319 lines
9.6 KiB
Python
319 lines
9.6 KiB
Python
from __future__ import annotations
|
|
|
|
from dataclasses import dataclass
|
|
from typing import Callable, Literal
|
|
|
|
|
|
CancellationCheck = Callable[[], bool]
|
|
AcceptedStepCallback = Callable[[float], None]
|
|
IntegrationStatus = Literal["completed", "cancelled", "failed"]
|
|
|
|
|
|
class _IntegrationCancelled(Exception):
|
|
pass
|
|
|
|
|
|
@dataclass(frozen=True)
|
|
class SolveIVPConfig:
|
|
t_start: float = 0.0
|
|
t_stop: float = 20.0
|
|
method: str = "BDF"
|
|
rtol: float = 1e-6
|
|
atol: float = 1e-8
|
|
max_step: float = 1e-3
|
|
first_step: float | None = None
|
|
|
|
|
|
@dataclass(frozen=True)
|
|
class ODESolution:
|
|
t: list[float]
|
|
y: list[list[float]]
|
|
success: bool
|
|
message: str
|
|
status: IntegrationStatus = "completed"
|
|
error: Exception | None = None
|
|
|
|
|
|
def _vector_add(a: list[float], b: list[float], scale: float = 1.0) -> list[float]:
|
|
return [x + scale * y for x, y in zip(a, b)]
|
|
|
|
|
|
def _append_solution_sample(
|
|
times: list[float],
|
|
states: list[list[float]],
|
|
time: float,
|
|
state: list[float],
|
|
) -> None:
|
|
if times and time <= times[-1] + 1e-12:
|
|
return
|
|
times.append(float(time))
|
|
for index, value in enumerate(state):
|
|
states[index].append(float(value))
|
|
|
|
|
|
def _runge_kutta_4(
|
|
rhs: Callable[[float, list[float]], list[float]],
|
|
initial_state: list[float],
|
|
config: SolveIVPConfig,
|
|
t_eval: list[float] | None,
|
|
cancel_check: CancellationCheck | None = None,
|
|
accepted_step_callback: AcceptedStepCallback | None = None,
|
|
) -> ODESolution:
|
|
if t_eval is None:
|
|
point_count = max(
|
|
2,
|
|
int((config.t_stop - config.t_start) / max(config.max_step, 1e-6)) + 1,
|
|
)
|
|
step = (config.t_stop - config.t_start) / (point_count - 1)
|
|
t_eval = [config.t_start + index * step for index in range(point_count)]
|
|
|
|
state = list(initial_state)
|
|
states = [[value] for value in state]
|
|
times = [float(t_eval[0])]
|
|
current_time = float(t_eval[0])
|
|
status: IntegrationStatus = "completed"
|
|
message = "Integrated with built-in RK4 fallback because SciPy is unavailable."
|
|
error: Exception | None = None
|
|
|
|
try:
|
|
for target_time in t_eval[1:]:
|
|
while current_time < target_time - 1e-15:
|
|
if cancel_check is not None and cancel_check():
|
|
raise _IntegrationCancelled
|
|
dt = min(config.max_step, target_time - current_time)
|
|
k1 = rhs(current_time, state)
|
|
k2 = rhs(current_time + 0.5 * dt, _vector_add(state, k1, 0.5 * dt))
|
|
k3 = rhs(current_time + 0.5 * dt, _vector_add(state, k2, 0.5 * dt))
|
|
k4 = rhs(current_time + dt, _vector_add(state, k3, dt))
|
|
state = [
|
|
value + (dt / 6.0) * (a + 2.0 * b + 2.0 * c + d)
|
|
for value, a, b, c, d in zip(state, k1, k2, k3, k4)
|
|
]
|
|
current_time += dt
|
|
if accepted_step_callback is not None:
|
|
accepted_step_callback(current_time)
|
|
|
|
_append_solution_sample(times, states, target_time, state)
|
|
except _IntegrationCancelled:
|
|
status = "cancelled"
|
|
message = "Simulation was stopped before reaching the requested end time."
|
|
_append_solution_sample(times, states, current_time, state)
|
|
except Exception as exc:
|
|
status = "failed"
|
|
message = str(exc)
|
|
error = exc
|
|
_append_solution_sample(times, states, current_time, state)
|
|
|
|
return ODESolution(
|
|
t=times,
|
|
y=states,
|
|
success=status == "completed",
|
|
message=message,
|
|
status=status,
|
|
error=error,
|
|
)
|
|
|
|
|
|
def _integrate_scipy_stepwise(
|
|
rhs: Callable[[float, list[float]], list[float]],
|
|
initial_state: list[float],
|
|
config: SolveIVPConfig,
|
|
t_eval: list[float] | None,
|
|
cancel_check: CancellationCheck,
|
|
accepted_step_callback: AcceptedStepCallback | None,
|
|
) -> ODESolution:
|
|
import numpy as np
|
|
from scipy.integrate import BDF, DOP853, LSODA, RK23, RK45, Radau
|
|
|
|
solver_types = {
|
|
"BDF": BDF,
|
|
"DOP853": DOP853,
|
|
"LSODA": LSODA,
|
|
"RK23": RK23,
|
|
"RK45": RK45,
|
|
"Radau": Radau,
|
|
}
|
|
solver_type = solver_types.get(config.method)
|
|
if solver_type is None:
|
|
raise ValueError(f"Unsupported integration method: {config.method}")
|
|
|
|
times = [float(config.t_start)]
|
|
states = [[float(value)] for value in initial_state]
|
|
last_accepted_time = float(config.t_start)
|
|
last_accepted_state = [float(value) for value in initial_state]
|
|
sample_times = list(t_eval or [])
|
|
sample_index = 0
|
|
while (
|
|
sample_index < len(sample_times)
|
|
and sample_times[sample_index] <= config.t_start + 1e-12
|
|
):
|
|
sample_index += 1
|
|
|
|
def cancellable_rhs(time, state):
|
|
if cancel_check():
|
|
raise _IntegrationCancelled
|
|
return rhs(float(time), [float(value) for value in state])
|
|
|
|
if cancel_check():
|
|
return ODESolution(
|
|
t=times,
|
|
y=states,
|
|
success=False,
|
|
message="Simulation was stopped before integration started.",
|
|
status="cancelled",
|
|
)
|
|
|
|
solver_options = {
|
|
"rtol": config.rtol,
|
|
"atol": config.atol,
|
|
"max_step": config.max_step,
|
|
}
|
|
if config.first_step is not None:
|
|
solver_options["first_step"] = config.first_step
|
|
|
|
try:
|
|
solver = solver_type(
|
|
cancellable_rhs,
|
|
config.t_start,
|
|
np.asarray(initial_state, dtype=float),
|
|
config.t_stop,
|
|
**solver_options,
|
|
)
|
|
except _IntegrationCancelled:
|
|
return ODESolution(
|
|
t=times,
|
|
y=states,
|
|
success=False,
|
|
message="Simulation was stopped before integration started.",
|
|
status="cancelled",
|
|
)
|
|
except Exception as exc:
|
|
return ODESolution(
|
|
t=times,
|
|
y=states,
|
|
success=False,
|
|
message=str(exc),
|
|
status="failed",
|
|
error=exc,
|
|
)
|
|
|
|
status: IntegrationStatus = "completed"
|
|
message = "The solver successfully reached the end of the integration interval."
|
|
error: Exception | None = None
|
|
|
|
while solver.status == "running":
|
|
if cancel_check():
|
|
status = "cancelled"
|
|
message = "Simulation was stopped before reaching the requested end time."
|
|
break
|
|
try:
|
|
step_message = solver.step()
|
|
except _IntegrationCancelled:
|
|
status = "cancelled"
|
|
message = "Simulation was stopped before reaching the requested end time."
|
|
break
|
|
except Exception as exc:
|
|
status = "failed"
|
|
message = str(exc)
|
|
error = exc
|
|
break
|
|
|
|
if solver.status == "failed":
|
|
status = "failed"
|
|
message = str(step_message or "Integration step failed.")
|
|
break
|
|
|
|
last_accepted_time = float(solver.t)
|
|
last_accepted_state = [float(value) for value in solver.y]
|
|
if sample_times:
|
|
dense_output = solver.dense_output()
|
|
while (
|
|
sample_index < len(sample_times)
|
|
and sample_times[sample_index] <= last_accepted_time + 1e-12
|
|
):
|
|
sample_time = float(sample_times[sample_index])
|
|
sample_state = [float(value) for value in dense_output(sample_time)]
|
|
_append_solution_sample(times, states, sample_time, sample_state)
|
|
sample_index += 1
|
|
else:
|
|
_append_solution_sample(
|
|
times,
|
|
states,
|
|
last_accepted_time,
|
|
last_accepted_state,
|
|
)
|
|
if accepted_step_callback is not None:
|
|
accepted_step_callback(last_accepted_time)
|
|
|
|
if status != "completed":
|
|
_append_solution_sample(
|
|
times,
|
|
states,
|
|
last_accepted_time,
|
|
last_accepted_state,
|
|
)
|
|
|
|
return ODESolution(
|
|
t=times,
|
|
y=states,
|
|
success=status == "completed",
|
|
message=message,
|
|
status=status,
|
|
error=error,
|
|
)
|
|
|
|
|
|
def integrate_ode(
|
|
rhs: Callable[[float, list[float]], list[float]],
|
|
initial_state: list[float],
|
|
config: SolveIVPConfig,
|
|
t_eval: list[float] | None = None,
|
|
cancel_check: CancellationCheck | None = None,
|
|
accepted_step_callback: AcceptedStepCallback | None = None,
|
|
):
|
|
"""Thin wrapper around scipy.integrate.solve_ivp with a pure-Python fallback."""
|
|
|
|
if abs(config.t_stop - config.t_start) <= 1e-15:
|
|
return ODESolution(
|
|
t=[float(config.t_start)],
|
|
y=[[value] for value in initial_state],
|
|
success=True,
|
|
message="Skipped integration because t_start equals t_stop.",
|
|
)
|
|
|
|
try:
|
|
from scipy.integrate import solve_ivp
|
|
except ImportError:
|
|
return _runge_kutta_4(
|
|
rhs,
|
|
initial_state,
|
|
config,
|
|
t_eval,
|
|
cancel_check,
|
|
accepted_step_callback,
|
|
)
|
|
|
|
if cancel_check is not None:
|
|
return _integrate_scipy_stepwise(
|
|
rhs,
|
|
initial_state,
|
|
config,
|
|
t_eval,
|
|
cancel_check,
|
|
accepted_step_callback,
|
|
)
|
|
|
|
solve_options = {
|
|
"fun": rhs,
|
|
"t_span": (config.t_start, config.t_stop),
|
|
"y0": initial_state,
|
|
"method": config.method,
|
|
"rtol": config.rtol,
|
|
"atol": config.atol,
|
|
"max_step": config.max_step,
|
|
"t_eval": t_eval,
|
|
}
|
|
if config.first_step is not None:
|
|
solve_options["first_step"] = config.first_step
|
|
return solve_ivp(**solve_options)
|