Source code for pde.solvers.scipy

Defines a solver using :mod:`scipy.integrate`
.. codeauthor:: David Zwicker <> 

from typing import Callable

import numpy as np

from ..fields.base import FieldBase
from ..pdes.base import PDEBase
from .base import SolverBase

[docs]class ScipySolver(SolverBase): """class for solving partial differential equations using scipy This class is a thin wrapper around :func:`scipy.integrate.solve_ivp`. In particular, it supports all the methods implemented by this function. """ name = "scipy" def __init__(self, pde: PDEBase, backend: str = "auto", **kwargs): r""" Args: pde (:class:`~pde.pdes.base.PDEBase`): The instance describing the pde that needs to be solved backend (str): Determines how the function is created. Accepted values are 'numpy` and 'numba'. Alternatively, 'auto' lets the code decide for the most optimal backend. **kwargs: All extra arguments are forwarded to :func:`scipy.integrate.solve_ivp`. """ super().__init__(pde) self.backend = backend self.solver_params = kwargs
[docs] def make_stepper( self, state: FieldBase, dt: float = None ) -> Callable[[FieldBase, float, float], float]: """return a stepper function Args: state (:class:`~pde.fields.FieldBase`): An example for the state from which the grid and other information can be extracted. dt (float): Initial time step for the simulation. If `None`, the solver will choose a suitable initial value. Returns: Function that can be called to advance the `state` from time `t_start` to time `t_end`. """ if self.pde.is_sde: raise RuntimeError("Cannot use scipy stepper for a stochastic equation") from scipy import integrate shape =["dt"] = dt["steps"] = 0["stochastic"] = False # obtain function for evaluating the right hand side rhs = self._make_pde_rhs(state, backend=self.backend) def rhs_helper(t: float, state_flat: np.ndarray) -> np.ndarray: """helper function to provide the correct call convention""" rhs_value = rhs(state_flat.reshape(shape), t) y = np.broadcast_to(rhs_value, shape).flat if np.any(np.isnan(y)): # this check is necessary, since solve_ivp does not deal correctly with # NaN, which might result in odd error messages or even a stalled # program raise RuntimeError("Encountered Not-A-Number (NaN) in evolution") return y # type: ignore def stepper(state: FieldBase, t_start: float, t_end: float) -> float: """use scipy.integrate.odeint to advance `state` from `t_start` to `t_end`""" if dt is not None: self.solver_params["first_step"] = min(t_end - t_start, dt) sol = integrate.solve_ivp( rhs_helper, t_span=(t_start, t_end), y0=np.ravel(, t_eval=[t_end], # only store necessary **self.solver_params, )["steps"] += sol.nfev[:] = sol.y.reshape(shape) return sol.t[0] # type: ignore if dt: f"Initialized {self.__class__.__name__} stepper with dt=%g", dt ) else:"Initialized {self.__class__.__name__} stepper") return stepper