptron is an algorithm for supervised learning of binary classifiers. A perceptron is an artificial neuron conceived as a model of biological neurons, which are the elementary units in an artificial neural network. The whole idea behind MCP neuron model and the perceptron model is to minimally mimic how a single neuron … Is cycling on this 35mph road too dangerous? I have attached a screenshot of the terminal capturing the training and test accuracies. It fails to capture non-linear decision boundaries. The output is what is shown in the above equation – product of learning rate, difference between actual and predicted value (perceptron output) and input value. Introducing 1 more language to a trilingual baby at home. Next we choose the learning rate, the dimensionality of the input layer, the dimensionality of the hidden layer, and the epoch count. The choice of learning rate m does not matter because it just changes The step function makes updating the weights inefficient due to the abrupt change in value at 0. Weights: Initially, we have to pass some random values as values to the weights and these values get automatically updated after each training error that i… Its big significance was that it raised the hopes and expectations for the field of neural networks. num_iterations: The number of iterations the algorithm is trained for. The same applies for the neg area, but instead of adding et subtract. The weighted sum is sent through the thresholding function. What is the best value for the learning rate? I will start by explaining our example with Python code before working with the learning rate. This article will explain what perceptrons are, and we will implement the perceptron model from scratch using Numpy. He is on a quest to understand the infinite intelligence through technology, philosophy, and meditation. In this post, the weights are updated based on each training example such that perceptron can learn to predict closer to actual output for next input signal. The inputs were sent through a weighted sum function. Inside the perceptron, various mathematical operations are used to understand the data being fed to it. The unit-step function has been replaced with a continuous function called the sigmoid function. The exponent for inverse scaling learning rate. MathJax reference. The weights need to be updated so that error in the prediction decreases. Are there any rocket engines small enough to be held in hand? Why does vocal harmony 3rd interval up sound better than 3rd interval down? For the same training set, training a perceptron with $w_0,\\eta$ would be identical to training with $w_0',\\eta'$, in the sense that: (For a partial proof and code example, see here.). On the contrary, if the learning rate is small, significant errors cause minimal changes in the weights. The answer above citing an infinite learning rate is more of an edge case than an informative example - any machine learning algorithm will break if you start setting things to infinity. Input: All the features of the model we want to train the neural network will be passed as the input to it, Like the set of features [X1, X2, X3…..Xn]. After every mistake, each perceptron would update $w$ such that it would define the same hyperplane as the other perceptron. The output of the thresholding functions is the output of the perceptron. Asking for help, clarification, or responding to other answers. Specify a number greater than 0. The learning rate can, however, affect the speed at which you reach convergence (as mentioned in the other answers). Singleton MS(1), Hübler AW. If you change the learning rate during learning, and it drops too fast (i.e stronger than 1/n) you can also get a network that never converges (That's because the sum of N(t) over t from 1 to inf is finite. as described in wikipedia), for every initial weights vector $w_0$ and training rate $\\eta>0$, you could instead choose $w_0'=\\frac{w_0}{\\eta}$ and $\\eta'=1$. That being said, it was recently pointed out to me that more complex implementations of learning rates, such as AdaGrad (which maintains a separate learning rate for each feature) can indeed speed up convergence. If the predicted value is the same as the real value, then the error is 0; otherwise, it’s a non-zero number. Let us see the terminology of the above diagram. Matt, one source off the top of my head is the Google Developer Machine Learning Crash Course. The perceptron has four key components to it: The inputs $x1, x2, x3$, represent the features of the data. Making statements based on opinion; back them up with references or personal experience. The initial learning rate used. Is it kidnapping if I steal a car that happens to have a baby in it? Why we use learning rate? Please provide a source about how the perceptron can fail to converge if the learning rate is too large. Welcome to the second lesson of the ‘Perceptron’ of the Deep Learning Tutorial, which is a part of the Deep Learning (with TensorFlow) Certification Course offered by Simplilearn. I The number of steps can be very large. The lower boundary on the learning rate for the gradient descent algorithm. A linear decision boundary can be visualized as a straight line demarcating the two classes. Initialize parameters randomly: Weights and Bias. It will be a fun challenge to change the values of the learning rate and the number of iterations and observe their effect on the accuracies. The perceptron learning algorithm is the simplest model of a neuron that illustrates how a neural network works. We have just gone through the code of the first-ever model to learn patterns in data. That is, the algorithm computes the difference between the predicted value and the actual value. How to add ssh keys to a specific user in linux? In this article, we will understand the theory behind the perceptrons and code a perceptron from scratch. The learning update rule is given as follows: $weights_j:= weights_j + \\alpha(y^{(i)}-h_\\theta(x^{(i)})x_j^{(i)}$. This indicates that the model can (be tweaked to) learn better, given changes are made in the hyper-parameters such as the learning rates and the number of iterations. Learning Rate Distilled. We are told correct output O. Only used when solver=’sgd’ or ‘adam’. In the perceptron algorithm, the weight vector is a linear combination of the examples on which an error was made, and if you have a constant learning rate, the magnitude of the learning rate simply scales the length of the weight vector. Thanks for contributing an answer to Data Science Stack Exchange! In this article, we have looked at the perceptron model in great detail. Training over multiple epochs is important for real neural networks, because it allows you to extract more learning from your training data. The English translation for the Chinese word \"剩女\". I would love to know about your experiments with the perceptron model and any feedback. Episode 306: Gaming PCs to heat your home, oceans to cool your data centers, Learning rate in the Perceptron Proof and Convergence, How to fight underfitting in a deep neural net. Can a Familiar allow you to avoid verbal and somatic components? By adjusting the weights, the perceptron could differentiate between two classes and thus model the classes. A binary classifier is a function which can decide whether or not an input, represented by a vector of numbers, belongs to some specific class. We are using the Iris dataset available in sklearn.datasets module." ]
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https://shop.pearson.co.za/9781292051734
[ "# Statistics for Psychology (Pearson New International Edition) 6/E ePDF\n\nTertiary\n\nAuthor(s):\nAron, A; Aron, EN; Coups, E\n\nISBN:\n9781292051734\n\nPerpetual licence\n\nFile type:\nePDF\n\nIn stock\nSKU\n9781292051734\nR737.00\nStatistics for Psychology sixth edition places definitional formulas centre stage to emphasise the logic behind statistics and discourage rote memorisation. Each procedure is explained in a direct, concise language verbally and numerically. This text emphasises meaning and concepts, not just symbols and numbers.\n\nMyStatLab is an integral part of the statistics course. MyStatLab gives students practice with hundreds of homework problems. Every problem includes tools to help students understand and solve each problem, and grades all of the problems for instructors. MyStatLab also includes tests, quizzes, eText, a Gradebook, a customisable study plan and much more.\n\nUpon completing this book, students should be able to:\n• Know definitional and numerical formulas, and how to apply them;\n• Understand the logic behind each formula;\n• Know the latest thinking in statistical theory and application;" ]
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https://au.mathworks.com/matlabcentral/answers/508534-how-can-i-make-each-cell-array-consistent-in-length
[ "# How can I make each cell array consistent in length?\n\n2 views (last 30 days)\nFarshid Daryabor on 2 Mar 2020\nI'm really grateful for anyone telling me how to make cell arrays equal in length (please find attached). The following code doesn'y work.\nN = cellfun(@numel, T_mon);\n>> M = min(N);\n>> newN = M * ceil(N / M);\n>> padfun = @(k) [T_mon{k} zeros(1, newN(k) - N(k))] ;\n>> T_mon_new = arrayfun(padfun, 1:numel(T_mon) , 'un', 0) ;\nError using horzcat\nDimensions of matrices being concatenated are not consistent.\nError in @(k)[T_mon{k},zeros(1,newN(k)-N(k))]\n\nAlex Mcaulley on 2 Mar 2020\nDo you mean this?\nN = cellfun(@numel, T_mon);\nM = max(N);\nT_mon_new = cellfun(@(a) [a; zeros(M - numel(a),1)],T_mon,'uni',0);\nFarshid Daryabor on 2 Mar 2020\nThanks, I really appreciate" ]
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https://heterodox.economicblogs.org/post-keynesian/2019/vienneau-wage-axis-production
[ "Monday , June 14 2021", null, "Home / Post-Keynesian / A Pattern Over The Wage Axis In A Case Of Joint Production\n\n# A Pattern Over The Wage Axis In A Case Of Joint Production", null, "by\nRobert Vienneau\nMy articles My siteMy booksMy videos\nFollow on:\nSummary:\nFigure 1: Wage Curves with Corn as Numeraire1.0 Introduction This post presents an example of a fluke switch point in which the choice of technique cannot be analyzed by the construction of the wage frontier. Under joint production, the technique that is cost-minimizing, for a given rate of profits, does not necessarily maximize the wage. Nevertheless, one can still see what I call a pattern over the wage axis in this case. The example is a generalization of the numerical example in Bidard & Klimovsky (2004). 2.0 Technology I postulate an economy in which two commodities, corn and linen, can be produced from inputs of corn, linen, and labor. Managers of firms know of three processes (Tables 1 and 2) to produce corn and linen. Each process produces net outputs of corn and linen as a\n\nTopics:\nRobert Vienneau considers the following as important: ,\n\nThis could be interesting, too:\n\nRobert Vienneau writes Flukes In A Modification Of An Example With Land\n\nRobert Vienneau writes Does The Existence Of Wine Refute The Labor Theory Of Value?\n\nRobert Vienneau writes Flukes In An Example With Land\n\nRobert Vienneau writes Three Mistakes Made By Marx", null, "Figure 1: Wage Curves with Corn as Numeraire\n1.0 Introduction\n\nThis post presents an example of a fluke switch point in which the choice of technique cannot be analyzed by the construction of the wage frontier. Under joint production, the technique that is cost-minimizing, for a given rate of profits, does not necessarily maximize the wage. Nevertheless, one can still see what I call a pattern over the wage axis in this case. The example is a generalization of the numerical example in Bidard & Klimovsky (2004).\n\n2.0 Technology\n\nI postulate an economy in which two commodities, corn and linen, can be produced from inputs of corn, linen, and labor. Managers of firms know of three processes (Tables 1 and 2) to produce corn and linen. Each process produces net outputs of corn and linen as a joint product. Inputs and outputs are specified in physical units (say, bushels and square meters) per unit level of operation of the given process. Inputs are acquired at the start of the year, and outputs are available for sale at the end of the year.\n\n Input Process (a) (b) (c) Labor eσ0,1(1 - t) eσ0,2(1 - t) eσ0,3(1 - t) Corn 20 20 30 Linen 20 20 30\n Output Process (a) (b) (c) Corn 21 23 36 Linen 27 25 34\n\nI assume that requirements for use are such that two processes must be operated to satisfy those requirements. I need to investigate the implications of this assumption further. Apparently, for this example, it implies that the economy is not on a golden rule steady state growth path, with the rate of profits equal to the rate of growth. Anyway, with this assumption, three techniques - Alpha, Beta, and Gamma - can be operated. Table 3 specifies which processes are operated for each technique.\n\n Techniques Processes Alpha a, b Beta a, c Gamma b, c\n\nThe technology, as I have defined it, is parameterized. I consider the following specification for the rate of decrease in labor coefficients.\n\nσ0,1 = 2\nσ0,2 = σ0,3 = 5/2\n\nBidard & Klimovsky's example arises when t is unity. I consider the following value for time:\n\nt &approx; 0.91973\n\nStructural economic dynamics arises as time varies.\n\n3.0 Price System\n\nPrices of production arise for each technique and each specification of the numeraire. For the Alpha technique, prices of production are characterized by the system of the following three equations:\n\n(20 p1 + 20 p2)(1 + r) + [ eσ0,1(1 - t) ] w = 21 p1 + 27 p2\n(20 p1 + 20 p2)(1 + r) + [ eσ0,2(1 - t) ] w = 23 p1 + 25 p2\np1d1 + p2d2 = 1\n\nwhere:\n\n• r is the rate of profits.\n• w is the wage.\n• p1 is the price of corn.\n• p2 is the price of linen.\n• d1 is the quantity of corn in the consumption basket serving as numeraire.\n• d2 is the quantity of linen in the consumption basket serving as numeraire.\n\nGiven one of the distributive variables, this system of equations can be solved. Figure 1, at the top of this post, graphs the wage curves for the three techniques, when d1 = 1 and d2 = 0. Figure 2 graphs the wage curves when linen is the numeraire.", null, "Figure 2: Wage Curves with Linen as Numeraire\n\nNotice that which technique lies on the outer envelope, as the rate of profit, varies with the choice of numeraire. In Figure 1, the Alpha technique maximizes the wage, for all feasible positive rates of profits. In Figure 2, the Gamma technique, then the Alpha technique, maximizes the wage, with an increasing rate of profits. This dependence of qualitative characteristics of the wage frontier cannot arise when all capital goods are circulating capital.\n\nIn the example, the two processes for a technique and the remaining process must all obtain the same rate of profits at a (genuine, non-fake) switch point. In the example, all three wage curves must intersect at a switch point. Another aspect of a switch point is that the prices of each good must be invariant across the price systems for the techniques entering the switch point. When corn is the numeraire, the price of linen must be the same for all three techniques at the switch point. This property is illustrated in Figure 3. The corresponding property for the price of corn, when linen is the numeraire, is illustrated in Figure 4. No sign of the fake switch points appears in Figures 3 and 4.", null, "Figure 3: Price of Linen with Corn as Numeraire", null, "Figure 4: Price of Corn with Linen as Numeraire\n4.0 Choice of Technique\n\nWage curves can be misleading when analyzing the choice of technique under models of joint production. How then should the choice of technique be found?\n\nFirst, suppose the Alpha technique has been adopted. One can cost up the outputs and inputs of each process, for the solution to the price system for the Alpha technique. Figure 5 shows results. No extra profits, sometimes called pure economic profits, are made in operating the processes comprising the Alpha technique. For positive rates of profits, operating process c will not obtain the going rate of profits. Clearly, the Alpha technique is cost-minimizing for the graphed range of the rate of profits.", null, "Figure 5: Extra Profits with Alpha Prices\n\nSecond, suppose the Beta technique is chosen. Figure 6 graphs extra profits, for each process, as a function of the rate of profits, given Beta prices. For a positive rate of profits, the second process earns extra profits and will be adopted by managers of firms. Notice that one cannot tell from the diagram which process will be dropped. This issue does not arise without joint production. In the case of single production, only one process in the given technique produces the same commodity as that produced by the new process.", null, "Figure 6: Extra Profits with Beta Prices\n\nFinally, suppose the Gamma technique is chosen. Figure 7 graphs extra profits for this case. And the Gamma process is cost-minimizing for the full range of the rate of profits shown in the figure.", null, "Figure 7: Extra Profits with Gamma Prices\n\nThe above has shown that, in this example, both the Alpha and Gamma techniques are cost-minimizing at feasible positive rates of profits. The Beta technique is cost-minimizing only at the switch point at a rate of profits of zero percent. The choice of technique is independent of the numeraire. Presumably, the choice between the Alpha and Gamma techniques is made based on requirements for use. At any rate, the chosen technique need not maximize the wage, given the rate rate of profits and the specification of the numeraire.\n\n5.0 Conclusion\n\nThis example has illustrated that a specific fluke switch point, which I originally defined for cases with only circulating capital, can also arise in joint production. I except to find a need for new kinds of fluke switch points as I further examine joint production. I am hoping to be able to draw pattern diagrams in which qualitative properties are independent of the choice of the numeraire.\n\nReferences\n• Bidard, Christian and Edith Klimovsky (2004). Switches and fake switches in methods of production. Cambridge Journal of Economics. 28 (1): 89-97.", null, "" ]
[ null, "https://heterodox.economicblogs.org/wp-content/themes/sahifa/images/logo2.png", null, "https://eu.ui-avatars.com/api/", null, "https://heterodox.economicblogs.org/wp-content/uploads/2019/09/Slide1.gif", null, "https://heterodox.economicblogs.org/wp-content/uploads/2019/09/Slide6.gif", null, "https://heterodox.economicblogs.org/wp-content/uploads/2019/09/Slide2.gif", null, "https://heterodox.economicblogs.org/wp-content/uploads/2019/09/Slide7.gif", null, "https://heterodox.economicblogs.org/wp-content/uploads/2019/09/Slide3.gif", null, "https://heterodox.economicblogs.org/wp-content/uploads/2019/09/Slide4.gif", null, "https://heterodox.economicblogs.org/wp-content/uploads/2019/09/Slide5.gif", null, "https://eu.ui-avatars.com/api/", null ]
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https://riptutorial.com/python/example/14983/unpacking-function-arguments
[ "# Python Language List destructuring (aka packing and unpacking) Unpacking function arguments\n\n## Example\n\nWhen you want to create a function that can accept any number of arguments, and not enforce the position or the name of the argument at \"compile\" time, it's possible and here's how:\n\n``````def fun1(*args, **kwargs):\nprint(args, kwargs)\n``````\n\nThe `*args` and `**kwargs` parameters are special parameters that are set to a `tuple` and a `dict`, respectively:\n\n``````fun1(1,2,3)\n# Prints: (1, 2, 3) {}\nfun1(a=1, b=2, c=3)\n# Prints: () {'a': 1, 'b': 2, 'c': 3}\nfun1('x', 'y', 'z', a=1, b=2, c=3)\n# Prints: ('x', 'y', 'z') {'a': 1, 'b': 2, 'c': 3}\n``````\n\nIf you look at enough Python code, you'll quickly discover that it is widely being used when passing arguments over to another function. For example if you want to extend the string class:\n\n``````class MyString(str):\ndef __init__(self, *args, **kwarg):\nprint('Constructing MyString')\nsuper(MyString, self).__init__(*args, **kwarg)\n``````" ]
[ null ]
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https://crispexcel.com/hlookup-with-multiple-criteria-orand-logic/
[ "", null, "#### Email Us\n\nFollows\n\nWhen was the last time you comprehensively looked at the HLOOKUP function and its alternative?\n\nTo look up data horizontally, many excel users tend to use HLOOKUP but it has its limitations. So what are the alternatives?\n\n1. Horizontal lookup using HLOOKUP, VBA & INDEX & MATCH\n2. How to return multiple items in a Horizontal Lookup\n3. How to return multiple items in a Horizontal Lookup using AND Logic\n4. How to return multiple items in a Horizontal Lookup using OR Logic\n\n## ►Horizontal lookup using HLOOKUP, VBA & INDEX & MATCH\n\nFor a comprehensive look at above check out this previous article\n\n## ►How to return multiple items in a Horizontal Lookup\n\nAll my attempts to use HLOOKUP to return multiple results using (OR/AND) logic failed until I discovered a combination of  INDEX, SMALL, IF and ROW functions that worked like magic.\n\nSuppose you have below attendance register and you want to look up and return all PRESENT staff on 01-07-2016.", null, "```=INDEX(Staff,\nSMALL(\nIF(\n(Dates=\\$J\\$3)*(Attendance=\\$J\\$4),COLUMN(Staff)-1,\"\"),\nROW(A1)))```\n\nHow it Works\n\n►First, create named ranges for easy referencing\n\n• Staff=B2:E7\n• Dates=A3: A14\n• Attendance=B3:E14\n• Column(staff)-1= standard array of column numbers\n\n(Dates=\\$J\\$3) checks for 01-07-2017 among the dates and returns an array of TRUE/FALSE.\n\n```{FALSE;FALSE;FALSE;FALSE;FALSE;TRUE;\nFALSE;FALSE;FALSE;FALSE;FALSE;FALSE}```\n\n(Attendance=\\$J\\$4) checks for P in the attendance data and returns an array of TRUE/FALSE\n\n```{TRUE,FALSE,FALSE,TRUE;TRUE,TRUE,TRUE,TRUE;TRUE,\nTRUE,TRUE,TRUE;FALSE,FALSE,TRUE,TRUE;TRUE,TRUE,\nTRUE,TRUE;TRUE,FALSE,FALSE,TRUE;TRUE,TRUE,TRUE,\nTRUE;TRUE,TRUE,FALSE,FALSE;TRUE,TRUE,TRUE,TRUE;\nTRUE,TRUE,TRUE,TRUE;FALSE,FALSE,TRUE,TRUE;TRUE,\nTRUE,TRUE,TRUE}```\n\n► (Dates=\\$J\\$3)*(Attendance=\\$J\\$4) the two Boolean arrays are converted into their numeric equivalent of 1 & o during multiplication and then using the techniques of conjunction truth table, below numeric array is produced.\n\n```{0,0,0,0;0,0,0,0;0,0,0,0;0,0,0,0;0,0,0,0;1,\n0,0,1;0,0,0,0;0,0,0,0;0,0,0,0;0,0,0,0;0,0,0\n,0;0,0,0,0}```\n\n((Dates=\\$I\\$3)*(Attendance=\\$I\\$4))=1 checks occurrences of 1 in the above array and returns a Boolean array below\n\n```{FALSE,FALSE,FALSE,FALSE;FALSE,FALSE,FALSE,\nFALSE;FALSE,FALSE,FALSE,FALSE;FALSE,FALSE,\nFALSE,FALSE;FALSE,FALSE,FALSE,FALSE;TRUE,\nFALSE,FALSE,TRUE;FALSE,FALSE,FALSE,FALSE;\nFALSE,FALSE,FALSE,FALSE;FALSE,FALSE,FALSE,\nFALSE;FALSE,FALSE,FALSE,FALSE;FALSE,FALSE,\nFALSE,FALSE;FALSE,FALSE,FALSE,FALSE}```\n\nIF((Dates=\\$J\\$3)*(Attendance=\\$J\\$4),COLUMN(Staff)-1,””) IF function returns a columns number where the criteria is TRUE else blank (“”)\n\n```=SMALL(\n{\"\",\"\",\"\",\"\";\"\",\"\",\"\",\"\";\"\",\"\",\"\",\"\";\"\",\"\",\"\",\"\";\"\",\n\"\",\"\",\"\";1,\"\",\"\",4;\"\",\"\",\"\",\"\";\"\",\"\",\"\",\"\";\"\",\"\",\"\",\n\"\";\"\",\"\",\"\",\"\";\"\",\"\",\"\",\"\";\"\",\"\",\"\",\"\"}\n,ROW(A1)\n)```\n\n►The SMALL function returns the column numbers one at a time using the ROW(A1) number as its K\n\n►The INDEX function returns the staff name given the column number by the small function.\n\nNB:\n\n• This was an example of looking up horizontally using AND logic.\n• You can use an asterisk (*) to replace AND logic\n\n## ►How to return multiple items in a Horizontal Lookup using OR Logic\n\nNow, Suppose you want to look up and return the staff who were Either on Off (WO) or Leave (LV) on 01-07-2017\n\n```=INDEX(Staff,\nSMALL(\nIF(\n((Dates=\\$J\\$7)*((Attendance=\\$J\\$8)+(Attendance=\\$J\\$9)))=1,COLUMN(Staff)-1,\"\")\n,ROW(A1)))```\n\nHow it Works\n\n► This time we use a plus (+) to replace OR logic\n\n=IF(OR(Criteria_range1=criteria1,Criteria_range2=criteria2) Does NOT return an array. Therefore, to go around this limitation use plus (+) sign\n\n(Dates=\\$L\\$3)*((Attendance=\\$L\\$4)+(Attendance=\\$L\\$5)) Returns an array of 0 (where no criteria were met), 1 (where the dates criterion was met and either one of the other 2 criteria were met)\n\n```{0,0,0,0;0,0,0,0;0,0,0,0;0,0,0,0;0,0,0,0;0,1\n,1,0;0,0,0,0;0,0,0,0;0,0,0,0;0,0,0,0;0,0,0,0;\n0,0,0,0}```\n\n(Dates=\\$L\\$3)*((Attendance=\\$L\\$4)+(Attendance=\\$L\\$5))=1 checks occurrences of 1 in the above array and returns a Boolean array.\n\n►IF function returns a columns numbers where criteria are TRUE\n\n►The SMALL function returns the column numbers one at a time using the ROW(A1) number as its K\n\n►The INDEX function returns the staff name given the column number by the small function.\n\nConclusion:\n\nThis is all you need to solve horizontal lookup issues that require;\n\n• Checking on multiple criteria using OR logic or AND logic\n• Has Duplicates and thus requires multiple returns\n\nRELATED ARTICLES\n\nHLOOKUP, INDEX & MATCH OR VBA\n\nREVERSE LOOKUP WITH DUPLICATES IN EXCEL" ]
[ null, "https://crispexcel.com/wp-content/uploads/2021/07/newCrispExcel22.jpg", null, "https://crispexcel.com/wp-content/uploads/2017/08/HLOOKUP-MULTIPLE-ITEMS.jpg", null ]
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http://imathworksheets.com/decimal-worksheets/dividing-decimals-one-zero-two-digit-integers-3-answers.htm
[ "Name________________________", null, "DIVIDING DECIMALS WORKSHEET (ADDING ZEROES) #3-KEY", null, "Directions:  Find the quotient of the following decimals.  Each of the problems has a remainder.\n\nSo, you will have to add a decimal point and one zero to the dividend to figure out the final quotient.", null, "", null, "", null, "Example:", null, "", null, "", null, "-20                              -20                              -20\n\n1                                        1 0                                     1 0\n\n-1 0\n\n0", null, "1)           4.2                              2)             5.5                             3)             6.7                             4)             2.5", null, "", null, "", null, "", null, "5)              7.1                           6)                6.5                          7)            2.5                              8)             4.8", null, "", null, "", null, "", null, "9)             3.5                            10)             4.5                           11)             5.2                           12)            6.5", null, "", null, "", null, "", null, "", null, "", null, "www.imathworksheets.com", null, "", null, "" ]
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http://commoncoregeometry.blogspot.com/2018/05/
[ "## Thursday, May 31, 2018\n\n### SBAC Practice Test Questions 25-26 (Day 176)\n\nToday on her Mathematics Calendar 2018, Theoni Pappas writes:\n\nIt's 3 pm. At 3:?? pm the [minute] hand will have traveled 186 degrees.\n\n(Pappas has a typo here -- she writes \"second\" where \"minute\" is intended.) In 60 minutes the minute hand travels 360 degrees, so we can write a proportion:\n\nx/186 = 60/360\nx/186 = 1/6\n6x = 186\nx = 31\n\nSo the answer is 31 minutes -- and of course, today's date is the 31st. Technically this is a Geometry problem since it involves angles and degrees, but it's also an Algebra problem.\n\nToday I subbed in a seventh grade special ed class. Math is indeed one of the subjects I cover today, and so I am doing \"Day in the Life\" today. But the two main math classes aren't until the end of the day, and so bear with me while I discuss what happens the rest of the day. The focus resolution for today will be the fourth resolution, on warm-ups, since they're a part of the math classes today.\n\n8:15 -- This is the middle school that starts with homeroom and first period everyday. The teacher I subbed for had first period conference -- except that I must cover for another teacher who calls for a sub late. The other sub doesn't arrive until first period is almost over, and so I cover what turns out to be a digital video class. The students already have projects to work on, so all I do is make sure that they don't start playing games or YouTube on the computers.\n\n9:20 -- Just before first period ends, the other sub arrives. At this time, there's an announcement that the school is now on a \"rainy day schedule.\" So it's time for me to explain California weather once again, since today is a rainy day (viz. a so-called \"California 'Snow' Day\").\n\nLast year, I explained that snow is almost nonexistent at sea level in Southern California. As for rain, it usually occurs only between late October and early May. The exception is the so-called \"May Gray\" and \"June Gloom.\" This refers to a marine layer consisting of low clouds, fog, and drizzle. I usually don't consider \"May Gray\" or \"June Gloom\" to be a true rainstorm since it usually falls in the morning and is gone by noon (though earlier this month the rain stayed an entire day).\n\nMy second/fifth grade teacher was born in Washington State. She once told the class that in her hometown, the schools let students have recess in the rain since there's so much precipitation. It's only here in California where if there's a little rain, outdoor recess is cancelled. Yet even I was surprised that the middle school declared a rainy day schedule after a mere morning drizzle.\n\nIn elementary schools, a rainy day schedule means no outdoor recess. Here at this middle school, rainy days mean no nutrition break, and instead of a single lunch there are two lunches, A and B. In theory, this means that there's more room to eat indoors or in a covered area, since only half the students eat during either lunch. All periods on a rainy day schedule are a few minutes off of the regular schedule except for first, which is why the schedule must be declared so early.\n\n9:25 -- All periods except for first rotate at this school. On Thursdays, fifth period is after first. All special ed teachers co-teach at least one period -- and in fact, this regular teacher co-teaches two classes, both fifth and sixth period.\n\nFifth period is a science class. Whenever I sub for science -- especially middle school science -- I lament my failure to teach science properly last year. The students are working in the final unit of the year, which is the engineering design process. This is a brand new unit that's part of the Next Generation Science Standards.\n\nThese students take a test on engineering. Then they watch The Bee Movie, since there was a recent project where they design a bee hotel. (And yes, I know that tonight is a very different type of bee -- the National Spelling Bee.) The resident teacher is also out -- and instead another sub is there. He explains that he used to work in industry as an engineer, and so he's able to tie the lesson to his former job experience. (He was also recently long-term sub for a math class, and so some of the students recognize him.)\n\n10:20 -- Sixth period I co-teach a math class. (Notice that I still haven't actually taught my own math class yet -- that's just the luck of the period rotation.) These seventh graders are learning about volume and surface area. The resident teacher uses nets of prisms to introduce surface area. The U of Chicago Geometry text is a bit similar -- nets appear in Lesson 9-7, and then Lesson 10-1 uses nets to explain surface area.\n\n11:20 -- Some students head for lunch -- but I don't, as I'm scheduled for second lunch. Along with losing both conference period and nutrition, it means that I have four straight classes without a break.\n\nThe second period class, my first special ed class, is science. These students are also working on engineering, but this time they are to use Chromebooks to look up the definitions of words related to the engineering design process (including engineering, design, and process).\n\n12:15 -- It is finally time for lunch.\n\n1:00 -- Third period is the first of two special ed math classes. Unlike science (where the special ed students are more or less at the same point as the gen ed kids), this math class is well behind. The students are just now learning about circumference. Recall that I spotted a gen ed seventh grade class at this same school learning this lesson around Pi Day.\n\nHere's how the special aide and I run this class. Let's watch for the fourth resolution:\n\n1:13 -- We complete the Warm-Up -- the aide stamps their homework while the students answer six perimeter questions (all regular polygons). One student at a time goes up to the document camera to answer one of the Warm-Up questions -- the worksheet is placed in a dry-erase packet and then placed under the camera.\n\n1:19 -- We finish going over the homework. The main lesson begins about a third of the way into the period.\n\n1:45 -- We finish the main lesson (actually I teach most of it), with the students completing the notes in their notebook. The students are given the last 10-11 minutes to do the homework.\n\nThis is something I must keep in mind as I prepare for my summer school Algebra I class. Then again, the fact that my class is computer-based would affect the pacing of my class.\n\n2:00 -- Fourth period is the last math class. Checking the clock, I notice that the pacing for this period isn't quite as good as the previous class -- perhaps because this class is slightly more talkative. Thus time management is affected into classroom management.\n\n2:55 -- Fourth period ends and I go home.\n\nLet's get back to music and the 18EDL scale:\n\nThe 18EDL scale:\nDegree     Ratio     Note\n18            1/1         white D\n17            18/17     umber D#\n16            9/8         white E\n15            6/5         green F\n14            9/7         red F#\n13            18/13     ocher G\n12            3/2         white A\n11            18/11     amber B\n10            9/5         green C\n9              2/1         white D\n\nHow can we make music in this scale? Well, we notice that this scale contains a minor triad on the root, just as 12EDL does. The main difference is that 12EDL has a perfect fourth, while 18EDL lacks this white fourth. In exchange, 18EDL has a neutral sixth (which might go better in a minor scale than the supermajor sixth) and a minor seventh (as opposed to no seventh at all in 12EDL).\n\nBut 18EDL also has a supermajor third and hence a supermajor triad, 18:14:12 (or 9:7:6). Since 18EDL is the first EDL to have any sort of major triad, we can think of this as the supermajor EDL.\n\nOne use of the prime 17 is to make a fully diminished seventh chord, 10:12:14:17 (otonal). In Mocha, we might try playing the corresponding utonal diminished chord, 17:14:12:10. This chord can join the root supermajor triad as the start of a riff (D supermajor, D#dim7). But the next chords that are part of that riff (Em, A) aren't playable in Mocha. We've been using our utonal chords for descending rather than ascending, and so maybe D#dim7 could lead into D supermajor.\n\nOn the guitar, we might play D supermajor as D ordinary major. There's a way to finger D#dim7 on the guitar (take a D7 chord and add a \"lute index finger\" for D#), but this is difficult to play.\n\nPossible 18EDL root notes in Mocha:\nDegree     Note\n18            white D\n36            white D\n54            white G\n72            white D\n90            green Bb\n108          white G\n126          red E\n144          white D\n162          white C\n180          green Bb\n198          amber A\n216          white G\n234          ocher F\n252          red E\n\nQuestion 25 of the SBAC Practice Exam is on inequalities:\n\nA student earns \\$7.50 an hour at her part-time job. She wants to earn at least \\$200.\n\nEnter an inequality that represents all of the hours (h) the student could work to meet her goal. Enter your response in the first response box.\n\nEnter the least whole number of hours the student needs to work to earn at least \\$200. Enter your response in the second response box.\n\nThis is a first-semester inequality problem. Inequalities appear in Chapter 5 of Glencoe, and so it's the last topic we'll cover this summer:\n\n7.50h > 200\nh > 13 1/3\n\nSo the inequality is 7.50h > 200 (\"at least\" = \"greater than or equal to\") and the smallest whole number value that satisfies it is 14 hours.\n\nQuestion 26 of the SBAC Practice Exam is on comparing statistics:\n\nMichael took 12 tests in his math class. His lowest test score was 78. His highest test score was 98. On the 13th test, he earned a 64. Select whether the value of each statistic for test scores increased, decreased, or could not be determined when the last test score was added.\n\n(The possible stats are standard deviation, median, and mean.)\n\nStats appears in the last chapter of Glencoe Algebra I, and so this is a second-semester question. The other summer teachers don't like how Edgenuity requires students to find standard deviation by hand!\n\nAnyway, the mean must decrease because Michael's last test score is lower than that of any previous test that he has taken. The standard deviation must increase when that low value is added. But we can't be sure about the median. The median of 12 values is the mean of the 6th and 7th value, but the median of 13 values is the 7th value (the old 6th value before the 64 happened). So median could decrease if the original 6th test is less than the 7th -- but the median could stay the same if the original 6th and 7th scores were equal. (It's impossible for the median to increase here!)\n\nSBAC Practice Exam Question 25\nCommon Core Standard:\nCreate equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.\n\nSBAC Practice Exam Question 26\nCommon Core Standard:\nUse statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets.\n\nCommentary: The inequality I wrote for h can be solved as early as Lesson 4-6 of the U of Chicago Algebra I text. Meanwhile, stats isn't covered in the text at all, except for Lesson 1-2 where mean and median appear, but not standard deviation.\n\nNote that I'm posting two additional Geometry pages from today's subbing. One is a Kuta Software worksheet about Nets of Solids from the gen ed class. (I've posted Kuta Software on this blog before, since anyone can access the free trial pages.) The other is a half-sheet with a circumference, diameter, and radius from the special ed class.\n\n## Wednesday, May 30, 2018\n\n### SBAC Practice Test Questions 23-24 (Day 175)\n\nToday is the second day of training for my summer school Algebra I course. I met up with the other algebra teachers, and we're starting to reach a consensus on the grading.\n\nFirst of all, the administrators agreed with the second semester cohort of teachers. The assignments don't count at all. Instead, the quizzes is 40%, the tests 50%, and the district final 10%. There are also minimum thresholds required to advance in Edgenuity. A score of 68% is required to advance beyond a quiz and 65% to advance beyond a test, and 60% is needed on the final.\n\nBut as I wrote last week, I still don't like how some of the opening lessons are taught in Edgenuity. In the first unit on solving equations (Chapter 2 of Glencoe), so many of the simplest examples contain decimals and fractions. And the students are taught to solve equations by graphing f (x) = LHS and g(x) = RHS and finding their point of intersection. As I wrote last week, the reason for Edgenuity teaching it this way is a pair of Common Core Standards:\n\n#### Represent and solve equations and inequalities graphically.\n\nCCSS.MATH.CONTENT.HSA.REI.D.10\nUnderstand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line).\nCCSS.MATH.CONTENT.HSA.REI.D.11\nExplain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.\n\nBut Glencoe teaches these standards in Lesson 3-2, after solving linear equations is covered. On Edgenuity, students are expected to graph linear equations in the plane first, and then they are taught to solve linear equations in one variable. This means that, for example, students aren't taught to convert a linear equation from standard form to slope-intercept form in order to graph it -- since at that point they don't know how to solve equations for y.\n\nOf course, keep in mind that many of Edgenuity's equations have decimal or fractional solutions -- which aren't exactly easy to graph, much less locate as the intersection of two graphs.\n\nIn fact, there's only two situations when I'd teach this as the primary method of solving equations. If the equation is nonlinear, then an algebraic method is impossible (such as 2^x = x + 3.) The other situation is when a graphing calculator is available, so it's easy to graph y_1 = LHS and y_2 = RHS on the calculator. Otherwise, I prefer to do it like Glencoe's Lesson 3-2 -- after solving equations, so that students can see the connection between equations and graphs in preparation for solving equations by graphing in the two aforementioned cases (nonlinear equation or calculator available).\n\nThe Algebra II teachers (and probably the Algebra 1B teachers as well) watch the first few Edgenuity videos as well, and they don't necessarily like how these lessons are set up either. One of them remark that the teaching method in the video is how she'd set up her Honors Algebra II class -- not a summer class where two-thirds of the students received F's during the school year.\n\nWe fear that by the end of the first week of classes, the students will be completely lost unless we resort to supplementing Edgenuity with packets. That's right -- I might have to bring back that old \"Packet Song\" from last year in music break. I could make the packets out of worksheets published by Glencoe -- or I might create my own worksheets based on the U of Chicago Algebra I text!\n\nLet's get back to Fawn Nguyen's Memorial Sunday post. She's describing how similar house cleaning is to lesson planning. Since we're still in the middle of lesson planning for summer school today, I'll post the rest of her list today.\n\nhttp://fawnnguyen.com/house-cleaning-and-lesson-planning/\n\n1. Swiffer products should be regarded as essentials like toothpaste and TP.\n2. The person who did not put the TV remote control away in a designated spot shall be banished from the home (or get punched in the face).\n3. Make your bed every morning.\n4. Never go to bed unless the kitchen is clean. (If you dread this, then don’t cook.)\n5. If you find the above 9 steps difficult to implement, then try step 1 again.\nAnd here's how Nguyen compares these house cleaning steps to lesson planning. For #6, she points out that the essential products of the classroom are equity and access. She admits that she isn't perfect when it comes to equity and access in her class. We summer school teachers are also worried about the accessibility of the Edgenuity lessons. One Algebra II teacher warns us that there will probably be a few special ed students in each class -- will Edgenuity be understandable to them? And one Algebra I teacher -- the one who's currently student teaching -- is worried about her current students who will be taking her class again in the summer.\n\nFor Nguyen, step #7 is all about respect. In lesson planning, this means that teachers should respect other teachers by giving proper credit to the source of each lesson, and sharing good lessons. This is exactly what she and I are doing on our respective blogs.\n\nSteps #8-9 are all about fresh starts or do-overs. Nguyen reminds us that just as we expect out students to persevere after a setback, we teachers need to pick ourselves up and move forward after lessons that don't work as well as they should have. And I've devoted numerous blog posts to unsuccessful lessons and how I'd improve upon them.\n\nFor the last step, Nguyen tells us that lesson planning can be a pain, especially on weekends. This is why we summer school teachers have been given these Wednesdays to do our lesson planning. I admit that Edgenuity has made the lesson planning easier, even though we don't necessarily like how the software presents some of the material.\n\nI want to use some of these posts to revisit my most popular posts from the past twelve months -- and that includes my Lee Canter classroom management post. Last summer, I looked at his Succeeding with Difficult Students and wrote about his worksheets #4-5. I considered three hypothetical, but common, classroom situations and how I'd handle them.\n\nI'd like to continue in this book especially in preparation for my summer class. But unfortunately, worksheets #4-5 are the only exercises I can do easily. Many of the worksheets require watching either a video that I can't access (the book was written a quarter-century ago, before YouTube) or students in our actual classrooms. I could go back to whom I remember of my class from last year (such as the \"special scholar\" from my January 6th post). I wish I'd thought about this book during the multi-day subbing assignments (such as the middle school Digital Video class from back in March, or the senior Economics class from about a month ago).\n\nThere's still some time to try out these exercises in these last few days of subbing before summer. I want to make sure that my management skills are much improved from last year.\n\nQuestion 23 of the SBAC Practice Exam is on comparing rates:\n\nNina has some money saved for a vacation she has planned.\n\n• The vacation will cost a total of \\$1600.\n• She will put \\$150 every week into her account to help pay for the vacation.\n• She will have enough money for the vacation in 8 weeks.\nIf Nina was able to save \\$200 a week instead of \\$150 a week, how many fewer weeks would it take her to save enough money for the vacation? Enter the result in the response box.\n\nOK, I'd count this as a first semester Algebra problem that our students might be required to solve this summer. First of all, let's ignore the given value \\$1600 completely, since it has nothing to do with the solution of this problem. What we want to know is, how long will it take Nina to save the same amount of money at \\$200/wk. as she does at \\$150/wk. for eight weeks? Thus this is the equation:\n\n200w = 150(8)\n200w = 1200\nw = 6\n\nSo it takes her six weeks to save the money as opposed to eight weeks. Therefore it will take her two fewer weeks (that is, 8 - 6) to save the money -- students should enter the number 2.\n\nSometimes students might forget that even though w = 6, they must enter the number 2, since the question is not how many weeks will she save, but how many fewer weeks. Sometimes I avoid this problem by letting x = 8 - w, so that as soon as I find x, I have the number I need to enter:\n\n200(8 - x) = 150(8)\n1600 - 200x = 1200\n-200x = -400\nx = 2\n\nI often solve Pappas problems this way -- using the variable x only for the final value that I need to find rather than any intermediate values. Also, if there's a system of equation and Pappas asks us to solve for x, I might eliminate y even if x is easier to eliminate, so that I find the actual asked-for value more directly.\n\nQuestion 24 of the SBAC Practice Exam is on quadrilaterals:\n\nConsider parallelogram ABCD with point X at the intersection of diagonal segments AC and BD.\n\nEvelyn claims that ABCD is a square. Select all the statements that must be true for Evelyn's claim to be true.\n\n• AB = BD\n• AD = AB\n• AC = BX\n• Angle ABC isn't 90\n• Angle AXB = 90\nHere's some Geometry -- yes, it's been some time since I posted Geometry on this Geometry blog. I'll look at the three length equations first. AD = AB is obviously true, since the sides of a square must indeed be congruent. On the other hand, AB = BD is definitely false -- the diagonal of a square is sqrt(2) times the length of a side, not the same length as a side. And AC = BX is false as well -- the diagonals of a square (or any rectangle) are congruent, and so AC can't be half of BD (which is what BX is, as the diagonals of a parallelogram bisect each other).\n\nNow let's look at the angle statements. The statement that ABC isn't 90 is obviously false -- the angles of a square must be exactly 90. The other statement that AXB = 90 is true, since the diagonals of a square are also perpendicular. So students must select two correct answers, AB = AD and AXB = 90.\n\nNotice that if all Evelyn knew about her parallelogram is AB = AD and AXB = 90, that would not be sufficient for her to conclude that it's a square. A rhombus, after all, also has congruent sides and perpendicular diagonals. (In fact, given that ABCD is a parallelogram, just one of these two is sufficient for her to conclude that ABCD is a rhombus.) On the other hand, adding the falsity of the claim that ABC isn't 90 (that is, the truth that ABC = 90) to either of the two selected statements is enough for Evelyn to conclude that ABCD is a square.\n\nSBAC Practice Exam Question 23\nCommon Core Standard:\nCreate equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.\n\nSBAC Practice Exam Question 24\nCommon Core Standard:\nProve theorems about parallelograms. Theorems include: opposite sides are congruent, opposite angles are congruent, the diagonals of a parallelogram bisect each other, and conversely, rectangles are parallelograms with congruent diagonals.\n\nCommentary: The first equation I wrote for w can be solved as early as Lesson 4-4 of the U of Chicago Algebra I text, although the distributive property in the x equation must wait for Lesson 6-8 a little later on. Meanwhile, the properties of rectangles, rhombuses, and squares are covered in Lesson 5-4 of the Geometry text.\n\n## Tuesday, May 29, 2018\n\n### SBAC Practice Test Questions 21-22 (Day 174)\n\nToday I subbed in a high school science class. There were three sections of Biology and two sections of Anatomy/Physiology. In the bio classes, students are supposed to create a comic strip where the characters are T-cells and other members of the immune system. I won't do a \"Day in the Life\" for today, but I do point out that several students in all three classes failed to complete three panels (and of these, half failed even to begin one panel) despite my repeating over and over again that I'd leave for the regular teacher the name of any student who didn't do three panels.\n\nThe Anatomy classes are mostly seniors, but one class has three juniors. This is significant because today is the infamous California Science Test -- the test that caused me many headaches when trying to set up my science classes last year. I haven't though much as much about the high school test as the middle school tests. I know that one grade (which could be any grade from 9-12) administers the test each year -- it makes sense that it would be juniors (since they test English and math as well).\n\nApparently, the California Science Test was supposed to be last week, but for some reason (computer failure?) it was delayed to this week. The three Anatomy juniors are sent to another classroom, presumably a science class with more juniors than Anatomy.\n\nMeanwhile, today there is a science Google Doodle -- S.P.L. Sorensen, the Danish chemist who developed the pH scale. It's too bad that I didn't sub in a Chemistry class today (instead of Biology) in order to fit the doodle. The pH scale is often mentioned in Algebra II classes as an application of the common logarithm. (During tutorial, I am able to help a few students in Algebra II. One student has a logarithm problem for review, but it's not a pH problem.)\n\nMeanwhile, the Queen of the MTBoS has made her latest post. That's Fawn Nguyen, in case you don't recall who our queen is:\n\nThis is what she writes on Memorial Sunday:\n\nThere is something else that I do way better than teaching mathematics, even though teaching has been a 25-year plus career. That something is house cleaning.\n\nNguyen proceeds by listing ten steps required for house cleaning. I'll post only the first five steps here, since you can just click the link if you really want the whole list:\n\n1. Throw everything out.\n2. When done with step 1, repeat step 1 again bc we both know you really didn’t throw everything out.\n3. With remaining [ideally just 3] items, ask, “Is it really really pretty?” If so, it should be displayed in your home in a pretty spot. Ask, “Is it useful, like a wine-bottle-opener type of necessity?” If so, keep it in a drawer.\n4. Unless it’s a piece of furniture, a houseplant, or a 4-legged friend, forbid it from touching your floor.\n5. Counter space is only for items that do not fit inside a drawer/cupboard and are used almost daily — e.g., toaster, Nutribullet, knife block.\nThen Nguyen compares these steps for house cleaning to those of lesson planning. I, of course, am currently thinking about lesson planning for my summer Algebra I course, so let's follow this closely.\n\nThe first two steps are to throw everything out. Well, last week's lesson planning was all about throwing things out -- the course as posted on Edgenuity is too long for a three-week course. But Nguyen goes on to explain that she often throws out questions in order to make some of her problems more open-ended. This I won't be able to do -- Edgenuity will ask the students questions, and it's difficult for a computer to evaluate open-ended answers.\n\nNguyen rejects the third step in her own classroom -- her students don't have time to make their work look \"pretty.\" It does remind me of Foldable notes, where students take time to decorate their Foldables before the unit begins. The idea of Foldables actually comes from the Glencoe text, and I was considering having my students make them to take notes from the text. But Nguyen's right -- there won't be time in a summer course for Foldables, and besides, the main text for the course is Edgenuity, not Glencoe. In a computer-based class, there's no time for Foldable notes.\n\nSteps 4-5 are connected to decorating the room itself. I don't know what my room will look like -- indeed, I probably won't have access to it until the Friday before summer school begins, since it's currently occupied by a regular school year class. So we'll worry about these two steps later.\n\nIt's time for our next musical scale. This week we'll look at 18EDL:\n\nThe 18EDL scale:\nDegree     Ratio     Note\n18            1/1         tonic\n17            18/17     septendecimal chromatic semitone (Arabic lute index finger)\n16            9/8         major tone\n15            6/5         minor third\n14            9/7         supermajor third\n13            18/13     tridecimal semiaugmented fourth\n12            3/2         perfect fifth\n11            18/11     undecimal neutral sixth\n10            9/5         minor seventh\n9              2/1         octave\n\nhttp://www.haplessgenius.com/mocha/\n\n10 INPUT N\n20 FOR D=9 TO 18\n30 SOUND 261-N*D,4\n40 NEXT D\n\nThis is a descending scale. To make the scale ascend, use:\n\n20 FOR D=18 TO 9 STEP -1\n\nWe notice that this scale contains a new prime, 17. Indeed, 18EDL is the only 17-limit EDL, and it contains the entire 17-limit tonality diamond.\n\nThe name \"septendecimal\" for the 17-limit is a bit awkward. It reminds us of the name \"hexadecimal\" for base 16 (going back to my last post, on number bases). But notice that linguistic purity is violated, as \"hexa-\" is Greek but \"septen-\" is Latin.\n\nOf course, this ordinarily isn't a problem. We know that number base enthusiasts don't even like odd bases, much less prime bases. But musical intervals are named for their prime limit. So it's unlikely we'll ever have to worry about confusing number bases with interval names. As a prime base, 17 will be ignored, so it doesn't matter whether it's \"septendecimal\" or \"heptadecimal.\" And intervals such as 16/13 won't be called \"hexadecimal\" or \"sexadecimal\" neutral third, but \"tridecimal\" neutral third, after the prime 13.\n\n(And besides, number bases often take Latin names anyway. There's been much discussion lately of base 6, called senary, not \"hexary.\" And base 11, when it appears, is \"undecimal,\" not \"hendecimal.\")\n\nLet's check out the notes of 18EDL using Kite's color notation:\n\nThe 18EDL scale:\nDegree     Ratio     Note\n18            1/1         white D\n17            18/17     umber D#\n16            9/8         white E\n15            6/5         green F\n14            9/7         red F#\n13            18/13     ocher G\n12            3/2         white A\n11            18/11     amber B\n10            9/5         green C\n9              2/1         white D\n\nThe new prime 17 requires two new colors -- \"tan\" for otonal and \"umber\" for utonal. Since EDL scales are utonal, the color \"umber\" appears in the scale, with \"umber D#\" the first note of that color.\n\nThe color \"umber\" is a odd choice, since it sounds so much like \"amber.\" In fact, Mocha has a note at Degree 187 (Sound 74) called \"umber-amber A#.\" But Kite, when choosing colors for his notation, was more concerned with the \"u,\" not the \"-mber\" part. He wanted each color to start with a different letter, and he needed a color starting with \"u,\" so \"umber\" it is. (His notation uses every letter of the alphabet except \"z.\")\n\nFinally, you might ask why our first umber note is called D# rather than Eb. Well, there are two reasons for preferring sharps over flats. In utonal music, fourths are preferred over fifths (since the largest prime of 4/3 is in its denominator, unlike 3/2). If Degree 17 is umber D#, then Degree 51 (that is, 17 * 3) is umber G# and Degree 153 is umber C#. Then Degree 459 would be umber F#, and Degree 1377 would be umber B (even though these last two are out of Mocha range). So at least in theory, we can reach notes without a classical accidental by proceeding fourthward from D#. On the other hand, proceeding fourthward from Eb takes us into more flats before reaching double flats.\n\nAnd here's another reason that Kite prefers sharps here. The interval 18/17 is 99 cents, while the interval 17/16 is 105 cents. Thus Degree 17, in cents, is closer to Degree 18 than to 16. And so we'd prefer 17 to have the same letter name as 18, which again means that D# is used over Eb. Both of these reasons generalize to higher primes, so if we have a choice between a flat name and a sharp name for a new prime, the latter is preferred.\n\nWhat good are umber notes, anyway? The use of the other limits is obvious -- the 3-limit gives us fifths while the 5-limit gives us thirds. The 7-limit is used in jazz (including barbershop). Even the 11- and 13-limits can be used for neutral intervals, plus we might want harmonic 11th and 13th chords (following the pattern for harmonic 7th chords). But 17 seems to be just a useless prime.\n\nWell, in Helmholtz-Ellis notation, the 17-limit can be indicated using a symbol for 256/255. This comma is so small that H-E calls it a \"schisma\" rather than a \"comma.\" (At 6.8 cents, it's slightly smaller than the 225/224 comma that Kite calls the \"sub.\")\n\nThe 256/255 schisma is one of the smallest intervals playable in Mocha. Degree 256 (Sound 5) is called \"white E,\" while Degree 255 (Sound 6) is called \"umber-green E\" (since 255 has the factor 5 as well as 17). In other words, the difference between \"white\" and \"umber-green\" is the schisma. As the color that cancels \"green\" is yellow, it follows that \"yellow\" differs from \"umber\" by the schisma.\n\nIn Mocha, otonal colors like \"yellow\" are unplayable, but utonal colors like \"umber\" are playable. So we can play major chords in Mocha using \"umber\" instead of \"yellow.\" For example, an A umber major triad would be Degrees 192:153:128 (Sounds 69-108-133). Unfortunately, there still aren't enough umber notes to make a complete major scale (so for now, green Bb major remains the only playable major scale).\n\nThere's one more thing I'd like to say about the prime 17. Let's look at the 18EDL scale once more:\n\nThe 18EDL scale:\nDegree     Ratio     Note\n18            1/1         tonic\n17            18/17     septendecimal chromatic semitone (Arabic lute index finger)\n16            9/8         major tone\n15            6/5         minor third\n14            9/7         supermajor third\n13            18/13     tridecimal semiaugmented fourth\n12            3/2         perfect fifth\n11            18/11     undecimal neutral sixth\n10            9/5         minor seventh\n9              2/1         octave\n\nHmm, that's a strange name for the 18/17 interval, \"Arabic lute index finger.\" I'm very curious about the reason for that name -- and I wonder if there's an \"Arabic lute index finger,\" are there also an \"Arabic lute middle finger,\" \"ring finger,\" and \"little finger\"?\n\nFirst of all, a \"lute\" is a string instrument, similar to the modern guitar. On a modern guitar, we can place an index finger on the first fret to raise the pitch -- for example, fretting the D string at the first fret produces D#. So perhaps we can place an index finger on an Arabic lute to raise its pitch by the semitone-like interval 18/17.\n\nWell, a traditional \"Arabic lute\" -- also known as an oud -- has no frets. Still, I can imagine raising the pitch of an oud string by using the index finger, thereby justifying the name.\n\nThe Xenharmonic website uses the name \"Arabic lute\" to refer to two intervals. One of these is 18/17, but the other is the \"Arabic lute acute fourth,\" 49/36:\n\nhttp://xenharmonic.wikispaces.com/49_36\n\nBut 49/36 is a septimal interval -- it has nothing to do with 17. And you'd think that as easy as it is to use Google to research ouds, no website seems to explain why 18/17 is \"Arabic lute index finger.\"\n\nWell, here's my conjecture -- 18/17 is actually part of a simple 18EDL system. The middle, ring, and little fingers can be placed on the strings to sound out 18/16, 18/15, and 18/14 -- that is, the fingers divide the string into 18 equal parts. But 18/16 isn't called \"Arabic lute middle finger\" because it reduces to 9/8, which already has a name (\"major tone\"). Likewise, 18/15 = 6/5 (minor third) and 18/14 = 9/7 (supermajor third), so these don't have Arabic names.\n\nThe next interval that could have an Arabic name would be 18/13 -- but by this point, we've run out of fingers! And besides, 18/13 is a sort of superfourth, while the interval between the strings are perfect fourths (just as they mostly are on a modern guitar). Thus once we reached the fourth, an oud player would just jump to the next string.\n\nFrom the perfect fourth, it's easy to use the middle finger to add 9/8 to this to obtain a perfect fifth, and the octave is likewise reached on the next string. And within each string, we can play a sort of semitone (18/17), whole tone (9/8), minor third (6/5), and major third (9/7). In other words, from 18EDL we have the beginning of a twelve-tone scale, centuries before 12EDO was created.\n\nBefore we leave music, I like to point out that for one of the higher primes, Kite actually has a color called \"fawn\" -- which reminds us of Fawn Nguyen, the Queen of the MTBoS. We'll find out what prime the color \"fawn\" corresponds to in a later post.\n\nWe'll continue our discussion of 18EDL on Thursday.\n\nQuestion 21 of the SBAC Practice Exam is on simplifying exponents:\n\nWrite an expression equivalent to b^11/b^4 in the form b^m.\n\nExponents are definitely a second-semester Algebra I topic. We know the Laws of Exponents, and the rule that to divide powers, we subtract exponents. Therefore the answer is b^(11 - 4) = b^7. The hardest part of students (provided they know the Laws of Exponents) is entering b^7 properly.\n\nQuestion 21 of the SBAC Practice Exam is on the average rate of change:\n\nThe depth of a river changes after a heavy rainstorm. Its depth, in feet, is modeled as a function of time, in hours. Consider this graph of the function.\n\n[The graph passes through many points, including (9, 18) and (18, 21) -- which, as you'll soon see, are the only two points that matter.]\n\nEnter the average rate of change for the depth of the river, measured as feet per hour, between hour 9 and hour 18. Round your answer to the nearest tenth.\n\nThis is considered to be a first-semester Algebra I problem, but it's worded strangely. The phrase \"average rate of change\" confuses many students and teachers alike.\n\nThe first time I, as a young student, ever heard the phrase \"average rate of change\" was in an AP Calculus class. Our teacher fave an average rate of change problem, and polled the students whether they needed to find an integral or a derivative to find the solution. I forgot which answer I chose, but I remember that the correct answer is neither. Here's the reason why, in a nutshell -- the word \"average\" implies an integral (as in \"the average value of a function\"), while \"rate of change\" obviously implies a derivative. Thus in \"average rate of change,\" the integration and differentiation cancel each other out, and so neither is needed (which had better be the case, otherwise this question has no business being on the SBAC).\n\nIn fact, the average rate of change of a function between is just the slope of the line passing through the two points. Here's somewhat of a proof, from Calculus:\n\n\"Average\" means integral:\n1/(b - a) times the integral from a to b of something dx\n\n\"Rate of change\" means that \"something\" is derivative:\n1/(b - a) times the integral from a to b of f '(x) dx\n\nBy the Fundamental Theorem of Calculus, the integral of f '(x) is f (x)\n1/(b - a) times f (x), evaluated from a to b\n1/(b - a) times (f (b) - f (a))\n((b) - (a))/(b - a)\n\nwhich is indeed the slope of the line through (a, f (a)) and (b, f (b)). QED\n\nOf course, Algebra I students don't deal with the proof. Instead, they're taught that the average rate of change through two points is simply the slope of the line passing through them. It's mentioned as a real-world example of slope and an instance of the Common Core Standards on modeling.\n\nOh yeah, let's solve the problem. The average rate of change, or slope, is:\n\n(21 - 18)/(18 - 9) = 1/3\n\nThe directions ask students to round this to the nearest tenth, so the correct answer is 0.3 ft./hr.\n\nSBAC Practice Exam Question 21\nCommon Core Standard:\nRewrite expressions involving radicals and rational exponents using the properties of exponents.\n\nSBAC Practice Exam Question 22\nCommon Core Standard:\nCalculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.\n\nCommentary: The standard listed for Question 21 is the closest standard in the high school section -- the true standard is an eighth grade standard. Quotients of Powers appear in Lesson 9-7 of the U of Chicago Algebra I text. The phrase \"average rate of change\" doesn't appear in the text, but \"rate of change\" appears in Lesson 8-1, with \"average\" implied. Constant rates of change appear in the next lesson. Notice that the first eight chapters of the U of Chicago text correspond to the first five chapters of Glencoe and the first semester in Edgenuity.\n\n## Friday, May 25, 2018\n\n### SBAC Practice Test Questions 19-20 (Day 173)\n\nToday on her Mathematics Calendar 2018, Theoni Pappas writes:\n\nWhat is the 10th (base two) root of 10000 (base five)?\n\nWell, 10 in base two is just two, so we're asking about the square root of 10000. Notice that the square root of 10000 in any base is 100 in that base -- that's because 10000 is just b^4 in base b, while 100 is just b^2, and sqrt(b^4) = b^2. Thus sqrt(10000) = 100 (base five) = 25. Therefore the answer is 25 -- and of course, today's date is the 25th.\n\nHold on a minute -- that's not a Geometry question, so why am I doing a Pappas question today? As these are the final weeks of school, I always celebrate by revisiting my most popular posts during the past year. My #1 post in hit count was a summer post on number bases. And so this is a good excuse to have another post on bases -- one of my favorite topics.\n\n(By the way, today I subbed in an eighth grade U.S. History class. Because all classes just watch a video -- Civil War by Ken Burns -- and take notes, I won't do a \"Day in the Life\" today.)\n\nThe two bases that appear in this Pappas problem are two (binary) and five (quinary). Even though binary is ubiquitous in computers, it's so small that it's considered well below the human scale -- large numbers take too long to write in binary.\n\nQuinary, at least, has its own thread at the Dozens Online website. (Recall that I have Dozens Online to thank for making number bases my most popular post of the year.)\n\nhttps://www.tapatalk.com/groups/dozensonline/quick-kid-quinary-t728.html?sid=23ef46302163fa278d02da09d5411b8f\n\nAt this thread, it's pointed out that humans could have developed quinary as the dominant base over decimal, since we do have five fingers on a hand. But quinary might still be a bit too small to be considered human-scale -- and besides, it's odd. Since even bases are generally preferred, we count two hands and use decimal as the dominant base.\n\nWhen I was young, my first scientific calculator, the TI-34, came with a manual. This calculator can convert numbers to binary as well as two binary-related bases, octal and hexadecimal. But in order to introduce the concept of number bases, the manual uses base five, the \"handal\" system.\n\n{5} (default quinary/handal)\n\nIn this base, 10 is simply called \"hand.\" The count goes as follows: one, two , three, four, hand, handy-one, handy-two, handy-three, handy-four, twandy (20). The other numbers also sound like decimal numbers with the syllable \"hand\" thrown in: thrandy (30), frandy (40), and of course, we must have one handred (100).\n\nThe manual didn't reach 1000. I suppose the easiest way to get my \"hand\" in is \"one thouhand.\" Then 10000, following the decimal pattern, would be \"hand thouhand.\" Perhaps it's better to change the Greek word \"myriad\" instead -- \"one myrihand.\" So today's Pappas problem becomes:\n\nThe square root of one myrihand is one handred.\n\n{a} (default decimal)\n\nSince handal is such as small base, it has many simple divisibility rules. Divisibility by 2 and 4 is covered by the omega, while 3 and 6 are covered by the alpha. The SPD rule -- used for divisibility by 5 in dozenal, applies to 13 (twandy-three) in handal, since 26 = 2 * 13. Here SPD is based on one more than the square of the base (square-alpha). There is also SPD based on square-omega. It's useless in even bases since any factor of square-omega is available in either alpha or omega. But in odd bases, an extra power of two (beyond alpha or omega) is available in square-omega. In this case, square-omega gives us 8 (handy-three), since 24 = 3 * 8.\n\nQuinary is small enough that SPD based on cube-alpha is also available. One more than 5^3 is 126, which factors as 2 * 7 * 9, so this gives us 7 (handy-two) and 9 (handy-four). For 7, we need to memorize 18 multiples of seven. This is fewer than the 29 multiples of five needed to do 5 in dozenal, but each multiple of seven has three quinary digits, so it's a wash. For 9, we only need to memorize 14 multiples of nine.\n\nSo quinary has feasible divisibility rules for factors 2-10. The useful numbers 2-6 have easier rules (divisor, alpha, omega) while the less useful 7-9 have more obscure rules (SPD).\n\nBut quinary has no simple rule for 11 (twandy-one). In fact, we can prove that 11 can't have a simple rule based on SPD for squares or cubes -- 11 can only have divisor, alpha, or omega rules. Thus decimal and dozenal are the smallest bases with an easy rule for 11 (along with undecimal of course).\n\nThe only possible SPD rule for 11 would be based on fifth powers. Since fifth powers are so large, this is infeasible for all bases -- except:\n\n{2} (default binary)\n\nIt's possible to use SPD for eleven (1011) in binary. Only three multiples need to be memorized, and all are trivial: 00000, 01011, and 10110.\n\n{a} (default decimal)\n\nIn ternary, 23 multiples of eleven must be memorized. This is fewer than 5 in dozenal, but the multiples contain five digits each, so it's difficult. Binary is below human-scale, but we can do 11 in bases 4, 8, and 16 by converting them to binary first.\n\nOK, let's get back to music. Today we wish to code Mocha for 16EDL music:\n\nThe 16EDL scale:\nDegree     Ratio     Note\n16            1/1         white E\n15            16/15     green F\n14            8/7         red F#\n13            16/13     ocher G\n12            4/3         white A\n11            16/11     amber B\n10            8/5         green C\n9              16/9       white D\n8              2/1         white E\n\nIn 12EDL, it's easy to alternate between the 12:10:8 (that is, 6:5:4) and 11:9:7 chords. For 16EDL, we must get a little more creative. Our main chord is 16:13:11, and so our secondary chord might end up being something like 15:12:10 (a just major triad). Here's a possibility:\n\n10 CLS\n20 N=16\n30 FOR A=0 TO 6\n40 B=4\n50 X=A-INT(A/2)*2\n60 IF X=0 THEN D=16 ELSE D=15\n70 PRINT D;\n80 L=RND(B)\n90 SOUND 261-N*D,4*L\n100 IF L>1 THEN FOR I=1 TO L-1:PRINT \"   \";:NEXT I\n110 B=B-L\n120 IF B>0 THEN D=17-RND(9):GOTO 70\n130 PRINT\n140 NEXT A\n150 PRINT 16\n160 SOUND 261-N*16,16\n\nSo in this song, each measure starts with either 16 or 15 to represent the root of the 16:13:11 and 15:12:10 triads, and then random notes fill out each measure.\n\nYesterday, I wrote about converting the \"Dren Song\" to EDL. We might program it like this:\n\nNEW\n10 N=20\n20 FOR V=1 TO 2\n30 FOR X=1 TO 12\n40 FOR Y=1 TO 7\n50 READ D\n60 IF V=1 THEN SOUND 261-N*D,4\n70 IF V=2 THEN SOUND 261-N*(20-D),4\n80 NEXT Y\n90 FOR I=1 TO 400\n100 NEXT I,X\n110 RESTORE\n120 NEXT V\n130 DATA 12,11,10,12,13,12,11\n140 DATA 13,12,11,13,12,11,10\n150 DATA 12,11,10,12,13,12,11\n160 DATA 13,12,11,13,12,11,12\n170 DATA 10,9,8,10,11,10,9\n180 DATA 12,11,10,12,13,12,11\n190 DATA 10,9,8,10,11,10,9\n200 DATA 11,10,9,11,10,9,10\n210 DATA 10,9,8,10,9,8,7\n220 DATA 11,10,9,11,10,9,8\n230 DATA 10,9,8,10,9,8,7\n240 DATA 9,8,7,9,8,7,8\n\nThis song begins with N=20, which gives us F minor. Another alternative is N=13, which would give us ocher C minor (to represent C# minor, the key in which I originally wrote the song).\n\nThe song consists of 24 lines, with the second 12 lines as the inversion of the first 12. The inversion is played by replacing D with 20 - D depending on whether it's the first (V=1) or second (V=2) verse.\n\nEach line consists of seven quarter notes followed by a quarter rest (the FOR I loop).\n\nWhat scale should we declare the song to be in. Here 12 is the root note, but it's not quite 12EDL because 13 is used. It's sort of like Bart Hopkin's mode 12 of the 16EDL scale. Since 15 isn't used, perhaps it's more accurate to call it mode 12 of the 14EDL scale. Then again, maybe we can simply call it 12EDL, add 13.\n\nThis just goes to show us that sometimes rather than having a span of one octave beginning and ending on the tonic, it's better to use a different sort of range. In this song, the range is 13-7, which 12 as the tonic.\n\nAs usual, with each EDL we play, I like to find EDO's we can convert it to. Let's run the EDO program I wrote a few years back, and input 16EDL. Here is the list of EDO's it outputs:\n\n1, 2, 4, 6, 7, 10, 24, 31, 41, 53, 87, 130, ...\n\nThe first non-trivial EDO we see here is 24EDO. Unlike 19EDO and 27EDO which are tricky to play (especially the latter), 24EDO is easier because it's closely related to 12EDO.\n\nhttp://xenharmonic.wikispaces.com/24edo\n\nAccording to this link, 24EDO is a contorted 12EDO in the 5-limit -- that is, all 5-limit intervals (white, green, yellow) are the same in 24EDO as in 12EDO. The twelve new notes are quarter tones (half of a semitone). The quarter tones are used to give us 11 and 13. As it turns out, using the quarter tones for 7 (subminor and supermajor) is slightly more accurate than simply using 12EDO.\n\nHere is some more information about 24EDO from the link, including Kite's colors. (As usual, all links will be dead after July.)\n\n# Basics\n\nThe 24edo system divides the octave into 24 equal parts of exactly 50 cents each. It is also known as quarter-tone tuning, since it evenly divides the 12-tone equal tempered semitone in two. Quarter-tones are the most commonly used microtonal tuning due to its retention of the familiar 12 tones and since it is the smallest microtonal equal temperament that contains all the 12 notes, and also because of its use in theory and occasionally in practice in Arabic music. It is easy to jump into this tuning and make microtonal music right away using common 12 equal software and even instruments - see this page\n\nCombining ups and downs notation with color notation, qualities can be loosely associated with colors:\nqualitycolormonzo formatexamples\ndownminorblue{a, b, 0, 1}7/6, 7/4\nminorfourthward white{a, b}, b < -132/27, 16/9\n\"green{a, b, -1}6/5, 9/5\nmidjade{a, b, 0, 0, 1}11/9, 11/6\n\"amber{a, b, 0, 0, -1}12/11, 18/11\nmajoryellow{a, b, 1}5/4, 5/3\n\"fifthward white{a, b}, b > 19/8, 27/16\nupmajorred{a, b, 0, -1}9/7, 12/7\n\nThe 11th harmonic, and most intervals derived from it, (11:10, 11:9, 11:8, 11:6, 12:11, 15:11, 16:11, 18:11, 20:11) are very well approximated in 24-tone equal temperament. The 24-tone interval of 550 cents is 1.3 cents flatter than 11:8 and is almost indistinguishable from it. In addition, the interval approximating 11:9 is 7 steps which is exactly half the perfect fifth.\n\nAlternatively, ups and downs notation can be used. Here are the blue, green, jade, yellow and red triads:\ncolor of the 3rdJI chordnotes as edostepsnotes of C chordwritten namespoken name\nblue6:7:90-5-14C Ebv GC.vmC downminor\ngreen10:12:150-6-14C Eb GCmC minor\njade18:22:270-7-14C Ev GC~C mid\nyellow4:5:60-8-14C E GCC major or C\nred14:18:270-9-14C E^ GC.^C upmajor or C dot up\n\nEven though we've been using \"d\" for quarter-flat, the quarter-sharp symbol isn't easy for me to write in ASCII format. So let's follow the suggestion and use \"^\" for up/quarter-sharp, and so \"v\" will be down/\"quarter-flat.\"\n\nHere is the 16EDL scale in E, converted to 24EDO:\n\nThe 16EDL scale, converted to 24EDO:\nDegree     Ratio     Note\n16            1/1         E\n15            16/15     F\n14            8/7         Gv\n13            16/13     G^\n12            4/3         A\n11            16/11     Bv\n10            8/5         C\n9              16/9       D\n8              2/1         E\n\nSince 24EDO agrees with 12EDO in the 5-limit, 24EDO tempers out both the syntonic comma and the Pythagorean comma. By tempering out the syntonic comma, 24EDO is a meantone tuning in which C-E is a major third. By tempering out the Pythagorean comma, G# and Ab are enharmonic, and B# and C are also enharmonic.\n\nA YouTube search for 24EDO reveals the following video of a quarter-tone guitar. (No, I will not be playing my 16EDL songs on the 24EDO guitar this summer.)\n\nOK, since I'm posting videos anyway, let me post the \"Be Sharps\" video from The Simpsons:\n\nHere are the key parts I wish to emphasize in this video. The song \"Coney Island Baby\" begins at the 0:24 mark of the video. It starts with Seymour (bass), Homer (baritone), Clancy (lead), and Apu (tenor) singing a barbershop 7th chord, with each singing the word \"Goodbye.\" The notes of this chord follow a 4:5:6:7 (otonal) pattern. The root of the chord is F, and so in septimal meantone, the notes are F-A-C-D#.\n\nThen at 0:48, the quartet sings a D chord (the lyric here is \"again\"). In septimal meantone, a D barbershop chord is D-F#-A-B#, and so the \"Be Sharps\" really do sing the note B#. (Later Barney replaces Clancy as the lead, and D-F#-A-B# occurs near the middle of \"Baby on Board,\" but there is no clean cut of this chord.)\n\nAgain 19EDO and 31EDO are good EDO's for septimal meantone. And 12EDO also supports septimal meantone, even though B# sounds as C. But 24EDO, while still meantone, isn't a septimal meantone EDO, since a 7/4 above D is now B quarter-sharp, not B#.\n\nThere are also higher EDO's that approximate the 13-limit. In fact, I can tie this to number bases -- you see, there was a debate on Dozens Online about the best EDO for 13-limit:\n\nhttps://www.tapatalk.com/groups/dozensonline/dare-i-admit-good-musical-things-about-decimal-t400.html\n\nThe original poster, Tony, asks, \"Dare I admit good musical things about decimal?\" He then points out that half of 100 in decimal is 50, and 50EDO approximate the 13-limit well. Indeed, 50EDL is also a septimal meantone EDO.\n\nBut notice that 50EDO doesn't appear in the list of good EDO's for 16EDL. Instead, another EDO emerges as a good EDO for 13-limit -- 72EDO. (Admittedly 72EDO doesn't appear in the 16EDL list, but it does appear in the list for 14EDL, which is also 13-limit.)\n\nAnother poster, Ebbe, explains that 72EDO, unlike 50EDO, isn't a meantone scale (much less septimal meantone). Indeed, the step size for 50EDO is about the size of the syntonic comma, and so it's not surprising that the best EDO's in this range are no longer meantone. (But 72EDO nonetheless tempers out the Pythagorean comma, so we still have enharmonics G#=Ab and B#=C.) And 72 is half of the dozenal hundred (gross), and so it's \"dozenal for the win again.\"\n\nIn 72EDO, six steps make a semitone and twelve steps make a whole tone. Thus each step of the scale can be called a twelfth-tone.\n\nThe major third above C is now one step below E -- that is, the scale maps the syntonic comma to a single step. The septimal comma is now two steps. The jade quarter-tone is now three steps (as 3/12 equals 1/4), and the ocher third-tone is now four steps (as 4/12 = 1/3). So we can see how ocher fits 72EDO better than 24EDO.\n\nIn fact, here are some of the notes of 72EDO, in sequence (listed as thirds above C)\n\nStep     Note     Color\n16        Eb-2     blue Eb (subminor 3rd above C)\n17        Eb-1     yellow Eb\n18        Eb        white Eb\n19        Eb+1    green Eb (minor 3rd above C)\n20        Eb+2    red Eb (emerald E)\n21        E-3       jade Eb (amber E, neutral 3rd above C)\n22        E-2       blue E (ocher Eb)\n23        E-1       yellow E (major 3rd above C)\n24        E          white E\n25        E+1      green E\n26        E+2      red E (supermajor 3rd above C)\n\nWithin each classical name, the rainbow is emerald-amber-blue-yellow-white-green-red-jade-ocher.\n\nHere's one more recent music-related post at the Dozens Online website:\n\nhttps://www.tapatalk.com/groups/dozensonline/why-the-golden-ratio-is-golden-t1875.html\n\nThe original poster Dan is writing about Phi, the Golden Ratio. In this post he ties Phi to music:\n\nOne practical use of \"almost rational\" irrational numbers is musical tuning.  For example, the equal-tempered major third has a frequency ratio of the cube root of two (1.259921 decimal, 1.315188 dozenal), approximating the just intonation ratio 5/4.  So, would a tuning based on setting the minor sixth to φ (or equivalently, setting the major fifth to (8/φ)^(1/4), or 691.7274 cents) sound dissonant?\n\n(It's too bad this wasn't posted before Phi Day of the Century.) Anyway, we know that the ratio of consecutive Fibonacci numbers approaches Phi, so let's start with these:\n\nRatio     Name\n1/1         unison\n2/1         octave\n3/2         perfect fifth\n5/3         major sixth\n8/5         minor sixth\n13/8       large tridecimal neutral sixth\n21/13     small tridecimal neutral sixth\n\nThe largest Fibonacci numbers within Mocha range are 144 and 233, so playing Degree 233 (Sound 28) and Degree 144 (Sound 117) best approximates Phi in Mocha.\n\nAmond EDO's, the aforementioned 72EDO approximates Phi well. If the root note is C, then Phi appears two steps above Ab (about 833 cents). We can refer to this note as either emerald A (to represent 13/8) or ocher-blue Ab (21/13).\n\nThe Xenharmonic site has its own page about applying Phi to music:\n\nhttp://xenharmonic.wikispaces.com/Golden%20ratio\n\nPhi taken as a musical ratio (ϕ*f where f=1/1) is about 833.1 cents. This is sometimes called \"acoustical phi\".\nAs the ratios of successive terms of the Fibonacci sequence converge on phi, the just intonation intervals 3/2, 5/3, 8/5, 13/8, 21/13, ... converge on ~833.1 cents.\n\n\"Logarithmic phi\", or 1200*ϕ cents = 1941.6 cents (or, octave-reduced, 741.6 cents) is also useful as a generator, for example in Erv Wilson's \"Golden Horagrams\".\n\n(\"Acoustical Phi\" is to \"Logarithmic Phi\" as EDL is to EDO. Thus Acoustical Phi appears in Fibonacci EDL's like 34EDL, while Logarithmic Phi appears in Fibonacci EDO's like 34EDO.)\n\nQuestion 19 of the SBAC Practice Exam is on solving equations:\n\nConsider this solution to a problem:\n\nProblem: -4(6 - y) + 4 = -4\nStep 1: -24 - 4y + 4 = -4\nStep 2: -20 - 4y = -4\nStep 3: -4y = 16\nStep 4: y = -4\n\nIn the first response box, enter the number of the step where the mistake is made.\nIn the second response box, enter the correct solution to the problem.\n\nThis is a strong first semester Algebra I problem. The original problem has lots of negative signs, and so the obvious error to search for is a sign error. And sure enough, there is a sign error right away -- -4 times -y should be 4y, not -4y. So the step that contains the mistake is step 1.\n\nThe solution is easy to correct. All we have to do is change all the signs on y:\n\nProblem: -4(6 - y) + 4 = -4\nStep 1: -24 + 4y + 4 = -4\nStep 2: -20 + 4y = -4\nStep 3: 4y = 16\nStep 4: y = 4\n\nQuestion 20 of the SBAC Practice Exam is on solving equations:\n\nConsider a sequence whose first five terms are: -1.75, -0.5, 0.75, 2, 3.25\n\nWhich function (with domain all integers n > 1) could be used to define and continue this sequence?\n\nA) f (n) = (7/4)(n - 1) - 5/4\nB) f (n) = (5/4)(n - 1) - 7/4\nC) f (n) = (7/4)n - 5/4\nD) f (n) = (5/4)n - 7/4\n\nBecause this is an arithmetic sequence, this is also considered to be first semester Algebra I. The first thing we notice is that the terms are listed as decimals, but the choices are all fractions. So the students must convert between decimals and fractions. There is an embedded calculator available, but that assumes that the students know how to use it to make the conversion. I used the calculator (powered by Desmos!) to divide to convert fractions to decimals. Some calculators can convert decimals to fractions, but I don't see that option on this calculator. So the first step would be to divide to convert 5/4 (a major 3rd!) and 7/4 (a barbershop 7th!) to fractions.\n\nWe find out that the first term -1.75 is -7/4 and the common difference is -1.25 or 5/4. But we can't use the first term unless we use the (n - 1) version of the formula, f (n) = f (1) + (n - 1)d. Plugging in to this formula, we obtain f (n) = -7/4 + (n - 1)5/4, which is rewritten as f (n) = (5/4)(n - 1) - 7/4. So the correct answer is B).\n\nToday is an activity day. Here the activities come from Chapter 6 of the U of Chicago Algebra I text, since this chapter matches these questions the best. Lesson 6-9 of the U of Chicago text is called \"Subtracting Quantities\" and emphasizes use of the Distributive Property with negatives, while Lesson 6-3 contains arithmetic sequences. The Exploration Question in the latter lesson is on programming in BASIC. Erase that music song using NEW so we can program Mocha to answer the activity question, or just skip that part of the activity.\n\nSBAC Practice Exam Question 19\nCommon Core Standard:\nExplain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.\n\nSBAC Practice Exam Question 20\nCommon Core Standard:\nCreate equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.\n\nCommentary: Distributing a negative sign correctly appears in Lesson 6-9 of the U of Chicago Algebra I text. But the method of finding explicit formulas in Lesson 6-3 -- finding the phantom \"zeroth term,\" doesn't work for Question 10. Instead, students must know and be able to use the formula f (n) = f (1) + (n - 1)d, which most likely appears in later texts based on the Common Core, such as Glencoe and Edgenuity.\n\nMonday is Memorial Day, and so my next post will be on Tuesday." ]
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https://www.geeksforgeeks.org/permutation-and-combination-set-2/?ref=lbp
[ "Related Articles\nPermutation and Combination | Set-2\n• Difficulty Level : Medium\n• Last Updated : 03 Dec, 2019\n\nQuestion 1: How many number greater than ten thousand can be formed from the digits 0, 1, 2, 3, 4 without repetation ?\nSolution : In order to form a number greater than 10000 we should have only 5 digits. Since, we have 5 digits we cannot take 0 in starting position.\n_ _ _ _\nFor first digit, we have 4 choices.\nFor second digit, again we have 4 choices because we can include 0 from here onwards.\nFor third digit, we have 3 choices.\nand for fourth digit only left 2 choices.\nTotal numbers = 4x4x3x2= 96\nHence, only 96 numbers possible.\n\nQuestion 2: In how many ways can 4 boys and 4 girls be seated around a circular table so that no two boys are in adjacent positions?\nSolution : If we first put 4 boys around the table, we can do this in 3! ways.\nOnce the 4 boys are placed, we have to place 4 girls around the same table.\nNow, we can see 4 vacant places are there between all 4 boys so we can do in 4! ways.\nTotal number of sitting arrangement = 3! x 4!\n\nQuestion 3: Out of the 11 points in a plane, 4 are collinear. How many straight line can be formed ?\nSolution : If all points were non-collinear then possible lines would have been 11C2.\nBut, 4 points are collinear lie on the same line. So, they are all counted as a single line.\nTotal number of straight line = 11C24C2 + 1\n= 11×10/2 – 4×3/2 + 1\n= 55 – 6 + 1\n= 50\n\nQuestion 4: Twenty people attend a party and shake hands with one another.In how many ways hand shake is possible?\nSolution : All people shake hands with one another except himself.\n1st person has 19 hand shakes and 2nd also has 19 hand shakes ………and so on\n20 people x 19 hand shakes\nand we know A handshake with B or B handshake with A, it is counted as 1 handshake.\nSo, total number of handshake = 20×19/2 = 190\nShortcut :\nfor n people there are always nC2 handshakes.\n\nQuestion 5: How many different sums of money can be formed from the four type of notes Rs 10, Rs 20, Rs 50 and Rs 100 ?\nSolution : Type of notes = 4\nSo, total number of sum can be formed = 24 – 1 = 15\n\nQuestion 6: Five chocolates of different flavours are to be distributed in three different children such that any child get at least 1 chocolate. What is the maximum number of different ways in which this can be distributed?\nSolution : Acc. to question\nChocolates can be distributed as [(3, 1, 1)(1, 3, 1)(1, 1, 3)]\nor [(2, 2, 1)(2, 1, 2)(1, 2, 2)]\nTotal number of ways = 3 x 5C3 x 2C1 x 1C1 + 3 x 5C2 x 3C2 x 1C1\n= 60 + 90\n= 150\n\nQuestion 7: Ram and his wife Sita both have five friends each. Ram has 2 boys and 3 girls. Sita has 3 boys and 2 girls. In how many maximum number of different ways can they invite 2 boys and 2 girls such that two of them are Ram’s friend and two are Sita’s friend?\nSolution : Selection can be done like that\ni) 2 boys from Ram’s friends and 2 girls from his wife Sita’s friends OR\nii) 1 boy and 1 girl from Ram’s friends and 1 boy and 1 girl from Sita’s friends OR\niii) 2 boys from his wife Sita’s friends and 2 girls from Ram’s friends\nTotal number of ways = 2C2.2C2 + 3C1 x 2C1 x 3C1 x 2C1 + 3C2.3C2\n= 1 + 36 + 9\n= 46 ways\n\nQuestion 8: In how many ways can 4 notebooks can be distributed to 5 students if each can get any number of notebooks?\nSolution : Since all the notebooks are identical or distinct we don’t know.\nSo, we take all are distinct and it can be distributed in 54 ways.\n\nQuestion 9: How many batting orders are possible for the Indian cricket team if there is a squad of 16 to choose from such that Virat Kohli and Rohit Sharma are always chosen?\nSolution : We need to select 9 players out of 14 players beacause two of them is already selected.\nThe selection of 11 players can be done in14C9 ways.\nBut batting order is also required to calculate for these 11 players so arrangements can be done in 11! ways.\nTotal number of batting orders possible = 14C9 . 11!\n\nQuestion 10: How many motor vehicle registration numbers plates can be formed for the state Haryana having code like (HR 12Q 8702) with the digits 0, 1, 2, 3, 4, 5, 6 and contains consonant at the alphabetical place(No digits being repeated).\nSolution : For Haryana state number plate always contains HR in starting.\nTwo consonants already used in HR so remaining consonant = 21 -2 = 19.\nSo, possible number of plates = 1(HR)x7x6x19(consonants)x5x4x3x2 = 95760\n\nMy Personal Notes arrow_drop_up" ]
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https://jprail.com/tag/toyohashi?amp=1
[ "',Y.captions&&l){var u=T(\"figcaption\");u.id=\"baguetteBox-figcaption-\"+t,u.innerHTML=l,s.appendChild(u)}n.appendChild(s);var c=T(\"img\");c.onload=function(){var n=document.querySelector(\"#baguette-img-\"+t+\" .baguetteBox-spinner\");s.removeChild(n),!Y.async&&e&&e()},c.setAttribute(\"src\",r),c.alt=a?a.alt||\"\":\"\",Y.titleTag&&l&&(c.title=l),s.appendChild(c),Y.async&&e&&e()}}function b(t){var e=t.href;if(t.dataset){var n=[];for(var o in t.dataset)\"at-\"!==o.substring(0,3)||isNaN(o.substring(3))||(n[o.replace(\"at-\",\"\")]=t.dataset[o]);for(var i=Object.keys(n).sort(function(t,e){return parseInt(t,10)=1?(M--,y(),C(M),t=!0):Y.animation&&(A.className=\"bounce-from-left\",setTimeout(function(){A.className=\"\"},400),t=!1),Y.onChange&&Y.onChange(M,V.length),t}function y(){var t=100*-M+\"%\";\"fadeIn\"===Y.animation?(A.style.opacity=0,setTimeout(function(){j.transforms?A.style.transform=A.style.webkitTransform=\"translate3d(\"+t+\",0,0)\":A.style.left=t,A.style.opacity=1},400)):j.transforms?A.style.transform=A.style.webkitTransform=\"translate3d(\"+t+\",0,0)\":A.style.left=t}function v(){var t=T(\"div\");return\"undefined\"!=typeof t.style.perspective||\"undefined\"!=typeof t.style.webkitPerspective}function w(){var t=T(\"div\");return t.innerHTML=\"\nCopied title and URL" ]
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https://it.mathworks.com/help/matlab/linear-algebra.html?s_tid=CRUX_lftnav
[ "# Linear Algebra\n\nLinear equations, eigenvalues, singular values, decomposition, matrix operations, matrix structure\n\nLinear algebra functions in MATLAB® provide fast, numerically robust matrix calculations. Capabilities include a variety of matrix factorizations, linear equation solving, computation of eigenvalues or singular values, and more. For an introduction, see Matrices in the MATLAB Environment.\n\n## Funzioni\n\nespandi tutto\n\n `mldivide` Solve systems of linear equations Ax = B for x `mrdivide` Solve systems of linear equations xA = B for x `pagemldivide` Page-wise left matrix divide `pagemrdivide` Page-wise right matrix divide `decomposition` Matrix decomposition for solving linear systems `lsqminnorm` Minimum norm least-squares solution to linear equation `linsolve` Solve linear system of equations `inv` Matrix inverse `pageinv` Page-wise matrix inverse `pinv` Moore-Penrose pseudoinverse `lscov` Least-squares solution in presence of known covariance `lsqnonneg` Solve nonnegative linear least-squares problem `sylvester` Solve Sylvester equation AX + XB = C for X\n `eig` Eigenvalues and eigenvectors `pageeig` Page-wise eigenvalues and eigenvectors `eigs` Subset of eigenvalues and eigenvectors `balance` Diagonal scaling to improve eigenvalue accuracy `svd` Singular value decomposition `pagesvd` Page-wise singular value decomposition `svds` Subset of singular values and vectors `svdsketch` Compute SVD of low-rank matrix sketch `gsvd` Generalized singular value decomposition `ordeig` Eigenvalues of quasitriangular matrices `ordqz` Reorder eigenvalues in QZ factorization `ordschur` Reorder eigenvalues in Schur factorization `polyeig` Polynomial eigenvalue problem `qz` QZ factorization for generalized eigenvalues `hess` Hessenberg form of matrix `schur` Schur decomposition `rsf2csf` Convert real Schur form to complex Schur form `cdf2rdf` Convert complex diagonal form to real block diagonal form\n `lu` LU matrix factorization `ldl` Block LDL' factorization for Hermitian indefinite matrices `chol` Cholesky factorization `cholupdate` Rank 1 update to Cholesky factorization `qr` QR decomposition `qrdelete` Remove column or row from QR factorization `qrinsert` Insert column or row into QR factorization `qrupdate` Rank 1 update to QR factorization `planerot` Givens plane rotation\n `transpose` Transpose vector or matrix `ctranspose` Complex conjugate transpose `pagetranspose` Page-wise transpose `pagectranspose` Page-wise complex conjugate transpose `mtimes` Matrix multiplication `pagemtimes` Page-wise matrix multiplication `mpower` Matrix power `sqrtm` Matrix square root `expm` Matrix exponential `logm` Matrix logarithm `funm` Evaluate general matrix function `kron` Kronecker tensor product `cross` Cross product `dot` Dot product\n `bandwidth` Lower and upper matrix bandwidth `tril` Lower triangular part of matrix `triu` Upper triangular part of matrix `isbanded` Determine if matrix is within specific bandwidth `isdiag` Determine if matrix is diagonal `ishermitian` Determine if matrix is Hermitian or skew-Hermitian `issymmetric` Determine if matrix is symmetric or skew-symmetric `istril` Determine if matrix is lower triangular `istriu` Determine if matrix is upper triangular\n `norm` Vector and matrix norms `pagenorm` Page-wise matrix or vector norm `normest` 2-norm estimate `vecnorm` Vector-wise norm `cond` Condition number for inversion `condest` 1-norm condition number estimate `rcond` Reciprocal condition number `condeig` Condition number with respect to eigenvalues `det` Matrix determinant `null` Null space of matrix `orth` Orthonormal basis for range of matrix `rank` Rank of matrix `rref` Reduced row echelon form (Gauss-Jordan elimination) `trace` Sum of diagonal elements `subspace` Angle between two subspaces" ]
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https://www.reference.com/web?q=Convert+Fluid+Ounces+to+Pounds&qo=contentPageRelatedSearch&o=600605&l=dir&sga=1
[ "ARTICLES\n\nTo convert milliliters to U.S. fluid ounces, multiply the number of milliliters by 0.033814. One milliliter equals approximately 0.033814 U.S. fluid ounces. If converting to U.K. fluid ounces, multiply milliliters by 0.0...\n\nwww.reference.com/article/convert-milliliters-fluid-ounces-632c6c28b5490e75\n\nOne U.S. fluid ounce is approximately 30 milliliters, so to convert 100 milliliters to its equivalent in fluid ounces, one simply needs to divide 100 by 30 to get the U.S. fluid-ounce equivalent of 3.33 per 100 millilite...\n\nwww.reference.com/science/conversion-100-milliliters-ounces-5baa45d585ddb9bc\n\nTo read an ounce conversion chart, find the number of ounces you wish to convert in the left hand column and find the corresponding unit of measurement in the next column of the same row. Some ounce conversion charts dis...\n\nRelated Search\nSIMILAR ARTICLES\n\nOne way to convert milliliters to ounces is by multiplying the number in milliliters by 0.03. This is because 1 milliliter is equal to 0.03 ounces.\n\nwww.reference.com/article/formula-convert-milliliters-ounces-cdd4ba03de437b75\n\nTo convert 40 milliliters to fluid ounces, divide 40 by 29.57. As there are 29.57 milliliters in a fluid ounce, 40 milliliters is equal to 1.35 fluid ounces.\n\nwww.reference.com/article/convert-40-ml-2f4a3e3be6a43fd\n\nThe first step in converting milliliters to ounces is understanding the volume conversion. Since 29.57ml equals 1 fluid ounce, convert 20 milliliters to fluid ounces by dividing 20ml by 29.57ml, which equals 0.67628 or 0...\n\nwww.reference.com/article/convert-20-ml-6dee0b024325d4c8\n\nA measurement of 50 milliliters is equivalent to 1.6907 U.S. fluid ounces. U.S. fluid ounces is slightly different from imperial ounces, with 1 U.S. fluid ounce measuring 29.5735295625 milliliters in the International Sy...\n\nwww.reference.com/article/equivalent-50-milliliters-u-s-fluid-ounces-bdc1b92cc0d081fd\n\nRelated Search\nToday's Top 10 Articles in science" ]
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https://www.ecologycenter.us/wastewater-treatment/info-tpx.html
[ "Info\n\nComposite behavior is sometimes an explanation for the observed results, i.e., a model consisting of a plug-flow reactor followed by one or more CSTRs.\n\nIn all combustion reactions, some CO is always formed. The following two-step global model accounts for this formation:\n\nVOC^CO-\n\nwhere, assuming excess oxygen, the following equations apply:\n\nQualitatively, the resulting concentration dependence is of the form shown in Figure 5.21.3. Under typical incinera-\n\nkey:\n\nc = Concentration at time t or exit concentration C0 = Initial concentration k1t= Product of rate coefficient x time, where t can be taken as the residence time at a given temperature\n\nFIG. 5.21.3 Qualitative relationship between VOC, CO, and CO2 concentration as a function of kjt.\n\ntion conditions, the preceding chemical sequence is irreversible. Using Cvoc (t = 0) = CvOC,i and Cœ,i = Cœ2,i = 0, the solution of Equations 5.21(7) to 5.21(9) is as follows:\n\n0 0" ]
[ null ]
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https://metanumbers.com/36296
[ "## 36296\n\n36,296 (thirty-six thousand two hundred ninety-six) is an even five-digits composite number following 36295 and preceding 36297. In scientific notation, it is written as 3.6296 × 104. The sum of its digits is 26. It has a total of 5 prime factors and 16 positive divisors. There are 16,704 positive integers (up to 36296) that are relatively prime to 36296.\n\n## Basic properties\n\n• Is Prime? No\n• Number parity Even\n• Number length 5\n• Sum of Digits 26\n• Digital Root 8\n\n## Name\n\nShort name 36 thousand 296 thirty-six thousand two hundred ninety-six\n\n## Notation\n\nScientific notation 3.6296 × 104 36.296 × 103\n\n## Prime Factorization of 36296\n\nPrime Factorization 23 × 13 × 349\n\nComposite number\nDistinct Factors Total Factors Radical ω(n) 3 Total number of distinct prime factors Ω(n) 5 Total number of prime factors rad(n) 9074 Product of the distinct prime numbers λ(n) -1 Returns the parity of Ω(n), such that λ(n) = (-1)Ω(n) μ(n) 0 Returns: 1, if n has an even number of prime factors (and is square free) −1, if n has an odd number of prime factors (and is square free) 0, if n has a squared prime factor Λ(n) 0 Returns log(p) if n is a power pk of any prime p (for any k >= 1), else returns 0\n\nThe prime factorization of 36,296 is 23 × 13 × 349. Since it has a total of 5 prime factors, 36,296 is a composite number.\n\n## Divisors of 36296\n\n1, 2, 4, 8, 13, 26, 52, 104, 349, 698, 1396, 2792, 4537, 9074, 18148, 36296\n\n16 divisors\n\n Even divisors 12 4 4 0\nTotal Divisors Sum of Divisors Aliquot Sum τ(n) 16 Total number of the positive divisors of n σ(n) 73500 Sum of all the positive divisors of n s(n) 37204 Sum of the proper positive divisors of n A(n) 4593.75 Returns the sum of divisors (σ(n)) divided by the total number of divisors (τ(n)) G(n) 190.515 Returns the nth root of the product of n divisors H(n) 7.90117 Returns the total number of divisors (τ(n)) divided by the sum of the reciprocal of each divisors\n\nThe number 36,296 can be divided by 16 positive divisors (out of which 12 are even, and 4 are odd). The sum of these divisors (counting 36,296) is 73,500, the average is 4,593,.75.\n\n## Other Arithmetic Functions (n = 36296)\n\n1 φ(n) n\nEuler Totient Carmichael Lambda Prime Pi φ(n) 16704 Total number of positive integers not greater than n that are coprime to n λ(n) 348 Smallest positive number such that aλ(n) ≡ 1 (mod n) for all a coprime to n π(n) ≈ 3851 Total number of primes less than or equal to n r2(n) 16 The number of ways n can be represented as the sum of 2 squares\n\nThere are 16,704 positive integers (less than 36,296) that are coprime with 36,296. And there are approximately 3,851 prime numbers less than or equal to 36,296.\n\n## Divisibility of 36296\n\n m n mod m 2 3 4 5 6 7 8 9 0 2 0 1 2 1 0 8\n\nThe number 36,296 is divisible by 2, 4 and 8.\n\n• Abundant\n\n• Polite\n\n## Base conversion (36296)\n\nBase System Value\n2 Binary 1000110111001000\n3 Ternary 1211210022\n4 Quaternary 20313020\n5 Quinary 2130141\n6 Senary 440012\n8 Octal 106710\n10 Decimal 36296\n12 Duodecimal 19008\n20 Vigesimal 4aeg\n36 Base36 s08\n\n## Basic calculations (n = 36296)\n\n### Multiplication\n\nn×i\n n×2 72592 108888 145184 181480\n\n### Division\n\nni\n n⁄2 18148 12098.7 9074 7259.2\n\n### Exponentiation\n\nni\n n2 1317399616 47816336462336 1735541748236947456 62993223294008244862976\n\n### Nth Root\n\ni√n\n 2√n 190.515 33.1095 13.8027 8.16529\n\n## 36296 as geometric shapes\n\n### Circle\n\n Diameter 72592 228054 4.13873e+09\n\n### Sphere\n\n Volume 2.00293e+14 1.65549e+10 228054\n\n### Square\n\nLength = n\n Perimeter 145184 1.3174e+09 51330.3\n\n### Cube\n\nLength = n\n Surface area 7.9044e+09 4.78163e+13 62866.5\n\n### Equilateral Triangle\n\nLength = n\n Perimeter 108888 5.70451e+08 31433.3\n\n### Triangular Pyramid\n\nLength = n\n Surface area 2.2818e+09 5.63521e+12 29635.6\n\n## Cryptographic Hash Functions\n\nmd5 bcffdc3d0dc34e21090d052d44e3eb2d 638c3a7a687533d1b04923fed254ebcb8066cf96 e97e8d9f2c4a9684dd6440081ba6046b107521258594514580d9c917e9ae5f69 005e133249555e2c88d22f108b3ef3816db601c793fc5ab1b91f6132da8f3de0f888ccf0175a59658a91fa3da1ea324e137f7079d0668021ebfe164b1acb3688 ad3f79abf0f1024e42ffdd629333a7ae57045796" ]
[ null ]
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https://www.brainysolutions.org/Course/Section/447/fsc-part-2-mathematics-complete-solutions-determine-whether-the-given-function--f---is-even-or-odd
[ "", null, "Fsc Part 2 Mathematics (Complete Solutions)\n\n# Q9 Determine whether the given function f is even or odd.\n\n## Determine whether the given function ƒ is even or odd.\n\n(i)     ƒ (x) = x3 + x\n(ii)     ƒ (x) = (x + 2)2\n(iii)     ƒ (x) = x  X2 + 5\n(iv)     ƒ (x) =\n x - 1 x + 1\n, x ≠ -1\n(v)     ƒ (x) = x 2/3 + 6\n(vi)     ƒ (x) =\n x3 - x x2 + 1\n\nSolution\n\n(i)     ƒ (x) = x3 + x\nConsider     ƒ (-x) = (-x)3 + (-x)\nƒ (-x) = -x3 - x\nƒ (-x) = -(x3 + x)\nƒ (-x) = -ƒ (x)\nHence ƒ (x) is an odd function.\n\n(ii)     ƒ (x) = (x + 2)2\nConsider     ƒ (-x) = (-x + 2)2\nƒ (-x) = (2 - x)2\nWhish cannot be compared with ƒ (x)\nHence ƒ (x) is neither even nor odd function.\n\n(iii)     ƒ (x) = x  X2 + 5\nConsider     ƒ (-x) = (-x)  (-x)2 + 5\nConsider     ƒ (-x) = -x  x2 + 5\nƒ (-x) = -ƒ (x)\nHence ƒ (x) is an odd function.\n\n(iv)     ƒ (x) =\n x - 1 x + 1\n, x ≠ -1\nConsider     ƒ (-x) =\n -x - 1 -x + 1\nƒ (-x) =\n -(x + 1) -(x - 1)\nƒ (-x) =\n x + 1 x - 1\nWhish cannot be compared with ƒ (x)\nHence ƒ (x) is neither even nor odd function.\n\n(v)     ƒ(x) = x 2/3 + 6\nConsider     ƒ (-x) = (-x) 2/3 + 6\nƒ (-x) = (-x 2) 1/3 + 6\nƒ (-x) = (x 2) 1/3 + 6\nƒ (-x) = x 2/3 + 6\nƒ (-x) = ƒ (x)\nHence ƒ (x) is an even function.\n\n(vi)     ƒ(x) =\n x3 - x x2 + 1\nConsider     ƒ (-x) =\n (-x)3 - (-x) (-x)2 + 1\nƒ (-x) =\n -x3 + x x2 + 1\nƒ (-x) =\n -(x3 - x) x2 + 1\nƒ (-x) = -ƒ (x)\nHence ƒ (x) is an odd function." ]
[ null, "https://www.brainysolutions.org/Content/Images/brainy-logo-90.png", null ]
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https://goformative.com/library/5d5805a6f782c17ec605479b
[ "Algebra 2 6-4 Guided Practice: Rational Exponents\nstarstarstarstarstarstarstarstarstarstar\nby Matthew Richardson\n| 25 Questions", null, "", null, "1\n2\n1\n10\nSolve It! On the canvas, show how to cut the three linked 1-squares into congruent pieces, each with size ¾.\n2\n10\nSolve It! Reasoning: Explain why you cannot cut them into congruent pieces, each with size 4/5.\nYou cannot cut the three 1-squares into congruent 4/5-pieces because 3 ÷ 4/5 is not a whole number.\nYou cannot cut the three 1-squares into congruent 4/5-pieces because 3 × 4/5 is not a whole number.\nYou cannot cut the three 1-squares into congruent 4/5-pieces because 3 is an odd number.", null, "", null, "3\n4\n5\n3\n10\nTake Note: Write the expression below in radical form.\n\n4\n10\nTake Note: Write the expression below in exponent form.\n\n5\n10\nTake Note: Define principal root.", null, "6\n6\n10\nProblem 1 Got It?\nA\nB\nC\nD", null, "7\n7\n10\nProblem 1 Got It?\nA\nB\nC\nD", null, "8\n8\n10\nProblem 1 Got It?\nA\nB\nC\nD", null, "", null, "9\n10\nProblem 2 Got It? What is the expression in radical form?\n\n10\n10\nProblem 2 Got It? What is the expression in radical form?\n\n11\n10\nProblem 2 Got It? What is the expression in exponential form?\n\n12\n10\nProblem 2 Got It? What is the expression in exponential form?\n\n13\n10\nProblem 2 Got It? Reasoning: Refer to the definition of rational exponent. Explain the need for the restriction that a ≠ 0 if m is negative. (In other words, if m is negative, why can't a be zero?)", null, "14\n14\n10\nProblem 3 Got It? Planetary Motion: Use the function\nwhere d is the distance from the planet to the sun in astronomical units (1 AU is about 93,000,000 miles, or the distance from Earth to the sun). About how many Earth years is a Venusian year if Venus is 0.72 AU from the sun?\nA\nB\nC\nD", null, "15\n15\n10\nProblem 3 Got It? Planetary Motion: Use the function\nwhere d is the distance from the planet to the sun in astronomical units (1 AU is about 93,000,000 miles, or the distance from Earth to the sun). About how many Earth years is a Jovian year if Jupiter is 5.46 AU from the sun?\nA\nB\nC\nD", null, "", null, "", null, "a\nTake Note: Take a moment to add the properties of rational exponents to your notes.", null, "", null, "", null, "", null, "16\n16\n10\nTake Note: Describe the process of simplifying radical expressions.\n◆ How do you know if you can simplify the expression in the first place?\n◆ What are the 2 steps for simplifying the expression?", null, "17\n17\n10\nProblem 4 Got It?\nA\nB\nC\nD", null, "18\n18\n10\nProblem 4 Got It?\nA\nB\nC\nD", null, "19\n19\n10\nProblem 4 Got It?\nA\nB\nC\nD", null, "", null, "20\n20\n10\nProblem 5 Got It?\nA\nB\nC\nD", null, "21\n21\n10\nProblem 5 Got It?\nA\nB\nC\nD", null, "22\n22\n10\nProblem 5 Got It?\nA\nB\nC\nD", null, "", null, "23\n23\n10\nProblem 6 Got It?\nA\nB\nC\nD", null, "24\n24\n10\nProblem 6 Got It?\nA\nB\nC\nD", null, "25\n25\n10\nTake Note: Summarize the content of this lesson." ]
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https://cs.stackexchange.com/questions/46893/algorithm-for-constructing-bst-from-post-order-traversal/46898
[ "# Algorithm for constructing BST from post-order traversal\n\nGiven a post-order traversal of Binary Search tree with $k$ nodes, find an algorithm that constructs the BST.\n\nMy Algortihm\n\nLet $n$ represent the next element to be inserted.\n\nLet $P(y)$ represent the parent of node $y$.\n\n1. We will read the traversal in reverse. The last element of the traversal is the root. Let $l = root$. $l$ will represent the element last inserted in the BST (except for the 3rd case below- where it will change to the parent).\n\nLoop the following till there's no element left to be inserted\n\n1. if $l<n$ then $n$ is the right child of $l$. For the next insertion, $l$ changes to it's right child and $n$ becomes the next element(in reverse order of traversal ).\n\n2. else, if $l>n$ and $P(l)<n$ then $n$ is the left child of $l$. For the next insertion, $l$ changes to it's left child and $n$ becomes the next element(in reverse order of traversal).\n\n3. else, if $l>n$ and $P(l)>n$ then $l$ becomes $P(l)$.($n$ hasn't been inserted - we loop with $l$ changed)\n\n[Let $P(root)=- \\infty$, so that the $2^{nd}$ case applies]\n\nComplexity Analysis : Every element may contribute at max 3 comparisons, 1 each for - left child, right child and for finally leaving i.e. subtree has been constructed. Even if I missed a comparison or two, It should be constant no. of comparisons per element and no. of operations for node construction will also be constant per element. Hence, giving $O(k)$ time complexity.\n\nActual Question\n\nIf the algorithm is correct, I need the correctness proof for it. Yes, I thought I had the proof but then brain got fried and I am stuck and unable to reason succinctly.\nIf the algorithm is incorrect, then why? And what is time complexity of the most efficient algorithm for the same question?\n\nAlso, is the $O(k)$ complexity correctly calculated - irrespective of the correctness of the algorithm?\n\n• @TerenceHang Do we have an $O(n)$ algo for constructing Binary tree from post and inorder traversal? Because for comparing two elements we will need to refer the inorder and that won't be constant time comparison. May be we can hash the indexes of elements in inorder traversal in $O(n)$ time and then we can compare the indexes, but that would require restriction on key values. Sep 8, 2015 at 3:24\n• An $O(n)$ algo exists, based on node matching instead of relative order. Take the inorder and postorder traversal as 2 stacks $In$ and $Post$, adding a 3rd stack $stk$. 1. pop the root off $Post$, inserting to $stk$, and set insert position at right child of root. 2. whenever top of $In$ matches top of $stk$, pop this node $x$ from both $In$ and $stk$, changing insert position to left child of $x$. 3. pop a new node $n$ from $post$, insert $n$ at current insert position, and push $n$ on $stk$, setting insert position to right child of $n$. Repeat 2,3 until all 3 stack are empty. Sep 8, 2015 at 5:00\n• Just find a $O(n)$ recursive algo (It is for construction binary tree from preorder and inorder. Scanning in reverse order and changing the target we can make it for construction from postorder and inorder.) Sep 8, 2015 at 5:26\n• What have you tried towards showing correctness, and where did you get stuck? Have you tried a more rigorous runtime analysis, too? See our reference questions for some pointers.\n– Raphael\nSep 8, 2015 at 7:17\n\nYou are in the right track. But the algorithm is incomplete. You missed the case inserting element on the left sub tree and back.\n\nHere is the modified algorithm: (Changes marked in bold)\n\nLet $n$ represent the next element to be inserted.\n\nLet $P(y)$ represent the parent of node $y$.\n\nLet $g=G(y)$ represent the first node g on the path $y\\to root$ such that $P(g)<g$.\n\n1. We will read the traversal in reverse. The last element of the traversal is the root. Let $l = root$. $l$ will represent the element last inserted in the BST (except for the 3rd case below- where it will change to the parent). Let $g=root$ tracking $G(l)$, initialize empty stack $stkG$ storing previous $g$'s on current path.\n\n2. Loop the following till there's no element left to be inserted\n\n1. if $l<n$ then $n$ is the right child of $l$. For the next insertion, $l$ changes to it's right child and $n$ becomes the next element(in reverse order of traversal ). Push $g$ on $stkG$, and let $g=l$.\n\n2. else, if $l>n$ and $\\textbf{P(g)<n}$ then $n$ is the left child of $l$. For the next insertion, $l$ changes to it's left child and $n$ becomes the next element(in reverse order of traversal).\n\n3. else, if $l>n$ and $\\textbf{P(g)>n}$ then $l$ becomes $\\textbf{P(g)}$ and pop $g$ from $stkG$.($n$ hasn't been inserted - we loop with $l$ changed)\n\n[Let $P(root)=- \\infty$, so that the $2^{nd}$ case applies]\n\nFor correctness, you can prove the following loop invariant:\n\n1. Root is the first inserted element. for each insertion except root, the parent element has been inserted before.\n2. Each insertion $n$ correctly maintains the order between $n$ and $l$. ($n<l$ if $n$ is left child of $l$, $n>l$ otherwise)\n3. After backtracking step 3, the next insertion always occurs on the left branch.\n\n1 and 3 ensures the post-order traversal, while 2 ensures the BST.\n\nFor complexity:\n\n1. insertion cost: each element is inserted exactly once.\n2. traversal and comparison: the algorithm actually performs a post-order traversal in reverse order, with $O(1)$ comparison on each step.\n3. $g$,$stkG$ maintain cost: each node, which is right child of parent, is pushed and popped from $stkG$ at most once.\n\nThus the time complexity is $O(k)$.\n\n## Alternative algorithm:\n\nUsing a recursive procedure:\n\nprocedure BST_from_postorder(post, len, target)\n/*\ninput: post[0..len-1] -- (partial) postorder traversal of BST\nlen -- length of post to be processed.\ntarget -- a cutoff value to stop processing\nOutput: tree_ptr -- pointer to root of tree/sub tree constructed from post[len_rest..len-1]\nlen_rest -- remaining length that has not been processed.\n*/\n1. if len <= 0 or post[len-1] <= target, then return null.\n2. root <- new Node created from from post[len-1].\n3. (root->right, new_len) <- BST_from_postorder(post, len-1, post[len-1])\n4. (root->left, rest_len) <- BST_from_postorder(post, newlen, target)\n5. return (pointer to root, rest_len)\n\n/* BST_from_postorder(post, length of post, -infinity)\nwill return the BST construct from given postorder traversal. */\n\n• Hey, thanks for the answer. I understood your algorithm. For the correctness part 1 - this may also be added : \"the right element is inserted before the left element\". Also, I think my algorithm is correct too. You maintain a stack, so that you can directly jump to $P(g)$ in the $3^{rd}$ case. Instead, my algo does redundant comparison during backtracking from a left-subtree but eventually does reach $P(g)$ and inserts in the correct position. What do you think? Sep 7, 2015 at 7:44\n• There are cases where $n<l<P(l)$, which fall into your $3^{rd}$ case, but you have to decide to insert to left child or to backtrack. $g$ is used not only for quick backtracking, but also for comparison. Sep 7, 2015 at 7:50\n• For correctness part, it is included in 3. ie. the traversal is always from right branch to left branch and never in reverse. Sep 7, 2015 at 7:53\n• Ah! for $n<l<p(l)$, my algorithm always backtracks. So, if $n<l<p(l)$ & $P(g)<n$ then it will try to insert $n$ as left child of $g$ but that's obviously wrong. Sep 7, 2015 at 8:42" ]
[ null ]
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https://solvedlib.com/n/carbon-monoxide-gas-reacts-with-gaseous-molecular-oxygen,15461952
[ "# Carbon monoxide gas reacts with gaseous molecular oxygen (O2) toform gaseous carbon dioxide. Initially, CO and O2 are separated inthe\n\n###### Question:\n\nCarbon monoxide gas reacts with gaseous molecular oxygen (O2) to form gaseous carbon dioxide. Initially, CO and O2 are separated in the glass apparatus shown. When the valve is opened, the reaction quickly goes to completion. What is the total pressure in the apparatus after the reaction occurs? Assume temperature remains constant at 75 °C.", null, "#### Similar Solved Questions\n\n##### A simple random sample of 60 items resulted in a sample mean of 90. The population...\nA simple random sample of 60 items resulted in a sample mean of 90. The population standard deviation is 13. 1)  Compute the 95% confidence interval for the population mean (to 1 decimal). 2) Assume that the same sample mean was obtained from a sample of 120 items. Provide a 95% confidence...\n##### Jo) ucit Itkc Iechenistn fac Na SHL DMSOEelloucd ~FeacHiba\nJo) ucit Itkc Iechenistn fac Na SHL DMSO Eelloucd ~FeacHiba...\n##### Abiologistis researching a newly-discovered species of bacteria: At time t=0.she puts an unknown number of bacteria into her petri dish After t=1 hour; there are 50O bacteria t24 hours. there are 2300 bacteria in her her petri dish After petri dish: exponentially and creates She assumes that the bacteria are growing graph of this growth; which is shown bclow. P(t)25002000'(4,,2300)15001000500500)Assuming that the bacteria are growing exponentially find J function Ptk the bacteri > popu\nAbiologistis researching a newly-discovered species of bacteria: At time t=0.she puts an unknown number of bacteria into her petri dish After t=1 hour; there are 50O bacteria t24 hours. there are 2300 bacteria in her her petri dish After petri dish: exponentially and creates She assumes that the b...\n##### PLEASE ANSWER QUESTIONS 1 - 3 (PLEASE SHOWWORK)Suppose that in a random sample of size 110, Pearson’s r is-0.203. You suspect there is a negative relationship in thepopulation.1) What is the standard score when you rescale Z?2) What is the probability of getting the sample correlation asextreme as we did if no relationship exists in the population?3) What can you conclude?\nPLEASE ANSWER QUESTIONS 1 - 3 (PLEASE SHOW WORK) Suppose that in a random sample of size 110, Pearson’s r is -0.203. You suspect there is a negative relationship in the population. 1) What is the standard score when you rescale Z? 2) What is the probability of getting the sample correlation a...\n##### A collection company has an antiquated high-capacity printer that needs to be updated. The company is...\nA collection company has an antiquated high-capacity printer that needs to be updated. The company is faced with two alternatives: the system either can be overhauled or replaced with a new system. The following data has been gathered concerning these two alternatives (ignore income taxes). The ...\n##### Give an arc-lenqh 2 Poraxelht ahaa S Uhich is J inkrekan Ha +oant Planus 6f 3 32 Tath Camscanner' = 0 449] Scanned\nGive an arc-lenqh 2 Poraxelht ahaa S Uhich is J inkrekan Ha +oant Planus 6f 3 32 Tath Camscanner' = 0 449] Scanned...\n##### Point)Two long, straight wires carry currents in the directions shown in the figure above. I1 = 5A,12 = 6A,a = 7 cm, b = 3 cm:a) Find the magnetic field strength at point P B =j)tb) What force would m of a third wire, carry a 6-A current out of the page, experience if place at P? F = j)N\npoint) Two long, straight wires carry currents in the directions shown in the figure above. I1 = 5A,12 = 6A,a = 7 cm, b = 3 cm: a) Find the magnetic field strength at point P B = j)t b) What force would m of a third wire, carry a 6-A current out of the page, experience if place at P? F = j)N...\n##### Problem 2: Find power series solutions about xo = 0 of the following ODEs: (a) y\" + xy +y = 0. 7 (b) (22 +l)y\" + 2ry' +y = 0.\nProblem 2: Find power series solutions about xo = 0 of the following ODEs: (a) y\" + xy +y = 0. 7 (b) (22 +l)y\" + 2ry' +y = 0....\n##### An object is placed 15 cm in front of a converging lens with a focal length f = +20 cm: The image formed is (Hint: Sketch the ray diagram:)\nAn object is placed 15 cm in front of a converging lens with a focal length f = +20 cm: The image formed is (Hint: Sketch the ray diagram:)...\n##### What kind of chromosom I changa occured prcducchrotnosonaeonaccnatGnodrOrden hinan (ntdanter Eprila, erd ornriamHanal\nWhat kind of chromosom I changa occured prcduc chrotnoson aeonaccnat Gnodr Orden hinan (ntdanter Eprila, erd ornriam Hanal...\n##### 2. [-12 Points) DETAILS SERCP11 7.1.OP.003. 0/6 Submissions Used MY NOTES ASK YOUR TEACHER A new...\n2. [-12 Points) DETAILS SERCP11 7.1.OP.003. 0/6 Submissions Used MY NOTES ASK YOUR TEACHER A new midsize car has tires with a diameter of 26.2 inches. The tires have a tread-life warranty of 58,000 miles. (a) How many radians will the tires rotate through within the full warranty length? rad ns TH l...\n##### How do the location and size of warehouses affect the performance of a firm ?\nHow do the location and size of warehouses affect the performance of a firm ?...\n##### The Georgia Corporation has a central copying facility. The copying facility has only two users, the...\nThe Georgia Corporation has a central copying facility. The copying facility has only two users, the Marketing Department and the Operations Department. The following data apply to the coming budget year: Budgeted costs of operating the copying facility for 300,000 to 500,000 copies:   &nb...\n##### Five cards are drawn with replacement from a standard deck of 52 cards consisting of four...\nFive cards are drawn with replacement from a standard deck of 52 cards consisting of four suits of thirteen cards each. Calculate the probability that the five cards result in a flush (all five cards are of the same suit and round to the fourth decimal)...\n##### With the complex numbers a =5.i+2 W =7-7.1 2 =-.i-1a(w - 2)2 + alw + 22\nWith the complex numbers a =5.i+2 W =7-7.1 2 =-.i-1 a(w - 2)2 + alw + 22...\n##### Given:CoClz (g) cO (g) Clz (g)This process nonspontaneous under standard conditions atroom temperature: In orderto make this eaction spontaneous: would you raise or lower the temperature? Please explain using your knowledge of Gibbs Equation:\nGiven: CoClz (g) cO (g) Clz (g) This process nonspontaneous under standard conditions atroom temperature: In orderto make this eaction spontaneous: would you raise or lower the temperature? Please explain using your knowledge of Gibbs Equation:...\n##### 2x\" lim 1 cos(5x)The limit does not exist.2 5 4\n2x\" lim 1 cos(5x) The limit does not exist. 2 5 4...\n##### Please i need the answer asap 1. Given the data below, compute for the following: a)...\nplease i need the answer asap 1. Given the data below, compute for the following: a) Forecasts for P5 to P12 using a 4-period simple moving average b) Forecasts for P5 to P12 using a 4-month weighted moving average with the following weights: Most recent period = 0.40 2nd most recent period = 0.30 ...\n##### 6. The exponential distribution Consider the random variable x that follows an exponential distribution, with p...\n6. The exponential distribution Consider the random variable x that follows an exponential distribution, with p - 10. The standard deviation of X is o = The parameter of the exponential distribution of X is A - What is the probability that X is less than 7? OP(X < 7) = 0.3935 OP(X < 7) = 0.503...\n##### (10 pts:] Consider the open sentences P(n) and Q(n) with domain NP(n) : n3 > 4nQ(n) 3l _ 2 is primeState each of the following in words (do not use the Symbols P; Q. ~, V, or 3) in your final answer. (Vn e N; P(n))(Jne N, Q(n))(Vn eN; P(n)Q(n))\n(10 pts:] Consider the open sentences P(n) and Q(n) with domain N P(n) : n3 > 4n Q(n) 3l _ 2 is prime State each of the following in words (do not use the Symbols P; Q. ~, V, or 3) in your final answer. (Vn e N; P(n)) (Jne N, Q(n)) (Vn eN; P(n) Q(n))...\n##### How do you integrate int (1-x^2)/((x-9)(x-3)(x-2)) using partial fractions?\nHow do you integrate int (1-x^2)/((x-9)(x-3)(x-2)) using partial fractions?...\n##### 1. Write the Ka\" expressions for each of the following reactions _ HOCN H,0 6 OcN + 1,0' (b) KSiF6 3H,O = 2KF H,SiO; + 4HF\n1. Write the Ka\" expressions for each of the following reactions _ HOCN H,0 6 OcN + 1,0' (b) KSiF6 3H,O = 2KF H,SiO; + 4HF...\n##### 5.0 [0/2 Points]DETAILSPREVIOUS ANSWERSLARCALC1I 13.R.047.Consider the following. In(x? + Y), X =2t, Y = 8 -dw (a) Find by using the appropriate Chain Rule_16t 422 _ t+8Findby converting w to function of before differentiating16t = 422 _ t+8dw\n5.0 [0/2 Points] DETAILS PREVIOUS ANSWERS LARCALC1I 13.R.047. Consider the following. In(x? + Y), X =2t, Y = 8 - dw (a) Find by using the appropriate Chain Rule_ 16t 422 _ t+8 Find by converting w to function of before differentiating 16t = 422 _ t+8 dw...\n##### There are three different reactions with alkenes that proceed via three-membered ring intermediates or produce a three-...\nThere are three different reactions with alkenes that proceed via three-membered ring intermediates or produce a three-membered ring product. 4. (4 Points) There are three different reactions with alkenes that proceed via three-membered ring intermediates or produce a three-membered ring product....\n##### POST LAB QUESTIONS Answer the following questions in your lab notebook: 1. Give the chemical formula...\nPOST LAB QUESTIONS Answer the following questions in your lab notebook: 1. Give the chemical formula for a single chemical reagent that would : (a) separate Ag from Cut b) separate AgCl from PbCl2 - separate Cu2+ from Mat (d) separate Fet from Zn2+ (e) Dissolve Zn(OH), but not Fe(OH)3 (f) separate B...\n##### Use the graph to evaluate the indicated limit and function value or state that it does not existf(c)Select ]6) lim_-0+ f (r)Select |cllimg_40 f (c)Select |lint,\nUse the graph to evaluate the indicated limit and function value or state that it does not exist f(c) Select ] 6) lim_-0+ f (r) Select | cllimg_40 f (c) Select | lint,...\n##### Use the Ksp value 1.0 x 10stto calculate the molar solubility of Pba(PO Jz in 1.00 x 10-6 M NazPOa.Use the glven molar solubility in pure water (S= 3.32 x 10-4) to calculate the Ke for Calz:\nUse the Ksp value 1.0 x 10stto calculate the molar solubility of Pba(PO Jz in 1.00 x 10-6 M NazPOa. Use the glven molar solubility in pure water (S= 3.32 x 10-4) to calculate the Ke for Calz:...\n##### C. At the 1% significance level, can you conclude that the average growth of the plant differs by acidity level?Yes since the p-value for Factor Bis less than significance level: Yes since the p value for Factor B is greater than significance level: No since the p-value for Factor B is less than significance level: No since the p-value for Factor B is greater than significance level.\nc. At the 1% significance level, can you conclude that the average growth of the plant differs by acidity level? Yes since the p-value for Factor Bis less than significance level: Yes since the p value for Factor B is greater than significance level: No since the p-value for Factor B is less than si..." ]
[ null, "https://cdn.numerade.com/previews/f0ab8d67-1d53-4572-b883-c4667fa3838f_large.jpg", null ]
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https://downloads.teradata.com/tag/day-interval
[ "Tags for day interval\nHow to calculate moving sums within variable size windows?\nHi! I am trying to calculate moving sums and row counts in a query, to do further arithmetic on the said values. For a range of 3 days, for example, I would sum the values given in the rows for those 3 days, and then divide them by the amount of rows in that same time period. In Oracle, the syntax would be:" ]
[ null ]
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https://innerzi.com/table-of-192/
[ "Becoming fluent in math tables is necessary if you want to do complex mathematical calculations fast. Memorizing the tables becomes very helpful during exams as well as in our day-to-day lives.\n\nHere’s the table of 192 which consists of the multiplication of 192 with the whole numbers:\n\n## Multiplication table of 192\n\nHere’s the multiplication table of 192 up to x20:\n\n192 times Equals\n192 x 1 192\n192 x 2 384\n192 x 3 576\n192 x 4 768\n192 x 5 960\n192 x 6 1152\n192 x 7 1344\n192 x 8 1536\n192 x 9 1728\n192 x 10 1920\n192 x 11 2112\n192 x 12 2304\n192 x 13 2496\n192 x 14 2688\n192 x 15 2880\n192 x 16 3072\n192 x 17 3264\n192 x 18 3456\n192 x 19 3648\n192 x 20 3840\n\n### 192 times table in words\n\n• 192 times 1 is equal to 192\n• 192 times 2 is equal to 384\n• 192 times 3 is equal to 576\n• 192 times 4 is equal to 768\n• 192 times 5 is equal to 960\n• 192 times 6 is equal to 1152\n• 192 times 7 is equal to 1344\n• 192 times 8 is equal to 1536\n• 192 times 9 is equal to 1728\n• 192 times 10 is equal to 1920\n• 192 times 11 is equal to 2112\n• 192 times 12 is equal to 2304\n• 192 times 13 is equal to 2496\n• 192 times 14 is equal to 2688\n• 192 times 15 is equal to 2880\n• 192 times 16 is equal to 3072\n• 192 times 17 is equal to 3264\n• 192 times 18 is equal to 3456\n• 192 times 19 is equal to 3648\n• 192 times 20 is equal to 3840\n\nAlso see:\n\n## Multiplication table of 192 in the form of addition\n\nMultiplication of natural numbers is repeated addition.\n\nIf you have to multiply 192 to 3 then it’s just the addition of 192 three times, i.e., 192 + 192 + 192 which ultimately gives you 576.\n\nLet’s take a look at the full table of 192 below:\n\n192 x 1 = 192 192\n192 x 2 = 384 192 + 192\n192 x 3 = 576 192 + 192 + 192\n192 x 4 = 768 192 + 192 + 192 + 192\n192 x 5 = 960 192 + 192 + 192 + 192 + 192\n192 x 6 = 1152 192 + 192 + 192 + 192 + 192 + 192\n192 x 7 = 1344 192 + 192 + 192 + 192 + 192 + 192 + 192\n192 x 8 = 1536 192 + 192 + 192 + 192 + 192 + 192 + 192 + 192\n192 x 9 = 1728 192 + 192 + 192 + 192 + 192 + 192 + 192 + 192 + 192\n192 x 10 = 1920 192 + 192 + 192 + 192 + 192 + 192 + 192 + 192 + 192 + 192\n\n## FAQs\n\n### 1. How to count or read the table of 192?\n\nYou can read the table of 192 by following the below lines:\n\n• 192 times one is 192\n• 192 times two is 384\n• 192 times three is 576\n• 192 times four is 768\n• 192 times five is 960\n• 192 times six is 1152\n• 192 times seven is 1344\n• 192 times eight is 1536\n• 192 times nine is 1728\n• 192 times ten is 1920\n\n### 2. Why memorizing tables is important?\n\nMemorizing tables makes mental calculations effortless and efficient, it makes people think. The multiplication tables come in very handy while doing geometry, algebra, trigonometry, calculus, number theory, etc.\n\n## Explore\n\nExplore other interesting stuff related to math and numbers." ]
[ null ]
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https://www.convertunits.com/from/cubic+centimeter/to/cubic+foot
[ "## ››Convert cubic centimetre to cubic foot\n\n cubic centimeter cubic foot\n\nHow many cubic centimeter in 1 cubic foot? The answer is 28316.846711688.\nWe assume you are converting between cubic centimetre and cubic foot.\nYou can view more details on each measurement unit:\ncubic centimeter or cubic foot\nThe SI derived unit for volume is the cubic meter.\n1 cubic meter is equal to 1000000 cubic centimeter, or 35.314666572222 cubic foot.\nNote that rounding errors may occur, so always check the results.\nUse this page to learn how to convert between cubic centimeters and cubic feet.\nType in your own numbers in the form to convert the units!\n\n## ››Want other units?\n\nYou can do the reverse unit conversion from cubic foot to cubic centimeter, or enter any two units below:\n\n## Enter two units to convert\n\n From: To:\n\n## ››Definition: Cubic centimeter\n\nA cubic centimetre (cm3) is equal to the volume of a cube with side length of 1 centimetre. It was the base unit of volume of the CGS system of units, and is a legitimate SI unit. It is equal to a millilitre (ml).\n\nThe colloquial abbreviations cc and ccm are not SI but are common in some contexts. It is a verbal shorthand for \"cubic centimetre\". For example 'cc' is commonly used for denoting displacement of car and motorbike engines \"the Mini Cooper had a 1275 cc engine\". In medicine 'cc' is also common, for example \"100 cc of blood loss\".\n\n## ››Definition: Cubic foot\n\nThe cubic foot (symbols ft³, cu. ft.) is a nonmetric unit of volume, used in U.S. customary units and Imperial units. It is defined as the volume of a cube with edges one foot in length.\n\n## ››Metric conversions and more\n\nConvertUnits.com provides an online conversion calculator for all types of measurement units. You can find metric conversion tables for SI units, as well as English units, currency, and other data. Type in unit symbols, abbreviations, or full names for units of length, area, mass, pressure, and other types. Examples include mm, inch, 100 kg, US fluid ounce, 6'3\", 10 stone 4, cubic cm, metres squared, grams, moles, feet per second, and many more!" ]
[ null ]
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http://isabelle.in.tum.de/repos/isabelle/file/a6b76247534d/src/HOL/Archimedean_Field.thy
[ "src/HOL/Archimedean_Field.thy\n author hoelzl Wed Apr 18 14:29:05 2012 +0200 (2012-04-18) changeset 47592 a6b76247534d parent 47307 5e5ca36692b3 child 54281 b01057e72233 permissions -rw-r--r--\n``` 1 (* Title: HOL/Archimedean_Field.thy\n```\n``` 2 Author: Brian Huffman\n```\n``` 3 *)\n```\n``` 4\n```\n``` 5 header {* Archimedean Fields, Floor and Ceiling Functions *}\n```\n``` 6\n```\n``` 7 theory Archimedean_Field\n```\n``` 8 imports Main\n```\n``` 9 begin\n```\n``` 10\n```\n``` 11 subsection {* Class of Archimedean fields *}\n```\n``` 12\n```\n``` 13 text {* Archimedean fields have no infinite elements. *}\n```\n``` 14\n```\n``` 15 class archimedean_field = linordered_field +\n```\n``` 16 assumes ex_le_of_int: \"\\<exists>z. x \\<le> of_int z\"\n```\n``` 17\n```\n``` 18 lemma ex_less_of_int:\n```\n``` 19 fixes x :: \"'a::archimedean_field\" shows \"\\<exists>z. x < of_int z\"\n```\n``` 20 proof -\n```\n``` 21 from ex_le_of_int obtain z where \"x \\<le> of_int z\" ..\n```\n``` 22 then have \"x < of_int (z + 1)\" by simp\n```\n``` 23 then show ?thesis ..\n```\n``` 24 qed\n```\n``` 25\n```\n``` 26 lemma ex_of_int_less:\n```\n``` 27 fixes x :: \"'a::archimedean_field\" shows \"\\<exists>z. of_int z < x\"\n```\n``` 28 proof -\n```\n``` 29 from ex_less_of_int obtain z where \"- x < of_int z\" ..\n```\n``` 30 then have \"of_int (- z) < x\" by simp\n```\n``` 31 then show ?thesis ..\n```\n``` 32 qed\n```\n``` 33\n```\n``` 34 lemma ex_less_of_nat:\n```\n``` 35 fixes x :: \"'a::archimedean_field\" shows \"\\<exists>n. x < of_nat n\"\n```\n``` 36 proof -\n```\n``` 37 obtain z where \"x < of_int z\" using ex_less_of_int ..\n```\n``` 38 also have \"\\<dots> \\<le> of_int (int (nat z))\" by simp\n```\n``` 39 also have \"\\<dots> = of_nat (nat z)\" by (simp only: of_int_of_nat_eq)\n```\n``` 40 finally show ?thesis ..\n```\n``` 41 qed\n```\n``` 42\n```\n``` 43 lemma ex_le_of_nat:\n```\n``` 44 fixes x :: \"'a::archimedean_field\" shows \"\\<exists>n. x \\<le> of_nat n\"\n```\n``` 45 proof -\n```\n``` 46 obtain n where \"x < of_nat n\" using ex_less_of_nat ..\n```\n``` 47 then have \"x \\<le> of_nat n\" by simp\n```\n``` 48 then show ?thesis ..\n```\n``` 49 qed\n```\n``` 50\n```\n``` 51 text {* Archimedean fields have no infinitesimal elements. *}\n```\n``` 52\n```\n``` 53 lemma ex_inverse_of_nat_Suc_less:\n```\n``` 54 fixes x :: \"'a::archimedean_field\"\n```\n``` 55 assumes \"0 < x\" shows \"\\<exists>n. inverse (of_nat (Suc n)) < x\"\n```\n``` 56 proof -\n```\n``` 57 from `0 < x` have \"0 < inverse x\"\n```\n``` 58 by (rule positive_imp_inverse_positive)\n```\n``` 59 obtain n where \"inverse x < of_nat n\"\n```\n``` 60 using ex_less_of_nat ..\n```\n``` 61 then obtain m where \"inverse x < of_nat (Suc m)\"\n```\n``` 62 using `0 < inverse x` by (cases n) (simp_all del: of_nat_Suc)\n```\n``` 63 then have \"inverse (of_nat (Suc m)) < inverse (inverse x)\"\n```\n``` 64 using `0 < inverse x` by (rule less_imp_inverse_less)\n```\n``` 65 then have \"inverse (of_nat (Suc m)) < x\"\n```\n``` 66 using `0 < x` by (simp add: nonzero_inverse_inverse_eq)\n```\n``` 67 then show ?thesis ..\n```\n``` 68 qed\n```\n``` 69\n```\n``` 70 lemma ex_inverse_of_nat_less:\n```\n``` 71 fixes x :: \"'a::archimedean_field\"\n```\n``` 72 assumes \"0 < x\" shows \"\\<exists>n>0. inverse (of_nat n) < x\"\n```\n``` 73 using ex_inverse_of_nat_Suc_less [OF `0 < x`] by auto\n```\n``` 74\n```\n``` 75 lemma ex_less_of_nat_mult:\n```\n``` 76 fixes x :: \"'a::archimedean_field\"\n```\n``` 77 assumes \"0 < x\" shows \"\\<exists>n. y < of_nat n * x\"\n```\n``` 78 proof -\n```\n``` 79 obtain n where \"y / x < of_nat n\" using ex_less_of_nat ..\n```\n``` 80 with `0 < x` have \"y < of_nat n * x\" by (simp add: pos_divide_less_eq)\n```\n``` 81 then show ?thesis ..\n```\n``` 82 qed\n```\n``` 83\n```\n``` 84\n```\n``` 85 subsection {* Existence and uniqueness of floor function *}\n```\n``` 86\n```\n``` 87 lemma exists_least_lemma:\n```\n``` 88 assumes \"\\<not> P 0\" and \"\\<exists>n. P n\"\n```\n``` 89 shows \"\\<exists>n. \\<not> P n \\<and> P (Suc n)\"\n```\n``` 90 proof -\n```\n``` 91 from `\\<exists>n. P n` have \"P (Least P)\" by (rule LeastI_ex)\n```\n``` 92 with `\\<not> P 0` obtain n where \"Least P = Suc n\"\n```\n``` 93 by (cases \"Least P\") auto\n```\n``` 94 then have \"n < Least P\" by simp\n```\n``` 95 then have \"\\<not> P n\" by (rule not_less_Least)\n```\n``` 96 then have \"\\<not> P n \\<and> P (Suc n)\"\n```\n``` 97 using `P (Least P)` `Least P = Suc n` by simp\n```\n``` 98 then show ?thesis ..\n```\n``` 99 qed\n```\n``` 100\n```\n``` 101 lemma floor_exists:\n```\n``` 102 fixes x :: \"'a::archimedean_field\"\n```\n``` 103 shows \"\\<exists>z. of_int z \\<le> x \\<and> x < of_int (z + 1)\"\n```\n``` 104 proof (cases)\n```\n``` 105 assume \"0 \\<le> x\"\n```\n``` 106 then have \"\\<not> x < of_nat 0\" by simp\n```\n``` 107 then have \"\\<exists>n. \\<not> x < of_nat n \\<and> x < of_nat (Suc n)\"\n```\n``` 108 using ex_less_of_nat by (rule exists_least_lemma)\n```\n``` 109 then obtain n where \"\\<not> x < of_nat n \\<and> x < of_nat (Suc n)\" ..\n```\n``` 110 then have \"of_int (int n) \\<le> x \\<and> x < of_int (int n + 1)\" by simp\n```\n``` 111 then show ?thesis ..\n```\n``` 112 next\n```\n``` 113 assume \"\\<not> 0 \\<le> x\"\n```\n``` 114 then have \"\\<not> - x \\<le> of_nat 0\" by simp\n```\n``` 115 then have \"\\<exists>n. \\<not> - x \\<le> of_nat n \\<and> - x \\<le> of_nat (Suc n)\"\n```\n``` 116 using ex_le_of_nat by (rule exists_least_lemma)\n```\n``` 117 then obtain n where \"\\<not> - x \\<le> of_nat n \\<and> - x \\<le> of_nat (Suc n)\" ..\n```\n``` 118 then have \"of_int (- int n - 1) \\<le> x \\<and> x < of_int (- int n - 1 + 1)\" by simp\n```\n``` 119 then show ?thesis ..\n```\n``` 120 qed\n```\n``` 121\n```\n``` 122 lemma floor_exists1:\n```\n``` 123 fixes x :: \"'a::archimedean_field\"\n```\n``` 124 shows \"\\<exists>!z. of_int z \\<le> x \\<and> x < of_int (z + 1)\"\n```\n``` 125 proof (rule ex_ex1I)\n```\n``` 126 show \"\\<exists>z. of_int z \\<le> x \\<and> x < of_int (z + 1)\"\n```\n``` 127 by (rule floor_exists)\n```\n``` 128 next\n```\n``` 129 fix y z assume\n```\n``` 130 \"of_int y \\<le> x \\<and> x < of_int (y + 1)\"\n```\n``` 131 \"of_int z \\<le> x \\<and> x < of_int (z + 1)\"\n```\n``` 132 then have\n```\n``` 133 \"of_int y \\<le> x\" \"x < of_int (y + 1)\"\n```\n``` 134 \"of_int z \\<le> x\" \"x < of_int (z + 1)\"\n```\n``` 135 by simp_all\n```\n``` 136 from le_less_trans [OF `of_int y \\<le> x` `x < of_int (z + 1)`]\n```\n``` 137 le_less_trans [OF `of_int z \\<le> x` `x < of_int (y + 1)`]\n```\n``` 138 show \"y = z\" by (simp del: of_int_add)\n```\n``` 139 qed\n```\n``` 140\n```\n``` 141\n```\n``` 142 subsection {* Floor function *}\n```\n``` 143\n```\n``` 144 class floor_ceiling = archimedean_field +\n```\n``` 145 fixes floor :: \"'a \\<Rightarrow> int\"\n```\n``` 146 assumes floor_correct: \"of_int (floor x) \\<le> x \\<and> x < of_int (floor x + 1)\"\n```\n``` 147\n```\n``` 148 notation (xsymbols)\n```\n``` 149 floor (\"\\<lfloor>_\\<rfloor>\")\n```\n``` 150\n```\n``` 151 notation (HTML output)\n```\n``` 152 floor (\"\\<lfloor>_\\<rfloor>\")\n```\n``` 153\n```\n``` 154 lemma floor_unique: \"\\<lbrakk>of_int z \\<le> x; x < of_int z + 1\\<rbrakk> \\<Longrightarrow> floor x = z\"\n```\n``` 155 using floor_correct [of x] floor_exists1 [of x] by auto\n```\n``` 156\n```\n``` 157 lemma of_int_floor_le: \"of_int (floor x) \\<le> x\"\n```\n``` 158 using floor_correct ..\n```\n``` 159\n```\n``` 160 lemma le_floor_iff: \"z \\<le> floor x \\<longleftrightarrow> of_int z \\<le> x\"\n```\n``` 161 proof\n```\n``` 162 assume \"z \\<le> floor x\"\n```\n``` 163 then have \"(of_int z :: 'a) \\<le> of_int (floor x)\" by simp\n```\n``` 164 also have \"of_int (floor x) \\<le> x\" by (rule of_int_floor_le)\n```\n``` 165 finally show \"of_int z \\<le> x\" .\n```\n``` 166 next\n```\n``` 167 assume \"of_int z \\<le> x\"\n```\n``` 168 also have \"x < of_int (floor x + 1)\" using floor_correct ..\n```\n``` 169 finally show \"z \\<le> floor x\" by (simp del: of_int_add)\n```\n``` 170 qed\n```\n``` 171\n```\n``` 172 lemma floor_less_iff: \"floor x < z \\<longleftrightarrow> x < of_int z\"\n```\n``` 173 by (simp add: not_le [symmetric] le_floor_iff)\n```\n``` 174\n```\n``` 175 lemma less_floor_iff: \"z < floor x \\<longleftrightarrow> of_int z + 1 \\<le> x\"\n```\n``` 176 using le_floor_iff [of \"z + 1\" x] by auto\n```\n``` 177\n```\n``` 178 lemma floor_le_iff: \"floor x \\<le> z \\<longleftrightarrow> x < of_int z + 1\"\n```\n``` 179 by (simp add: not_less [symmetric] less_floor_iff)\n```\n``` 180\n```\n``` 181 lemma floor_mono: assumes \"x \\<le> y\" shows \"floor x \\<le> floor y\"\n```\n``` 182 proof -\n```\n``` 183 have \"of_int (floor x) \\<le> x\" by (rule of_int_floor_le)\n```\n``` 184 also note `x \\<le> y`\n```\n``` 185 finally show ?thesis by (simp add: le_floor_iff)\n```\n``` 186 qed\n```\n``` 187\n```\n``` 188 lemma floor_less_cancel: \"floor x < floor y \\<Longrightarrow> x < y\"\n```\n``` 189 by (auto simp add: not_le [symmetric] floor_mono)\n```\n``` 190\n```\n``` 191 lemma floor_of_int [simp]: \"floor (of_int z) = z\"\n```\n``` 192 by (rule floor_unique) simp_all\n```\n``` 193\n```\n``` 194 lemma floor_of_nat [simp]: \"floor (of_nat n) = int n\"\n```\n``` 195 using floor_of_int [of \"of_nat n\"] by simp\n```\n``` 196\n```\n``` 197 lemma le_floor_add: \"floor x + floor y \\<le> floor (x + y)\"\n```\n``` 198 by (simp only: le_floor_iff of_int_add add_mono of_int_floor_le)\n```\n``` 199\n```\n``` 200 text {* Floor with numerals *}\n```\n``` 201\n```\n``` 202 lemma floor_zero [simp]: \"floor 0 = 0\"\n```\n``` 203 using floor_of_int [of 0] by simp\n```\n``` 204\n```\n``` 205 lemma floor_one [simp]: \"floor 1 = 1\"\n```\n``` 206 using floor_of_int [of 1] by simp\n```\n``` 207\n```\n``` 208 lemma floor_numeral [simp]: \"floor (numeral v) = numeral v\"\n```\n``` 209 using floor_of_int [of \"numeral v\"] by simp\n```\n``` 210\n```\n``` 211 lemma floor_neg_numeral [simp]: \"floor (neg_numeral v) = neg_numeral v\"\n```\n``` 212 using floor_of_int [of \"neg_numeral v\"] by simp\n```\n``` 213\n```\n``` 214 lemma zero_le_floor [simp]: \"0 \\<le> floor x \\<longleftrightarrow> 0 \\<le> x\"\n```\n``` 215 by (simp add: le_floor_iff)\n```\n``` 216\n```\n``` 217 lemma one_le_floor [simp]: \"1 \\<le> floor x \\<longleftrightarrow> 1 \\<le> x\"\n```\n``` 218 by (simp add: le_floor_iff)\n```\n``` 219\n```\n``` 220 lemma numeral_le_floor [simp]:\n```\n``` 221 \"numeral v \\<le> floor x \\<longleftrightarrow> numeral v \\<le> x\"\n```\n``` 222 by (simp add: le_floor_iff)\n```\n``` 223\n```\n``` 224 lemma neg_numeral_le_floor [simp]:\n```\n``` 225 \"neg_numeral v \\<le> floor x \\<longleftrightarrow> neg_numeral v \\<le> x\"\n```\n``` 226 by (simp add: le_floor_iff)\n```\n``` 227\n```\n``` 228 lemma zero_less_floor [simp]: \"0 < floor x \\<longleftrightarrow> 1 \\<le> x\"\n```\n``` 229 by (simp add: less_floor_iff)\n```\n``` 230\n```\n``` 231 lemma one_less_floor [simp]: \"1 < floor x \\<longleftrightarrow> 2 \\<le> x\"\n```\n``` 232 by (simp add: less_floor_iff)\n```\n``` 233\n```\n``` 234 lemma numeral_less_floor [simp]:\n```\n``` 235 \"numeral v < floor x \\<longleftrightarrow> numeral v + 1 \\<le> x\"\n```\n``` 236 by (simp add: less_floor_iff)\n```\n``` 237\n```\n``` 238 lemma neg_numeral_less_floor [simp]:\n```\n``` 239 \"neg_numeral v < floor x \\<longleftrightarrow> neg_numeral v + 1 \\<le> x\"\n```\n``` 240 by (simp add: less_floor_iff)\n```\n``` 241\n```\n``` 242 lemma floor_le_zero [simp]: \"floor x \\<le> 0 \\<longleftrightarrow> x < 1\"\n```\n``` 243 by (simp add: floor_le_iff)\n```\n``` 244\n```\n``` 245 lemma floor_le_one [simp]: \"floor x \\<le> 1 \\<longleftrightarrow> x < 2\"\n```\n``` 246 by (simp add: floor_le_iff)\n```\n``` 247\n```\n``` 248 lemma floor_le_numeral [simp]:\n```\n``` 249 \"floor x \\<le> numeral v \\<longleftrightarrow> x < numeral v + 1\"\n```\n``` 250 by (simp add: floor_le_iff)\n```\n``` 251\n```\n``` 252 lemma floor_le_neg_numeral [simp]:\n```\n``` 253 \"floor x \\<le> neg_numeral v \\<longleftrightarrow> x < neg_numeral v + 1\"\n```\n``` 254 by (simp add: floor_le_iff)\n```\n``` 255\n```\n``` 256 lemma floor_less_zero [simp]: \"floor x < 0 \\<longleftrightarrow> x < 0\"\n```\n``` 257 by (simp add: floor_less_iff)\n```\n``` 258\n```\n``` 259 lemma floor_less_one [simp]: \"floor x < 1 \\<longleftrightarrow> x < 1\"\n```\n``` 260 by (simp add: floor_less_iff)\n```\n``` 261\n```\n``` 262 lemma floor_less_numeral [simp]:\n```\n``` 263 \"floor x < numeral v \\<longleftrightarrow> x < numeral v\"\n```\n``` 264 by (simp add: floor_less_iff)\n```\n``` 265\n```\n``` 266 lemma floor_less_neg_numeral [simp]:\n```\n``` 267 \"floor x < neg_numeral v \\<longleftrightarrow> x < neg_numeral v\"\n```\n``` 268 by (simp add: floor_less_iff)\n```\n``` 269\n```\n``` 270 text {* Addition and subtraction of integers *}\n```\n``` 271\n```\n``` 272 lemma floor_add_of_int [simp]: \"floor (x + of_int z) = floor x + z\"\n```\n``` 273 using floor_correct [of x] by (simp add: floor_unique)\n```\n``` 274\n```\n``` 275 lemma floor_add_numeral [simp]:\n```\n``` 276 \"floor (x + numeral v) = floor x + numeral v\"\n```\n``` 277 using floor_add_of_int [of x \"numeral v\"] by simp\n```\n``` 278\n```\n``` 279 lemma floor_add_neg_numeral [simp]:\n```\n``` 280 \"floor (x + neg_numeral v) = floor x + neg_numeral v\"\n```\n``` 281 using floor_add_of_int [of x \"neg_numeral v\"] by simp\n```\n``` 282\n```\n``` 283 lemma floor_add_one [simp]: \"floor (x + 1) = floor x + 1\"\n```\n``` 284 using floor_add_of_int [of x 1] by simp\n```\n``` 285\n```\n``` 286 lemma floor_diff_of_int [simp]: \"floor (x - of_int z) = floor x - z\"\n```\n``` 287 using floor_add_of_int [of x \"- z\"] by (simp add: algebra_simps)\n```\n``` 288\n```\n``` 289 lemma floor_diff_numeral [simp]:\n```\n``` 290 \"floor (x - numeral v) = floor x - numeral v\"\n```\n``` 291 using floor_diff_of_int [of x \"numeral v\"] by simp\n```\n``` 292\n```\n``` 293 lemma floor_diff_neg_numeral [simp]:\n```\n``` 294 \"floor (x - neg_numeral v) = floor x - neg_numeral v\"\n```\n``` 295 using floor_diff_of_int [of x \"neg_numeral v\"] by simp\n```\n``` 296\n```\n``` 297 lemma floor_diff_one [simp]: \"floor (x - 1) = floor x - 1\"\n```\n``` 298 using floor_diff_of_int [of x 1] by simp\n```\n``` 299\n```\n``` 300\n```\n``` 301 subsection {* Ceiling function *}\n```\n``` 302\n```\n``` 303 definition\n```\n``` 304 ceiling :: \"'a::floor_ceiling \\<Rightarrow> int\" where\n```\n``` 305 \"ceiling x = - floor (- x)\"\n```\n``` 306\n```\n``` 307 notation (xsymbols)\n```\n``` 308 ceiling (\"\\<lceil>_\\<rceil>\")\n```\n``` 309\n```\n``` 310 notation (HTML output)\n```\n``` 311 ceiling (\"\\<lceil>_\\<rceil>\")\n```\n``` 312\n```\n``` 313 lemma ceiling_correct: \"of_int (ceiling x) - 1 < x \\<and> x \\<le> of_int (ceiling x)\"\n```\n``` 314 unfolding ceiling_def using floor_correct [of \"- x\"] by simp\n```\n``` 315\n```\n``` 316 lemma ceiling_unique: \"\\<lbrakk>of_int z - 1 < x; x \\<le> of_int z\\<rbrakk> \\<Longrightarrow> ceiling x = z\"\n```\n``` 317 unfolding ceiling_def using floor_unique [of \"- z\" \"- x\"] by simp\n```\n``` 318\n```\n``` 319 lemma le_of_int_ceiling: \"x \\<le> of_int (ceiling x)\"\n```\n``` 320 using ceiling_correct ..\n```\n``` 321\n```\n``` 322 lemma ceiling_le_iff: \"ceiling x \\<le> z \\<longleftrightarrow> x \\<le> of_int z\"\n```\n``` 323 unfolding ceiling_def using le_floor_iff [of \"- z\" \"- x\"] by auto\n```\n``` 324\n```\n``` 325 lemma less_ceiling_iff: \"z < ceiling x \\<longleftrightarrow> of_int z < x\"\n```\n``` 326 by (simp add: not_le [symmetric] ceiling_le_iff)\n```\n``` 327\n```\n``` 328 lemma ceiling_less_iff: \"ceiling x < z \\<longleftrightarrow> x \\<le> of_int z - 1\"\n```\n``` 329 using ceiling_le_iff [of x \"z - 1\"] by simp\n```\n``` 330\n```\n``` 331 lemma le_ceiling_iff: \"z \\<le> ceiling x \\<longleftrightarrow> of_int z - 1 < x\"\n```\n``` 332 by (simp add: not_less [symmetric] ceiling_less_iff)\n```\n``` 333\n```\n``` 334 lemma ceiling_mono: \"x \\<ge> y \\<Longrightarrow> ceiling x \\<ge> ceiling y\"\n```\n``` 335 unfolding ceiling_def by (simp add: floor_mono)\n```\n``` 336\n```\n``` 337 lemma ceiling_less_cancel: \"ceiling x < ceiling y \\<Longrightarrow> x < y\"\n```\n``` 338 by (auto simp add: not_le [symmetric] ceiling_mono)\n```\n``` 339\n```\n``` 340 lemma ceiling_of_int [simp]: \"ceiling (of_int z) = z\"\n```\n``` 341 by (rule ceiling_unique) simp_all\n```\n``` 342\n```\n``` 343 lemma ceiling_of_nat [simp]: \"ceiling (of_nat n) = int n\"\n```\n``` 344 using ceiling_of_int [of \"of_nat n\"] by simp\n```\n``` 345\n```\n``` 346 lemma ceiling_add_le: \"ceiling (x + y) \\<le> ceiling x + ceiling y\"\n```\n``` 347 by (simp only: ceiling_le_iff of_int_add add_mono le_of_int_ceiling)\n```\n``` 348\n```\n``` 349 text {* Ceiling with numerals *}\n```\n``` 350\n```\n``` 351 lemma ceiling_zero [simp]: \"ceiling 0 = 0\"\n```\n``` 352 using ceiling_of_int [of 0] by simp\n```\n``` 353\n```\n``` 354 lemma ceiling_one [simp]: \"ceiling 1 = 1\"\n```\n``` 355 using ceiling_of_int [of 1] by simp\n```\n``` 356\n```\n``` 357 lemma ceiling_numeral [simp]: \"ceiling (numeral v) = numeral v\"\n```\n``` 358 using ceiling_of_int [of \"numeral v\"] by simp\n```\n``` 359\n```\n``` 360 lemma ceiling_neg_numeral [simp]: \"ceiling (neg_numeral v) = neg_numeral v\"\n```\n``` 361 using ceiling_of_int [of \"neg_numeral v\"] by simp\n```\n``` 362\n```\n``` 363 lemma ceiling_le_zero [simp]: \"ceiling x \\<le> 0 \\<longleftrightarrow> x \\<le> 0\"\n```\n``` 364 by (simp add: ceiling_le_iff)\n```\n``` 365\n```\n``` 366 lemma ceiling_le_one [simp]: \"ceiling x \\<le> 1 \\<longleftrightarrow> x \\<le> 1\"\n```\n``` 367 by (simp add: ceiling_le_iff)\n```\n``` 368\n```\n``` 369 lemma ceiling_le_numeral [simp]:\n```\n``` 370 \"ceiling x \\<le> numeral v \\<longleftrightarrow> x \\<le> numeral v\"\n```\n``` 371 by (simp add: ceiling_le_iff)\n```\n``` 372\n```\n``` 373 lemma ceiling_le_neg_numeral [simp]:\n```\n``` 374 \"ceiling x \\<le> neg_numeral v \\<longleftrightarrow> x \\<le> neg_numeral v\"\n```\n``` 375 by (simp add: ceiling_le_iff)\n```\n``` 376\n```\n``` 377 lemma ceiling_less_zero [simp]: \"ceiling x < 0 \\<longleftrightarrow> x \\<le> -1\"\n```\n``` 378 by (simp add: ceiling_less_iff)\n```\n``` 379\n```\n``` 380 lemma ceiling_less_one [simp]: \"ceiling x < 1 \\<longleftrightarrow> x \\<le> 0\"\n```\n``` 381 by (simp add: ceiling_less_iff)\n```\n``` 382\n```\n``` 383 lemma ceiling_less_numeral [simp]:\n```\n``` 384 \"ceiling x < numeral v \\<longleftrightarrow> x \\<le> numeral v - 1\"\n```\n``` 385 by (simp add: ceiling_less_iff)\n```\n``` 386\n```\n``` 387 lemma ceiling_less_neg_numeral [simp]:\n```\n``` 388 \"ceiling x < neg_numeral v \\<longleftrightarrow> x \\<le> neg_numeral v - 1\"\n```\n``` 389 by (simp add: ceiling_less_iff)\n```\n``` 390\n```\n``` 391 lemma zero_le_ceiling [simp]: \"0 \\<le> ceiling x \\<longleftrightarrow> -1 < x\"\n```\n``` 392 by (simp add: le_ceiling_iff)\n```\n``` 393\n```\n``` 394 lemma one_le_ceiling [simp]: \"1 \\<le> ceiling x \\<longleftrightarrow> 0 < x\"\n```\n``` 395 by (simp add: le_ceiling_iff)\n```\n``` 396\n```\n``` 397 lemma numeral_le_ceiling [simp]:\n```\n``` 398 \"numeral v \\<le> ceiling x \\<longleftrightarrow> numeral v - 1 < x\"\n```\n``` 399 by (simp add: le_ceiling_iff)\n```\n``` 400\n```\n``` 401 lemma neg_numeral_le_ceiling [simp]:\n```\n``` 402 \"neg_numeral v \\<le> ceiling x \\<longleftrightarrow> neg_numeral v - 1 < x\"\n```\n``` 403 by (simp add: le_ceiling_iff)\n```\n``` 404\n```\n``` 405 lemma zero_less_ceiling [simp]: \"0 < ceiling x \\<longleftrightarrow> 0 < x\"\n```\n``` 406 by (simp add: less_ceiling_iff)\n```\n``` 407\n```\n``` 408 lemma one_less_ceiling [simp]: \"1 < ceiling x \\<longleftrightarrow> 1 < x\"\n```\n``` 409 by (simp add: less_ceiling_iff)\n```\n``` 410\n```\n``` 411 lemma numeral_less_ceiling [simp]:\n```\n``` 412 \"numeral v < ceiling x \\<longleftrightarrow> numeral v < x\"\n```\n``` 413 by (simp add: less_ceiling_iff)\n```\n``` 414\n```\n``` 415 lemma neg_numeral_less_ceiling [simp]:\n```\n``` 416 \"neg_numeral v < ceiling x \\<longleftrightarrow> neg_numeral v < x\"\n```\n``` 417 by (simp add: less_ceiling_iff)\n```\n``` 418\n```\n``` 419 text {* Addition and subtraction of integers *}\n```\n``` 420\n```\n``` 421 lemma ceiling_add_of_int [simp]: \"ceiling (x + of_int z) = ceiling x + z\"\n```\n``` 422 using ceiling_correct [of x] by (simp add: ceiling_unique)\n```\n``` 423\n```\n``` 424 lemma ceiling_add_numeral [simp]:\n```\n``` 425 \"ceiling (x + numeral v) = ceiling x + numeral v\"\n```\n``` 426 using ceiling_add_of_int [of x \"numeral v\"] by simp\n```\n``` 427\n```\n``` 428 lemma ceiling_add_neg_numeral [simp]:\n```\n``` 429 \"ceiling (x + neg_numeral v) = ceiling x + neg_numeral v\"\n```\n``` 430 using ceiling_add_of_int [of x \"neg_numeral v\"] by simp\n```\n``` 431\n```\n``` 432 lemma ceiling_add_one [simp]: \"ceiling (x + 1) = ceiling x + 1\"\n```\n``` 433 using ceiling_add_of_int [of x 1] by simp\n```\n``` 434\n```\n``` 435 lemma ceiling_diff_of_int [simp]: \"ceiling (x - of_int z) = ceiling x - z\"\n```\n``` 436 using ceiling_add_of_int [of x \"- z\"] by (simp add: algebra_simps)\n```\n``` 437\n```\n``` 438 lemma ceiling_diff_numeral [simp]:\n```\n``` 439 \"ceiling (x - numeral v) = ceiling x - numeral v\"\n```\n``` 440 using ceiling_diff_of_int [of x \"numeral v\"] by simp\n```\n``` 441\n```\n``` 442 lemma ceiling_diff_neg_numeral [simp]:\n```\n``` 443 \"ceiling (x - neg_numeral v) = ceiling x - neg_numeral v\"\n```\n``` 444 using ceiling_diff_of_int [of x \"neg_numeral v\"] by simp\n```\n``` 445\n```\n``` 446 lemma ceiling_diff_one [simp]: \"ceiling (x - 1) = ceiling x - 1\"\n```\n``` 447 using ceiling_diff_of_int [of x 1] by simp\n```\n``` 448\n```\n``` 449 lemma ceiling_diff_floor_le_1: \"ceiling x - floor x \\<le> 1\"\n```\n``` 450 proof -\n```\n``` 451 have \"of_int \\<lceil>x\\<rceil> - 1 < x\"\n```\n``` 452 using ceiling_correct[of x] by simp\n```\n``` 453 also have \"x < of_int \\<lfloor>x\\<rfloor> + 1\"\n```\n``` 454 using floor_correct[of x] by simp_all\n```\n``` 455 finally have \"of_int (\\<lceil>x\\<rceil> - \\<lfloor>x\\<rfloor>) < (of_int 2::'a)\"\n```\n``` 456 by simp\n```\n``` 457 then show ?thesis\n```\n``` 458 unfolding of_int_less_iff by simp\n```\n``` 459 qed\n```\n``` 460\n```\n``` 461 subsection {* Negation *}\n```\n``` 462\n```\n``` 463 lemma floor_minus: \"floor (- x) = - ceiling x\"\n```\n``` 464 unfolding ceiling_def by simp\n```\n``` 465\n```\n``` 466 lemma ceiling_minus: \"ceiling (- x) = - floor x\"\n```\n``` 467 unfolding ceiling_def by simp\n```\n``` 468\n```\n``` 469 end\n```" ]
[ null ]
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https://windrawwin-prediction.com/betting/how-many-ways-can-we-get-an-even-sum-when-two-distinguishable-dice-are-rolled.html
[ "# How many ways can we get an even sum when two distinguishable dice are rolled?\n\nContents\n\n## How many even sums are possible with 2 dice?\n\nThe probability that two coins when tossed together turn up the same is 12, even though two of the three visible possibilities are “favorable”. To answer the question: 5/11 and 6/11. The possible sum of rolling two dice is 2,3,4…..,12. Total 11 possibilities, 5 odds and 6 evens.\n\n## What is the probability of getting an even sum?\n\n5 Answers. Now, note that P(even|first was even)=P(second is even)=1/2. Similarly, P(even|first was odd)=P(second is odd)=1/2. Thus, we have P(even sum)=1/2(P(first was even)+P(first was odd))=1/2(1)=1/2.\n\n## What is the probability of getting an even number?\n\nWhat is the probability of getting an even number? Assuming a perfect die (all numbers equally likely), then there are 3 even and 3 odd numbers. Since each outcome is equally likely, the probability of an even number is 50% (sometimes shown as . 5).\n\n## What is the sum of two dice?\n\nYou compute it by multiplying each value x of the random variable by the probability P(X=x), and then adding up the results. So the average sum of dice is: E(X) = 2 . 1/36 + 3 . 2/36 + ….\n\nIT IS SURPRISING:  Can you bet in Wisconsin?\n\n## What is the probability of rolling a 2 with two dice?\n\nTwo (6-sided) dice roll probability table\n\nRoll a… Probability\n2 1/36 (2.778%)\n3 2/36 (5.556%)\n4 3/36 (8.333%)\n5 4/36 (11.111%)\n\n## How many ways are there in getting a double when two dice are rolled?\n\nThere are 6 ways we can roll doubles out of a possible 36 rolls (6 x 6), for a probability of 6/36, or 1/6, on any roll of two fair dice. So you have a 16.7% probability of rolling doubles with 2 fair six-sided dice.\n\n## How many ways can two dice be rolled such that their sum is not more than 7?\n\nAs the table shows there are 36 possible outcomes. For each of the possible outcomes add the numbers on the two dice and count how many times this sum is 7. If you do so you will find that the sum is 7 for 6 of the possible outcomes.\n\n## How many ways can two dice be rolled such that their sum is not more than 10?\n\nIf you roll two dice, there are 6×6=36 possible outcomes." ]
[ null ]
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https://www.selfridges.com/SG/zh/cat/maje-small-leather-goods-220suitu_R00075675/?previewAttribute=BLACK
[ "## 以当地货币和语言购买\n\n• 澳大利亚 / 澳元 \\$\n• 加拿大 / 加元 \\$\n• 中国 / 人民币 ¥\n• 法国 / 欧元 €\n• 德国 / 欧元 €\n• 香港 / 港元 \\$\n• 爱尔兰 / 欧元 €\n• 意大利 / 欧元 €\n• 日本 / 日元 ¥\n• 科威特 / 美元 \\$\n• 澳门 / 港元 \\$\n• 荷兰 / 欧元 €\n• 卡塔尔 / 美元 \\$\n• 沙特阿拉伯 / 美元 \\$\n• 新加坡 / 新加坡元 \\$\n• 韩国 / 韩元 ₩\n• 西班牙 / 欧元 €\n• 台湾 / 新台币 \\$\n• 阿拉伯联合酋长国 / 美元 \\$\n• 英国 / 英镑 £\n• 美国 / 美元 \\$\n• 不符合您的要求？阅读更多\n• 简体中文\n• 英语\n• 英语\n• 简体中文\n• 英语\n• 英语\n• 英语\n• 简体中文\n• 英语\n• 英语\n• 英语\n• 英语\n• 英语\n• 简体中文\n• 英语\n• 英语\n• 英语\n• 英语\n• 简体中文\n• 英语\n• 英语\n• 英语\n• 简体中文\n• 英语\n• 英语\n• 简体中文\n• 英语\n• 英语\n• 简体中文\n\n## 国际送货\n\nselfridges.com 上几乎所有的商品均可提供国际配送服务，您的订单可发往全世界 130 个国家/地区，包括北美、澳洲、中东及中国。\n\n• 阿尔及利亚\n• 安道尔\n• 安提瓜和巴布达\n• 阿鲁巴\n• 澳大利亚\n• 奥地利\n• 阿塞拜疆\n• 巴林\n• 孟加拉国\n• 巴巴多斯\n• 白俄罗斯\n• 比利时\n• 伯利兹\n• 百慕大\n• 玻利维亚\n• 博兹瓦纳\n• 文莱\n• 保加利亚\n• 柬埔寨\n• 加拿大\n• 开曼群岛\n• 智利\n• 中国大陆\n• 哥伦比亚\n• 哥斯达黎加\n• 克罗地亚\n• 塞浦路斯\n• 捷克共和国\n• 丹麦\n• 多米尼克\n• 多米尼加共和国\n• 厄瓜多尔\n• 埃及\n• 萨尔瓦多\n• 爱沙尼亚\n• 芬兰\n• 法国\n• 法属圭亚那\n• 德国\n• 直布罗陀\n• 希腊\n• 格林纳达\n• 瓜德罗普岛\n• 危地马拉\n• 根西岛\n• 圭亚那\n• 洪都拉斯\n• 香港\n• 匈牙利\n• 冰岛\n• 印度\n• 印度尼西亚\n• 爱尔兰\n• 以色列\n• 意大利\n• 牙买加\n• 日本\n• 泽西岛\n• 约旦\n• 哈萨克斯坦\n• 肯尼亚\n• 科威特\n• 老挝\n• 拉脱维亚\n• 黎巴嫩\n• 莱索托\n• 列支敦士登\n• 立陶宛\n• 卢森堡\n• 澳门\n• 马来西亚\n• 马尔代夫\n• 马耳他\n• 马提尼克岛\n• 马约特岛\n• 墨西哥\n• 摩纳哥\n• 蒙特塞拉特\n• 摩洛哥\n• 缅甸\n• 纳米比亚\n• 荷兰\n• 新西兰\n• 尼加拉瓜\n• 尼日利亚\n• 挪威\n• 阿曼\n• 巴基斯坦\n• 巴拿马\n• 巴拉圭\n• 秘鲁\n• 菲律宾\n• 波兰\n• 葡萄牙\n• 波多黎各\n• 卡塔尔\n• 留尼汪岛\n• 罗马尼亚\n• 卢旺达\n• 圣基茨与尼维斯\n• 圣卢西亚\n• 圣马丁岛（法属）\n• 圣马力诺\n• 沙特阿拉伯\n• 塞尔维亚\n• 新加坡\n• 斯洛伐克\n• 斯洛文尼亚\n• 南非\n• 韩国\n• 西班牙\n• 斯里兰卡\n• 苏里南\n• 斯威士兰\n• 瑞典\n• 瑞士\n• 台湾\n• 坦桑尼亚\n• 泰国\n• 特立尼达和多巴哥\n• 土耳其\n• 乌干达\n• 乌克兰\n• 阿拉伯联合酋长国\n• 英国\n• 美国\n• 乌拉圭\n• 委内瑞拉\n• 越南\n\n# MAJE 小皮具-220SUITU\n\n\\$75.00 \\$107.00\n\n*关税和税金在购物车中另行计算", null, "BLACK", null, "BLUE SKY", null, "CARMINE RED", null, "FUCHSIA\n\nMaje 卡夹\n100% 皮革\n\nCroc-压花，双M标识，金色硬件，两个卡槽，主隔层\n\n## 英国和欧洲\n\n\\$20.00\n• 无限英国定时、指定日和标准配送\n• 英国境内次日配送（英国时间下午 6 点前下单）\n• 无限欧盟地区标准配送\n• 免费退货\n• 无人购买的产品\n\n## 全球\n\n\\$75.00\n• 订单金额超过\\$ 75.00英国时间，指定日期和标准交货时间不受限制\n• 订单金额超过\\$ 75.00全球不限次数的送货" ]
[ null, "https://images.selfridges.com/is/image/selfridges/R00075675_BLACK_SW", null, "https://images.selfridges.com/is/image/selfridges/R00075675_BLUESKY_SW", null, "https://images.selfridges.com/is/image/selfridges/R00075675_CARMINERED_SW", null, "https://images.selfridges.com/is/image/selfridges/R00075675_FUCHSIA_SW", null ]
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https://www.thelittleaussiebakery.com/should-you-put-desired-salary-on-application/
[ "", null, "# Should you put desired salary on application?\n\n## Should you put desired salary on application?\n\nBut what do you put for desired salary when the application asks for it? Ideally, you should either leave the desired salary field blank or put “negotiable.” If you can only insert numerals, set a realistic salary range based on your market value, like \\$45,000-\\$Feb 2020\n\n## How do you calculate a 2% raise?\n\nHow to calculate salary increase: PercentageFirst, multiply the percentage by the employee’s current annual wages: \\$50,000 X .04 = \\$2,000.Next, add the employee’s current annual salary to the raise amount: \\$50,000 + \\$2,000 = \\$52,000.Take the employee’s new annual salary and divide it by 26: \\$52,000 / 26 = \\$2,000.\n\n## How much is a 3% raise per hour?\n\nIf your employee makes \\$15/hour, then you have: 15x. 03=. 45. So your employee’s increase is 45 cents per hour.\n\n## How much is a 1 dollar raise per year?\n\nHow Much is a Dollar Raise Annually? If you are paid for 40-hours per week, and 52-weeks per year, a \\$1 an hour raise will add up to \\$2,080 extra per year.\n\n## How much is a 2 dollar raise per year?\n\nYour hourly wage of 2 dollars would end up being about \\$4,160 per year in salary.\n\n## How much more is \\$1 an hour?\n\nOf course, that’s all assuming you work for an hourly rate and that you work roughly 2000 hours per year. If any of those things change, the rates will have to be adjusted accordingly. But regardless, \\$1/hour = \\$2000/year is always a very handy number to keep in your mental math toolbag.\n\n## How much is 20 dollars an hour annually?\n\nAssuming 40 hours a week, that equals 2,080 hours in a year. Your hourly wage of 20 dollars would end up being about \\$41,600 per year in salary." ]
[ null, "https://museunaif.com/wp-content/uploads/2018/11/cropped-business-computer-connection-450035-2.jpg", null ]
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https://studysoup.com/tsg/710651/operating-system-concepts-9-edition-chapter-6-problem-6-31
[ "×\n×\n\n# Consider two processes, P1 and P2, where p1 = 50, t1 = 25, p2 = 75, andt2 = 30.a. Can", null, "ISBN: 9781118063330 327\n\n## Solution for problem 6.31 Chapter 6\n\nOperating System Concepts | 9th Edition\n\n• Textbook Solutions\n• 2901 Step-by-step solutions solved by professors and subject experts\n• Get 24/7 help from StudySoup virtual teaching assistants", null, "Operating System Concepts | 9th Edition\n\n4 5 1 249 Reviews\n11\n1\nProblem 6.31\n\nConsider two processes, P1 and P2, where p1 = 50, t1 = 25, p2 = 75, andt2 = 30.a. Can these two processes be scheduled using rate-monotonicscheduling? Illustrate your answer using a Gantt chart such asthe ones in Figure 6.16Figure 6.19.b. Illustrate the scheduling of these two processes using earliestdeadline-first(EDF) scheduling.\n\nStep-by-Step Solution:\nStep 1 of 3\n\nEXSC223:Weekof9/12/16 NotesfromthetextbookCh.3.10 3.10Thecellcycleconsistsofinterphaseandamitoticphase • Cellcycle:changesacellgoesthroughfromwhenitisformedtowhenitreproduces • Twomajorperiodsforthecell o Interphase:cellgrowsandcarriesoutnormalactivities...\n\nStep 2 of 3\n\nStep 3 of 3\n\n##### ISBN: 9781118063330\n\nUnlock Textbook Solution" ]
[ null, "https://studysoup.com/cdn/79cover_2670976", null, "https://studysoup.com/cdn/79cover_2670976", null ]
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https://brainmass.com/economics/economic-growth/calculations-real-gdp-for-2004-2005-23223
[ "Explore BrainMass\n\n# Calculations of real GDP for 2004 and 2005\n\nNot what you're looking for? Search our solutions OR ask your own Custom question.\n\nThis content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!\n\nUse the following data to answer questions 1-3 (be sure to provide all calculations).\n\n1. Calculate real GDP for 2004 and 2005 using 2004 prices. By what percent did real GDP grow?\n\n2. Calculate the value of the price index for GDP for 2005 using 2004 as the base year. By what percent did prices increase?\n\n3. Now calculate real GDP for 2004 and 2005 using 2005 prices. By what percent did real GDP grow?\n\nReview the GDP information for the past few years from the Bureau of Economic Analysis's Website. Provide a brief summary of the GDP trends over that timeframe and discuss two or three events which may have caused these trends.\n\nhttps://brainmass.com/economics/economic-growth/calculations-real-gdp-for-2004-2005-23223\n\n#### Solution Preview\n\nUse the following data to answer questions 1-3 (be sure to provide all calculations).\n. Quantities Produced Prices\n. CDs Tennis Racquets CDs Tennis Racquets\nYear 2004 100 200 20 110\nYear 2005 120 210 22 120\n1. Calculate real GDP for 2004 and 2005 using 2004 prices. By what percent did real GDP grow?\nIn 2004, there were 100 CD's produced and each CD costs \\$20; and 200 tennis racquets were produced and each racquet costs \\$110.\n2004 Nominal GDP = 100*20 + 200*110 = 2000 + 22,000 = \\$24,000\nIn 2005, there were 120 CD's produced and each CD costs \\$22; ...\n\n#### Solution Summary\n\nThe solution calculates real GDP for 2004 and 2005 for a company.\n\n\\$2.49" ]
[ null ]
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https://botbark.com/category/seaborn/
[ "", null, "# How to Create 3d Interactive Graph using Plotly\n\nLike matplotlib and seaborn we have plotly, that is a data visualization library used for creating graphical, 3d and interactive graph. You can install plotly using below command pip install plotly Then you can import it in Jupyter notebook as below. import plotly.express as pex Let us use the famous iris dataset to create the … Continue reading How to Create 3d Interactive Graph using Plotly\n\n# Scatter Plot using Lmplot Function of Seaborn\n\nApart from the methods scatterplot and regplot, seaborn also provides lmplot as another function to draw a scatterplot. However when we create scatter plots using seaborn’s lmplot, it will introduce a regression line in the plot. Let us first import libraries and load the data required to create the plot. import numpy as np import … Continue reading Scatter Plot using Lmplot Function of Seaborn\n\n# Scatter Plot using Regplot Function of Seaborn\n\nThough we have an obvious method named, scatterplot, provided by seaborn to draw a scatterplot, seaborn provides other methods as well to draw scatter plot. One of the other method is regplot. However when we create scatter plots using seaborn's regplot method, it will introduce a regression line in the plot as regplot is based … Continue reading Scatter Plot using Regplot Function of Seaborn" ]
[ null, "https://i0.wp.com/botbark.com/wp-content/uploads/2019/12/3d-plot-interactive.png", null ]
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https://man.linuxreviews.org/man3/cggsvp3.f.3.html
[ "# cggsvp3.f\n\nSection: LAPACK (3)\nUpdated: Tue Nov 14 2017\nPage Index\n\ncggsvp3.f\n\n## SYNOPSIS\n\n### Functions/Subroutines\n\nsubroutine cggsvp3 (JOBU, JOBV, JOBQ, M, P, N, A, LDA, B, LDB, TOLA, TOLB, K, L, U, LDU, V, LDV, Q, LDQ, IWORK, RWORK, TAU, WORK, LWORK, INFO)\nCGGSVP3\n\n## Function/Subroutine Documentation\n\n### subroutine cggsvp3 (character JOBU, character JOBV, character JOBQ, integer M, integer P, integer N, complex, dimension( lda, * ) A, integer LDA, complex, dimension( ldb, * ) B, integer LDB, real TOLA, real TOLB, integer K, integer L, complex, dimension( ldu, * ) U, integer LDU, complex, dimension( ldv, * ) V, integer LDV, complex, dimension( ldq, * ) Q, integer LDQ, integer, dimension( * ) IWORK, real, dimension( * ) RWORK, complex, dimension( * ) TAU, complex, dimension( * ) WORK, integer LWORK, integer INFO)\n\nCGGSVP3\n\nPurpose:\n\n``` CGGSVP3 computes unitary matrices U, V and Q such that\n\nN-K-L K L\nU**H*A*Q = K ( 0 A12 A13 ) if M-K-L >= 0;\nL ( 0 0 A23 )\nM-K-L ( 0 0 0 )\n\nN-K-L K L\n= K ( 0 A12 A13 ) if M-K-L < 0;\nM-K ( 0 0 A23 )\n\nN-K-L K L\nV**H*B*Q = L ( 0 0 B13 )\nP-L ( 0 0 0 )\n\nwhere the K-by-K matrix A12 and L-by-L matrix B13 are nonsingular\nupper triangular; A23 is L-by-L upper triangular if M-K-L >= 0,\notherwise A23 is (M-K)-by-L upper trapezoidal. K+L = the effective\nnumerical rank of the (M+P)-by-N matrix (A**H,B**H)**H.\n\nThis decomposition is the preprocessing step for computing the\nGeneralized Singular Value Decomposition (GSVD), see subroutine\nCGGSVD3.\n```\n\nParameters:\n\nJOBU\n\n``` JOBU is CHARACTER*1\n= 'U': Unitary matrix U is computed;\n= 'N': U is not computed.\n```\n\nJOBV\n\n``` JOBV is CHARACTER*1\n= 'V': Unitary matrix V is computed;\n= 'N': V is not computed.\n```\n\nJOBQ\n\n``` JOBQ is CHARACTER*1\n= 'Q': Unitary matrix Q is computed;\n= 'N': Q is not computed.\n```\n\nM\n\n``` M is INTEGER\nThe number of rows of the matrix A. M >= 0.\n```\n\nP\n\n``` P is INTEGER\nThe number of rows of the matrix B. P >= 0.\n```\n\nN\n\n``` N is INTEGER\nThe number of columns of the matrices A and B. N >= 0.\n```\n\nA\n\n``` A is COMPLEX array, dimension (LDA,N)\nOn entry, the M-by-N matrix A.\nOn exit, A contains the triangular (or trapezoidal) matrix\ndescribed in the Purpose section.\n```\n\nLDA\n\n``` LDA is INTEGER\nThe leading dimension of the array A. LDA >= max(1,M).\n```\n\nB\n\n``` B is COMPLEX array, dimension (LDB,N)\nOn entry, the P-by-N matrix B.\nOn exit, B contains the triangular matrix described in\nthe Purpose section.\n```\n\nLDB\n\n``` LDB is INTEGER\nThe leading dimension of the array B. LDB >= max(1,P).\n```\n\nTOLA\n\n``` TOLA is REAL\n```\n\nTOLB\n\n``` TOLB is REAL\n\nTOLA and TOLB are the thresholds to determine the effective\nnumerical rank of matrix B and a subblock of A. Generally,\nthey are set to\nTOLA = MAX(M,N)*norm(A)*MACHEPS,\nTOLB = MAX(P,N)*norm(B)*MACHEPS.\nThe size of TOLA and TOLB may affect the size of backward\nerrors of the decomposition.\n```\n\nK\n\n``` K is INTEGER\n```\n\nL\n\n``` L is INTEGER\n\nOn exit, K and L specify the dimension of the subblocks\ndescribed in Purpose section.\nK + L = effective numerical rank of (A**H,B**H)**H.\n```\n\nU\n\n``` U is COMPLEX array, dimension (LDU,M)\nIf JOBU = 'U', U contains the unitary matrix U.\nIf JOBU = 'N', U is not referenced.\n```\n\nLDU\n\n``` LDU is INTEGER\nThe leading dimension of the array U. LDU >= max(1,M) if\nJOBU = 'U'; LDU >= 1 otherwise.\n```\n\nV\n\n``` V is COMPLEX array, dimension (LDV,P)\nIf JOBV = 'V', V contains the unitary matrix V.\nIf JOBV = 'N', V is not referenced.\n```\n\nLDV\n\n``` LDV is INTEGER\nThe leading dimension of the array V. LDV >= max(1,P) if\nJOBV = 'V'; LDV >= 1 otherwise.\n```\n\nQ\n\n``` Q is COMPLEX array, dimension (LDQ,N)\nIf JOBQ = 'Q', Q contains the unitary matrix Q.\nIf JOBQ = 'N', Q is not referenced.\n```\n\nLDQ\n\n``` LDQ is INTEGER\nThe leading dimension of the array Q. LDQ >= max(1,N) if\nJOBQ = 'Q'; LDQ >= 1 otherwise.\n```\n\nIWORK\n\n``` IWORK is INTEGER array, dimension (N)\n```\n\nRWORK\n\n``` RWORK is REAL array, dimension (2*N)\n```\n\nTAU\n\n``` TAU is COMPLEX array, dimension (N)\n```\n\nWORK\n\n``` WORK is COMPLEX array, dimension (MAX(1,LWORK))\nOn exit, if INFO = 0, WORK(1) returns the optimal LWORK.\n```\n\nLWORK\n\n``` LWORK is INTEGER\nThe dimension of the array WORK.\n\nIf LWORK = -1, then a workspace query is assumed; the routine\nonly calculates the optimal size of the WORK array, returns\nthis value as the first entry of the WORK array, and no error\nmessage related to LWORK is issued by XERBLA.\n```\n\nINFO\n\n``` INFO is INTEGER\n= 0: successful exit\n< 0: if INFO = -i, the i-th argument had an illegal value.\n```\n\nAuthor:\n\nUniv. of Tennessee\n\nUniv. of California Berkeley\n\nNAG Ltd.\n\nDate:\n\nAugust 2015\n\nFurther Details:\n\n``` The subroutine uses LAPACK subroutine CGEQP3 for the QR factorization\nwith column pivoting to detect the effective numerical rank of the\na matrix. It may be replaced by a better rank determination strategy.\n\nCGGSVP3 replaces the deprecated subroutine CGGSVP.\n```\n\nDefinition at line 280 of file cggsvp3.f.\n\n## Author\n\nGenerated automatically by Doxygen for LAPACK from the source code." ]
[ null ]
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https://diplomaticar.it/a-uniform-rod-of-length-l-and-mass-m-is-free-to-rotate.html
[ "### Hearing 2 knocks in your sleep\n\nA uniform rod (mass = 2.0 kg, length = 0.60 m) is free to rotate about a frictionless pivot at one end. The rod is released from rest in the horizontal position. What is the magnitude of the angular acceleration of the rod at the instant it is 60° below the horizontal?\n\n## 1 2 a geometry word puzzle\n\nFeb 15, 2020 · A thin uniform rod of mass M and length L is free to rotate in vertical plane about a horizontal - YouTube A thin uniform rod of mass M and length L is free to rotate in vertical plane about a...\n\n## 270 accubond ammo\n\nSep 20, 2020 · September 20, 2020. The slender homogeneous rod AB of mass m and length L is free to rotate about a horizontal axle through its mass center G. The axle is supported by a frame of negligible mass which is free to rotate about the vertical CD. Knowing that, initially, θ= θ0, show that the rod will oscillate about the horizontal axle and determine (a) the range of values of angle u during this motion, (b) the maximum value of ˙ θ, (c) the minimum value of ϕ.\n\n## 3 stages of pisces\n\nA uniform rod of length L and mass M is free to rotate about a frictionless pivot at one end. The rod is released from rest in the horizontal position. length l of a simple pendulum were measured. 1. A body of mass 𝑚, moving at velocity 𝑣, collides with a stationary body of the same mass and sticks to it. Masses are suspended from its lower end. The load on the lower end is increased from zero and then decreased again back to zero.\n\n5zig reborn\n\n## Aquifer pediatrics anki\n\nA unifrom rod of length l and mass m is free to rotate in a vertical plane about A, Fig. The rod initially in horizontal position is released. The initial angular acceleration of the rod is (MI \"of rod about\" A \"is\" (ml^(2))/(3))\n\n## Redshift for katana\n\nExample: Uniform Rigid Rod Calculate the moment of inertia of a uniform rigid rod of length L and mass M about an axis perpendicular to the rod (the y axis) and passing through its center of mass. The shaded length element dx has a mass where l is the mass per unit length." ]
[ null ]
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https://phys.libretexts.org/Bookshelves/Quantum_Mechanics/Advanced_Quantum_Mechanics_(Kok)/14%3A_Atomic_Orbitals
[ "$$\\newcommand{\\vecs}{\\overset { \\rightharpoonup} {\\mathbf{#1}} }$$ $$\\newcommand{\\vecd}{\\overset{-\\!-\\!\\rightharpoonup}{\\vphantom{a}\\smash {#1}}}$$$$\\newcommand{\\id}{\\mathrm{id}}$$ $$\\newcommand{\\Span}{\\mathrm{span}}$$ $$\\newcommand{\\kernel}{\\mathrm{null}\\,}$$ $$\\newcommand{\\range}{\\mathrm{range}\\,}$$ $$\\newcommand{\\RealPart}{\\mathrm{Re}}$$ $$\\newcommand{\\ImaginaryPart}{\\mathrm{Im}}$$ $$\\newcommand{\\Argument}{\\mathrm{Arg}}$$ $$\\newcommand{\\norm}{\\| #1 \\|}$$ $$\\newcommand{\\inner}{\\langle #1, #2 \\rangle}$$ $$\\newcommand{\\Span}{\\mathrm{span}}$$ $$\\newcommand{\\id}{\\mathrm{id}}$$ $$\\newcommand{\\Span}{\\mathrm{span}}$$ $$\\newcommand{\\kernel}{\\mathrm{null}\\,}$$ $$\\newcommand{\\range}{\\mathrm{range}\\,}$$ $$\\newcommand{\\RealPart}{\\mathrm{Re}}$$ $$\\newcommand{\\ImaginaryPart}{\\mathrm{Im}}$$ $$\\newcommand{\\Argument}{\\mathrm{Arg}}$$ $$\\newcommand{\\norm}{\\| #1 \\|}$$ $$\\newcommand{\\inner}{\\langle #1, #2 \\rangle}$$ $$\\newcommand{\\Span}{\\mathrm{span}}$$$$\\newcommand{\\AA}{\\unicode[.8,0]{x212B}}$$\nFor other atoms, there are additional electrons. The energy levels that we have calculated for Hydrogen can very easily be adapted to take into account a nucleus with more protons— all you have to do is multiply all of the energy levels by $$Z^{2}$$, the square of the number of protons in the nucleus (which is also the positive charge of the nucleus). We can then approximate other atoms by putting electrons into all of these energy levels. Because electrons are fermions, we can only put two into any given orbital. (Two because there are two possible spin states for an electron.) However, this implicitly assumes that the electrons are interacting only with the nucleus, and not with each other. That approximation will allow us to get a lot of insight into the structure of (for example) the Periodic Table of the elements, but is too much of an approximation to be able to figure out precise energy levels." ]
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https://novaresearch.unl.pt/en/publications/the-cauchy-singular-integral-operator-on-weighted-variable-lebesg
[ "# The Cauchy singular integral operator on weighted variable Lebesgue spaces\n\nResearch output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review\n\n27 Citations (Scopus)\n\n## Abstract\n\nLet $p:\\R\\to(1,\\infty)$ be a globally log-H\\\"older continuous variable exponentand $w:\\R\\to[0,\\infty]$ be a weight. We prove that the Cauchy singular integraloperator $S$ is bounded on the weighted variable Lebesgue space$L^{p(\\cdot)}(\\R,w)=\\{f:fw\\in L^{p(\\cdot)}(\\R)\\}$ if and only if the weight $w$satisfies$\\sup_{-\\infty<a<b<\\infty}\\frac{1}{b-a}\\|w\\chi_{(a,b)}\\|_{p(\\cdot)}\\|w^{-1}\\chi_{(a,b)}\\|_{p'(\\cdot)}<\\infty\\quad (1/p(x)+1/p'(x)=1).$\nOriginal language Unknown Operator Theory: Advances and Applications 275-291 978-3-0348-0648-0 https://doi.org/10.1007/978-3-0348-0648-0_17 Published - 1 Jan 2014 Concrete Operators, Spectral Theory, Operators in Harmonic Analysis and Approximation. 22nd International Workshop in Operator Theory and its Applications, Sevilla, July 2011 - Duration: 1 Jan 2011 → …\n\n### Conference\n\nConference Concrete Operators, Spectral Theory, Operators in Harmonic Analysis and Approximation. 22nd International Workshop in Operator Theory and its Applications, Sevilla, July 2011 1/01/11 → …" ]
[ null ]
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https://www.yogihosting.com/gridview-column-sum/
[ "# How to show sum of columns in the footer of the GridView with jQuery", null, "When working with GridView in ASP.NET Web Forms, there are requirements to show the sum of all the columns in the footer of the GridView. Well, let me tell you don’t write lengthy C# codes in .aspx.cs for these simple things, instead you can achieve this by using only a few lines of jQuery.\n\nI decided to write this tutorial so that I can tell you some simplest ways to show sum of columns in the footer of the GridView with a few lines of jQuery.\n\n## GridView’s Column Sum\n\nMy GridView shows the product data report and has 5 columns which are:\n\n• 1. Id\n• 2. Name\n• 3. Quantity\n• 4. Price\n• 5. Total\n\nOut of these 5 columns, Id, Name, Quantity & Price values are Bind from the database or .asp.cs page, while the 5th column (Total) will show the multiplication of Product * Price for each row of the GridView.\n\nWant to learn ASP.NET Core from the start? Do check my 100+ tutorials written on this topic. Link – ASP.NET Core Tutorials\n\nThe GridView will also have a footer which will show 3 values:\n\n• 1. Sum of all Quantity column values.\n• 2. Sum of all Price column values.\n• 3. Sum of all Total column values.\nThe GridView code in the .aspx page is shown below\n```<asp:GridView ID=\"gridView\" runat=\"server\" AutoGenerateColumns=\"false\" ShowFooter=\"true\" FooterStyle-BackColor=\"#ff0066\">\n<Columns>\n<ItemTemplate>\n<asp:Label ID=\"nameLabel\" runat=\"server\" Text='<%#Bind(\"Name\") %>'></asp:Label>\n</ItemTemplate>\n</asp:TemplateField>\n<ItemTemplate>\n<asp:Label ID=\"quantityLabel\" runat=\"server\" Text='<%# Bind(\"Quantity\") %>' CssClass=\"quantityCSS\"></asp:Label>\n</ItemTemplate>\n<FooterTemplate>\n<span class=\"quantitySpan\"></span>\n</FooterTemplate>\n</asp:TemplateField>\n<ItemTemplate>\n\\$<asp:Label ID=\"priceLabel\" runat=\"server\" Text='<%# Bind(\"Price\") %>' CssClass=\"priceCSS\"></asp:Label>\n</ItemTemplate>\n<FooterTemplate>\n<span class=\"priceSpan\"></span>\n</FooterTemplate>\n</asp:TemplateField>\n<ItemTemplate>\n<asp:Label ID=\"totalLabel\" runat=\"server\" CssClass=\"totalCSS\"></asp:Label>\n</ItemTemplate>\n<FooterTemplate>\n<span class=\"totalSpan\"></span>\n</FooterTemplate>\n</asp:TemplateField>\n</Columns>\n</asp:GridView>\n```\n\nNotice ShowFooter=”true” properly which will show the footer in the GridView. Also see the 3 columns given in the FooterTemplate of the GridView like:\n\n```<FooterTemplate>\n<span class=\"quantitySpan\"></span>\n</FooterTemplate>\n…\n<FooterTemplate>\n<span class=\"priceSpan\"></span>\n</FooterTemplate>\n…\n<FooterTemplate>\n<span class=\"totalSpan\"></span>\n</FooterTemplate>\n```\nThe GridView binding code in the .aspx.cs page is shown below\n\n```protected void Page_Load(object sender, EventArgs e)\n{\nif (!IsPostBack)\nBindGridView();\n}\n\npublic void BindGridView()\n{\nDataTable dataTable = new DataTable();\nDataColumn[] dataColumn = new DataColumn[]\n{\nnew DataColumn(\"Id\"),\nnew DataColumn(\"Name\"),\nnew DataColumn(\"Quantity\"),\nnew DataColumn(\"Price\")\n};\n\ndataTable.Rows.Add(new object[] { 1, \"Pants\", 5, 10.10 });\ndataTable.Rows.Add(new object[] { 2, \"Shirts\", 6, 5 });\ndataTable.Rows.Add(new object[] { 3, \"Shoes\", 7, 8.98 });\ndataTable.Rows.Add(new object[] { 4, \"Socks\", 8, 9.80 });\ndataTable.Rows.Add(new object[] { 5, \"TVs\", 4, 99.99 });\n\ngridView.DataSource = dataTable;\ngridView.DataBind();\n}\n```\n\nNotice that I have used a DataTable object to bind the GridView with some dummy data.\n\nNow if you run your page in the browser the GridView will look like:\n\nNow let me use jQuery to show the sum of columns in the GridView.\n\nShowing Sum of Quantities columns in the footer\n\n```<script src=\"https://code.jquery.com/jquery-3.2.1.min.js\"></script>\n\n<script type=\"text/javascript\">\nvar quantityTotal = 0;\n\\$.each(\\$(\".quantityCSS\"), function (index, value) {\nquantityTotal += parseInt(\\$(value).text());\n});\n\\$(\".quantitySpan\").text(quantityTotal);\n});\n</script>\n```\n\nI have used jQuery .each method to loop through all the ‘Quantity’ columns of the GridView. These columns have the CSS class called quantityCSS.\n\nI have defined a variable to store the sum:\n\n``var quantityTotal = 0;``\n\nTo this variable I am adding the sum like:\n\n``quantityTotal += parseInt(\\$(value).text());``\n\nFinally, I am showing the sum of the quantity column, inside the footer column which has the CSS class called ‘quantitySpan’:\n\n``\\$(\".quantitySpan\").text(quantityTotal);``\n\nNow reload the page in the browser, and you will see the sum of quantity column, which is 30, is displayed in the footer column, see the below image:\n\nShowing Sum of Price columns in the footer\n\n``````var priceTotal = 0;\n\n\\$.each(\\$(\".priceCSS\"), function (index, value) {\npriceTotal += parseFloat(\\$(value).text());\n});\n\n\\$(\".priceSpan\").text(priceTotal);``````\n\nIn this code I am looping through all the ‘Price’ columns of the GridView (they have priceCSS as their CSS class). Then I adding the values of each column in a variable called priceTotal.\n\nFinally showing this sum inside the footer column which has a CSS class called priceSpan.\n\nNotice that the values of the Price columns are in decimals therefore I have used parseFloat() function to convert them to float values before adding them to the priceTotal variable.\n\nNow reload the page in the browser and you will see the total of all the Price columns in the footer of the GridView like shown by this image below:\n\nShowing Multiplication of Price * Quantity in the Total column\n\nThe total column will show the multiplication of Price * Quantity of each row. Therefore to do this add the below jquery code inside the document.ready method:\n\n```\\$.each(\\$(\".totalCSS\"), function (index, value) {\nvar q = \\$(this).parents(\"tr\").find(\".quantityCSS\").text();\nvar p = \\$(this).parents(\"tr\").find(\".priceCSS\").text();\n\\$(this).text(p * q);\n});\n```\n\nThe total column has a CSS class called totalCSS. So with the .each() method of jQuery I am looping through them.\n\nNext, inside the .each() method I am finding the values of Quantity and Price columns of each row of the GridView.\n\n``````var q = \\$(this).parents(\"tr\").find(\".quantityCSS\").text();\nvar p = \\$(this).parents(\"tr\").find(\".priceCSS\").text();``````\n\nI am using the parents() method to find the current ‘tr’ element, and then with the find() method I am able to get the Quantity and Price columns.\n\nNot to mention that with the text() method I get the values of these columns.\n\nOn the final code line – \\$(this).text(p * q), which shows the multiplication value in the current ‘total’ column.\n\nIn this way all the total columns are provided with the multiplication of Price and Quantity.\n\nReload the web page to see the ‘Total’ columns now have the multiplication values, check the below image:\n\nShowing Sum of Total columns in the footer\n\nTo show the sum of Total columns in the footer of the GridView add the below code to the document.ready method:\n\n```var totals =0\n\\$.each(\\$(\".totalCSS\"), function (index, value) {\ntotals += parseFloat(\\$(value).text());\n});\n\\$(\".totalSpan\").text(totals);\n```\n\nHere to I am looping through all the Total columns and adding their values in a variable called ‘totals’. This variable value is finally shown inside the footer column.\n\nReload the web page and you will now see the footer now shows the sum of all the values in the ‘Total’ columns, see below image:", null, "" ]
[ null, "https://www.yogihosting.com/wp-content/uploads/2020/05/sum-of-columns-gridview-footer.png", null, "https://www.yogihosting.com/wp-content/themes/yogi-yogihosting/Images/yh.png", null ]
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http://slh.alljournals.cn/search.aspx?subject=mathematical_chemical&major=sx&orderby=referenced&field=institution&q=%20Dover%2019901
[ "", null, "首页 | 本学科首页 官方微博 | 高级检索\n\n 按 中文标题 英文标题 中文关键词 英文关键词 中文摘要 英文摘要 作者中文名 作者英文名 单位中文名 单位英文名 基金中文名 基金英文名 杂志中文名 杂志英文名 栏目英文名 栏目英文名 DOI 责任编辑 分类号 杂志ISSN号 检索 检索词:\n\n 收费全文 59篇 国内免费 1篇 完全免费 4篇\n 数学 64篇\n 2017年 1篇 2016年 2篇 2014年 5篇 2013年 4篇 2012年 2篇 2011年 11篇 2010年 21篇 2009年 5篇 2008年 2篇 2007年 1篇 2006年 2篇 2004年 2篇 2001年 2篇 1998年 1篇 1995年 1篇 1992年 1篇 1955年 1篇\n\n1.\n2.\nIn this paper, we study the Korteweg-de Vries (KdV) equation having time dependent coefficients from the Lie symmetry point of view. We obtain Lie point symmetries admitted by the equation for various forms for the time-dependent coefficients. We use the symmetries to construct the group-invariant solutions for each of the cases of the arbitrary coefficients. Subsequently, the 1-soliton solution is obtained by the aid of solitary wave ansatz method. It is observed that the soliton solution will exist provided that these time-dependent coefficients are all Riemann integrable.  相似文献\n3.\nThis paper carries out the integration of Burgers equation by the aid of tanh method. This leads to the complex solutions for the Burgers equation, KdV-Burgers equation, coupled Burgers equation and the generalized time-delayed Burgers equation. Finally, the perturbed Burgers equation in (1+1) dimensions is integrated by the ansatz method.  相似文献\n4.\n5.\nThis paper develops algorithms for solving an undetermined coefficient problem for a wave equation. The algorithms are based on an integral representation for the solution to the wave equation obtained by using transmutation. The convergence of the algorithm is studied and numerical experiments are performed.  相似文献\n6.\nInvariant factors of bivariate orthogonal polynomials inherit most of the properties of univariate orthogonal polynomials and play an important role in the research of Stieltjes type theorems and location of common zeros of bivariate orthogonal polynomials. The aim of this paper is to extend our study of invariant factors from two variables to several variables. We obtain a multivariate Stieltjes type theorem, and the relationships among invariant factors, multivariate orthogonal polynomials and the corresponding Jacobi matrix. We also study the location of common zeros of multivariate orthogonal polynomials and provide some examples of tri-variate.  相似文献\n7.\nThe probability distribution of the number of players in the last round of a matching problem is analyzed and the existence of the limiting distribution is proved by using convolution method.  相似文献\n8.\nProblem solving and justification of a diversified group of two-year college students was compared with approaches of younger elementary and secondary school students working on the same tasks. The students in this study were engaged in thoughtful mathematics. Both groups found patterns, justified that their patterns were reasonable and, utilized similar strategies for their solutions and methods of justification. They were also able to make connections and build isomorphisms among the various problems.  相似文献\n9.\nIn this paper, we consider the problem of constructing partitions of the points of a Hermitian unital into pairwise disjoint blocks, commonly known as spreads. We generalize a construction of Baker et al. (In Finite Geometry and Combinatorics, Vol. 191 of London Math. Soc. Lecture Not Ser., pages 17–30. Cambridge University Press, Cambridge, 1993.) to provide a new infinite family of spreads. Morover, we develop a structural connection between these new spreads of the Hermitian unital in PG(2, q2) and the subregular spreads of PG(3, q), allowing us to christen a new “subregular” family of spreads in the Hermitian unital in PG(2, q2).  相似文献\n10." ]
[ null, "http://slh.alljournals.cn/ch/ext_images/logo.jpg", null ]
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https://answers.everydaycalculation.com/multiply-fractions/40-3-times-6-70
[ "Solutions by everydaycalculation.com\n\n## Multiply 40/3 with 6/70\n\n1st number: 13 1/3, 2nd number: 6/70\n\nThis multiplication involving fractions can also be rephrased as \"What is 40/3 of 6/70?\"\n\n40/3 × 6/70 is 8/7.\n\n#### Steps for multiplying fractions\n\n1. Simply multiply the numerators and denominators separately:\n2. 40/3 × 6/70 = 40 × 6/3 × 70 = 240/210\n3. After reducing the fraction, the answer is 8/7\n4. In mixed form: 11/7\n\nMathStep (Works offline)", null, "Download our mobile app and learn to work with fractions in your own time:" ]
[ null, "https://answers.everydaycalculation.com/mathstep-app-icon.png", null ]
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https://docs.oracle.com/en/database/oracle/oracle-database/21/sqlrf/TO_NUMBER.html#SQLRF51915
[ "## TO_NUMBER\n\nSyntax", null, "Description of the illustration to_number.eps\n\nPurpose\n\n`TO_NUMBER` converts `expr` to a value of `NUMBER` data type.\n\n`expr` can be any expression that evaluates to a character string of type `CHAR`, `VARCHAR2`, `NCHAR`, or `NVARCHAR2`, a numeric value of type `NUMBER`, `BINARY_FLOAT`, or `BINARY_DOUBLE`, or null. If `expr` is `NUMBER`, then the function returns `expr`. If `expr` evaluates to null, then the function returns null. Otherwise, the function converts `expr` to a `NUMBER` value.\n\n• If you specify an `expr` of `CHAR`, `VARCHAR2`, `NCHAR`, or `NVARCHAR2` data type, then you can optionally specify the format model `fmt`.\n\n• If you specify an `expr` of `BINARY_FLOAT` or `BINARY_DOUBLE` data type, then you cannot specify a format model because a float can be interpreted only by its internal representation.\n\nRefer to for information on number formats.\n\nThe `'nlsparam'` argument in this function has the same purpose as it does in the `TO_CHAR` function for number conversions. Refer to TO_CHAR (number) for more information.\n\nThis function does not support `CLOB` data directly. However, `CLOB`s can be passed in as arguments through implicit data conversion.\n\nExamples\n\nThe following examples convert character string data into a number:\n\n```UPDATE employees SET salary = salary +\nTO_NUMBER('100.00', '9G999D99')\nWHERE last_name = 'Perkins';\n```\n```SELECT TO_NUMBER('-AusDollars100','L9G999D99',\n' NLS_NUMERIC_CHARACTERS = '',.''\nNLS_CURRENCY = ''AusDollars''\n') \"Amount\"\nFROM DUAL;\n\nAmount\n----------\n-100```\n\nThe following example returns the default value of `0` because the specified expression cannot be converted to a `NUMBER` value:\n\n```SELECT TO_NUMBER('2,00' DEFAULT 0 ON CONVERSION ERROR) \"Value\"\nFROM DUAL;\n\nValue\n--------\n0\n```" ]
[ null, "https://docs.oracle.com/en/database/oracle/oracle-database/21/sqlrf/img/to_number.gif", null ]
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https://docstore.mik.ua/orelly/perl/cookbook/ch02_10.htm
[ "home | O'Reilly's CD bookshelfs | FreeBSD | Linux | Cisco | Cisco Exam\n\n#", null, "## 2.9. Making Numbers Even More Random\n\n### Problem\n\nYou want to generate numbers that are more random than Perl's random numbers. Limitations of your C library's random number generator seeds will sometimes cause problems. The sequence of pseudo-random numbers may repeat too soon for some applications.\n\n### Solution\n\nUse a different random number generator, such as those provided by the Math::Random and Math::TrulyRandom modules from CPAN:\n\n```use Math::TrulyRandom;\n\\$random = truly_random_value();\n\nuse Math::Random;\n\\$random = random_uniform();```\n\n### Discussion\n\nPerl uses the standard C library routine rand (3) to generate pseudo-random numbers. (This can be changed at build time, however.) Some implementations of the ``` rand``` function return only 16-bit random numbers or have algorithmic weaknesses and may not be sufficiently random.\n\nThe Math::TrulyRandom module uses the inadequacies of your system's timers to generate the random numbers. This takes a while, so it isn't useful for generating a lot of random numbers.\n\nThe Math::Random module uses the ``` randlib``` library to generate random numbers. It also includes a wide range of related functions.\n\nThe ``` srand``` and ``` rand``` functions in perlfunc (1) and Chapter 3 of Programming Perl ; Recipe 2.7 ; Recipe 2.8 ; the documentation for the CPAN modules Math::Random and Math::TrulyRandom", null, "", null, "", null, "2.8. Generating Different Random Numbers", null, "2.10. Generating Biased Random Numbers" ]
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https://math.stackexchange.com/questions/2489107/extended-euclidean-algorithm-issue/2489119
[ "# Extended Euclidean algorithm issue.\n\nThis question is related to RSA cryptosystem.\n\nFor simplicity I will work through the example given on Wikipedia on the following address: https://en.wikipedia.org/wiki/RSA_(cryptosystem)#Example (under the example header)\n\nunder the subheading: \"Compute d, the modular multiplicative inverse of e (mod λ(n))\" I have done the following which has given me the wrong answer.\n\nCan someone please correct me in stating what I've done wrong or not yet done. Thank you.\n\np=61 and q=53\nn = pq = 3233\n(this other value confuses me, why is it calculated?) LCM of (60,52) = 780. I'm sure other examples used n for this??\ne= 17\n\n\ncalculating d\n\nTo do this the modular multiplicative inverse of e(mod(n)) must be found.\n\nThe worked example give the formula d * e % n = 1\n\nThus d * 17 % 780 = 1\n\nTo solve d here I tried to use Extended Euclidean algorithm here is what I get:\n\nGCD(17, 780)\n\n780 = 45 * 17 + 15\n17 = 1 * 15 + 2\n15 = 7 * 2 + 1 <<<< Final one as the next remainder is 0\n\n1 = 15 - 7 * 2\n1 = 15 - 7 * (17-1*15)\n1 = 8 * 15 - 7 * 17\n1 = 8 * (780 - 45 * 17) - 7 * 17\n1 = 8(780) - 367(17)\n\n\nThis is not what I need for d\n\nedit: d in this instance should be 413\n\nEdit 2, let me run through a whole example I had earlier and set out my concerns more clearly:\n\n• P1 picks two primes p and q\n\np=17 q=19 n = pq = 323\n\n• P1 chooses another prime e\n\ne = 7\n\n• P1 makes n and e public\n\n• P2 wants to send P1 'H', 'H' in Ascii is 72\n\n• P2 does the following 72^e % 323 = c. 72^7 % 323 = c = 13\n• P2 sends P1 c\n\n• P1 needs to use p and q to decrypt c\n\n• P1 calculates D in order to do so.\n• (7xD)(mod((p-1)*(q-1)))=1\n• (7xD)(mod((16)*(18))) = 1\n• (7xD)(mod(288) = 1\n• which is the same as 7*D = 1 mod 288 << Am I correct there?\n\nExtended Euclidean algorithm\n\nGCD(7, 288)\n\n288 = 41 * 7 + 1\n7 = 7 * 1 + 0\n\n288 = 41 * 7 + 1 << (no winding up??)\n\n\n(Something happens here which I am unsure of)\n\n• D = 247\n• To decode the message c^D mod n is used\n• 13^247 mod 323 = 72\n• 72 in Ascii = 'H'\n\nYou made a mistake in the last line of your calculation: $8\\cdot 45 + 7$ is not equal to $343$.\n\nThere is an easier and less error-prone way to do this calculation.\n\nThe idea is to write equations $z = 780x + 17y$ and to combine them until we get an equation with $z=\\gcd(780,17)=1$\n\n$780 = 780\\cdot 1 + 17\\cdot 0$\n\n$17 = 780\\cdot 0 + 17\\cdot 1$\n\nSince $\\lfloor 780/17\\rfloor=45$, subtract $45$ times the second equation from the first:\n\n$15=780\\cdot 1 - 17\\cdot 45$\n\nand continue doing this until the left-hand side becomes $1$.\n\nIn fact, you don't need to write all the equations in full; you can simply make a table with the values of $z$, $x$ and $y$.\n\nNote that $-367\\equiv 413\\pmod{780}$\n\nConcerning the value of $n$.\n\nIn the article, $n = pq$ is the public modulus. It is used for encryption and decryption: you encrypt $M$ as $M^e\\pmod{n}$. The value $\\mbox{lcm}(p-1,q-1)$ is used when you prepare your public key: after you choose $p$ and $q$, you choose a public key $e$ and compute your private key $d$ as you did. You do this only once.\n\nYou need to have $M^{ed}\\equiv M\\pmod{pq}$, which is equivalent to $M^{ed}\\equiv M\\pmod{p}$ and $M^{ed}\\equiv M\\pmod{q}$.\n\nBy Fermat's Little theorem, if $p$ is prime and $\\gcd(a,p)=1$, $a^{p-1}\\equiv 1\\pmod{p}$.\n\nThis means that you must have $ed\\equiv 1\\pmod{p-1}$ and $ed\\equiv 1\\pmod{q-1}$. This implies that you must have $ed\\equiv 1\\pmod{\\mbox{lcm}(p-1,q-1)}$.\n\nOn the other hand, if you find $ed\\equiv 1\\pmod{(p-1)(q-1)}$, this will imply the previous condition. However, you may find a larger value for $d$, but the value will be the same $\\pmod{\\mbox{lcm}(p-1,q-1)}$. In that case, the algorithm will still work. However, the number of operations required to compute $M^d\\pmod{pq}$ will be larger. As we are dealing with very large numbers, this is significant.\n\n• Amended, thanks – Joe Blogs Oct 25 '17 at 13:01\n• Can you see why I'm not getting the correct values for d? – Joe Blogs Oct 25 '17 at 13:06\n• Seems now correct. Then $-367\\equiv 17\\mod 780$. – Wuestenfux Oct 25 '17 at 13:23\n• Maybe this is the wrong place to ask this question, but maybe my issue is my value for n. I have seen two values being used 1) 'n = LCM(p,q)' 2) 'n = ((p-1)*(q-1))'. D I believe is found by 'd*e%n = 1' then using Extended Euclidean algorithm on that. Am I correct? and what should I be using for n – Joe Blogs Oct 25 '17 at 13:42\n• I updated the answer to give additional information (it is too long for a comment). – wsj84 Oct 25 '17 at 14:28" ]
[ null ]
{"ft_lang_label":"__label__en","ft_lang_prob":0.86508745,"math_prob":0.99844533,"size":1922,"snap":"2020-10-2020-16","text_gpt3_token_len":681,"char_repetition_ratio":0.081334725,"word_repetition_ratio":0.037647057,"special_character_ratio":0.4219563,"punctuation_ratio":0.06855792,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9998915,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-03-31T23:45:16Z\",\"WARC-Record-ID\":\"<urn:uuid:49bdfaf4-785e-4c9d-9c09-9e82b796c8b7>\",\"Content-Length\":\"150361\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:64d9c242-9f15-4123-8328-99870754e9d8>\",\"WARC-Concurrent-To\":\"<urn:uuid:cafba88a-571a-46bd-841b-a53a05444bca>\",\"WARC-IP-Address\":\"151.101.129.69\",\"WARC-Target-URI\":\"https://math.stackexchange.com/questions/2489107/extended-euclidean-algorithm-issue/2489119\",\"WARC-Payload-Digest\":\"sha1:P7SY5Q7UDW54ILNWZRXGXEDKP5BDO3HL\",\"WARC-Block-Digest\":\"sha1:TMQJ63JF3ROICTPHVSIP4YHE5ESCKU43\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-16/CC-MAIN-2020-16_segments_1585370504930.16_warc_CC-MAIN-20200331212647-20200401002647-00306.warc.gz\"}"}
https://www.enlightenment.org/develop/api/ref/c/key/efl_ui_layout_finger_size_multiplier_set?do=
[ "# Efl.Ui.Layout_Base.finger_size_multiplier\n\n## Description\n\nSet a multiplier for applying finger size to the layout.\n\nBy default, any widget which inherits from this class will apply the finger_size global config value with a 1:1 width:height ratio during sizing calculations. This will cause the widget to scale its size based on the finger_size config value.\n\nTo disable finger_size in a layout's sizing calculations, set the multipliers for both axes to 0.\n\nSince 1.23\n\n## Values\n\n• multiplier_x - Multiplier for X axis.\n• multiplier_y - Multiplier for Y axis.\n\n## Signature\n\n```@property finger_size_multiplier {\nget {}\nset {}\nvalues {\nmultiplier_x: uint;\nmultiplier_y: uint;\n}\n}```\n\n## C signature\n\n```void efl_ui_layout_finger_size_multiplier_get(const Eo *obj, unsigned int *multiplier_x, unsigned int *multiplier_y);\nvoid efl_ui_layout_finger_size_multiplier_set(Eo *obj, unsigned int multiplier_x, unsigned int multiplier_y);```\n\n## Implemented by", null, "" ]
[ null, "https://www.enlightenment.org/lib/exe/indexer.php", null ]
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https://cs.stackexchange.com/questions/76919/rod-cutting-without-using-dynamic-approach
[ "# Rod Cutting without using dynamic approach\n\n## Question\n\nI want to Implement Rod cutting Algorithm without Dynamic Programming Approach.\n\nLet me Describe the problem statement.\n\nGiven a rod of length $n$ inches and a table of prices $p_{i}$ for $i=1,2,3,4,\\,.\\,.\\,.$ determine the maximum revenue $r_n$ obtainable by cutting up the rod and selling the pieces.\n\nIn cormen, the Algorithm is implemented as -:\n\nCUT-ROD (p,n)\n1 if n == 0\n2 return 0\n3 q = - inifinity\n4 for i = 1 to n\n5 q =max(q, p[i]+CUT-ROD(p,n-i))\n6 return q\n\n\nI got this algorithm , i may explain it with a example-:\n\nSay we want to determine maximum revenue for $n=4$,\n\nand the profit associated with each inches i.e $i=1,2,3,4$is given as follows-:\n\n$p=1,p=5,p=8,p=9$\n\nNow Moving to the algorithm ,if we want to find maximum revenue for Length 4 inch ,we need to call CUT-ROD$(p,4)$.How will it process , i mean what will be its sequence!?i can explain-:\n\nCUT-ROD$(p,4)$ will be computed by\n\nmaximum value of\n\n• $p+$CUT-ROD$(p,3)$\n• $p+$CUT-ROD$(p,2)$\n• $p+$CUT-ROD$(p,1)$\n• $p+$CUT-ROD$(p,0)$\n\nfor $i=1,2,3,4$ respectively.\n\nNow when $i=1$, it will encounter CUT-ROD$(p,3)$\n\nCUT-ROD$(p,3)$ will be computed by\n\nmaximum value of\n\n• $p+$CUT-ROD$(p,2)$\n• $p+$CUT-ROD$(p,1)$\n• $p+$CUT-ROD$(p,0)$\n\nfor $i=1,2,3$ respectively.\n\nCUT-ROD$(p,2)$ will be computed by\n\nmaximum value of\n\n• $p+$CUT-ROD$(p,1)$\n• $p+$CUT-ROD$(p,0)$\n\nfor $i=1,2$ respectively.\n\nCUT-ROD$(p,1)$ will be computed by\n\nmaximum value of\n\n• $p+$CUT-ROD$(p,0)$\n\nfor $i=1$\n\nCUT-ROD$(p,1)$=1,CUT-ROD$(p,2)$=$max(1+1,5)=5$\n\nCUT-ROD$(p,3)$=$max(1+5,5+1,8+0)=8$\n\nCUT-ROD$(p,4)$=$max(1+8,5+5,8+1,9+0)=10$\n\n## MY Doubt\n\nI implemented the $C$ code,but it is giving wrong result.I don't know why!\n\nI guess that the sequence of the function call is wrong .Here is the code.\n\n#include<stdio.h>\nint p;\nint result=-9999;\nint count=0;\nint max(int x,int y)\n{\nreturn (x > y)? x : y;\n}\nint recrsv_top_down(int sizee)\n{\nint i;\nif (sizee<=0)\n{\nreturn 0;\n}\nfor(i=1;i<=sizee;i++)\n{\nresult=max(result,(p[i]+(recrsv_top_down(sizee-i))));\n}\nreturn result;\n}\nint main()\n{\nint size,i,result;\nprintf(\"enter the size of rod\\n\");\nscanf(\"%d\",&size);\nprintf(\"enter the profit of assocaited length\\n\");\nfor(i=1;i<=size;i++)\n{\nprintf(\"enter profit assocaited with length %d \\n \",i);\nscanf(\"%d\",&p[i]);\n}\nprintf(\"\\n***************OUTPUT*****************\\n\");\nresult=recrsv_top_down(size);\nprintf(\"Maximum profit is %d\\n\",result);\nreturn 0;\n}\n\n\nSorry for the long post , but i have no option!!!\n\nIn recrsv_top_down, declare result = -1000 as a local variable.\n• @laura Well, your problem was the fact that the global result got tampered by recursive calls. Actually, in professional software development, usage of globals is most likely an indication of a design error. Jun 17 '17 at 18:21" ]
[ null ]
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https://math.stackexchange.com/questions/1800842/completeness-theorem-for-second-order-logic-in-the-language
[ "# Completeness theorem for second-order logic in the language $\\{\\}$\n\nIt is well-known that the completeness theorem fails for second-order logic. In particular, there is no calculus $C$ that proves exactly those second-order sentences $\\phi$ in the language $\\{0, s, +, \\cdot\\}$ which are valid (valid means true in every interpretation/model). This is because of Gödels Incompleteness theorem: If there was such a calculus $C$, this would contradict the assertion of Gödels Incompleteness theorem, since the sentence $\\mathrm {PA}\\rightarrow \\varphi$ is valid if and only if $\\varphi$ is true in the standard model $\\mathbb N$ of the peano axioms. ($\\mathrm{PA}$ denotes the conjunction of the second-order peano axioms.)\n\nMy question is: Is there a complete calculus for second-order logic in the empty language $\\{\\}$ with no constant symbols, no function symbols and no relation symbols? That is to say: Is there a calculus $C$ that proves exactly those second-order sentences $\\phi$ in the language $\\{\\}$ which are valid?\n\n• Trying to understand. What is an example of a sentence in the language $\\{\\}$? You do have the predicate ‘=’ anyway? So I guess you have a sentence $(\\forall x) (\\exists y) x=y$. So is it true that all this language can do is express properties of equality? – GEdgar May 26 '16 at 13:59\n• Yes, $=$ is allowed. For example, $\\exists a\\exists b(a\\not = b)$ would be a sentence in the language $\\{\\}$ – thisismyname May 26 '16 at 14:02\n\nNo, second-order logic over the empty language is basically as powerful as second-order logic over an arbitrary language. To see this, suppose $\\varphi$ is a second-order sentence with some non-logical symbols; let $\\psi$ be the sentence gotten by \"universally quantifying out\" the non-logical symbols in $\\varphi$. For example, if $\\varphi$ is the sentence $$\\forall x\\exists y(xRy),$$ then $\\psi$ would be $$\\forall R\\forall x\\exists y(xRy).$$ It's not hard to see that $\\psi$ is valid iff $\\varphi$ is valid, but $\\psi$ uses no non-logical symbols." ]
[ null ]
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http://boscoh.com/protein/magic-numbers-and-unit-conversions-in-structural-biology.html
[ "Magic Numbers and unit conversions in Structural Biology\n\nIf you end up doing any kind of energy calculation in proteins or organic chemistry – and that includes messing around with Molecular Dynamic trajectories – you may end up dealing with actual numbers.\n\nAnd that means you'll have to get your head around physical units and their conversions.\n\nI've spent days trying to figure out magic numbers in equations and source-code. Diving into the guts of someone else's source-code is not the nicest place to figure such things out. Do it enough, and you'll start seeing the same numbers pop up everywhere. As I've never seen anyone bother to describe some very common magic numbers in biochemistry, I'll list a bunch of them right here.\n\nFirst let's get acquainted with the standard units:\n\n1. positions of atoms and molecules are always expressed in Ångstroms which is 10-10 m. Ånstroms are preferred because the radius of a hydrogen atom is ~1.0 Å, a useful magnitude to describe molecules. That's why PDB protein structure files use Ångstroms.\n2. masses are expressed in Da, which is g·mol-1 or 10-3 kg·mol-1 (where mol-1 is 1.0 / 6.02×10-23). This unit is the work-horse of chemistry and the masses of atoms (or at least their protons) can almost be pulled directly out of the periodic table. Once again, the mass of a hydrogen nucleus is ~1.0 Da.\n3. charges are expressed in multiples of e (the charge of an electron). A hydrogen nucleus has charge +1 e.\n4. energy is usually expressed kcal·mol-1, which biochemists and nutritions use but not engineers of physicists. At room temperature, 300 K, the average kinetic energy available to most atoms is about 1 kcal·mol-1. The hydrogen bond binding energy is about 2 kcal·mol-1.\n\nThese units are pretty universal across a whole bunch of structural biology programs, and are chosen because they have a reasonable order of magnitudes for biological molecules at room temperatures. This is important to avoid overflow and underflow problems in floating-point operations.\n\nWhere magic numbers come in is making all the other physical properties match this set of units. One of the most common calculations is the electrostatic interaction. Namely the electrostatic potential energy k·q1·q2/r.\n\nNow, we ideally would like the result in kcal·mol-1. Given that q1 and q2 are in e, and r is in Å, this imposes a set of unit conversions on k (=1/4πε) which gives the magic number k = 332.24.\n\nYou will see this everywhere, and the first place I saw it was in the ubiquitous secondary structure evaluation program DSSP that defines hydrogen bonds in terms of the electrostatic energy calculated by this equation for bacbkone O and H atoms.\n\nSince the energy and distance units are fixed, this means that the calculated force units are, not in terms of Newtons, but in terms kcal·mol-1Å-1. This is because forces in MD are mostly central forces taken from the energy potentials where F = dE/dr.\n\nNotice I've said nothing about time. There is no particular consensus on what time units are used in Molecular Dynamics simulations.Some MD simulations choose fs (10-15 s) as this is the smallest time-step, which allows ~10 steps for the fastest vibrations (bond vibrations involving H atoms). Others choose ps (10-12 s) as this is closer to what can be observed with experiment.\n\nEven with ps, this causes problems with velocities, due in part to the floating point representation. In NAMD, velocity values are stored in the PDB which has only 3 decimal figures in the coordinate fields. Given that velocities are outputed as Å/ps, the 3 decimal places lose a lot of precision. As a result NAMD multiplies the velocities by 10 before storing. So you have to divide by 10 when you read NAMD velocities.\n\nBut the programs mess around with time and velocity units internally, ostensibly to avoid a single floating point multiplication in the main loop. In both NAMD and AMBER, the kinetic energy E = 0.5·m·v2 is stored as kcal·mol-1. If time was stored as ps or fs, then the kinetic energy calculation would require a unit conversion to get kcal·mol-1.\n\nIn NAMD, the base time unit is fs (10-15 s). As mass is in Da and position is in Ånstroms, directly plugging these values in the kinetic energy calculation results in an energy unit that is 2388.45897 kcal·mol-1. To abstract away that 2388.45897, they find the square root of 2388.46, so that can you can slide one square root each into one of the velocities in the v2 term in the kinetic energy. The velocity is of course, distance/time. Since they don't want to mess around with the distances in Ångstroms, they divide their time (which is in fs) by the NAMD magic time-factor of √ 2388.45897 = 48.89. Now you can plug it all in 0.5·m·(d/t)2 and get the energy directly in kcal·mol-1.\n\nIn AMBER on the other hand, the base time unit is ps (10-12 s). AMBER too, uses Da and Å. Plugging these time, mass and distance units in gives the kinetic energy as 0.00238846 kcal·mol-1. In this case, AMBER takes the square root of the inverse of this number which is 418.68. They multiply time (in ps) by the AMBER magic time-factor of √418.6 = 20.46.\n\nTwo different MD packages. In one, you multiply time by 20.46. In the other, you divide time by 48.89. Same problem, two magic numbers." ]
[ null ]
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http://www.gdzpgc.com/article/show_article.php?id=1329
[ "14的圆钢一米多少公斤：0.00617×14×14=1.20932kg\n\n18的圆钢每米多少公斤：0.00617×18×18=1.99908kg\n\n20圆钢每米多少公斤：0.00617×20×20=2.468kg\n\n25的圆钢一米多少公斤：0.00617×25×25=3.85625kg\n\n32的圆钢一米多少公斤：0.00617×32×32=6.31808kg\n\n40的圆钢一米多少公斤：0.00617×40×40=9.872kg", null, "" ]
[ null, "http://www.gdzpgc.com/template/default/images/foot_logo.png", null ]
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https://thetwomeatmeal.wordpress.com/2010/11/21/banach-tarski-part-2/
[ "Gracious Living\n\nBanach-Tarski part 2\nNovember 21, 2010, 23:30\nFiled under: Algebra, Math | Tags: , , , , ,\n\nSo I sort of left you hanging last time.  We talked about equidecomposability, showed that", null, "$F_2$ was paradoxical under its own action on itself, and embedded", null, "$F_2$ into", null, "$SO(3)$.  From here, it just becomes a matter of putting all the steps together: first the sphere, then the ball minus its center, then the whole ball.\n\nFirst, let’s look at the sphere.  Here’s a simple fact about group actions: any group action on a set restricts to a group action on a subset of that set if and only if that subset is a union of orbits.  For", null, "$SO(3)$, the orbit of a point is the sphere about the origin containing it, since all orthogonal matrices preserve distance.  In particular,", null, "$SO(3)$ acts on the unit sphere, and since this is just one orbit, the action is transitive (for any pair of points, an element of", null, "$SO(3)$ takes the first to the second).\n\nIn addition, group actions restrict to subgroup actions, so the copy of", null, "$F_2$ in", null, "$SO(3)$ also acts on the sphere.  Recall that this is generated by rotations of", null, "$\\arccos(3/5)$ around the", null, "$x$– and", null, "$z$-axes, called", null, "$a$ and", null, "$b$ respectively.  It’s clear that this is countable: we can just list the words in increasing order of length.  It also partitions the sphere into orbits.\n\nAgain, we partition this group into four sets,", null, "$W(a),W(a^{-1}),W(b),W(b^{-1})$, such that", null, "$aW(a^{-1})\\sqcup W(a)=bW(b^{-1})\\sqcup W(b)=F_2$.  Then we pick a point out of each orbit in the sphere of", null, "$F_2$, calling this set", null, "$X$.  Then the sets", null, "$W(a)X,W(a^{-1})X,W(b)X,W(b^{-1})X$ are disjoint, partition the sphere (since the action is free), and we also have partitions", null, "$aW(a^{-1})X\\sqcup W(a)X=bW(b^{-1})\\sqcup W(b)X=S^2$!  Geometrically, what we’ve done is split the sphere into these four sets, and each of them can be rotated by a certain angle so that it completely covers two others.  If we rotate", null, "$W(a^{-1})X$ by", null, "$a$, then together with", null, "$W(a)X$, we have a whole sphere — then we just have to translate this to the side, and rotate", null, "$W(b^{-1})X$, and get a second sphere.  This paradoxical decomposition of the sphere is called the Hausdorff paradox.\n\nThere are three things that need to be said about this proof.  One is a deliberate error that I hope you caught, one isn’t considered an error now but would have been when the proof was published, and one is why this isn’t that strange.\n\nThe first thing is: the action of", null, "$F_2$ on the sphere is not free.  Since all the elements are rotations, they each fix two points, where their axis of rotation intersects the sphere.  What this means is that the partition of", null, "$F_2$ doesn’t necessarily give a partition of", null, "$S^2$ when it acts on", null, "$X$: rather, points in", null, "$X$ that get fixed could wind up sent to the same place twice, meaning that the sets overlap and potentially breaking our proof.\n\nBut fortunately, this doesn’t happen.  The reason why goes back all the way to our studies of cardinality:", null, "$F_2$, and thus the set of points fixed by any rotation in", null, "$F_2$, is countable, and the sphere is not.  If we remove this countable fixed point set (call it", null, "$C$) from the sphere, then the action of", null, "$F_2$ on", null, "$S^2-C$ is free, and so we can paradoxically decompose", null, "$S^2-C$.  We just have to show that", null, "$S^2-C$ is equidecomposable with", null, "$S^2$, which really only requires the same trick we did on the circle last time.  Pick any irrational rotation", null, "$r\\in SO(3)-F_2$.  Then the axis of rotation of", null, "$r$ is disjoint from", null, "$C$, so", null, "$C,rC,r^2C,\\dotsc$ are all disjoint.  Then applying", null, "$r$ to", null, "$C\\cup rC\\cup r^2C\\cup\\dotsb$ gives", null, "$rC\\cup r^2C\\cup\\dotsb$, which is the original set minus", null, "$C$.  So", null, "$S^2\\sim S^2-C\\sim S^2-C\\sqcup S^2-C\\sim S^2\\sqcup S^2$.\n\nThe second thing is the sentence “pick an element out of each orbit of", null, "$F_2$.”  Without the Axiom of Choice, there’s no reason we should be able to do this.  Most mathematicians today use choice without reservation, but in Hausdorff, Banach, and Tarski’s day, this raised some eyebrows.  In fact, the Banach-Tarski paradox was one of the main sources of fuel behind the anti-choice (or, as I like to call it, “pro-life”) movement.  Without choice, the paradox disappears, but I feel that some very beautiful mathematics disappears as well.\n\nThe third thing is that the Hausdorff paradox really isn’t as bad as it seems.  Why?  Because in", null, "$\\mathbb{R}^3$, surface area isn’t well-defined.  I find it easier to think about the analogous problem with length in", null, "$\\mathbb{R}^2$.  Imagine measuring the coastline of Great Britain.  If you’re looking at a map, you can just say “well, it looks like a triangle” and use the perimeter of that triangle as a first approximation.  Then you can zoom in on the map, measure each of the tiny lines, and get a larger approximation.  Then you can actually go there and start measuring it with surveying equipment, and your approximation will be bigger.  If you go back with a yardstick, the approximation will be bigger still.  As you increase your level of detail, you uncover more kinks in the coastline, making your approximation longer, and this sequence won’t, in general, converge!  (Fortunately, this isn’t a problem with differentiable curves — we can just integrate the length of the tangent vector.)\n\nIn", null, "$\\mathbb{R}^2$, we can approximate any area to any level of precision — for example, it must be less than the area of any disk containing it.  But in", null, "$\\mathbb{R}^3$, we again have the problem of craggy landscapes, and it’s entirely possible that the area of a bounded surface can be infinite!  Since the paradoxical decomposition given in the Hausdorff paradox is really weird (so weird that we need the axiom of choice to prove it exists), it’s not really that surprising that we can double the area of a surface through isometries.\n\nWhat Banach and Tarski did was extend the Hausdorff Paradox to the ball, which has volume.  We expect to be able to measure volume in", null, "$\\mathbb{R}^3$.  But if we connect each point on", null, "$S^2$ to the origin by a line segment (not including the origin itself), then", null, "$F_2$ acts (almost) freely on the set of those segments, whose union is, of course, the ball minus its center.  Repeating the above steps, we get", null, "$B^3-\\{0\\}\\sim(B^3-\\{0\\})\\sqcup(B^3-\\{0\\})$.\n\nFinally, imagine a small circle through the origin and inside the unit ball.  We showed in the previous post that such a circle was equidecomposable with itself minus a point under the group of rotations about its center.  Such rotations are in", null, "$SE(3)$ (to rotate about an axis not going through the origin, you just have to conjugate by a translation sending the origin to it in a perpendicular direction — investigate this).  So under the", null, "$SE(3)$ action, the ball is equidecomposable to itself minus its center.  Putting this all together, we have that the ball is equidecomposable with two balls.", null, "$\\square$, bitches!\n\nThe implications of this are extensive.  There are two directions I want to go.  First, in order for this to make sense, at least one of the sets in the paradoxical decomposition must have no definable volume.  This naturally leads us to asking when we can define volume (or length, area, et cetera) at all, a question at the heart of measure theory.  Second, the reason we can do this in", null, "$\\mathbb{R}^3$ but not", null, "$\\mathbb{R}^2$ is due to certain abstract group-theoretic properties of", null, "$SE(3)$.  We can continue our discussion of group theory by examining these properties, and follow up the Banach-Tarski paradox with von Neumann’s extension to", null, "$\\mathbb{R}^2$, where a paradoxical decomposition is possible if we extend the acting group to the group of all transformations that preserve area,", null, "$SA(2)$.  Of course, I also want to head back to topology at some point — we’ve yet to discuss metric spaces, which are relevant here, and there are a bunch of other cool topics to address.", null, "" ]
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https://www.groundai.com/project/gaussian-entanglement-revisited/
[ "Gaussian entanglement revisited\n\n# Gaussian entanglement revisited\n\nLudovico Lami    Alessio Serafini    Gerardo Adesso\n###### Abstract\n\nWe present a novel approach to the problem of separability versus entanglement in Gaussian quantum states of bosonic continuous variable systems, as well as a collection of closely related results. We derive a simplified necessary and sufficient separability criterion for arbitrary Gaussian states of vs modes, which relies on convex optimisation over marginal covariance matrices on one subsystem only. We further revisit the currently known results stating the equivalence between separability and positive partial transposition (PPT) for specific classes of multimode Gaussian states. Using techniques based on matrix analysis, such as Schur complements and matrix means, we then provide a unified treatment and compact proofs of all these results. In particular, we recover the PPT-separability equivalence for Gaussian states of vs modes, for arbitrary . We then proceed to show the novel result that Gaussian states invariant under partial transposition are separable. Next, we provide a previously unknown extension of the PPT-separability equivalence to arbitrary Gaussian states of vs modes that are symmetric under the exchange of any two modes belonging to one of the parties. Further, we include a new proof of the sufficiency of the PPT criterion for separability of isotropic Gaussian states, not relying on their mode-wise decomposition. In passing, we also provide an alternative proof of the recently established equivalence between separability of an arbitrary Gaussian state and its complete extendability with Gaussian extensions. Finally, we prove that Gaussian states which remain PPT under passive optical operations cannot be entangled by them either; this is not a foregone conclusion per se (since Gaussian bound entangled states do exist) and settles a question that had been left unanswered in the existing literature on the subject. This paper, enjoyable by both the quantum optics and the matrix analysis communities, overall delivers technical and conceptual advances which are likely to be useful for further applications in continuous variable quantum information theory, beyond the separability problem.\n\nplus 0.3ex\n\n\\@xsect\n\nGaussian states have played a privileged role in quantum optics and bosonic field theories, essentially since the very early steps of such theories, due to their ease of theoretical description and relevance to experimental practice. Over the last twenty years, such a privilege has carried over to quantum information science, where Gaussian states form the core of the ‘continuous variable’ toolbox introeisert (); biblioparis (); adesso07 (); weedbrook12 (); adesso14 (); bucco (). The analysis of quantum Gaussian states from the information theoretic standpoint brought up new subtle elements and much previously unknown insight into their structure. For, while Gaussian dynamics may essentially be dealt with entirely at the phase space level (typically by normal mode decomposition, so that Gaussian dynamics are often trivialised as ‘quasi-free’ in field theory), the analysis of quantum information properties requires one to confront the Hilbert space description of the quantum states. Hence, while Gaussian dynamics might well be exactly solvable with elementary tools, the properties of Gaussian states related to the Hilbert space and tensor product structures are far from being equally transparent.\n\nThe problem of Gaussian separability, that is, determining whether a bipartite Gaussian state is separable or entangled adesso07 (), exemplifies such a situation very well. Necessary and sufficient conditions for Gaussian separability in the general vs -mode case are available Werner01 (); Giedke01 (), yet they are recast in terms of convex optimisation problems whose solution (albeit numerically efficient) does not admit, in general, a closed analytical form. For non-separable states, a closely related question is whether their entanglement is distillable or bound HorodeckiBound (). In the case of arbitrary multimode Gaussian states, while entanglement can never be distilled by Gaussian operations alone nogo1 (); nogo2 (); nogo3 (), it is known that entanglement distillability under general local operations and classical communications is equivalent to violation of the positivity of the partial transposition (PPT) criterion Giedke01 (); GiedkeQIC (). In turn, the PPT criterion, which is as well efficiently computable at the level of covariance matrices for Gaussian states, and is in general only necessary for separability Peres (), has been proven to be also sufficient in some important cases, notably when the bipartite Gaussian state under examination pertains to a vs -mode system Simon00 (); Werner01 (), when it is ‘bi-symmetric’ Serafini05 (), i.e. invariant under local permutations of any two modes within any of the two subsystems, and when it is ‘isotropic’, i.e. with a fully degenerate symplectic spectrum of its covariance matrix holwer (); botero03 (); giedkemode (). Outside of these special families, bound entangled Gaussian states can occur, as first shown in the vs -mode case in Werner01 ().\n\nIn this paper we provide significant advances towards the characterisation of separability and entanglement distillability in Gaussian quantum states. On one hand, we revisit the existing results, providing in particular a new compact proof for the equivalence between PPT and separability in vs -mode Gaussian states, which encompasses the seminal vs -mode case originally tackled by Simon Simon00 () and its extension settled by Werner and Wolf Werner01 (). Key to our proof is the intensive use of Schur complements, which have enjoyed applications in various areas of (Gaussian) quantum information theory Giedke01 (); giedkemode (); nogo1 (); nogo2 (); nogo3 (); eisemi (); gian (); Simon16 (); Lami16 (), and — as further reinforced by this work — may be appreciated as a mathematical cornerstone for continuous variable quantum technology.\n\nOn the other hand, we derive a number of novel results. In particular, a marginal extension of the techniques applied in the aforementioned proof allow us to prove that Gaussian states invariant under partial transposition are necessarily separable, a result previously known only for the partial transposition of qubit subsystems sep 2xN (). We then show that the vs -mode PPT-separability equivalence can be further extended to a class of arbitrary bipartite multimode Gaussian states that we call ‘mono-symmetric’, i.e., invariant under local exchanges of any two modes on one of the two subsystems (see Fig. LABEL:mononucleosi). This result, which (to the best of our knowledge) is observed and proven here for the first time, generalises the case of bi-symmetric states studied in Serafini05 (), providing as a byproduct a simplified proof for the latter as well.\n\nAs for isotropic Gaussian states, in the traditional approach the sufficiency of PPT for their separability follows from a well known ‘mode-wise’ decomposition of pure-state covariance matrices holwer (); botero03 (); giedkemode (), and from the fact that the covariance matrix of an isotropic state is just a multiple of the covariance matrix of a pure Gaussian state. Here, we derive the sufficiency of the PPT criterion for isotropic Gaussian states following a completely different and arguably more direct approach. Main ingredients of this novel proof are advanced matrix analysis tools such as the operator geometric mean, already found to be useful in the context of quantum optics Lami16 ().\n\nWe also consider the well known class of Gaussian passive operations (i.e., the ones that preserve the average number of excitations of the input state, such as beam splitters and phase shifters), which play a central role in quantum optics introeisert (); adesso14 (); bucco (), and we prove that a Gaussian state that always remains PPT under such a set of operations must also always stay separable. This novel result complements the seminal study of passive (), in that the latter only considered the possibility of turning a PPT state into a non-PPT one through passive operations — essentially, the question of generating distillable entanglement — which is not the same as the question of generating inseparability, because Gaussian PPT bound entangled states do exist Werner01 (). Here we settle the latter, more general and fundamental question.\n\nAll the previous results enable us to substantially extend the range of equivalence between Gaussian separability and PPT in contexts of strong practical relevance. Last but not the least — in fact, first and foremost in the paper — we address the separability problem directly, and derive a simplified necessary and sufficient condition for Gaussian separability. For a bipartite state, this requires convex optimisation over marginal covariance matrices on one subsystem only, yielding a significant simplification over the existing criteria, which instead require optimisation on both parties Werner01 (); Giedke01 (); eisemi ().", null, "Figure 1: Mono-symmetric Gaussian states of two parties A (with m modes) and B (with n modes) are invariant under exchange of any two modes within party A. By means of a suitable symplectic transformation on subsystem A, these states can be reduced to a 1 vs n-mode Gaussian state and a collection of m−1 uncorrelated single-mode states on A’s side. Since PPT is equivalent to separability for 1 vs n-mode Gaussian states, it follows that PPT is necessary and sufficient for separability of all m vs n-mode mono-symmetric Gaussian states. In the schematics, entanglement between pairs of modes from the same party is depicted as a single solid (black) line, while entanglement across a mode from A and a mode from B is depicted as a double (dark red) line.\n\nThis paper is organised as follows: in Sec. LABEL:methods, the definition and basic properties of Schur complements and matrix means that will be used in our derivations are recalled, and the Gaussian notation is set; Sec. LABEL:secp contains our main novel finding: a simplified necessary and sufficient condition for Gaussian separability in the general vs -mode case; Sec. LABEL:ppt contains a new proof of the sufficiency of the PPT criterion for separability of vs -mode Gaussian states achieved in a few, swift Schur complements’ manipulation; Sec. LABEL:inva shows that invariance under partial transposition implies separability; in Sec. LABEL:symm we prove that mono-symmetric states are amenable, under local unitary operations, to the vs -mode case, thus implying that PPT is sufficient for them too (see Fig. LABEL:mononucleosi); in Sec. LABEL:mode-wise we provide the reader with a new proof of the sufficiency of PPT for separability of isotropic Gaussian states, not relying on their mode-wise decomposition; Sec. LABEL:pass contains our novel analysis of entanglement generation under passive operations. Sec. LABEL:outro concludes the paper with a brief summary and some future perspectives related to this work.\n\n\\@xsect\n\nOne of the messages of the present paper is to lend further support to the fact that methods based on Schur complements and matrix means can be successfully exmployed to derive fundamental results in continuous variable quantum information, following a streak of applications to various contexts including separability, distillability, steerability, entanglement monogamy, characterisation of Gaussian maps, and related problems Giedke01 (); giedkemode (); nogo1 (); nogo2 (); nogo3 (); eisemi (); gian (); Simon16 (); Lami16 (). As a divertissement to set the stage, let us present a compact, essential compendium of such methods.\n\n\\@xsect\n\nGiven a square matrix partitioned into blocks as\n\n M=(AXYB), (0)\n\nthe Schur complement of its (square, invertible) principal submatrix , denoted by , is defined as\n\n M/A\\vbox\\scriptsize.\\scriptsize.=B−YA−1X. (0)\n\nA useful reference on Schur complements is the monograph ZHANG05 (). Here we limit ourselves to stress some of the properties we will make use of in the present paper. As it turns out, Schur complements are the answer 42 () to a number of questions that arise pretty naturally in matrix analysis. Many of these applications stem from the fact that the positivity conditions of hermitian block matrices can be easily written in terms of Schur complements.\n\n###### Lemma 1.\n\nConsider a hermitian matrix\n\n H=(AXX†B). (0)\n\nThen is strictly positive definite () if and only if and . Then, by taking suitable limits, is semidefinite positive () if and only if and for all .\n\nA consequence of this result that will be relevant to us is the following.\n\n###### Corollary 2.\n\nLet be a hermitian matrix partitioned as in (LABEL:H_part). Then, if ,\n\n H/A=sup{~B=~B†: H>0⊕~B}. (0)\n\nHere we mean that the matrix set on the right-hand side has a supremum (i.e. a minimum upper bound) with respect to the Löwner partial order ( if and only if is positive semidefinite), and that this supremum is given by the Schur complement on the left-hand side.\n\nWe note in passing that from the above variational representation it follows immediately that is monotone and concave in .\n\n\\@xsect\n\nSomehow related to Schur complements are the so-called matrix means. As one might expect from their name, these are functions taking two positive matrices as inputs and yielding another positive matrix as output. For an excellent introduction to this topic, we refer the reader to (BHATIA, , Chapter 4). Here, we review only some basic facts that we will find useful throughout the paper. Given two strictly positive matrices , the simplest mean one can define is the arithmetic mean , whose generalisation from scalars to matrices does not present difficulties. Another easily defined object is the harmonic mean parallel sum (); ando79 (), denoted by and given by\n\n A!B\\vbox\\scriptsize.\\scriptsize.=(A−1+B−12)−1. (0)\n\nIncidentally, the harmonic mean can be also defined as a Schur complement, with the help of the identity , which immediately implies that is monotone and jointly concave in and , i.e. concave in the pair .\n\nThe least trivially defined among the elementary means is undoubtedly the geometric mean between strictly positive matrices geometric mean (); ando79 (), which can be constructed as\n\n A#B\\vbox\\scriptsize.\\scriptsize.=max{X=X†: A≥XB−1X}, (0)\n\nwhere the above maximisation is with respect to the Löwner partial order, and the fact that the particular set of matrices we chose admits an absolute maximum is already nontrivial. With a bit of work one can show that is explicitly given by\n\n A#B=A1/2(A−1/2BA−1/2)1/2A1/2. (0)\n\nHaving multiple expressions for a single matrix mean is always useful, as some properties that are not easy to prove within one formulation may become apparent when a different approach is taken. For instance, the fact that is covariant under congruences, i.e.  for all invertible , is far from transparent if one looks at (LABEL:geom_expl), while it becomes almost obvious when (LABEL:geometric) is used. On the contrary, the fact that when is not easily seen from (LABEL:geometric), but it is readily verified employing (LABEL:geom_expl).\n\nAs it happens with scalars, the inequality\n\n A!B≤A#B≤A+B2 (0)\n\nholds true for all . In view of the above inequality, it could be natural to wonder, how the geometric mean between the leftmost and rightmost sides of (LABEL:hga) compares to . That this could be a fruitful thought is readily seen by asking the same question for real numbers. In fact, when it is elementary to verify that . Our first result is a little lemma extending this to the non-commutative case. We were not able to find a proof in the literature, so we provide one.\n\n###### Lemma 3.\n\nFor strictly positive matrices, the identity\n\n A#B=(A+B2)#(A!B) (0)\n\nholds true.\n\n###### Proof.\n\nWe start by defining , . It is easy to see that , for instance because . Therefore, the identity holds. Now, on the one hand the congruence covariance of the geometric mean implies that\n\n ~A#~B=((A+B)−1/2A(A+B)−1/2)#((A+B)−1/2B(A+B)−1/2)=(A+B)−1/2(A#B)(A+B)−1/2.\n\nOn the other hand,\n\n ~A~B =(A+B)−1/2A(A+B)−1B(A+B)−1/2= =(A+B)−1/2(B−1(A+B)A−1)−1(A+B)−1/2=12(A+B)−1/2(A!B)(A+B)−1/2.\n\nPutting all together, we see that\n\n (A+B)−1/2(A#B)(A+B)−1/2=~A#~B=(~A~B)1/2=1√2((A+B)−1/2(A!B)(A+B)−1/2)1/2.\n\nConjugating by , we obtain\n\n A#B=1√2(A+B)1/2((A+B)−1/2(A!B)(A+B)−1/2)1/2(A+B)1/2=(A+B2)#(A!B), (0)\n\nwhere the last step is an application of (LABEL:geom_expl). ∎\n\n\\@xsect\n\nIn the remainder of this Section, we provide a brief introduction to the main concepts of the Gaussian formalism. Quantum continuous variables just describe quantum mechanics applied to an infinite-dimensional Hilbert space equipped with position and momentum operators () satisfying the so-called canonical commutation relations (in natural units, ). Such a Hilbert space describes, for instance, a collection of quantum harmonic oscillators, or modes of the electromagnetic radiation field. The operators are often grouped together to form a single vector of operators . The canonical commutation relations then take the form\n\n [r,rT]=i Ω\\vbox\\scriptsize.\\scriptsize.=i ω⊕n,ω\\vbox\\scriptsize.%.=(01−10). (0)\n\nAn important object one can form is the displacement operator. For any , we define\n\n Dz\\vbox\\scriptsize.\\scriptsize.=eizTΩr. (0)\n\nIt turns out that Nature has a special preference for quadratic Hamiltonians. A prominent example is the free-field Hamiltonian . Not surprisingly, thermal states of quadratic Hamiltonians are extremely easily produced in the lab, in fact so easily that they deserve a special name: Gaussian states introeisert (); biblioparis (); adesso07 (); weedbrook12 (); adesso14 (); bucco (). As the name suggests, they can be fully described by a real displacement vector and a real, quantum covariance matrix (QCM) , defined respectively as and . By quantum covariance matrix we mean a real, symmetric, strictly positive matrix that moreover satisfies the Heisenberg uncertainty relation simon94 ()\n\n V+iΩ≥0. (0)\n\nNote that (LABEL:Heisenberg) can equivalently be written as upon applying transposition (as , ).\n\nThe Gaussian state with QCM and displacement vector admits the representation\n\n ρG(V,w)=∫d2nu(2π)n e−14uTVu−iwTrDΩr, (0)\n\nwhich justifies the alternative definition of Gaussian states as the continuous variable states associated with a Gaussian characteristic function.\n\nClearly, linear transformations that preserve the commutation relations (LABEL:CCR) play a special role within this framework. Any such transformation is described by a symplectic matrix, i.e. a matrix with the property that . Symplectic matrices form a non-compact, connected Lie group that is additionally closed under transposition, and is typically denoted by pramana (). The importance of these operations arises from the fact that for any symplectic there is a unitary evolution on the Hilbert space such that . Most importantly, such a unitary is the product of a finite number of factors , where is a quadratic Hamiltonian, and as such it can be easily implemented in laboratory. Under conjugation by , Gaussian states transform as\n\n U†SρG(V,w)US=ρG(SVST,Sw). (0)\n\nIt turns out that all Gaussian states can be brought into a remarkably simple normal form via unitary transformations induced by quadratic Hamiltonians. In fact, a theorem by Williamson willy (); willysim () implies that for all strictly positive matrices there is a symplectic transformation and a diagonal matrix such that\n\n SVST=N\\vbox\\scriptsize.\\scriptsize.=% diag(ν1,ν1,…,νn,νn). (0)\n\nThe diagonal elements , each taken with multiplicity one, are called symplectic eigenvalues of , and are uniquely determined by (up to their order, which can be assumed decreasing by convention with no loss of generality). Accordingly, we will refer to as the symplectic spectrum of . Notably, Heisenberg uncertainty relation (LABEL:Heisenberg) can be conveniently restated as , or equivalently for all . A Gaussian state can be shown to be pure if and only if all of its symplectic eigenvalues are equal to , which corresponds to the matrix equality . Correspondingly, a QCM satisfying for all (or equivalently ) will be called a pure QCM. Note that pure QCMs are themselves symplectic matrices, , and are the extremal elements in the convex set of QCMs.\n\nFinally, note that displacement vector is often irrelevant since it can be made to vanish by local unitaries, resulting from the action of the displacement operator of (LABEL:displacement) on each individual mode. Since all the physically relevant informational properties such as purity and entanglement are invariant under local unitaries, all the results we are going to present will not depend on the first moments. Therefore, in what follows, we will completely specify any Gaussian state under our investigation as in terms of its QCM alone.\n\n\\@xsect\n\nThe QCM of a Gaussian state pertaining to a -mode bipartite system can be naturally written in block form according to the splitting between the subsystems and :\n\n VAB=(VAXXTVB). (0)\n\nAccording to the same splitting, the matrix appearing in (LABEL:CCR) takes the form\n\n ΩAB=(ΩA00ΩB)=ΩA⊕ΩB, (0)\n\nwith and .\n\nThe entanglement properties of a bipartite Gaussian state can thus be conveniently translated at the level of QCMs. Recall that, in general, a bipartite quantum state is separable if and only if it can be written as a convex mixture of product states, , with being probabilities Werner89 (). For a Gaussian state of a bipartite continuous variable system, we have then the following.\n\n###### Lemma 4 (Proposition 1 in Werner01 ()).\n\nA Gaussian state with -mode QCM is separable if and only if there exist an -mode QCM and an mode QCM such that\n\n VAB≥γA⊕γB. (0)\n\nIn view of the above result, a QCM satisfying (LABEL:sep_eq) for some marginal QCMs , will itself be called separable from now on. The criterion in (LABEL:sep_eq) is necessary and sufficient for separability of QCMs, and can be evaluated numerically via convex optimisation Giedke01 (); eisemi (), however such optimisation runs over both marginal QCMs, hence scaling (polynomially) with both and .\n\nThe first main result of this paper is to show that the necessary and sufficient separability condition (LABEL:sep_eq), for any and , can be further simplified. This result is quite neat and of importance in its own right. In particular, it allows us to recast the Gaussian separability problem as a convex optimisation over the marginal QCM of one subsystem only (say without loss of generality), resulting in an appreciable reduction of computational resources, especially in case party comprises a much smaller number of modes than party .\n\n###### Theorem 5 (Simplified separability condition for an arbitrary QCM).\n\nA QCM of modes is separable if and only if there exists an -mode QCM such that\n\n VAB≥γA⊕iΩB. (0)\n\nIn terms of the block form (LABEL:V_explicit) of , when the above condition is equivalent to the existence of a real matrix satisfying\n\n iΩA≤γA≤VA−X(VB−iΩB)−1XT. (0)\n\nIf is not invertible, we require instead for all .\n\n###### Proof.\n\nSince both sets of QCMs defined by (LABEL:sep_eq) and (LABEL:simp_sep_1) are clearly topologically closed, we can just show without loss of generality that their interiors coincide. This latter condition can be rephrased as an equivalence between the two following statements: (i) for some QCMs ; and (ii) for some QCM .\n\nNow, once is fixed, the supremum of all the matrices satisfying is given by the Schur complement , as the variational characterisation (LABEL:variational) reveals. Therefore, statement (i) is equivalent to the existence of such that . This is the same as to require , as the positivity conditions of Lemma LABEL:pos_cond immediately show.\n\nUntil now, we have proven that the separability of can be restated as for some appropriate QCM . Employing Lemma LABEL:pos_cond, we see that this is turn equivalent to (LABEL:simp_sep_2), or to its -modified version when is not invertible. ∎\n\n###### Remark 1.\n\nIt has been recently observed Bhat16 () that condition (LABEL:simp_sep_2) is equivalent to the corresponding Gaussian state with QCM being completely extendable with Gaussian extensions. We remind the reader that a bipartite state is said to be completely extendable if for all there exists a state that is: (i) symmetric under exchange of any two systems; and (ii) an extension of in the sense that . When the original state is Gaussian, it is natural to consider extensions of Gaussian form as well. Interestingly enough, the above Theorem LABEL:simp_sep_lemma provides a simple alternative proof of the remarkable fact (also proven in Bhat16 ()) that Gaussian states are separable if and only if completely extendable with Gaussian extensions.\n\n###### Remark 2.\n\nIt is worth noticing that both Lemma LABEL:sep and Theorem LABEL:simp_sep_lemma extend straightforwardly to encompass the case of full separability of multipartite Gaussian states. In the case of Lemma LABEL:sep, this extension was already formulated in Werner01 (); 3-mode sep (). As for Theorem LABEL:simp_sep_lemma, the corresponding necessary and sufficient condition for the full separability of a -partite QCM would read for appropriate QCMs .\n\n\\@xsect\n\nWe now focus on investigating known and new conditions under which separability becomes equivalent to PPT for Gaussian states, so that the problem of deciding whether a given QCM is separable or not admits a handy formulation.\n\nFor any bipartite state , recall that the PPT criterion provides a useful necessary condition for separability Peres ():\n\n ρAB is separable  ⇒  ρTBAB≥0, (0)\n\nwhere the suffix denotes transposition with respect to the degrees of freedom of subsystem only. In finite-dimensional systems, PPT is also a sufficient condition for separability when H3 ().\n\nIn continuous variable systems, the PPT criterion turns out to be also sufficient for separability of QCMs when either or is composed of one mode only Simon00 (); Werner01 ().\n\n###### Theorem 6 (PPT is sufficient for Gaussian states of 1 vs n modes).\n\nLet be a bipartite QCM such that either or are composed of one mode only. Then is separable if and only if\n\n VAB≥(iΩA00±iΩB)=iΩA⊕(±iΩB), (0)\n\nwhich amounts to the corresponding Gaussian state being PPT, .\n\nFor completeness, we recall that the partial transpose of an -mode QCM (i.e., the covariance matrix of the partially transposed density operator ) is given by , where with respect to a mode-wise decomposition on the subsystem the matrix can be written as , with Simon00 (). Accordingly, we can say that the QCM is PPT if and only if is a valid QCM obeying (LABEL:Heisenberg), which is equivalent to (LABEL:PPT).\n\nThe original proof of Theorem LABEL:PPT_thm came in two steps. Firstly, Simon Simon00 () proved it in the particular case when both and are made of one mode only by performing an explicit analysis of the symplectic invariants of ; this seminal analysis is quite straightforward to follow and particularly instructive, but eventually a bit cumbersome, since it requires to distinguish between three cases, according to the sign of , where is the off-diagonal block of the QCM partitioned as in (LABEL:V_explicit). Later on, Werner and Wolf Werner01 () reduced the problem for the vs -mode case with arbitrary to the vs -mode case; the proof of this reduction is geometric in nature and rather elegant, but also relatively difficult.\n\nOur purpose in this Section is to use Schur complements to provide the reader with a simple, direct proof of Theorem LABEL:PPT_thm. Before coming to that, there is a preliminary lemma we want to discuss.\n\n###### Lemma 7.\n\nLet be hermitian matrices. There is a real symmetric matrix satisfying if and only if , where denotes complex conjugation.\n\n###### Proof.\n\nThe only complex entry in a hermitian matrix is in the off-diagonal element. Suppose without loss of generality that and (both conditions in the statement are in fact symmetric under complex conjugation of or ). It is easy to verify that a such that and always exists, and we see that is a real symmetric matrix. Moreover, since belongs to the segment joining and we conclude that . ∎\n\n###### Remark 3.\n\nLemma LABEL:2x2_interval admits an appealing physical interpretation which also leads to an intuitive proof. This interpretation is based on the fact that hermitian matrices can be seen as events in -dimensional Minkowski space-time through the correspondence . Furthermore, translates in Minkowski space-time to ‘ is in the absolute future of ’, since the remarkable determinantal identity holds true. Now, the complex conjugation at the matrix level becomes nothing but a spatial reflection with respect to a fixed spatial plane in Minkowski space-time. Thus, our original question is: is it true that whenever both an event and its spatial reflection are in the absolute future of a reference event then there is another event which is: (i) in the absolute future of ; (ii) in the absolute past of both and ; and (iii) lies right on the reflection plane? The answer is clearly yes, and there is a simple way to obtain it. Start from and shoot a photon to the location of that event between and that will happen on the other side of the reflection plane. After some time the photon hits the plane, and this event clearly satisfies all requirements.\n\nNow we are ready to give our direct proof of the equivalence between PPT and separability for vs -mode Gaussian states, leveraging the simplified separability condition of Theorem LABEL:simp_sep_lemma.\n\n###### Proof of Theorem LABEL:PPT_thm.\n\nSuppose without loss of generality that is composed of one mode only. As in the proof of Theorem LABEL:simp_sep_lemma, since both sets of QCMs defined by (LABEL:sep_eq) and (LABEL:PPT) are topologically closed, we can assume that is in the interior of the PPT set, i.e. that . Our goal will be to show that in this case belongs to the separable set, as characterized by Theorem LABEL:simp_sep_lemma. Since is taken to be invertible, the PPT condition reads\n\n VA−X(VB∓iΩB)−1XT≥iΩA.\n\nNow, define and , and observe that . Thanks to Lemma LABEL:2x2_interval, we can find a real matrix such that\n\n VA−X(VB∓iΩB)−1XT≥γA≥iΩA.\n\nChoosing the negative sign in the above inequality, we see that the second condition (LABEL:simp_sep_2) in Theorem LABEL:simp_sep_lemma is met, and therefore is separable. ∎\n\n\\@xsect\n\nAs a further example of application of Theorem LABEL:simp_sep_lemma, we study here the separability of a special class of PPT Gaussian states, i.e. those that are invariant under partial transposition of one of the subsystems. This problem has an analogue in finite-dimensional quantum information, already studied in sep 2xN (), where it was shown that bipartite states on that are invariant under partial transpose on the first system are necessarily separable.\\hyper@linkstartlink\\@currentHref-\\@mpfn.\\@textsuperscript0\\hyper@linkend\\hb@xt@1.8em\\@textsuperscript0The proof reported in sep 2xN () is rather long, so here we provide a shorter one, again based on Schur complements. A state on that is invariant under partial transposition on the first subsystem can be represented in block form as . By a continuity argument, we can suppose without loss of generality that . Rewrite . Both terms are positive by Lemma LABEL:pos_cond. Since the second one is separable, let us deal only with the first one, call it . We have , where is hermitian. Denoting by its spectral decomposition, we obtain the following manifestly separable representation of :\n\n\\@finalstrut\n\nHere we show that for Gaussian states an even stronger statement holds, in that invariance under partial transposition implies separability for any number of local modes.\n\n###### Corollary 8.\n\nA bipartite Gaussian state that is invariant under partial transposition of one of the two subsystems is necessarily separable.\n\n###### Proof.\n\nWithout loss of generality, we can assume that the partial transpose on the system leaves the state invariant. We now show that under the this assumption the separability condition (LABEL:simp_sep_2) is immediately satisfied, since the rightmost side is already a real, symmetric matrix. In fact, equating the original QCM (LABEL:V_explicit) with the one obtained after partial transpose on the system, we get the identities and , where, as previously set, according to a mode-wise decomposition of the system, and . As a consequence,\n\n X(VB−iΩB)−1XT=XΘB(VB−iΩB)−1ΘBXT=X(ΘB(VB−iΩB)ΘB)−1XT=X(VB+iΩB)−1XT,\n\nwhere we used also . This shows that is equal to its complex conjugate, and is therefore (despite appearances) a real symmetric matrix. Hence the separability condition (LABEL:simp_sep_2) is satisfied with . ∎\n\n\\@xsect\n\nThroughout this Section, we show how the PPT criterion is also necessary and sufficient for deciding the separability of bipartite Gaussian states of vs modes that are symmetric under the exchange of any two among the first modes. These states will be referred to as mono-symmetric (with respect to the first party ). As can be easily seen, this novel result (see Fig. LABEL:mononucleosi for a graphical visualisation) is a generalisation of both Theorem LABEL:PPT_thm and of one of the main results in Serafini05 (), where the subclass of bi-symmetric states was considered instead, bi-symmetric meaning that they are invariant under swapping any two modes either within the first or within the last (that is, they are mono-symmetric in both and ).\n\n###### Theorem 9 (Symplectic localisation of mono-symmetric states).\n\nLet be a mono-symmetric Gaussian state of modes, i.e. specified by a QCM that is symmetric under the exchange of any two of the modes of subsystem . Then there exists a local unitary operation on corresponding to a symplectic transformation that transforms into the tensor product of uncorrelated single-mode Gaussian states () and a bipartite Gaussian state of vs modes. At the QCM level, this reads\n\n (SA⊕\\mathds1B)VAB(STA⊕\\mathds1B)=(m⨁j=2~VAj)⊕~VA1B. (0)\n\nThe separability properties of and are equivalent, in particular is separable if and only if it is PPT.\n\n###### Proof.\n\nWe will prove (LABEL:monolocale) directly at the QCM level, by constructing a suitable local symplectic . By virtue of the symmetry under the exchange of any two modes of subsystem , if we decompose as in (LABEL:V_explicit), the submatrices and have the following structure:\n\n (0)\n\nwhere each one of the blocks in (LABEL:strucaz) is a real matrix, with and symmetric adescaling ().\n\nWe can now decompose the real space of the first modes as . According to this decomposition, we may rewrite and as follows:\n\n VA=\\mathds1m⊗(α−ε)+m|+⟩⟨+|⊗ε,X=√mn∑j=1|+⟩⟨j|⊗κj, (0)\n\nwhere , with denoting the standard basis for . Observe that the symplectic form on subsystem decomposes accordingly as . If is an orthogonal matrix such that , we easily see that on the one hand , i.e.  is symplectic, while on the other hand\n\n O⊗\\mathds12 VA OT⊗\\mathds12 (0) O⊗\\mathds12 X (0)\n\nTherefore, the initial QCM has been decomposed as a direct sum of one-mode QCMs , and of one -mode QCM , via a local symplectic operation on subsystem , given precisely by . This proves (LABEL:monolocale) constructively. Applying Theorem LABEL:PPT_thm, one then gets immediately that the PPT condition is necessary and sufficient for separability in this case. ∎\n\n###### Remark 4.\n\nThis original result yields a substantial enlargement to the domain of validity of PPT as a necessary and sufficient criterion for separability of multimode Gaussian states, reaching beyond any existing literature. In practice, Theorem LABEL:PPt_sym tells us that, in any mono-symmetric Gaussian state, all the correlations (including and beyond entanglement) shared among the whole modes of and the whole modes of can be localised onto correlations between a single mode of vs the whole , by means of a local unitary (symplectic at the QCM level) operation at ’s side only. Being unitary, this operation is fully reversible, meaning that the correlations with can be redistributed back and forth between and the whole set of modes with no information loss. This also means that quantitative results on any measure of such correlations between and encoded in can be conveniently evaluated in the much simpler vs -mode normal form constructed in the proof Theorem LABEL:PPt_sym, ignoring the uncorrelated modes.\n\nIn the special case of being the QCM of a bi-symmetric state, i.e. with full permutation symmetry within both and , it is immediate to observe that applying a similar construction by means of a local unitary at ’s side as well fully reduces to a two-mode QCM , with equivalent entanglement properties as the original , plus a collection of uncorrelated single modes. This reproduces the findings of Serafini05 ().\n\nSimilarly to what discussed in Remark LABEL:remulti, the results of Theorem LABEL:PPt_sym can also be straightforwardly extended to characterise full separability and, conversely, multipartite entanglement of arbitrary multimode Gaussian states which are partitioned into subsystems, with the requirement of local permutation invariance within some of these subsystems. It is clear that, by suitable local symplectic transformations, each of those locally symmetric parties can be localised onto a single mode correlated with the remaining parties, thus removing the redundancy in the QCM. Gaussian states of this sort generalise the so-called multi-symmetric states studied in moleculo (), where local permutation invariance was enforced within all of the subsystems, resulting in a direct multipartite analogue of bi-symmetric states.\n\n\\@xsect\n\nIt is well known that the PPT criterion is in general sufficient, as well as obviously necessary, for pure bipartite states to be separable Peres (). This may be seen by a direct inspection of the Schmidt decomposition of a pure state. Let us note, incidentally, that a stronger statement holds, namely any bound entangled state (in any dimension) must have at least rank chen08 ().\n\nThe Schmidt decomposition theorem is in fact so important that a Gaussian version of it, that is, the determination of a normal form of pure QCMs under local symplectic operations, is of central importance in continuous variable quantum information. As can be shown at the covariance matrix level holwer (); giedkemode () or at the density operator level botero03 (), every pure bipartite Gaussian state can be brought into a tensor product of two-mode squeezed vacuum states and single-mode vacuum states by means of local unitaries with respect to the vs partition. In particular, by acting correspondingly with local symplectic transformations, any pure QCM (where pure means ) can be transformed into a direct sum of (pure) two-mode squeezed vacuum QCMs and (pure) single-mode vacuum QCMs. More precisely, at the level of QCMs, one can formulate this fundamental result as follows.\n\n###### Theorem 10 (Mode-wise decomposition of pure Gaussian states holwer (); botero03 (); giedkemode ()).\n\nLet be a bipartite QCM of modes , assuming (with no loss of generality). If is a pure QCM, i.e. all its symplectic eigenvalues are equal to (which amounts to ), then there exist local symplectic transformations , mapping into the following normal form:\n\n (SA⊕SB)VAB(STA⊕STB)=m⨁j=1¯VAjBj(rj)⊕n⨁k=m+1\\mathds1Bk, (0)\n\nwhere with and , for a real squeezing parameter , is the pure QCM of a two-mode squeezed vacuum state of modes and , and is the pure QCM of the single-mode vacuum state of mode . In particular, with respect to the block form (LABEL:V_explicit), for any pure QCM the marginal QCMs and have matching symplectic spectra, given by and .\n\nLeaving apart its far-reaching applications, in the context of the present paper this result is mainly instrumental for assessing the separability of so-called isotropic multimode Gaussian states. The QCM of any such state of modes is characterised by the property of having a completely degenerate symplectic spectrum, i.e. formed of only one distinct symplectic eigenvalue (repeated times). This means that the QCM of any isotropic state is proportional by a factor to a pure QCM. Hence, Theorem LABEL:mode-wise_thm tells us that can be brought into a direct sum of two-mode QCMs via a local symplectic congruence (local with respect to any partition into groups of modes and ), as first observed in holwer (). Thanks to Theorem LABEL:PPT_thm, this guarantees the following.\n\n###### Theorem 11.\n\nThe PPT criterion is necessary and sufficient for separability of all isotropic Gaussian states of an arbitrary number of modes.\n\nHowever, notwithstanding the importance of Theorem LABEL:mode-wise per se, one could strive to seek a more direct way to obtain Theorem LABEL:iso_thm. Our purpose in this Section is in fact to provide an alternative proof of this result, which does not appeal to the mode-wise decomposition theorem at all, and uses directly Lemma LABEL:sep instead, leveraging matrix analysis tools such as the notions of matrix means introduced in Section LABEL:secMM.\n\nNote that, in almost all the remainder of this Section, for a single system of modes, we will find it more convenient to reorder the vector of canonical operators as , corresponding to a position-momentum block structure. The symplectic form appearing in (LABEL:CCR) is accordingly rewritten as\n\n Ω\\vbox\\scriptsize.\\scriptsize.=(0\\mathds1−\\mathds10). (0)\n\nWe will then write any QCM , as well as any symplectic operation acting on it, with respect to this alternative block structure, unless explicitly stated otherwise.\n\nLet us start with a preliminary result, equivalent to Proposition 12 of manuceau () or Lemma 13 of Lami16 (). We include a proof for the sake of completeness.\n\n###### Lemma 12.\n\nLet be a positive matrix. Then is a pure QCM if and only if , and it obeys (LABEL:Heisenberg) if and only if\n\n V≥V#(ΩTV−1Ω). (0)\n###### Proof.\n\nLet the Williamson form of be given by (LABEL:Williamson), where (in the convention of this Section) , with . Then we can write\n\n ΩTV−1Ω=ΩTS−T(Λ−1⊕Λ−1)S−1Ω=SΩT(Λ−1⊕Λ−1)ΩST=S(Λ−1⊕Λ−1)ΩTΩST=S(Λ−1⊕Λ−1)ST,\n\nwhere we used in order: (i) the identities , , all consequences of the defining symplectic identity ; (ii) the fact that commutes with ; and (iii) the orthogonality relation . Now the first claim becomes obvious, since if and only if is a pure QCM. In general, as it can be seen from the above expression, and are brought in Williamson form by simultaneous congruences with the same symplectic matrix . Hence, the covariance of the geometric mean under congruence ensures that\n\n V#(ΩV−1ΩT)=(S(Λ00Λ)ST)#(S(Λ−100Λ−1)ST)=S((Λ00Λ)#(Λ−100Λ−1))ST=SST,\n\nwhere the last passage is an easy consequence of the fact that for all . By comparison with (LABEL:Williamson), we see that the Heisenberg uncertainty relation can be rephrased as , which reproduces (LABEL:WalterWhite), proving the second claim. ∎\n\n###### Remark 5.\n\nFrom the above proof it is also apparent how, for any positive , the matrix is a pure QCM (independently of the nature of ).\n\nNow we are ready to explain our direct argument to show separability of PPT isotropic Gaussian states, alternative to the use of the mode-wise decomposition.\n\n###### Proof of Theorem LABEL:iso_thm.\n\nWe start by rewriting the PPT condition (LABEL:PPT) for a QCM as\n\n ΘBVΘB,≥iΩ,\n\nwhere in the convention of this Section . Thanks to Lemma LABEL:QCM_geom_lemma, this becomes in turn\n\n ΘBVΘB≥(ΘBVΘB)#(ΩΘBV−1ΘBΩT)\n\nand finally\n\n V≥V#(ΘBΩΘBV−1ΘBΩTΘB)=(gV)#(ZΩ(gV)−1ΩTZ)\n\nafter conjugating by , applying once more the covariance of the geometric mean under congruences, introducing a real parameter (to be fixed later), and defining . Now, we apply Lemma LABEL:lemma_ha=g to the above expression, obtaining\n\n V≥(gV+ZΩ(gV)−1ΩTZ2)#((gV)!(ZΩ(gV)−1ΩTZ))\n\nAlthough it is not yet transparent, we are done, as the right-hand side of the above inequality is exactly of the form when is the QCM of an isotropic Gaussian state. In fact, let be such that is a pure QCM, satisfying , where we have now reverted to a block decomposition with respect to the vs splitting. Then on the one hand since we find\n\n gV+ZΩ(gV)−1ΩTZ2=(P00Q),\n\nwhile on the other hand\n\n (gV)!(ZΩ(gV)−1ΩTZ) =2((gV)−1+ZΩ(gV)ΩTZ)−1=2Ω(Ω(gV)−1ΩT+Z(gV)Z)−1ΩT=\n\nwhere we used the definition (LABEL:harmonic) of harmonic mean and the fact that . Putting all together, we find\n\n V≥(P00Q)#(ΩP−1ΩT00ΩQ−1ΩT)=(P#ΩP−1ΩT00Q#ΩQ−1ΩT)=γA⊕γB.\n\nSince we already observed that is a QCM for any (and analogously for ), a direct invocation of Lemma LABEL:sep allows us to conclude the proof. ∎\n\n\\@xsect\n\nThroughout this Section, we finally complete the solution of a problem posed in passive () and there addressed under some additional constraints. Let us start by recalling that symplectic operations can be divided into two main categories, namely those such as squeezers that require an exchange of energy between the system and the apparatus, called active, and those that can be implemented using only beam splitters and phase plates, called passive. A symplectic matrix represents a passive transformation if and only if it is also orthogonal, meaning that (it may be worth adding that symplectic orthogonal transformations form the maximal compact subgroup of the symplectic group). As it turns out, symplectic orthogonal matrices can be represented in an especially simple form if we resort to a position-momentum block decomposition. Namely, one has the parametrisation bucco ()\n\n K=W†(UU∗)W, (0)\n\nwhere\n\n W\\vbox\\scriptsize.\\scriptsize.=1√2(\\mathds1i\\mathds1\\mathds1−i\\mathds1)\n\nand is a generic, unitary matrix, with denoting its complex conjugate.\n\nSince the implementation of passive operations is so inexpensive in quantum optics and entangled states so useful for quantum technologies, the question first posed in passive () was a natural one: “What bipartite Gaussian states are such that they can be entangled via a global, passive operation?” However, in this full generality the problem was left unanswered in passive (). Instead, another related question was investigated and answered there, namely whether distillable Gaussian entanglement can be produced in the same fashion. For Gaussian states, as mentioned in the Introduction, distillability is well known to be equivalent to non-positivity of the partial transpose Giedke01 (); GiedkeQIC (), so the authors of passive () proceeded to identify the class of Gaussian states that can be made PPT with a passive transformation. However, it is important to realise that since PPT and separability are not the same for general multimode Gaussian states, the two questions are a priori different. Here we show that the answer to the original question above turns out to be yet another situation where the PPT condition is necessary and sufficient to ensure separability of Gaussian states. In other words, we will prove that a bipartite Gaussian state that cannot be made distillable (i.e. non-PPT) via passive operations is necessarily separable, and thus it stays separable under the application of said passive operations. Let us start with a technical lemma that we deduce from recent results obtained in bhatia15 ()." ]
[ null, "https://storage.googleapis.com/groundai-web-prod/media%2Fusers%2Fuser_38794%2Fproject_40243%2Fimages%2Fx1.png", null ]
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https://www.tutorialspoint.com/datetime-subtract-method-in-chash
[ "# DateTime.Subtract() Method in C#\n\nCsharpServer Side ProgrammingProgramming\n\nThe DateTime.Subtract() method in C# is used to subtract the specified DateTime or span.\n\n## Syntax\n\nFollowing is the syntax −\n\npublic TimeSpan Subtract (DateTime value);\npublic DateTime Subtract (TimeSpan value);\n\n## Example\n\nLet us now see an example to implement the DateTime.Subtract() method −\n\nusing System;\npublic class Demo {\npublic static void Main() {\nDateTime d1 = new DateTime(2019, 10, 10, 8, 10, 40);\nDateTime d2 = new DateTime(2017, 11, 06, 8, 10, 40);\nConsole.WriteLine(\"Date 1 = \"+d1);\nConsole.WriteLine(\"Date 2 = \"+d2);\nTimeSpan res = d1.Subtract(d2);\nConsole.WriteLine(\"TimeSpan between two dates = {0} \",res);\n}\n}\n\n## Output\n\nThis will produce the following output −\n\nDate 1 = 10/10/2019 8:10:40 AM\nDate 2 = 11/6/2017 8:10:40 AM\nTimeSpan between two dates = 703.00:00:00\n\n## Example\n\nLet us now see another example to implement the DateTime.Subtract() method −\n\nusing System;\npublic class Demo {\npublic static void Main() {\nDateTime d = new DateTime(2019, 10, 10, 8, 10, 40);\nTimeSpan t = new TimeSpan(1, 10, 10, 12);\nConsole.WriteLine(\"Date = \"+d);\nDateTime res = d.Subtract(t);\nConsole.WriteLine(\"DateTime between date d and timespan t = {0} \",res);\n}\n}\n\n## Output\n\nThis will produce the following output −\n\nDate = 10/10/2019 8:10:40 AM\nDateTime between date d and timespan t = 10/8/2019 10:00:28 PM" ]
[ null ]
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https://metanumbers.com/26395
[ "## 26395\n\n26,395 (twenty-six thousand three hundred ninety-five) is an odd five-digits composite number following 26394 and preceding 26396. In scientific notation, it is written as 2.6395 × 104. The sum of its digits is 25. It has a total of 2 prime factors and 4 positive divisors. There are 21,112 positive integers (up to 26395) that are relatively prime to 26395.\n\n## Basic properties\n\n• Is Prime? No\n• Number parity Odd\n• Number length 5\n• Sum of Digits 25\n• Digital Root 7\n\n## Name\n\nShort name 26 thousand 395 twenty-six thousand three hundred ninety-five\n\n## Notation\n\nScientific notation 2.6395 × 104 26.395 × 103\n\n## Prime Factorization of 26395\n\nPrime Factorization 5 × 5279\n\nComposite number\nDistinct Factors Total Factors Radical ω(n) 2 Total number of distinct prime factors Ω(n) 2 Total number of prime factors rad(n) 26395 Product of the distinct prime numbers λ(n) 1 Returns the parity of Ω(n), such that λ(n) = (-1)Ω(n) μ(n) 1 Returns: 1, if n has an even number of prime factors (and is square free) −1, if n has an odd number of prime factors (and is square free) 0, if n has a squared prime factor Λ(n) 0 Returns log(p) if n is a power pk of any prime p (for any k >= 1), else returns 0\n\nThe prime factorization of 26,395 is 5 × 5279. Since it has a total of 2 prime factors, 26,395 is a composite number.\n\n## Divisors of 26395\n\n1, 5, 5279, 26395\n\n4 divisors\n\n Even divisors 0 4 2 2\nTotal Divisors Sum of Divisors Aliquot Sum τ(n) 4 Total number of the positive divisors of n σ(n) 31680 Sum of all the positive divisors of n s(n) 5285 Sum of the proper positive divisors of n A(n) 7920 Returns the sum of divisors (σ(n)) divided by the total number of divisors (τ(n)) G(n) 162.465 Returns the nth root of the product of n divisors H(n) 3.3327 Returns the total number of divisors (τ(n)) divided by the sum of the reciprocal of each divisors\n\nThe number 26,395 can be divided by 4 positive divisors (out of which 0 are even, and 4 are odd). The sum of these divisors (counting 26,395) is 31,680, the average is 7,920.\n\n## Other Arithmetic Functions (n = 26395)\n\n1 φ(n) n\nEuler Totient Carmichael Lambda Prime Pi φ(n) 21112 Total number of positive integers not greater than n that are coprime to n λ(n) 10556 Smallest positive number such that aλ(n) ≡ 1 (mod n) for all a coprime to n π(n) ≈ 2899 Total number of primes less than or equal to n r2(n) 0 The number of ways n can be represented as the sum of 2 squares\n\nThere are 21,112 positive integers (less than 26,395) that are coprime with 26,395. And there are approximately 2,899 prime numbers less than or equal to 26,395.\n\n## Divisibility of 26395\n\n m n mod m 2 3 4 5 6 7 8 9 1 1 3 0 1 5 3 7\n\nThe number 26,395 is divisible by 5.\n\n## Classification of 26395\n\n• Arithmetic\n• Semiprime\n• Deficient\n\n• Polite\n\n• Square Free\n\n### Other numbers\n\n• LucasCarmichael\n\n## Base conversion (26395)\n\nBase System Value\n2 Binary 110011100011011\n3 Ternary 1100012121\n4 Quaternary 12130123\n5 Quinary 1321040\n6 Senary 322111\n8 Octal 63433\n10 Decimal 26395\n12 Duodecimal 13337\n20 Vigesimal 35jf\n36 Base36 kd7\n\n## Basic calculations (n = 26395)\n\n### Multiplication\n\nn×i\n n×2 52790 79185 105580 131975\n\n### Division\n\nni\n n⁄2 13197.5 8798.33 6598.75 5279\n\n### Exponentiation\n\nni\n n2 696696025 18389291579875 485385351250800625 12811746346264882496875\n\n### Nth Root\n\ni√n\n 2√n 162.465 29.7742 12.7462 7.66133\n\n## 26395 as geometric shapes\n\n### Circle\n\n Diameter 52790 165845 2.18874e+09\n\n### Sphere\n\n Volume 7.70289e+13 8.75494e+09 165845\n\n### Square\n\nLength = n\n Perimeter 105580 6.96696e+08 37328.2\n\n### Cube\n\nLength = n\n Surface area 4.18018e+09 1.83893e+13 45717.5\n\n### Equilateral Triangle\n\nLength = n\n Perimeter 79185 3.01678e+08 22858.7\n\n### Triangular Pyramid\n\nLength = n\n Surface area 1.20671e+09 2.1672e+12 21551.4" ]
[ null ]
{"ft_lang_label":"__label__en","ft_lang_prob":0.61443925,"math_prob":0.9909578,"size":4519,"snap":"2020-34-2020-40","text_gpt3_token_len":1592,"char_repetition_ratio":0.12026578,"word_repetition_ratio":0.02827381,"special_character_ratio":0.44921443,"punctuation_ratio":0.07522698,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9985756,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-09-28T08:18:29Z\",\"WARC-Record-ID\":\"<urn:uuid:8a477f45-5181-4e11-93d6-a526c94f22e9>\",\"Content-Length\":\"48188\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:70daa9eb-0e61-4d44-8f3c-0dccc69c2d32>\",\"WARC-Concurrent-To\":\"<urn:uuid:510a9f32-f176-42a3-a2d6-e342b864be1a>\",\"WARC-IP-Address\":\"46.105.53.190\",\"WARC-Target-URI\":\"https://metanumbers.com/26395\",\"WARC-Payload-Digest\":\"sha1:IZ4Y67D6A7IWIWB2WQWB24OM65RI67YH\",\"WARC-Block-Digest\":\"sha1:674OQNTKAYHILMJUUKLWJZSODMA7XJJS\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-40/CC-MAIN-2020-40_segments_1600401598891.71_warc_CC-MAIN-20200928073028-20200928103028-00292.warc.gz\"}"}
http://blade.nagaokaut.ac.jp/cgi-bin/scat.rb/ruby/ruby-talk/77823
[ "```\"Josef 'Jupp' Schugt\" <jupp / gmx.de> wrote:\n>\n> [...] Even the most trivial computations are\n> nontrivial when one has a closer look at them:\n>\n> 1.upto(16) { |i|\n> puts 1.0 + (0.1 ** i) - 1.0 - (0.1 ** i)\n> }\n>\n> on my machine results in:\n>\n> 8.32667268468867e-17\n> [snipped some]\n> -1 e-16\n>\n> The mathematical results of course all are 0.\n>\n> Josef 'Jupp' Schugt\n>\n\nJust trollin', but is it right that Float#to_f\nshould be a no-op when it could have saved\ndoing 'to_s.to_f' (or other) below ?:\n\nexpect = [ nil,\n8.32667268468867e-17,\n6.93889390390723e-18,\n-1.10371781159024e-16,\n-1.10317571050400e-17,\n6.55095281406476e-17,\n]\n\n1.upto(5) do |i|\nans = 1.0 + (0.1 ** i) - 1.0 - (0.1 ** i)\nunless ans == expect[i]\np [ans, expect[i]]\nputs 'Oops' unless Float === ans and Float === expect[i]\nif ans.to_s.to_f == expect[i] # <<----#####\n# ans.to_f short-circuits (just returns self)\nputs \"Not equal but equal\"; puts\nend\nend\nend\n\n#-> [8.32667268468867e-17, 8.32667268468867e-17]\n#-> Not equal but equal\n#->\n#-> [6.93889390390723e-18, 6.93889390390723e-18]\n#-> Not equal but equal\n#->\n#-> [-1.10371781159024e-16, -1.10371781159024e-16]\n#-> Not equal but equal\n#->\n#-> [-1.103175710504e-17, -1.103175710504e-17]\n#-> Not equal but equal\n#->\n#-> [6.55095281406476e-17, 6.55095281406476e-17]\n#-> Not equal but equal\n\ndaz\n\n```" ]
[ null ]
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https://www.excelmadeeasy.com/excel-calculation-table-generator-school.php
[ "## Math worksheet to learn basic operations\n\nMath is an important topic to learn and teaching it well takes time. We provide you here with some help with an excel sheet that can generate worksheet for training your kid at home or your pupils at school. It can also be a math quiz or math test for your students.\n\nThis math calculation worksheet is made of three parts.", null, "Part one is the Generator. It create the calculation table in Excel.\n\nPart 2 is the Exercise Table and part 3 is the printablemath worksheet.", null, "You first select in the math calculation worksheet the boundaries. Like numbers between 1 and 10 or numbers between 10 and 100 or 10 and 20, etc… this depends on the current abilities of the students.\n\nThen select the operation: if your students only know basic operation like addition, then just select the “plus” by entering OK in the plus blue cell and leave the other one empty. If you want to use also subtraction or multiplication or division then add OK next these.\n\nThis will create per default 40 operations. To use it, copy the green area into the next sheet by only copying the text as explained in the sheet or on this page “how to convert a formula to text”.", null, "To finally print it out, use the 3rd sheet that will let you print out the full exercise.", null, "We hope you like our calculation worksheet for first, second graders and for you if you want to train bigger numbers head calculation." ]
[ null, "https://www.excelmadeeasy.com/images/image-excel-math-worksheet-kids-grade2.png", null, "https://www.excelmadeeasy.com/images/image-excel-math-worksheet-kids-grade1.png", null, "https://www.excelmadeeasy.com/images/image-excel-math-worksheet-kids-grade3.png", null, "https://www.excelmadeeasy.com/images/image-excel-math-worksheet-kids-grade4.png", null ]
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https://dgtal.org/doc/1.3/testLabels_8cpp.html
[ "DGtal 1.3.0\nSearching...\nNo Matches\ntestLabels.cpp File Reference\n#include <cstdio>\n#include <cmath>\n#include <iostream>\n#include <algorithm>\n#include <vector>\n#include <bitset>\n#include \"DGtal/base/Common.h\"\n#include \"DGtal/base/Labels.h\"\n\nGo to the source code of this file.\n\n## Functions\n\ntemplate<typename Container1 , typename Container2 >\nbool isEqual (Container1 &c1, Container2 &c2)\n\ntemplate<typename VContainer1 , typename LContainer2 >\nvoid insert (VContainer1 &c1, LContainer2 &c2, unsigned int idx)\n\ntemplate<typename VContainer1 , typename LContainer2 >\nbool checkInsert (VContainer1 &v, LContainer2 &l, unsigned int nb)\n\ntemplate<typename VContainer1 , typename LContainer2 >\nvoid erase (VContainer1 &c1, LContainer2 &c2, unsigned int idx)\n\ntemplate<typename VContainer1 , typename LContainer2 >\nbool checkErase (VContainer1 &v, LContainer2 &l, unsigned int nb)\n\nint main ()\n\n## Detailed Description\n\nThis program is free software: you can redistribute it and/or modify it under the terms of the GNU Lesser General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version.\n\nThis program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.\n\nYou should have received a copy of the GNU General Public License along with this program. If not, see http://www.gnu.org/licenses/.\n\nDate\n2012/07/02\n\nThis file is part of the DGtal library\n\nDefinition in file testLabels.cpp.\n\n## ◆ checkErase()\n\ntemplate<typename VContainer1 , typename LContainer2 >\n bool checkErase ( VContainer1 & v, LContainer2 & l, unsigned int nb )\n\nDefinition at line 88 of file testLabels.cpp.\n\n90{\n91 for ( unsigned int i = 0; i < nb; ++i )\n92 {\n93 unsigned int idx = rand() % ( l.size() );\n94 erase( v, l, idx );\n95 }\n96 return isEqual( v, l );\n97}\nvoid erase(VContainer1 &c1, LContainer2 &c2, unsigned int idx)\nDefinition: testLabels.cpp:80\nbool isEqual(Container1 &c1, Container2 &c2)\nDefinition: testLabels.cpp:45\n\nReferences erase(), and isEqual().\n\nReferenced by main().\n\n## ◆ checkInsert()\n\ntemplate<typename VContainer1 , typename LContainer2 >\n bool checkInsert ( VContainer1 & v, LContainer2 & l, unsigned int nb )\n\nDefinition at line 68 of file testLabels.cpp.\n\n70{\n71 for ( unsigned int i = 0; i < nb; ++i )\n72 {\n73 unsigned int idx = rand() % ( l.size() );\n74 insert( v, l, idx );\n75 }\n76 return isEqual( v, l );\n77}\nvoid insert(VContainer1 &c1, LContainer2 &c2, unsigned int idx)\nDefinition: testLabels.cpp:60\n\nReferences insert(), and isEqual().\n\nReferenced by main().\n\n## ◆ erase()\n\ntemplate<typename VContainer1 , typename LContainer2 >\n void erase ( VContainer1 & c1, LContainer2 & c2, unsigned int idx )\n\nDefinition at line 80 of file testLabels.cpp.\n\n81{\n82 c1.reset( idx );\n83 c2.reset( idx );\n84}\n\nReferenced by checkErase(), and main().\n\n## ◆ insert()\n\ntemplate<typename VContainer1 , typename LContainer2 >\n void insert ( VContainer1 & c1, LContainer2 & c2, unsigned int idx )\n\nDefinition at line 60 of file testLabels.cpp.\n\n61{\n62 c1.set( idx );\n63 c2.set( idx );\n64}\n\nReferenced by checkInsert(), and main().\n\n## ◆ isEqual()\n\ntemplate<typename Container1 , typename Container2 >\n bool isEqual ( Container1 & c1, Container2 & c2 )\n\nDefinition at line 45 of file testLabels.cpp.\n\n46{\n47 if ( c1.size() == c2.size() )\n48 {\n49 for ( unsigned int i = 0; i < c1.size(); ++i )\n50 {\n51 if ( c1.test( i ) != c2.test( i ) )\n52 return false;\n53 }\n54 return true;\n55 }\n56 return false;\n57}\n\nReferenced by checkErase(), checkInsert(), and main().\n\n## ◆ main()\n\n int main ( void )\n\nDefinition at line 100 of file testLabels.cpp.\n\n101{\n102 typedef Labels<80, DGtal::uint32_t> MyLabels;\n103 typedef MyLabels::ConstIterator LabelsConstIterator;\n104 typedef std::bitset<80> MyBitset;\n105\n106 BOOST_CONCEPT_ASSERT(( boost::ForwardIterator< LabelsConstIterator > ));\n107\n108 unsigned int nb = 0;\n109 unsigned int nbok = 0;\n110 trace.beginBlock ( \"Testing Labels\" );\n111 MyLabels l;\n112 MyBitset v;\n113 ++nb; nbok += isEqual( v, l ) ? 1 : 0;\n114 std::cout << \"(\" << nbok << \"/\" << nb << \") l=\" << l << std::endl;\n115 insert( v, l, 15 );\n116 insert( v, l, 4 );\n117 ++nb; nbok += isEqual( v, l ) ? 1 : 0;\n118 std::cout << \"(\" << nbok << \"/\" << nb << \") l=\" << l << std::endl;\n119 insert( v, l, 62 );\n120 insert( v, l, 4 );\n121 insert( v, l, 78 );\n122 insert( v, l, 31 );\n123 insert( v, l, 32 );\n124 ++nb; nbok += isEqual( v, l ) ? 1 : 0;\n125 std::cout << \"(\" << nbok << \"/\" << nb << \") l=\" << l << std::endl;\n126 checkInsert( v, l, 40 );\n127 ++nb; nbok += isEqual( v, l ) ? 1 : 0;\n128 std::cout << \"(\" << nbok << \"/\" << nb << \") l=\" << l << std::endl;\n129 checkErase( v, l, 200 );\n130 ++nb; nbok += isEqual( v, l ) ? 1 : 0;\n131 std::cout << \"(\" << nbok << \"/\" << nb << \") l=\" << l << std::endl;\n132 for ( LabelsConstIterator it = l.begin(), it_end = l.end();\n133 it != it_end; ++it )\n134 std::cout << \" \" << *it;\n135 std::cout << std::endl;\n136\n137 trace.endBlock();\n138\n139 // Test related to pull request #971 & #972\n140 typedef Labels<32, DGtal::uint32_t> MySmallLabels;\n141 typedef MySmallLabels::ConstIterator SmallLabelsConstIterator;\n142 typedef std::bitset<32> MySmallBitset;\n143\n144 trace.beginBlock ( \"Testing one word long Labels\" );\n145 MySmallLabels ll;\n146 MySmallBitset vv;\n147\n148 ++nb; nbok += isEqual( vv, ll ) ? 1 : 0;\n149 std::cout << \"(\" << nbok << \"/\" << nb << \") small_l=\" << ll << std::endl;\n150\n151 insert( vv, ll, 15 );\n152 insert( vv, ll, 4 );\n153 insert( vv, ll, 31 );\n154 ++nb; nbok += isEqual( vv, ll ) ? 1 : 0;\n155 std::cout << \"(\" << nbok << \"/\" << nb << \") small_l=\" << ll << std::endl;\n156\n157 erase( vv, ll, 15 );\n158 ++nb; nbok += isEqual( vv, ll ) ? 1 : 0;\n159 std::cout << \"(\" << nbok << \"/\" << nb << \") small_l=\" << ll << std::endl;\n160\n161 // Check insertion at index 0\n162 insert( vv, ll, 0 );\n163 ++nb; nbok += isEqual( vv, ll ) ? 1 : 0;\n164 std::cout << \"(\" << nbok << \"/\" << nb << \") small_l=\" << ll << std::endl;\n165\n166 // Check bit count computation\n167 ++nb; nbok += ll.count() == 3 ? 1 : 0;\n168 std::cout << \"(\" << nbok << \"/\" << nb << \") small_l.count()=\" << ll.count() << std::endl;\n169\n170 // Compare with size computed with iterators\n171 unsigned int cnt = 0;\n172 for ( SmallLabelsConstIterator it = ll.begin(), it_end = ll.end(); it != it_end; ++cnt, ++it) {}\n173 ++nb; nbok += cnt == 3 ? 1 : 0;\n174 std::cout << \"(\" << nbok << \"/\" << nb << \") small_l bit count with iterators=\" << cnt << std::endl;\n175\n176 trace.endBlock();\n177\n178 return ( nb == nbok ) ? 0 : 1;\n179}\nAim: Stores a set of labels in {O..L-1} as a sequence of bits.\nDefinition: Labels.h:72\nvoid beginBlock(const std::string &keyword=\"\")\ndouble endBlock()\nTrace trace\nDefinition: Common.h:154\nGo to http://www.sgi.com/tech/stl/ForwardIterator.html.\nDefinition: Boost.dox:40\nbool checkInsert(VContainer1 &v, LContainer2 &l, unsigned int nb)\nDefinition: testLabels.cpp:68\nbool checkErase(VContainer1 &v, LContainer2 &l, unsigned int nb)\nDefinition: testLabels.cpp:88" ]
[ null ]
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https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Book%3A_Quantum_States_of_Atoms_and_Molecules_(Zielinksi_et_al)/06%3A_Vibrational_States/6.0S%3A_6.S%3A_Vibrational_States_(Summary)
[ "# 6.S: Vibrational States (Summary)\n\nIn this chapter we developed the quantum mechanical description of the harmonic oscillator for a diatomic molecule and applied it to the normal modes of molecular vibrations. We examined the functional form of the wavefunctions and the associated energy level structure. We can calculate expectation values (average values) and standard deviations for the displacement, the momentum, the square of the displacement, and the square of the momentum. The wavefunctions, which form an orthonormal set, were used to determine electric dipole selection rules for spectroscopic transitions, and in the problems at the end of the chapter, they are used to calculate several properties of the harmonic oscillator. The phenomenon of quantum mechanical tunneling through a potential-energy barrier was introduced and its relationship to real chemical phenomena was illustrated by consideration of hydrogen bonding in DNA. We finally looked at the nature of low-resolution IR spectra and introduced the anharmonicity concept to account for forbidden overtone transitions in spectra. The presence of combination bands in spectra was attributed to second derivative terms in the expansion of the dipole moment operator in terms of the normal coordinates. The simple harmonic oscillator model works well for molecules at room temperature because the molecules are in the lower vibrational levels where the effects of anharmonicity are small.\n\nSelf-Assessment Quiz\n\n1. Write a definition of a normal vibrational mode.\n2. Write a definition of a normal vibrational coordinate.\n3. List the steps in a methodology for finding the normal vibrational coordinates and frequencies.\n4. What is a harmonic oscillator?\n5. How is the harmonic oscillator relevant to molecular properties?\n6. Write the Hamiltonian operator for a one-dimensional harmonic oscillator.\n7. What are the major steps in the procedure to solve the Schrödinger equation for the harmonic oscillator?\n8. What are the three parts of a harmonic oscillator wavefunction?\n9. How is the quantum number v produced in solving the Schrödinger equation for the harmonic oscillator?\n10. What are the allowed energies for a quantum harmonic oscillator?\n11. What determines the frequency of a quantum harmonic oscillator?\n12. What information about a molecular vibration is provided by the harmonic oscillator wavefunction for a normal coordinate?\n13. Sketch graphs of the harmonic oscillator potential energy and a few wavefunctions.\n14. Draw the harmonic oscillator energy level diagram.\n15. Why is the lowest possible energy of the quantum oscillator not zero?\n16. Compute the approximate energy for the first overtone transition in HBr given that the fundamental is 2564 cm-1.\n17. If a transition from vibrational energy level v = 3 to v = 4 were observed in an infrared spectrum, where would that spectral line appear relative to the one for the transition from v = 0 to v = 1?\n18. What is the harmonic oscillator selection rule for vibrational excitation by infrared radiation?\n19. Explain why the infrared absorption coefficient is larger for some normal modes than for others.\n20. Why is it possible for quantum particles to tunnel through potential barriers?\n21. What are the values of integrals like $$\\int \\limits _{-\\infty}^{\\infty} \\psi ^*_n (Q) \\psi _m (Q) dQ$$ using harmonic oscillator wavefunctions?" ]
[ null ]
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http://isabelle.in.tum.de/repos/isabelle/file/f7333f055ef6/src/HOL/Isar_examples/BasicLogic.thy
[ "src/HOL/Isar_examples/BasicLogic.thy\n author oheimb Wed Jan 31 10:15:55 2001 +0100 (2001-01-31) changeset 11008 f7333f055ef6 parent 10636 d1efa59ea259 child 12387 fe2353a8d1e8 permissions -rw-r--r--\nimproved theory reference in comment\n 1 (* Title: HOL/Isar_examples/BasicLogic.thy\n\n 2 ID: $Id$\n\n 3 Author: Markus Wenzel, TU Muenchen\n\n 4\n\n 5 Basic propositional and quantifier reasoning.\n\n 6 *)\n\n 7\n\n 8 header {* Basic logical reasoning *}\n\n 9\n\n 10 theory BasicLogic = Main:\n\n 11\n\n 12\n\n 13 subsection {* Pure backward reasoning *}\n\n 14\n\n 15 text {*\n\n 16 In order to get a first idea of how Isabelle/Isar proof documents may\n\n 17 look like, we consider the propositions $I$, $K$, and $S$. The\n\n 18 following (rather explicit) proofs should require little extra\n\n 19 explanations.\n\n 20 *}\n\n 21\n\n 22 lemma I: \"A --> A\"\n\n 23 proof\n\n 24 assume A\n\n 25 show A by assumption\n\n 26 qed\n\n 27\n\n 28 lemma K: \"A --> B --> A\"\n\n 29 proof\n\n 30 assume A\n\n 31 show \"B --> A\"\n\n 32 proof\n\n 33 show A by assumption\n\n 34 qed\n\n 35 qed\n\n 36\n\n 37 lemma S: \"(A --> B --> C) --> (A --> B) --> A --> C\"\n\n 38 proof\n\n 39 assume \"A --> B --> C\"\n\n 40 show \"(A --> B) --> A --> C\"\n\n 41 proof\n\n 42 assume \"A --> B\"\n\n 43 show \"A --> C\"\n\n 44 proof\n\n 45 assume A\n\n 46 show C\n\n 47 proof (rule mp)\n\n 48 \tshow \"B --> C\" by (rule mp)\n\n 49 show B by (rule mp)\n\n 50 qed\n\n 51 qed\n\n 52 qed\n\n 53 qed\n\n 54\n\n 55 text {*\n\n 56 Isar provides several ways to fine-tune the reasoning, avoiding\n\n 57 excessive detail. Several abbreviated language elements are\n\n 58 available, enabling the writer to express proofs in a more concise\n\n 59 way, even without referring to any automated proof tools yet.\n\n 60\n\n 61 First of all, proof by assumption may be abbreviated as a single dot.\n\n 62 *}\n\n 63\n\n 64 lemma \"A --> A\"\n\n 65 proof\n\n 66 assume A\n\n 67 show A .\n\n 68 qed\n\n 69\n\n 70 text {*\n\n 71 In fact, concluding any (sub-)proof already involves solving any\n\n 72 remaining goals by assumption\\footnote{This is not a completely\n\n 73 trivial operation, as proof by assumption may involve full\n\n 74 higher-order unification.}. Thus we may skip the rather vacuous body\n\n 75 of the above proof as well.\n\n 76 *}\n\n 77\n\n 78 lemma \"A --> A\"\n\n 79 proof\n\n 80 qed\n\n 81\n\n 82 text {*\n\n 83 Note that the \\isacommand{proof} command refers to the $\\idt{rule}$\n\n 84 method (without arguments) by default. Thus it implicitly applies a\n\n 85 single rule, as determined from the syntactic form of the statements\n\n 86 involved. The \\isacommand{by} command abbreviates any proof with\n\n 87 empty body, so the proof may be further pruned.\n\n 88 *}\n\n 89\n\n 90 lemma \"A --> A\"\n\n 91 by rule\n\n 92\n\n 93 text {*\n\n 94 Proof by a single rule may be abbreviated as double-dot.\n\n 95 *}\n\n 96\n\n 97 lemma \"A --> A\" ..\n\n 98\n\n 99 text {*\n\n 100 Thus we have arrived at an adequate representation of the proof of a\n\n 101 tautology that holds by a single standard rule.\\footnote{Apparently,\n\n 102 the rule here is implication introduction.}\n\n 103 *}\n\n 104\n\n 105 text {*\n\n 106 Let us also reconsider $K$. Its statement is composed of iterated\n\n 107 connectives. Basic decomposition is by a single rule at a time,\n\n 108 which is why our first version above was by nesting two proofs.\n\n 109\n\n 110 The $\\idt{intro}$ proof method repeatedly decomposes a goal's\n\n 111 conclusion.\\footnote{The dual method is $\\idt{elim}$, acting on a\n\n 112 goal's premises.}\n\n 113 *}\n\n 114\n\n 115 lemma \"A --> B --> A\"\n\n 116 proof intro\n\n 117 assume A\n\n 118 show A .\n\n 119 qed\n\n 120\n\n 121 text {*\n\n 122 Again, the body may be collapsed.\n\n 123 *}\n\n 124\n\n 125 lemma \"A --> B --> A\"\n\n 126 by intro\n\n 127\n\n 128 text {*\n\n 129 Just like $\\idt{rule}$, the $\\idt{intro}$ and $\\idt{elim}$ proof\n\n 130 methods pick standard structural rules, in case no explicit arguments\n\n 131 are given. While implicit rules are usually just fine for single\n\n 132 rule application, this may go too far with iteration. Thus in\n\n 133 practice, $\\idt{intro}$ and $\\idt{elim}$ would be typically\n\n 134 restricted to certain structures by giving a few rules only, e.g.\\\n\n 135 \\isacommand{proof}~($\\idt{intro}$~\\name{impI}~\\name{allI}) to strip\n\n 136 implications and universal quantifiers.\n\n 137\n\n 138 Such well-tuned iterated decomposition of certain structures is the\n\n 139 prime application of $\\idt{intro}$ and $\\idt{elim}$. In contrast,\n\n 140 terminal steps that solve a goal completely are usually performed by\n\n 141 actual automated proof methods (such as\n\n 142 \\isacommand{by}~$\\idt{blast}$).\n\n 143 *}\n\n 144\n\n 145\n\n 146 subsection {* Variations of backward vs.\\ forward reasoning *}\n\n 147\n\n 148 text {*\n\n 149 Certainly, any proof may be performed in backward-style only. On the\n\n 150 other hand, small steps of reasoning are often more naturally\n\n 151 expressed in forward-style. Isar supports both backward and forward\n\n 152 reasoning as a first-class concept. In order to demonstrate the\n\n 153 difference, we consider several proofs of $A \\conj B \\impl B \\conj 154 A$.\n\n 155\n\n 156 The first version is purely backward.\n\n 157 *}\n\n 158\n\n 159 lemma \"A & B --> B & A\"\n\n 160 proof\n\n 161 assume \"A & B\"\n\n 162 show \"B & A\"\n\n 163 proof\n\n 164 show B by (rule conjunct2)\n\n 165 show A by (rule conjunct1)\n\n 166 qed\n\n 167 qed\n\n 168\n\n 169 text {*\n\n 170 Above, the $\\idt{conjunct}_{1/2}$ projection rules had to be named\n\n 171 explicitly, since the goals $B$ and $A$ did not provide any\n\n 172 structural clue. This may be avoided using \\isacommand{from} to\n\n 173 focus on $\\idt{prems}$ (i.e.\\ the $A \\conj B$ assumption) as the\n\n 174 current facts, enabling the use of double-dot proofs. Note that\n\n 175 \\isacommand{from} already does forward-chaining, involving the\n\n 176 \\name{conjE} rule here.\n\n 177 *}\n\n 178\n\n 179 lemma \"A & B --> B & A\"\n\n 180 proof\n\n 181 assume \"A & B\"\n\n 182 show \"B & A\"\n\n 183 proof\n\n 184 from prems show B ..\n\n 185 from prems show A ..\n\n 186 qed\n\n 187 qed\n\n 188\n\n 189 text {*\n\n 190 In the next version, we move the forward step one level upwards.\n\n 191 Forward-chaining from the most recent facts is indicated by the\n\n 192 \\isacommand{then} command. Thus the proof of $B \\conj A$ from $A 193 \\conj B$ actually becomes an elimination, rather than an\n\n 194 introduction. The resulting proof structure directly corresponds to\n\n 195 that of the $\\name{conjE}$ rule, including the repeated goal\n\n 196 proposition that is abbreviated as $\\var{thesis}$ below.\n\n 197 *}\n\n 198\n\n 199 lemma \"A & B --> B & A\"\n\n 200 proof\n\n 201 assume \"A & B\"\n\n 202 then show \"B & A\"\n\n 203 proof -- {* rule \\name{conjE} of $A \\conj B$ *}\n\n 204 assume A B\n\n 205 show ?thesis .. -- {* rule \\name{conjI} of $B \\conj A$ *}\n\n 206 qed\n\n 207 qed\n\n 208\n\n 209 text {*\n\n 210 In the subsequent version we flatten the structure of the main body\n\n 211 by doing forward reasoning all the time. Only the outermost\n\n 212 decomposition step is left as backward.\n\n 213 *}\n\n 214\n\n 215 lemma \"A & B --> B & A\"\n\n 216 proof\n\n 217 assume ab: \"A & B\"\n\n 218 from ab have a: A ..\n\n 219 from ab have b: B ..\n\n 220 from b a show \"B & A\" ..\n\n 221 qed\n\n 222\n\n 223 text {*\n\n 224 We can still push forward-reasoning a bit further, even at the risk\n\n 225 of getting ridiculous. Note that we force the initial proof step to\n\n 226 do nothing here, by referring to the -'' proof method.\n\n 227 *}\n\n 228\n\n 229 lemma \"A & B --> B & A\"\n\n 230 proof -\n\n 231 {\n\n 232 assume ab: \"A & B\"\n\n 233 from ab have a: A ..\n\n 234 from ab have b: B ..\n\n 235 from b a have \"B & A\" ..\n\n 236 }\n\n 237 thus ?thesis .. -- {* rule \\name{impI} *}\n\n 238 qed\n\n 239\n\n 240 text {*\n\n 241 \\medskip With these examples we have shifted through a whole range\n\n 242 from purely backward to purely forward reasoning. Apparently, in the\n\n 243 extreme ends we get slightly ill-structured proofs, which also\n\n 244 require much explicit naming of either rules (backward) or local\n\n 245 facts (forward).\n\n 246\n\n 247 The general lesson learned here is that good proof style would\n\n 248 achieve just the \\emph{right} balance of top-down backward\n\n 249 decomposition, and bottom-up forward composition. In general, there\n\n 250 is no single best way to arrange some pieces of formal reasoning, of\n\n 251 course. Depending on the actual applications, the intended audience\n\n 252 etc., rules (and methods) on the one hand vs.\\ facts on the other\n\n 253 hand have to be emphasized in an appropriate way. This requires the\n\n 254 proof writer to develop good taste, and some practice, of course.\n\n 255 *}\n\n 256\n\n 257 text {*\n\n 258 For our example the most appropriate way of reasoning is probably the\n\n 259 middle one, with conjunction introduction done after elimination.\n\n 260 This reads even more concisely using \\isacommand{thus}, which\n\n 261 abbreviates \\isacommand{then}~\\isacommand{show}.\\footnote{In the same\n\n 262 vein, \\isacommand{hence} abbreviates\n\n 263 \\isacommand{then}~\\isacommand{have}.}\n\n 264 *}\n\n 265\n\n 266 lemma \"A & B --> B & A\"\n\n 267 proof\n\n 268 assume \"A & B\"\n\n 269 thus \"B & A\"\n\n 270 proof\n\n 271 assume A B\n\n 272 show ?thesis ..\n\n 273 qed\n\n 274 qed\n\n 275\n\n 276\n\n 277\n\n 278 subsection {* A few examples from Introduction to Isabelle'' *}\n\n 279\n\n 280 text {*\n\n 281 We rephrase some of the basic reasoning examples of\n\n 282 \\cite{isabelle-intro}, using HOL rather than FOL.\n\n 283 *}\n\n 284\n\n 285 subsubsection {* A propositional proof *}\n\n 286\n\n 287 text {*\n\n 288 We consider the proposition $P \\disj P \\impl P$. The proof below\n\n 289 involves forward-chaining from $P \\disj P$, followed by an explicit\n\n 290 case-analysis on the two \\emph{identical} cases.\n\n 291 *}\n\n 292\n\n 293 lemma \"P | P --> P\"\n\n 294 proof\n\n 295 assume \"P | P\"\n\n 296 thus P\n\n 297 proof -- {*\n\n 298 rule \\name{disjE}: \\smash{$\\infer{C}{A \\disj B & \\infer*{C}{[A]} & \\infer*{C}{[B]}}$}\n\n 299 *}\n\n 300 assume P show P .\n\n 301 next\n\n 302 assume P show P .\n\n 303 qed\n\n 304 qed\n\n 305\n\n 306 text {*\n\n 307 Case splits are \\emph{not} hardwired into the Isar language as a\n\n 308 special feature. The \\isacommand{next} command used to separate the\n\n 309 cases above is just a short form of managing block structure.\n\n 310\n\n 311 \\medskip In general, applying proof methods may split up a goal into\n\n 312 separate cases'', i.e.\\ new subgoals with individual local\n\n 313 assumptions. The corresponding proof text typically mimics this by\n\n 314 establishing results in appropriate contexts, separated by blocks.\n\n 315\n\n 316 In order to avoid too much explicit parentheses, the Isar system\n\n 317 implicitly opens an additional block for any new goal, the\n\n 318 \\isacommand{next} statement then closes one block level, opening a\n\n 319 new one. The resulting behavior is what one would expect from\n\n 320 separating cases, only that it is more flexible. E.g.\\ an induction\n\n 321 base case (which does not introduce local assumptions) would\n\n 322 \\emph{not} require \\isacommand{next} to separate the subsequent step\n\n 323 case.\n\n 324\n\n 325 \\medskip In our example the situation is even simpler, since the two\n\n 326 cases actually coincide. Consequently the proof may be rephrased as\n\n 327 follows.\n\n 328 *}\n\n 329\n\n 330 lemma \"P | P --> P\"\n\n 331 proof\n\n 332 assume \"P | P\"\n\n 333 thus P\n\n 334 proof\n\n 335 assume P\n\n 336 show P .\n\n 337 show P .\n\n 338 qed\n\n 339 qed\n\n 340\n\n 341 text {*\n\n 342 Again, the rather vacuous body of the proof may be collapsed. Thus\n\n 343 the case analysis degenerates into two assumption steps, which are\n\n 344 implicitly performed when concluding the single rule step of the\n\n 345 double-dot proof as follows.\n\n 346 *}\n\n 347\n\n 348 lemma \"P | P --> P\"\n\n 349 proof\n\n 350 assume \"P | P\"\n\n 351 thus P ..\n\n 352 qed\n\n 353\n\n 354\n\n 355 subsubsection {* A quantifier proof *}\n\n 356\n\n 357 text {*\n\n 358 To illustrate quantifier reasoning, let us prove $(\\ex x P \\ap (f \\ap 359 x)) \\impl (\\ex x P \\ap x)$. Informally, this holds because any $a$\n\n 360 with $P \\ap (f \\ap a)$ may be taken as a witness for the second\n\n 361 existential statement.\n\n 362\n\n 363 The first proof is rather verbose, exhibiting quite a lot of\n\n 364 (redundant) detail. It gives explicit rules, even with some\n\n 365 instantiation. Furthermore, we encounter two new language elements:\n\n 366 the \\isacommand{fix} command augments the context by some new\n\n 367 arbitrary, but fixed'' element; the \\isacommand{is} annotation\n\n 368 binds term abbreviations by higher-order pattern matching.\n\n 369 *}\n\n 370\n\n 371 lemma \"(EX x. P (f x)) --> (EX y. P y)\"\n\n 372 proof\n\n 373 assume \"EX x. P (f x)\"\n\n 374 thus \"EX y. P y\"\n\n 375 proof (rule exE) -- {*\n\n 376 rule \\name{exE}: \\smash{$\\infer{B}{\\ex x A(x) & \\infer*{B}{[A(x)]_x}}$}\n\n 377 *}\n\n 378 fix a\n\n 379 assume \"P (f a)\" (is \"P ?witness\")\n\n 380 show ?thesis by (rule exI [of P ?witness])\n\n 381 qed\n\n 382 qed\n\n 383\n\n 384 text {*\n\n 385 While explicit rule instantiation may occasionally improve\n\n 386 readability of certain aspects of reasoning, it is usually quite\n\n 387 redundant. Above, the basic proof outline gives already enough\n\n 388 structural clues for the system to infer both the rules and their\n\n 389 instances (by higher-order unification). Thus we may as well prune\n\n 390 the text as follows.\n\n 391 *}\n\n 392\n\n 393 lemma \"(EX x. P (f x)) --> (EX y. P y)\"\n\n 394 proof\n\n 395 assume \"EX x. P (f x)\"\n\n 396 thus \"EX y. P y\"\n\n 397 proof\n\n 398 fix a\n\n 399 assume \"P (f a)\"\n\n 400 show ?thesis ..\n\n 401 qed\n\n 402 qed\n\n 403\n\n 404 text {*\n\n 405 Explicit $\\exists$-elimination as seen above can become quite\n\n 406 cumbersome in practice. The derived Isar language element\n\n 407 \\isakeyword{obtain}'' provides a more handsome way to do\n\n 408 generalized existence reasoning.\n\n 409 *}\n\n 410\n\n 411 lemma \"(EX x. P (f x)) --> (EX y. P y)\"\n\n 412 proof\n\n 413 assume \"EX x. P (f x)\"\n\n 414 then obtain a where \"P (f a)\" ..\n\n 415 thus \"EX y. P y\" ..\n\n 416 qed\n\n 417\n\n 418 text {*\n\n 419 Technically, \\isakeyword{obtain} is similar to \\isakeyword{fix} and\n\n 420 \\isakeyword{assume} together with a soundness proof of the\n\n 421 elimination involved. Thus it behaves similar to any other forward\n\n 422 proof element. Also note that due to the nature of general existence\n\n 423 reasoning involved here, any result exported from the context of an\n\n 424 \\isakeyword{obtain} statement may \\emph{not} refer to the parameters\n\n 425 introduced there.\n\n 426 *}\n\n 427\n\n 428\n\n 429\n\n 430 subsubsection {* Deriving rules in Isabelle *}\n\n 431\n\n 432 text {*\n\n 433 We derive the conjunction elimination rule from the corresponding\n\n 434 projections. The proof is quite straight-forward, since\n\n 435 Isabelle/Isar supports non-atomic goals and assumptions fully\n\n 436 transparently.\n\n 437 *}\n\n 438\n\n 439 theorem conjE: \"A & B ==> (A ==> B ==> C) ==> C\"\n\n 440 proof -\n\n 441 assume \"A & B\"\n\n 442 assume r: \"A ==> B ==> C\"\n\n 443 show C\n\n 444 proof (rule r)\n\n 445 show A by (rule conjunct1)\n\n 446 show B by (rule conjunct2)\n\n 447 qed\n\n 448 qed\n\n 449\n\n 450 text {*\n\n 451 Note that classic Isabelle handles higher rules in a slightly\n\n 452 different way. The tactic script as given in \\cite{isabelle-intro}\n\n 453 for the same example of \\name{conjE} depends on the primitive\n\n 454 \\texttt{goal} command to decompose the rule into premises and\n\n 455 conclusion. The actual result would then emerge by discharging of\n\n 456 the context at \\texttt{qed} time.\n\n 457 *}\n\n 458\n\n 459 end" ]
[ null ]
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https://discourse.julialang.org/t/possible-speedup-in-matrix-diagonal-products/68474
[ "", null, "# Possible speedup in matrix-diagonal products?\n\nRight multiplication by a `Diagonal` matrix effectively scales the columns of a matrix. Currently the default `Matrix`-`Diagonal` product appears to use `copy_similar`:\n\n``````(*)(A::AbstractMatrix, D::Diagonal) =\nrmul!(copy_similar(A, promote_op(*, eltype(A), eltype(D.diag))), D)\n``````\n\nwhich seems a bit wasteful. Wouldn’t an uninitialized matrix be better as the destination here? I compare a naive implementation of this matrix product with and without bounds-checking disabled, and it appears that the present implementation is even less performant than the version with bounds checking.\n\n``````julia> A = ones(3000, 2000); D = Diagonal(ones(2000));\n\njulia> @btime \\$A * \\$D;\n42.105 ms (4 allocations: 45.78 MiB)\n\njulia> Base.@propagate_inbounds function muldiag(A::Matrix{T}, D::Diagonal{R}) where {R,T}\n@assert size(A,2) == size(D,1) \"sizes are incompatible\"\nC = similar(A, promote_type(T, R)) # some promotion operation\nd = diag(D);\nfor (j, dj) in enumerate(d), i in axes(C, 1)\nC[i, j] = dj * A[i, j]\nend\nreturn C\nend\nmuldiag (generic function with 1 method)\n\njulia> @btime muldiag(\\$A, \\$D);\n36.357 ms (3 allocations: 45.79 MiB)\n\njulia> @btime @inbounds muldiag(\\$A, \\$D);\n28.553 ms (3 allocations: 45.79 MiB)\n\njulia> A * D == muldiag(A, D)\ntrue\n``````\n\nPerhaps there are instances where the copy is essential, but it seems to be an expensive operation\n\n``````julia> @btime LinearAlgebra.copy_similar(\\$A, Float64);\n34.992 ms (2 allocations: 45.78 MiB)\n``````\n\nand it appears that we may do without it after all?\n\nUsing `mul!` instead of `rmul!` seems to resolve this:\n\n``````julia> muldiag(A, D) = mul!(similar(A, promote_type(eltype(A), eltype(D))), A, D);\n\njulia> @btime muldiag(\\$A, \\$D);\n28.734 ms (4 allocations: 45.78 MiB)\n``````\n5 Likes\n\nI’ve created a PR to add this for matrices of numbers\n\n3 Likes\n\nThis post was temporarily hidden by the community for possibly being off-topic, inappropriate, or spammy." ]
[ null, "https://aws1.discourse-cdn.com/business5/uploads/julialang/original/2X/1/12829a7ba92b924d4ce81099cbf99785bee9b405.png", null ]
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https://doorsgeek.blogspot.com/2013/05/100-zombies-level-59-walkthrough.html
[ "## Monday, May 6, 2013\n\n### 100 Zombies Level 59 Walkthrough\n\n 1. This one is a bit tricky... Figure the pattern on the each column of numbers. Now fill \"?\" spots with the corresponding white number above the door. The correct order is this one Red column: 24, 16, 6, 12 (they divide by 2) Green column: 35, 14, 42, 7 (they divide by 7) Blue column: 27, 9, 18 (they divide by 3) Now sum the numbers in each column and you have the code: 24 + 16 + 6 + 12 = 58 35  +14 + 42 + 7 = 98 27 + 9 + 18 = 54 So the final code is: 58 98 54 This level is bugged now and the code that works is 809854 It will probably be fixed in the next update." ]
[ null ]
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https://www.igus.co.uk/info/linear-guides-drylin-zlw-drive-torque-load
[ "# drylin® ZLW - Toothed belt axis - Drive torque and load\n\n### Drive torque and fill weight of the ZLW-1040/1080\n\n#### Required drive torque*Vertical orientation – ZLW-1040/1080, Version basic 02", null, "X = Load capacity[kg]\nY = drive torque [Nm]", null, "X = Load capacity[kg]\nY = drive torque [Nm]\n\n#### Required drive torque*Vertical orientation – ZLW-1040/1080, Version standard 02", null, "X = Load capacity[kg]\nY = drive torque [Nm]", null, "X = Load capacity[kg]\nY = drive torque [Nm]\n\n* Supposition: The moving mass is located in a circumscribed circle with a max. R = 100 mm to the middle of the rail, max. permissible torque, version 01: 1.3 Nm, a= 0 m/s² ; version 02: 2.4 Nm, a= 0 m/s²; constant drive without nominal value acceleration.\n\n#### Sag between unsupported end blocksZLW-1040/1080, Version basic 02 and standard 02.", null, "X = load of the carriage [N]\nY = speed of the carriage [m/s]\n\nThe diagram accounts for the sum of all forces active on the carriage. ED = On-time", null, "X = Support length [mm]\n\nSag permissible up to maximum 2 mm .\n\n### Drive torque and load of the ZLW-0630\n\n#### Required drive torque*Installation position vertical - ZLW-0630, basic version 02", null, "X = Load capacity[kg]\nY = drive torque [Nm]", null, "X = Load capacity[kg]\nY = drive torque [Nm]\n\n#### Required drive torque*Installation position vertical - ZLW-0630, standard version 02", null, "X = Load capacity[kg]\nY = drive torque [Nm]", null, "X = Load capacity[kg]\nY = drive torque [Nm]\n\n* Supposition: The mass to be moved is in a circumscribed circle with a max. R = 100 mm to the centre of the guide rail, max. permitted torque, version 01: 1.3 Nm, a= 0 m/s² ; version 02: 2.4 Nm, a= 0 m/s²; constant drive without nominal value acceleration.\n\n#### Bending under load based on the width between supportsZLW-0630, basic version 02 and standard 02", null, "X = load of the carriage [N]\nY = speed of the carriage [m/s]\n\nThe diagram accounts for the sum of all forces active on the carriage. ED = On-time", null, "X = Support lenght [mm]\n\nSag permissible up to maximum 2 mm .\n\n### Drive torque and fill weight of the ZLW-1660\n\n#### Required drive torque*Vertical orientation – ZLW-1660, Version standard 02", null, "X = payload [kg]\nY = torque [Nm]", null, "X = payload [kg]\nY = torque [Nm]\n\n*Assumption: the moving mass is located in a circumscribed circle with a Max. R = 100 mm to the middle of the guiding rail, max. permissible torque Version 01: 1.3 Nm, a = 0 m/s²; Version 02: 2.4 Nm, a = 0 m/s²; constant drive without nominal acceleration value\n\n#### Maximum load,horizontal orientation; the diagram accounts for the sum of all forces active on the carriage.", null, "X = Carriage load[N]\nY = Carriage speed [m/s]" ]
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http://ep.jhu.edu/programs-and-courses/625.717-advanced-differential-equations-partial-differential-equations
[ "This course presents practical methods for solving partial differential equations (PDEs). The course covers solutions of hyperbolic, parabolic, and elliptic equations in two or more independent variables. Topics include Fourier series, separation of variables, existence and uniqueness theory for general higher-order equations, eigenfunction expansions, numerical methods, Green’s functions, and transform methods. MATLAB, a high-level computing language, is used in the course to complement the analytical approach and to motivate numerical methods.\nCourse prerequisite(s):\nEN.625.604 Ordinary Differential Equations or equivalent graduate-level ODE class and knowledge of eigenvalues and eigenvectors from matrix theory. (Note: The standard undergraduate-level ODE class alone is not sufficient to meet the prerequisites for this class.)\n\nView Course Homepage(s) for this course.\n\nCourse instructor(s) :" ]
[ null ]
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http://www.unitarium.com/area
[ "How to use\n• Type your value into appropriate edit box.\n• Converter will translate the value into other systems automatically as you type.\n\nAccuracy - number of significant decimal digits:\n Metric Units Imperial and US Units millimeter2 [mm2] square inch [in2] centimeter2 [cm2] square foot [ft2] decimeter2 [dm2] square yard [yd2] meter2 [m2] square mile [mi2] kilometer2 [km2] acre (intl) are [a] acre (US) hectare [ha]\nSquare Foot Conversion Example\nIf your area is given in square meters and you want to know square footage of it, you should type quantity of square meters in the edit box labeled 'meter2'. You will get square footage of the area in the edit box labeled 'square foot'. On the other hand, if you want to know how many square meters/centimeters/inches/yards are in an 1 square foot area, type '1' in the edit box labeled 'square foot' and your answer will appear in the appriopriate box.\n\nFundamental unit of area in the International System Of Units (SI) is:\nsquare meter [m2].\nUnitin square meters\nMetric Unit System\nsquare milimeter [mm2]0.000001\nsquare centimeter [cm2]0.0001\nsquare decimeter [dm2]0.01\nsquare meter [m2]1\nsquare kilometer [km2]1000000\nare [ar]100\nhectare [ha]10000\nImperial and US Unit System\nsquare inch [in2]0.00064513460025\nsquare foot [ft2]0.09290304\nsquare yard [jard2]0.83612736\nsquare mile [mi2]2589886.1433037824\ninternational acre4046.8564224\nUS acre4046.87261\n\nAll our online converters are free to use. We try to keep our software free of bugs and errors but we do not take any responsibility for any problems caused through the use of these calculators and converters." ]
[ null ]
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https://tools.carboncollective.co/compound-interest/65501-at-13-percent-in-27-years/
[ "# What is the compound interest on $65501 at 13% over 27 years? If you want to invest$65,501 over 27 years, and you expect it will earn 13.00% in annual interest, your investment will have grown to become $1,775,684.91. If you're on this page, you probably already know what compound interest is and how a sum of money can grow at a faster rate each year, as the interest is added to the original principal amount and recalculated for each period. The actual rate that$65,501 compounds at is dependent on the frequency of the compounding periods. In this article, to keep things simple, we are using an annual compounding period of 27 years, but it could be monthly, weekly, daily, or even continuously compounding.\n\nThe formula for calculating compound interest is:\n\n$$A = P(1 + \\dfrac{r}{n})^{nt}$$\n\n• A is the amount of money after the compounding periods\n• P is the principal amount\n• r is the annual interest rate\n• n is the number of compounding periods per year\n• t is the number of years\n\nWe can now input the variables for the formula to confirm that it does work as expected and calculates the correct amount of compound interest.\n\nFor this formula, we need to convert the rate, 13.00% into a decimal, which would be 0.13.\n\n$$A = 65501(1 + \\dfrac{ 0.13 }{1})^{ 27}$$\n\nAs you can see, we are ignoring the n when calculating this to the power of 27 because our example is for annual compounding, or one period per year, so 27 × 1 = 27.\n\n## How the compound interest on $65,501 grows over time The interest from previous periods is added to the principal amount, and this grows the sum a rate that always accelerating. The table below shows how the amount increases over the 27 years it is compounding: Start Balance Interest End Balance 1$65,501.00 $8,515.13$74,016.13\n2 $74,016.13$9,622.10 $83,638.23 3$83,638.23 $10,872.97$94,511.20\n4 $94,511.20$12,286.46 $106,797.65 5$106,797.65 $13,883.69$120,681.35\n6 $120,681.35$15,688.58 $136,369.92 7$136,369.92 $17,728.09$154,098.01\n8 $154,098.01$20,032.74 $174,130.75 9$174,130.75 $22,637.00$196,767.75\n10 $196,767.75$25,579.81 $222,347.56 11$222,347.56 $28,905.18$251,252.74\n12 $251,252.74$32,662.86 $283,915.60 13$283,915.60 $36,909.03$320,824.63\n14 $320,824.63$41,707.20 $362,531.83 15$362,531.83 $47,129.14$409,660.96\n16 $409,660.96$53,255.93 $462,916.89 17$462,916.89 $60,179.20$523,096.08\n18 $523,096.08$68,002.49 $591,098.58 19$591,098.58 $76,842.81$667,941.39\n20 $667,941.39$86,832.38 $754,773.77 21$754,773.77 $98,120.59$852,894.36\n22 $852,894.36$110,876.27 $963,770.63 23$963,770.63 $125,290.18$1,089,060.81\n24 $1,089,060.81$141,577.91 $1,230,638.72 25$1,230,638.72 $159,983.03$1,390,621.75\n26 $1,390,621.75$180,780.83 $1,571,402.58 27$1,571,402.58 $204,282.33$1,775,684.91\n\nWe can also display this data on a chart to show you how the compounding increases with each compounding period.\n\nAs you can see if you view the compounding chart for $65,501 at 13.00% over a long enough period of time, the rate at which it grows increases over time as the interest is added to the balance and new interest calculated from that figure. ## How long would it take to double$65,501 at 13% interest?\n\nAnother commonly asked question about compounding interest would be to calculate how long it would take to double your investment of $65,501 assuming an interest rate of 13.00%. We can calculate this very approximately using the Rule of 72. The formula for this is very simple: $$Years = \\dfrac{72}{Interest\\: Rate}$$ By dividing 72 by the interest rate given, we can calculate the rough number of years it would take to double the money. Let's add our rate to the formula and calculate this: $$Years = \\dfrac{72}{ 13 } = 5.54$$ Using this, we know that any amount we invest at 13.00% would double itself in approximately 5.54 years. So$65,501 would be worth $131,002 in ~5.54 years. We can also calculate the exact length of time it will take to double an amount at 13.00% using a slightly more complex formula: $$Years = \\dfrac{log(2)}{log(1 + 0.13)} = 5.67\\; years$$ Here, we use the decimal format of the interest rate, and use the logarithm math function to calculate the exact value. As you can see, the exact calculation is very close to the Rule of 72 calculation, which is much easier to remember. Hopefully, this article has helped you to understand the compound interest you might achieve from investing$65,501 at 13.00% over a 27 year investment period." ]
[ null ]
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https://discuss.pytorch.org/t/bidirectional-rnn-implementation/90668
[ "# Bidirectional RNN Implementation\n\nHi I am trying to understand bidirectional RNN.\n\n``````> class RNN(nn.Module):\n>\n\n>\n> def __init__(self,n_vocab,n_embed,hidden_size,output_size):\n>\n> super().__init__()\n>\n> self.hidden_size = hidden_size\n>\n> self.embedding = nn.Embedding(n_vocab+1,n_embed) ## n_vocab is unique words in dictionary ## n_embed is hyperparameter\n\n> self.rnn = nn.RNN(n_embed, hidden_size, num_layers = 1, batch_first = True,bidirectional = True) #\n>\n> self.fc = nn.Linear(hidden_size,output_size)\n>\n> def forward(self,x):>\n>\n> x = x # input batch_size * seq_length\n>\n> batch_size = x.size(0)\n>\n> #print('Batch Size is',batch_size)\n>\n> x = self.embedding(x) # batch-size x seq_length x embedding_dimension\n>\n> x,hidden =self.rnn(x) #batch-size x seq_length x hidden_size\n>\n>\n>\n> return x,hidden\n``````\n\nI am returning both hidden state and output while going through tutorials some says that I need to concatenate hidden state (torch.cat((hidden[-2,:,:], hidden[-1,:,:]), dim = 1)) and in some tutorials take output state (x[:,-1,:]) but both of results come difference.\n\nWhat is the correct way of doing Bidirectional RNN.\n\n1 Like" ]
[ null ]
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https://www.studystack.com/flashcard-2816611
[ "Save", null, "or", null, "or", null, "taken", null, "why\n\nMake sure to remember your password. If you forget it there is no way for StudyStack to send you a reset link. You would need to create a new account.\n\nfocusNode\nDidn't know it?\nclick below\n\nKnew it?\nclick below\nDon't know (0)\nRemaining cards (0)\nKnow (0)\n0:00\nEmbed Code - If you would like this activity on your web page, copy the script below and paste it into your web page.\n\nNormal Size     Small Size show me how\n\n# Physics Final\n\n### Physics Final (6/6)\n\nA stationary point that allows observers to see motion because the distance between the object and this changes. Reference point\nThe distance traveled in a certain amount of time (how fast) Speed\nWhat is the unit for speed? m/sec\nThe speed at a certain instant of time Instantaneous speed\nTraveling equal distances in equal amounts of time Constant speed\nThe total distance traveled in a certain amount of time Average speed\nThe speed in a certain direction (how fast and which way) Velocity\nIf Lauren can run 15 meters in 10 seconds, what is her speed? 1.5 m/s\nCovering equal distances in equal amounts of time without changing direction Constant velocity\nAny change in velocity Acceleration\nA car accelerates from rest to a final speed of 10m/s in 5 seconds. What is the acceleration of the car? 2 m/sec/sec\nA car speeds up from 10 m/s to 20 m/s in 4 seconds. What is the acceleration of the car? 2.5 m/sec/sec\nA car slows down from a speed of 25 m/s to 10 m/s in 3 seconds. What is the acceleration of the car? -5 m/sec/sec\nA car is traveling at 10 m/s. How much time will it take to accelerate to a final speed of 30 m/s if it can accelerate at 4 m/s? 5 seconds\nA car that is at rest begins to accelerate at 5 m/sec/sec. What is the car's speed after 6 seconds? 30 m/s\nA car that is traveling at 10 m/s begins to accelerate at 5 m/sec/sec. What is the car's speed after 6 seconds? 40 m/s\nA car accelerates from rest at 4 m/sec/sec. Calculate the distance traveled after 0 seconds. 0 m\nA car accelerates from rest at 4 m/sec/sec. Calculate the distance traveled after 2 seconds. 8 m\nA car accelerates from rest at 4 m/sec/sec. Calculate the distance traveled after 3 seconds. 18 m\nA car accelerates from rest at 4 m/sec/sec. Calculate the distance traveled after 10 seconds. 200 m\nA car accelerates from rest at 4 m/sec/sec. Calculate the final velocity after 0 seconds. 0 m/s\nA car accelerates from rest at 4 m/sec/sec. Calculate the final velocity after 2 seconds. 8 m/s\nA car accelerates from rest at 4 m/sec/sec. Calculate the final velocity after 3 seconds. 12 m/s\nA car accelerates from rest at 4 m/sec/sec. Calculate the final velocity after 10 seconds. 40 m/s\nIf the slope on a distance vs time graph is flat, that means the object is...? a) Not moving b) Constant speed c) Acceleration A\nIf the slope on an acceleration vs time graph is flat, that means the object is...? a) Not moving b) Constant acceleration B\nIf the slope on a velocity vs time graph is slanted, that means the object is...? a) Constant speed b) Acceleration B\nIf the slope on a velocity vs time graph is flat, that means the object is...? a) Constant speed b) Acceleration A\nIf the slope on a distance vs time graph is curved, that means the object is...? a) Not moving b) Constant speed c) Acceleration C\nIf the slope on a distance vs time graph is slanted, that means the object is...? a) Not moving b) Constant speed c) Acceleration B\nThe slope of a distance vs time graph shows _________. Speed\nThe slope of a velocity vs time graph shows _____________. Acceleration\nAny push or pull of an object Force\nThe unit for force is__________. Newtons\nThe overall force on an object Net force\nShows all the forces acting on the object Force diagram\nA nonzero net force that causes an object to accelerate Unbalanced force\nA zero net force that does not cause an object to accelerate Balanced force\nThe amount of matter in an object Mass\nThe force of gravity pulling on an object Weight\nWeight = mass * _________ Gravity\nWhen you go to the moon, your __________ (mass/weight) stays the same. Mass\nA force that opposes motion and slows down moving objects Friction\nIf the texture of a surface is rough, that means that there is _________ (more/less) friction More\nThe two forms of friction are ________________ and _______________, which means that one is stationary and the other is moving, respectfully. Static; kinetic\nThe three types of kinetic friction are ______________, __________________, and _______________, where in one, a surface slides over another, in the second, a surface rolls over another, and in the third, a surface moves through a fluid. Sliding friction; rolling friction; fluid friction\nWhen the only force acting on an object is gravity. Free fall\nIf two different objects of different mass are dropped from the same height, the ________________ (will/will not) fall to the ground at the same time because they are in free fall. Will\nSuppose a basketball is dropped from rest from a very, very high tower. What is its acceleration after 5 seconds? 9.8 m/sec/sec\nSuppose a basketball is dropped from rest from a very, very high tower. What is its velocity after 5 seconds? 49 m/s\nWhen the downward force of gravity is cancelled out by the upward force of air resistance; the object no longer accelerates. It moves at a constant speed Terminal velocity\nAn object that is in free fall and moves horizontally at the same time Projectile\nThe ability to do work or cause change Energy\nWhat are the two forms of energy? Kinetic; potential\nWhat are the three types of potential energy? Gravitational; elastic; chemical\nWhat is the formula for KE? 1/2mv^2\nWhat is the unit for energy? Joules\nWhat is the formula for GPE? mgh\nHow much kinetic energy does a 0.15 baseball have if its speed is 40 m/s? 120 J\nHow much gravitational potential energy is stored in a 0.15 baseball if it is held 2m off the ground? 2.943 J\nWhat law is this? Energy cannot be created or destroyed, but it can be transformed from one form to another Law of Conservation of Energy\nWhat are the six forms of energy? (List in the order as in the acronym MENCHE) Mechanical; electromagnetic; nuclear; chemical; heat; electrical\nWhat form of energy is this? Energy that's stored in the nucleus of an atom Sun:Fusion-2 nuclei collide together at high speeds, releasing energy as they fuse together Power plants:Fission-nucleus breaks into 2 or more nuclei which releases energy Nuclear\nWhat form of energy is this? Energy that is stored in the chemical bonds between atoms (food, batteries, burning coal, gasoline) Chemical\nWhat form of energy is this? Energy associated with moving electric charges (batteries, power plants sending electric currents, laptop sending electrical signals through circuits, brain controls body through electrical impulses) Electrical\nWhat form of energy is this? Energy associated with the temperature of an object. Moving particles produce heat energy through friction (chemical reactions, heating/cooling surroundings, change in the state of matter) Heat\nWhat form of energy is this? Energy that is carried in massless waves that are part electric and part magnetic (visible light, invisible inferred heat waves, invisible x-rays) Electromagnetic\nWhat form of energy is this? Energy associated with the motion or position of an object (living a mass, running, kicking a football) Mechanical\nWhat principle is this? The buoyant force on an object is equal to the weight of the fluid displaced by that object Archimedes' Principle\nSuppose you jump into a pool. What is the volume of water you displace if you go halfway under? 1/2 your volume\nSuppose you jump into a pool and go all the way under. What is the buoyant force? The weight of you\nIf an object has the same volume as water, but it weights more, it will _____. Sink\nIf the object ______, the object weights less than that much water. Floats\nWhat principle is this? As the speed of a moving fluid increases, the pressure inside of that fluid decreases? Bernoulli's Principle\nThe pressure inside a moving fluid is ___________ (more than/less than) the pressure of the surrounding slower moving or stationary fluid. Less than\nWhich of Newton's laws is this? (Just put number) • Objects at rest stay at rest • Object in motion stay in motion • All of the above unless acted on by an unbalanced force with makes it accelerate • Also known as the Law of Inertia 1\nWhich of Newton's laws is this? (Just put number) • For every action, there is an equal and opposite reaction force • Action/reaction force pairs DO NOT cancel out because they act on different objects 3\nWhich of Newton's laws is this? (Just put number) • Describes the relationship between force, mass, and acceleration • If the force is constant, then as mass increases, the acceleration decreases • F=ma 2\nWhat law is this? Opposite charges attract, while like charges repel. Law of Electric Charges\nFor positive charges, the arrows point ____________ (out/in) Out\nThe quantity that keeps an object in its state of motion Momentum\nThe formula for momentum is: P=mv\nThe unit for momentum is: Kg * m/s\nWhat is the momentum of a 5 Kg cart traveling at a velocity of 3 m/s? 15 Kg * m/s\nA force of attraction or repulsion between two types of metals (Ni, Fe, or Co) caused by the identical spin of electrons within each substance Magnetic force\nThe magnetic force depends on: Size + distance\nThe average kinetic energy of all the molecules in a substance Temperature\nThe movement of thermal energy from one substance to another Heat\nThe transfer of thermal energy by direct contact Conduction\nEasily transfer thermal energy Conductors\nDo not easily transfer thermal energy Insulators\nThe transfer of thermal energy by electromagnetic waves Radiation\nThe transfer of thermal energy by the movement of currents in a fluid Convection\nWhen heated, objects __________ (expand/contract) Expand\nCreated by: oliva.muchnik\n\nVoices\n\nUse these flashcards to help memorize information. Look at the large card and try to recall what is on the other side. Then click the card to flip it. If you knew the answer, click the green Know box. Otherwise, click the red Don't know box.\n\nWhen you've placed seven or more cards in the Don't know box, click \"retry\" to try those cards again.\n\nIf you've accidentally put the card in the wrong box, just click on the card to take it out of the box.\n\nYou can also use your keyboard to move the cards as follows:\n\n• SPACEBAR - flip the current card\n• LEFT ARROW - move card to the Don't know pile\n• RIGHT ARROW - move card to Know pile\n• BACKSPACE - undo the previous action\n\nIf you are logged in to your account, this website will remember which cards you know and don't know so that they are in the same box the next time you log in.\n\nWhen you need a break, try one of the other activities listed below the flashcards like Matching, Snowman, or Hungry Bug. Although it may feel like you're playing a game, your brain is still making more connections with the information to help you out.\n\nTo see how well you know the information, try the Quiz or Test activity.\n\n# Pass complete!\n\n \"Know\" box contains: Time elapsed: Retries:\nrestart all cards" ]
[ null, "https://sstk.biz/images/studystacklogo.svg", null, "https://sstk.biz/images/blackeye.png", null, "https://sstk.biz/images/greenCheckMark.svg", null, "https://sstk.biz/images/blackeye.png", null ]
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https://forum.freecodecamp.org/t/how-to-sum-these-variables-into-one-variable/377779
[ "# How to sum these variables into one variable?\n\nSo I stored object property values inside these variables, and i want to sum them.\nHow to do that, and what would be a better way without making variable for each property?\n\n``````console.log(frequencyCounter1);//{a: 5, b: 2, r: 2, c: 1, d: 1}\nlet A = frequencyCounter1.a;\nlet E = frequencyCounter1.e;\nlet I = frequencyCounter1.i;\nlet O = frequencyCounter1.o;\nlet U = frequencyCounter1.u;\nconsole.log(A); //returns 5\n\n``````\n\nyou cant sum variables its NaN\n\nDon’t your variables contain numbers?\n\nthey do, but try to sum them and see the output\n\nI don’t know what you mean." ]
[ null ]
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https://www.cs.ox.ac.uk/people/jakub.oprsal/
[ "# Jakub Opršal", null, "Dr Jakub Opršal\n\nResearch Associate\n\nLeaving date: 31st May 2022\n\n## Interests\n\nMy work lies at the interface of mathematics and computer science. I am seeking to answer what inherent mathematical quality makes a computational problem hard, and which allows us to design an efficient algorithm to solve this problem. In essence, we are asking if P ≠ NP, how can we distinguish problems that are in P from those that are NP-complete?\n\nTo answer these questions, I investigate the complexity of constraint satisfaction problems and its variants including approximation, and I use deep mathematical theories, including universal algebra, topology, and topological combinatorics for this goal." ]
[ null, "https://www.cs.ox.ac.uk/files/13230//d9c0f279-f368-45ba-bc31-6f3889f12914.jpg", null ]
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https://www.jiskha.com/questions/1246596/is-x-y-2-equal-to-x2-y2-explain-why-or-why-not-using-an-example-to-support-your
[ "# math\n\nIs (x+y)2 equal to (x2+y2)? Explain why or why not using an example to support your answer.\n\n1. 👍\n2. 👎\n3. 👁\n1. Online \"^\" is used to indicate an exponent, e.g., x^2 = x squared.\n\n(x+y)^2 = (x+y)(x+y)\n\nMultiply them out.\n\n1. 👍\n2. 👎\n\n## Similar Questions\n\n1. ### social studies\n\nwhich of the following was one way different regions of the the country agreed? A. support of slavery B. support for the war of 1812 C. support for foreign policies D. support of economic stability i think its B. am i right?\n\n2. ### language arts\n\nWhat is the purpose of reasons in a persuasive essay?(1 point) They are opinions based on evidence. They are facts used to support a claim. They are ideas used to support a claim. They are specific details used to support an idea.\n\n3. ### ELA\n\nWhat is evidence?(1 point) specific information that supports an idea reasons to support a claim a statement put forth in support of an argument*** an opinion formed based on facts What is the purpose of reasons in a persuasive\n\n4. ### math\n\n7. The tennis team is selling key chains as a fundraiser. If its goal is to raise is at least 180, how many key chains must it sell at \\$2.25 each to meet that goal? Write and solve an inequality. a. 2.25k (greater than or equal\n\n1. ### Math\n\nplease check my work. 1. The number of words (x) Tina can type per minute is at Least 50. write and graph and inequality. (I broke it down to these 2 choices because the A & D was incorrect) B. x is less than or equal to 50 C. x\n\n2. ### Math\n\nHi everyone, my name is Emerson. I was wondering if anybody could help me on a test. I'm stuck on some, but I think I know some others. Thank you! 1. Translate the phrase \"nine more than two times a number\" in to an algebraic\n\n3. ### Science\n\nName two types of evidence used to support the theory of evolution explain how scientists use each type of evidence to provide support for evolution. give one example of each\n\n4. ### physics\n\nA 3.0 m long rigid beam with a mass of 100 kg is supported at each end. An 60 kg student stands 2.0 m from support 1. How much upward force does each support exert on the beam? support 1- support 2-\n\n1. ### Algebra--Correction?\n\nSolve x^2 -3x is greater than or equal to 10 Would the solutions be x=5 and x= -2? Here's how I figured it. x^2-3x is greater than or equal to 10. I subtracted 10 from both sides. This left me with x^2-3x-10 is greater than or\n\n2. ### Calculus\n\nTwo particles move along the x -axis. For 0 is less than or equal to t is less than or equal to 6, the position of particle P at time t is given by p(t)=2cos((pi/4)t), while the position of particle R at time t is given by\n\n3. ### Science\n\nName two types of evidence used to support the theory of evolution. Explain how scientists use each type of evidence to provide support for evolution. Give one example of each.\n\n4. ### math\n\nplease check my work. 1. The number of words (x) Tina can type per minute is at Least 50. write and graph and inequality. (I broke it down to these 2 choices because the A & D was incorrect) B. x is less than or equal to 50 C. x" ]
[ null ]
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https://minuteshours.com/110-17-hours-to-minutes
[ "# 110.17 hours to minutes\n\n## Result\n\n110.17 hours equals 6610.2 minutes\n\nYou can also convert 110.17 hours to hours and minutes.\n\n## Conversion formula\n\nMultiply the amount of hours by the conversion factor to get the result in minutes:\n\n110.17 hr × 60 = 6610.2 min\n\n## How to convert 110.17 hours to minutes?\n\nThe conversion factor from hours to minutes is 60, which means that 1 hours is equal to 60 minutes:\n\n1 hr = 60 min\n\nTo convert 110.17 hours into minutes we have to multiply 110.17 by the conversion factor in order to get the amount from hours to minutes. We can also form a proportion to calculate the result:\n\n1 hr → 60 min\n\n110.17 hr → T(min)\n\nSolve the above proportion to obtain the time T in minutes:\n\nT(min) = 110.17 hr × 60 min\n\nT(min) = 6610.2 min\n\nThe final result is:\n\n110.17 hr → 6610.2 min\n\nWe conclude that 110.17 hours is equivalent to 6610.2 minutes:\n\n110.17 hours = 6610.2 minutes\n\n## Result approximation\n\nFor practical purposes we can round our final result to an approximate numerical value. In this case one hundred ten point one seven hours is approximately six thousand six hundred ten point two minutes:\n\n110.17 hours ≅ 6610.2 minutes\n\n## Conversion table\n\nFor quick reference purposes, below is the hours to minutes conversion table:\n\nhours (hr) minutes (min)\n111.17 hours 6670.2 minutes\n112.17 hours 6730.2 minutes\n113.17 hours 6790.2 minutes\n114.17 hours 6850.2 minutes\n115.17 hours 6910.2 minutes\n116.17 hours 6970.2 minutes\n117.17 hours 7030.2 minutes\n118.17 hours 7090.2 minutes\n119.17 hours 7150.2 minutes\n120.17 hours 7210.2 minutes\n\n## Units definitions\n\nThe units involved in this conversion are hours and minutes. This is how they are defined:\n\n### Hours\n\nAn hour (symbol: h; also abbreviated hr.) is a unit of time conventionally reckoned as 1⁄24 of a day and scientifically reckoned as 3,599–3,601 seconds, depending on conditions. The seasonal, temporal, or unequal hour was established in the ancient Near East as 1⁄12 of the night or daytime. Such hours varied by season, latitude, and weather. It was subsequently divided into 60 minutes, each of 60 seconds. Its East Asian equivalent was the shi, which was 1⁄12 of the apparent solar day; a similar system was eventually developed in Europe which measured its equal or equinoctial hour as 1⁄24 of such days measured from noon to noon. The minor variations of this unit were eventually smoothed by making it 1⁄24 of the mean solar day, based on the measure of the sun's transit along the celestial equator rather than along the ecliptic. This was finally abandoned due to the minor slowing caused by the Earth's tidal deceleration by the Moon. In the modern metric system, hours are an accepted unit of time equal to 3,600 seconds but an hour of Coordinated Universal Time (UTC) may incorporate a positive or negative leap second, making it last 3,599 or 3,601 seconds, in order to keep it within 0.9 seconds of universal time, which is based on measurements of the mean solar day at 0° longitude.\n\n### Minutes\n\nThe minute is a unit of time or of angle. As a unit of time, the minute (symbol: min) is equal to 1⁄60 (the first sexagesimal fraction) of an hour, or 60 seconds. In the UTC time standard, a minute on rare occasions has 61 seconds, a consequence of leap seconds (there is a provision to insert a negative leap second, which would result in a 59-second minute, but this has never happened in more than 40 years under this system). As a unit of angle, the minute of arc is equal to 1⁄60 of a degree, or 60 seconds (of arc). Although not an SI unit for either time or angle, the minute is accepted for use with SI units for both. The SI symbols for minute or minutes are min for time measurement, and the prime symbol after a number, e.g. 5′, for angle measurement. The prime is also sometimes used informally to denote minutes of time. In contrast to the hour, the minute (and the second) does not have a clear historical background. What is traceable only is that it started being recorded in the Middle Ages due to the ability of construction of \"precision\" timepieces (mechanical and water clocks). However, no consistent records of the origin for the division as 1⁄60 part of the hour (and the second 1⁄60 of the minute) have ever been found, despite many speculations." ]
[ null ]
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https://nyuscholars.nyu.edu/en/publications/a-fast-numerical-method-for-solving-the-three-dimensional-stokes-
[ "# A fast numerical method for solving the three-dimensional stokes' equations in the presence of suspended particles\n\nAaron L. Fogelson, Charles S. Peskin\n\nResearch output: Contribution to journalArticlepeer-review\n\n## Abstract\n\nA new fast numerical method for solving the three-dimensional Stokes' equations in the presence of suspended particles is presented. The fluid dynamics equations are solved on a lattice. A particle is represented by a set of points each of which moves at the local fluid velocity and is not constrained to lie on the lattice. These points are coupled by forces which resist deformation of the particle. These forces contribute to the force density in the Stokes' equations. As a result, a single set of fluid dynamics equations holds at all points of the domain and there are no internal boundaries. Particle size, shape, and deformability may be prescribed. Computational work increases only linearly with the number of particles, so large numbers (500-1000) of particles may be studied efficiently. The numerical method involves implicit calculation of the particle forces by minimizing an energy function and solution of a finite-difference approximation to the Stokes' equations using the Fourier-Toeplitz method. The numerical method has been implemented to run on all CRAY computers: the implementation exploits the CRAY's vectorized arithmetic, and on machines with insufficient central memory, it performs efficient disk 1/O while storing most of the data on disk. Applications of the method to sedimentation of one-, two-, and many-particle systems are described. Trajectories and settling speeds for two-particle sedimentation, and settling speed for multiparticle sedimentation from initial distributions on a cubic lattice or at random give good quantitative agreement with existing theories.\n\nOriginal language English (US) 50-69 20 Journal of Computational Physics 79 1 https://doi.org/10.1016/0021-9991(88)90003-4 Published - Nov 1988\n\n## ASJC Scopus subject areas\n\n• Numerical Analysis\n• Modeling and Simulation\n• Physics and Astronomy (miscellaneous)\n• Physics and Astronomy(all)\n• Computer Science Applications\n• Computational Mathematics\n• Applied Mathematics\n\n## Fingerprint\n\nDive into the research topics of 'A fast numerical method for solving the three-dimensional stokes' equations in the presence of suspended particles'. Together they form a unique fingerprint." ]
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