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from itertools import count
from functools import reduce
from .tracer import trace, primitive, toposort, Node, Box, isbox, getval
from .util import func, subval
# -------------------- reverse mode --------------------
def make_vjp(fun, x):
start_node = VJPNode.new_root()
end_value, end_node = trace(start_node, fun, x)
if end_node is None:
def vjp(g): return vspace(x).zeros()
else:
def vjp(g): return backward_pass(g, end_node)
return vjp, end_value
def backward_pass(g, end_node):
outgrads = {end_node : (g, False)}
for node in toposort(end_node):
outgrad = outgrads.pop(node)
ingrads = node.vjp(outgrad[0])
for parent, ingrad in zip(node.parents, ingrads):
outgrads[parent] = add_outgrads(outgrads.get(parent), ingrad)
return outgrad[0]
class VJPNode(Node):
__slots__ = ['parents', 'vjp']
def __init__(self, value, fun, args, kwargs, parent_argnums, parents):
self.parents = parents
try:
vjpmaker = primitive_vjps[fun]
except KeyError:
fun_name = getattr(fun, '__name__', fun)
raise NotImplementedError("VJP of {} wrt argnums {} not defined"
.format(fun_name, parent_argnums))
self.vjp = vjpmaker(parent_argnums, value, args, kwargs)
def initialize_root(self):
self.parents = []
self.vjp = lambda g: ()
primitive_vjps = {}
def defvjp_argnums(fun, vjpmaker):
primitive_vjps[fun] = vjpmaker
def defvjp_argnum(fun, vjpmaker):
def vjp_argnums(argnums, *args):
vjps = [vjpmaker(argnum, *args) for argnum in argnums]
return lambda g: (vjp(g) for vjp in vjps)
defvjp_argnums(fun, vjp_argnums)
def defvjp(fun, *vjpmakers, **kwargs):
argnums = kwargs.get('argnums', count())
vjps_dict = {argnum : translate_vjp(vjpmaker, fun, argnum)
for argnum, vjpmaker in zip(argnums, vjpmakers)}
def vjp_argnums(argnums, ans, args, kwargs):
L = len(argnums)
# These first two cases are just optimizations
if L == 1:
argnum = argnums[0]
try:
vjpfun = vjps_dict[argnum]
except KeyError:
raise NotImplementedError(
"VJP of {} wrt argnum 0 not defined".format(fun.__name__))
vjp = vjpfun(ans, *args, **kwargs)
return lambda g: (vjp(g),)
elif L == 2:
argnum_0, argnum_1 = argnums
try:
vjp_0_fun = vjps_dict[argnum_0]
vjp_1_fun = vjps_dict[argnum_1]
except KeyError:
raise NotImplementedError(
"VJP of {} wrt argnums 0, 1 not defined".format(fun.__name__))
vjp_0 = vjp_0_fun(ans, *args, **kwargs)
vjp_1 = vjp_1_fun(ans, *args, **kwargs)
return lambda g: (vjp_0(g), vjp_1(g))
else:
vjps = [vjps_dict[argnum](ans, *args, **kwargs) for argnum in argnums]
return lambda g: (vjp(g) for vjp in vjps)
defvjp_argnums(fun, vjp_argnums)
def translate_vjp(vjpfun, fun, argnum):
if vjpfun is None:
return lambda ans, *args, **kwargs: lambda g: vspace(args[argnum]).zeros()
elif callable(vjpfun):
return vjpfun
else:
raise Exception("Bad VJP '{}' for '{}'".format(vjpfun, fun.__name__))
# -------------------- forward mode --------------------
def make_jvp(fun, x):
def jvp(g):
start_node = JVPNode.new_root(g)
end_value, end_node = trace(start_node, fun, x)
if end_node is None:
return end_value, vspace(end_value).zeros()
else:
return end_value, end_node.g
return jvp
class JVPNode(Node):
__slots__ = ['g']
def __init__(self, value, fun, args, kwargs, parent_argnums, parents):
parent_gs = [parent.g for parent in parents]
try:
jvpmaker = primitive_jvps[fun]
except KeyError:
name = getattr(fun, '__name__', fun)
raise NotImplementedError("JVP of {} wrt argnums {} not defined"
.format(name, parent_argnums))
self.g = jvpmaker(parent_argnums, parent_gs, value, args, kwargs)
def initialize_root(self, g):
self.g = g
primitive_jvps = {}
def defjvp_argnums(fun, jvpmaker):
primitive_jvps[fun] = jvpmaker
def defjvp_argnum(fun, jvpmaker):
def jvp_argnums(argnums, gs, ans, args, kwargs):
return sum_outgrads(jvpmaker(argnum, g, ans, args, kwargs)
for argnum, g in zip(argnums, gs))
defjvp_argnums(fun, jvp_argnums)
def defjvp(fun, *jvpfuns, **kwargs):
argnums = kwargs.get('argnums', count())
jvps_dict = {argnum : translate_jvp(jvpfun, fun, argnum)
for argnum, jvpfun in zip(argnums, jvpfuns)}
def jvp_argnums(argnums, gs, ans, args, kwargs):
return sum_outgrads(jvps_dict[argnum](g, ans, *args, **kwargs)
for argnum, g in zip(argnums, gs))
defjvp_argnums(fun, jvp_argnums)
def translate_jvp(jvpfun, fun, argnum):
if jvpfun is None:
return lambda g, ans, *a, **k: vspace(ans).zeros()
elif jvpfun == 'same':
return (lambda g, ans, *args, **kwargs:
fun(*subval(args, argnum, g), **kwargs))
elif callable(jvpfun):
return jvpfun
else:
raise Exception("Bad JVP '{}' for '{}'".format(jvpfun, fun.__name__))
def def_linear(fun):
"""Flags that a function is linear wrt all args"""
defjvp_argnum(fun, lambda argnum, g, ans, args, kwargs:
fun(*subval(args, argnum, g), **kwargs))
# -------------------- vector behavior --------------------
def add_outgrads(prev_g_flagged, g):
sparse = type(g) in sparse_object_types
if prev_g_flagged:
vs = vspace(g)
prev_g, mutable = prev_g_flagged
if mutable:
if sparse:
return sparse_add(vs, prev_g, g), True
else:
return vs.mut_add(prev_g, g), True
else:
if sparse:
prev_g_mutable = vs.mut_add(None, prev_g)
return sparse_add(vs, prev_g_mutable, g), True
else:
return vs.add(prev_g, g), True
else:
if sparse:
return sparse_add(vspace(g), None, g), True
else:
return g, False
def sum_outgrads(gs):
return reduce(add_outgrads, gs, None)[0]
@primitive
def sparse_add(vs, x_prev, x_new):
x_prev = x_prev if x_prev is not None else vs.zeros()
return x_new.mut_add(x_prev)
class VSpace(object):
__slots__ = []
mappings = {}
iscomplex = False
def __init__(self, value): pass
def zeros(self): assert False, repr(self)
def ones(self): assert False, repr(self)
def standard_basis(self): assert False, repr(self)
def randn(self): assert False, repr(self)
@primitive
def mut_add(self, x_prev, x_new):
x_prev = x_prev if x_prev is not None else self.zeros()
return self._mut_add(x_prev, x_new)
@primitive
def add(self, x_prev, x_new): return self._add(x_prev, x_new)
@primitive
def scalar_mul(self, x, a): return self._scalar_mul(x, a)
@primitive
def inner_prod(self, x, y): return self._inner_prod(x, y)
@primitive
def covector(self, x): return self._covector(x)
def _add(self, x, y): return x + y
def _mut_add(self, x, y): x += y; return x
def _scalar_mul(self, x, a): return x * a
def _inner_prod(self, x, y): assert False
def _covector(self, x): return x
def __eq__(self, other):
return type(self) == type(other) and self.__dict__ == other.__dict__
def __repr__(self):
return "{}_{}".format(type(self).__name__, self.__dict__)
@classmethod
def register(cls, value_type, vspace_maker=None):
if vspace_maker:
VSpace.mappings[value_type] = vspace_maker
else:
VSpace.mappings[value_type] = cls
def vspace(value):
try:
return VSpace.mappings[type(value)](value)
except KeyError:
if isbox(value):
return vspace(getval(value))
else:
raise TypeError("Can't find vector space for value {} of type {}. "
"Valid types are {}".format(
value, type(value), VSpace.mappings.keys()))
class SparseBox(Box):
__slots__ = []
class SparseObject(object):
__slots__ = ['vs', 'mut_add']
def __init__(self, vs, mut_add):
self.vs = vs
self.mut_add = mut_add
VSpace.register(SparseObject, lambda x : x.vs)
SparseBox.register(SparseObject)
sparse_object_types = {SparseObject, SparseBox}
# -------------------- core reverse mode grads --------------------
identity_vjp = lambda argnums, *args: lambda g: g
defvjp(sparse_add, None, identity_vjp, identity_vjp)
defvjp(func(VSpace.add ), None, identity_vjp, identity_vjp)
defvjp(func(VSpace.mut_add), None, identity_vjp, identity_vjp)
defvjp(func(VSpace.inner_prod), None,
lambda ans, vs, x, y: lambda g: vs.covector(vs.scalar_mul(y, g)),
lambda ans, vs, x, y: lambda g: vs.covector(vs.scalar_mul(x, g)))
defvjp(func(VSpace.covector), None,
lambda ans, vs, x: lambda g: vs.covector(g))
defvjp(func(VSpace.scalar_mul), None,
lambda ans, vs, x, a: lambda g: vs.covector(vs.scalar_mul(vs.covector(g), a)),
lambda ans, vs, x, a: lambda g: vs.inner_prod(g, vs.covector(x)))
# -------------------- core forward mode grads --------------------
identity_jvp = lambda g, *args, **kwargs: g
defjvp(sparse_add, None, identity_jvp, identity_jvp)
defjvp(func(VSpace.mut_add), None, identity_jvp, identity_jvp)
defjvp(func(VSpace.add), None, identity_jvp, identity_jvp)
defjvp(func(VSpace.scalar_mul), None, 'same', 'same')
defjvp(func(VSpace.inner_prod), None, 'same', 'same')
defjvp(func(VSpace.covector), None, 'same')
# -------------------- deprecation warnings -----------------------
import warnings
deprecated_defvjp_message = '''
The {} method is deprecated. See the update guide and tutorial:
https://github.com/HIPS/autograd/blob/master/docs/updateguide.md
https://github.com/HIPS/autograd/blob/master/docs/tutorial.md'''
def deprecated_defvjp(primitive_fun):
deprecation_msg = deprecated_defvjp_message.format('defvjp')
vjpfuns = {}
def defvjp_unstaged(vjpmaker, argnum=0):
warnings.warn(deprecation_msg)
def staged_vjpmaker(ans, *args, **kwargs):
def vjp(g):
vs, gvs = vspace(args[argnum]), vspace(g)
return vjpmaker(g, ans, vs, gvs, *args, **kwargs)
return vjp
vjpfuns[argnum] = staged_vjpmaker
argnums, vjpmakers = zip(*[(argnum, vjpfuns[argnum])
for argnum in sorted(vjpfuns.keys())])
defvjp(primitive_fun, *vjpmakers, argnums=argnums)
return defvjp_unstaged
def deprecated_defvjp_is_zero(primitive_fun):
deprecation_msg = deprecated_defvjp_message.format('defvjp_is_zero')
zero_vjps = [set()]
def defvjp_is_zero(argnums=(0,)):
warnings.warn(deprecation_msg)
zero_vjps[0] |= set(argnums)
nones = [None] * len(zero_vjps[0])
defvjp(primitive_fun, *nones, argnums=sorted(zero_vjps[0]))
return defvjp_is_zero
def deprecated_defgrad(primitive_fun):
deprecation_msg = deprecated_defvjp_message.format('defgrad')
gradfuns = {}
def defgrad(gradfun, argnum=0):
warnings.warn(deprecation_msg)
gradfuns[argnum] = gradfun
argnums, vjpmakers = zip(*[(argnum, gradfuns[argnum])
for argnum in sorted(gradfuns.keys())])
defvjp(primitive_fun, *vjpmakers, argnums=argnums)
return defgrad
primitive_ = primitive
def primitive_with_deprecation_warnings(f_raw):
f_wrapped = primitive_(f_raw)
f_wrapped.defvjp = deprecated_defvjp(f_wrapped)
f_wrapped.defvjp_is_zero = deprecated_defvjp_is_zero(f_wrapped)
f_wrapped.defgrad = deprecated_defgrad(f_wrapped)
return f_wrapped
primitive = primitive_with_deprecation_warnings
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