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"""
Solves a first-order ordinary differential equation (or system of first-order ODEs)
dy/dt = f(t, y) with initial condition y(t0) = y0.
"""
import numpy as np
from scipy.integrate import solve_ivp
from typing import Callable, List, Tuple, Dict, Any, Union
import matplotlib.pyplot as plt
from maths.differential_equations.ode_interface_utils import parse_float_list, parse_time_span, string_to_ode_func
import gradio as gr
ODEFunc = Callable[[float, Union[np.ndarray, List[float]]], Union[np.ndarray, List[float]]]
def solve_first_order_ode(
ode_func: ODEFunc,
t_span: Tuple[float, float],
y0: List[float],
t_eval_count: int = 100,
method: str = 'RK45',
**kwargs: Any
) -> Dict[str, Union[np.ndarray, str, bool]]:
# ...existing code...
try:
y0_np = np.array(y0, dtype=float)
t_eval = np.linspace(t_span[0], t_span[1], t_eval_count)
sol = solve_ivp(ode_func, t_span, y0_np, method=method, t_eval=t_eval, **kwargs)
plot_path = None
if sol.success:
try:
plt.figure(figsize=(10, 6))
if y0_np.ndim == 0 or len(y0_np) == 1 : # Single equation
plt.plot(sol.t, sol.y[0], label=f'y(t), y0={y0_np[0] if y0_np.ndim > 0 else y0_np}')
else: # System of equations
for i in range(sol.y.shape[0]):
plt.plot(sol.t, sol.y[i], label=f'y_{i+1}(t), y0_{i+1}={y0_np[i]}')
plt.xlabel("Time (t)")
plt.ylabel("Solution y(t)")
plt.title(f"Solution of First-Order ODE ({method})")
plt.legend()
plt.grid(True)
plot_path = "ode_solution_plot.png"
plt.savefig(plot_path)
plt.close() # Close the plot to free memory
except Exception as e_plot:
print(f"Warning: Could not generate plot: {e_plot}")
plot_path = None
return {
't': sol.t,
'y': sol.y,
'message': sol.message,
'success': sol.success,
'plot_path': plot_path
}
except Exception as e:
return {
't': np.array([]),
'y': np.array([]),
'message': f"Error during ODE solving: {str(e)}",
'success': False,
'plot_path': None
}
# --- Gradio Interface for First-Order ODEs ---
first_order_ode_interface = gr.Interface(
fn=lambda ode_str, t_span_str, y0_str, t_eval_count, method: solve_first_order_ode(
string_to_ode_func(ode_str, ('t', 'y')),
parse_time_span(t_span_str),
parse_float_list(y0_str),
int(t_eval_count),
method
),
inputs=[
gr.Textbox(label="ODE Function (lambda t, y: ...)",
placeholder="e.g., lambda t, y: -y*t OR for system lambda t, y: [y[1], -0.1*y[1] - y[0]]",
info="Define dy/dt or a system [dy1/dt, dy2/dt,...]. `y` is a list/array for systems."),
gr.Textbox(label="Time Span (t_start, t_end)", placeholder="e.g., 0,10"),
gr.Textbox(label="Initial Condition(s) y(t_start)", placeholder="e.g., 1 OR for system 1,0"),
gr.Slider(minimum=10, maximum=1000, value=100, step=10, label="Evaluation Points Count"),
gr.Radio(choices=['RK45', 'LSODA', 'BDF', 'RK23', 'DOP853'], value='RK45', label="Solver Method")
],
outputs=[
gr.Image(label="Solution Plot", type="filepath", show_label=True, visible=lambda res: res['success'] and res['plot_path'] is not None),
gr.Textbox(label="Solver Message"),
gr.Textbox(label="Success Status"),
gr.JSON(label="Raw Data (t, y values)", visible=lambda res: res['success']) # For users to copy if needed
],
title="First-Order ODE Solver",
description="""
Solves dy/dt = f(t, y) or a system of first-order ODEs.
- Enter a Python lambda for the ODE (e.g., `lambda t, y: -y*t`).
- For systems, use `y` as a list: `lambda t, y: [y[1], -0.1*y[1] - y[0]]`.
- Initial conditions: single value (e.g., `1`) or comma-separated for systems (e.g., `1,0`).
**Examples:**
- Simple: `lambda t, y: -y*t`, y0: `1`, t_span: `0,5`
- System: `lambda t, y: [y[1], -0.1*y[1] - y[0]]`, y0: `1,0`, t_span: `0,20`
- Lotka-Volterra: `lambda t, y: [1.5*y[0] - 0.8*y[0]*y[1], 0.5*y[0]*y[1] - 0.9*y[1]]`, y0: `10,5`, t_span: `0,20`
WARNING: Uses eval() for the ODE function string - potential security risk.
""",
flagging_mode="manual"
)
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