add padding function to imgScalePadding()
This commit is contained in:
@@ -1,192 +0,0 @@
|
||||
import numpy as np
|
||||
from scipy.integrate import ode
|
||||
from .common import validate_tol, validate_first_step, warn_extraneous
|
||||
from .base import OdeSolver, DenseOutput
|
||||
|
||||
|
||||
class LSODA(OdeSolver):
|
||||
"""Adams/BDF method with automatic stiffness detection and switching.
|
||||
|
||||
This is a wrapper to the Fortran solver from ODEPACK [1]_. It switches
|
||||
automatically between the nonstiff Adams method and the stiff BDF method.
|
||||
The method was originally detailed in [2]_.
|
||||
|
||||
Parameters
|
||||
----------
|
||||
fun : callable
|
||||
Right-hand side of the system. The calling signature is ``fun(t, y)``.
|
||||
Here ``t`` is a scalar, and there are two options for the ndarray ``y``:
|
||||
It can either have shape (n,); then ``fun`` must return array_like with
|
||||
shape (n,). Alternatively it can have shape (n, k); then ``fun``
|
||||
must return an array_like with shape (n, k), i.e. each column
|
||||
corresponds to a single column in ``y``. The choice between the two
|
||||
options is determined by `vectorized` argument (see below). The
|
||||
vectorized implementation allows a faster approximation of the Jacobian
|
||||
by finite differences (required for this solver).
|
||||
t0 : float
|
||||
Initial time.
|
||||
y0 : array_like, shape (n,)
|
||||
Initial state.
|
||||
t_bound : float
|
||||
Boundary time - the integration won't continue beyond it. It also
|
||||
determines the direction of the integration.
|
||||
first_step : float or None, optional
|
||||
Initial step size. Default is ``None`` which means that the algorithm
|
||||
should choose.
|
||||
min_step : float, optional
|
||||
Minimum allowed step size. Default is 0.0, i.e., the step size is not
|
||||
bounded and determined solely by the solver.
|
||||
max_step : float, optional
|
||||
Maximum allowed step size. Default is np.inf, i.e., the step size is not
|
||||
bounded and determined solely by the solver.
|
||||
rtol, atol : float and array_like, optional
|
||||
Relative and absolute tolerances. The solver keeps the local error
|
||||
estimates less than ``atol + rtol * abs(y)``. Here `rtol` controls a
|
||||
relative accuracy (number of correct digits), while `atol` controls
|
||||
absolute accuracy (number of correct decimal places). To achieve the
|
||||
desired `rtol`, set `atol` to be smaller than the smallest value that
|
||||
can be expected from ``rtol * abs(y)`` so that `rtol` dominates the
|
||||
allowable error. If `atol` is larger than ``rtol * abs(y)`` the
|
||||
number of correct digits is not guaranteed. Conversely, to achieve the
|
||||
desired `atol` set `rtol` such that ``rtol * abs(y)`` is always smaller
|
||||
than `atol`. If components of y have different scales, it might be
|
||||
beneficial to set different `atol` values for different components by
|
||||
passing array_like with shape (n,) for `atol`. Default values are
|
||||
1e-3 for `rtol` and 1e-6 for `atol`.
|
||||
jac : None or callable, optional
|
||||
Jacobian matrix of the right-hand side of the system with respect to
|
||||
``y``. The Jacobian matrix has shape (n, n) and its element (i, j) is
|
||||
equal to ``d f_i / d y_j``. The function will be called as
|
||||
``jac(t, y)``. If None (default), the Jacobian will be
|
||||
approximated by finite differences. It is generally recommended to
|
||||
provide the Jacobian rather than relying on a finite-difference
|
||||
approximation.
|
||||
lband, uband : int or None
|
||||
Parameters defining the bandwidth of the Jacobian,
|
||||
i.e., ``jac[i, j] != 0 only for i - lband <= j <= i + uband``. Setting
|
||||
these requires your jac routine to return the Jacobian in the packed format:
|
||||
the returned array must have ``n`` columns and ``uband + lband + 1``
|
||||
rows in which Jacobian diagonals are written. Specifically
|
||||
``jac_packed[uband + i - j , j] = jac[i, j]``. The same format is used
|
||||
in `scipy.linalg.solve_banded` (check for an illustration).
|
||||
These parameters can be also used with ``jac=None`` to reduce the
|
||||
number of Jacobian elements estimated by finite differences.
|
||||
vectorized : bool, optional
|
||||
Whether `fun` is implemented in a vectorized fashion. A vectorized
|
||||
implementation offers no advantages for this solver. Default is False.
|
||||
|
||||
Attributes
|
||||
----------
|
||||
n : int
|
||||
Number of equations.
|
||||
status : string
|
||||
Current status of the solver: 'running', 'finished' or 'failed'.
|
||||
t_bound : float
|
||||
Boundary time.
|
||||
direction : float
|
||||
Integration direction: +1 or -1.
|
||||
t : float
|
||||
Current time.
|
||||
y : ndarray
|
||||
Current state.
|
||||
t_old : float
|
||||
Previous time. None if no steps were made yet.
|
||||
nfev : int
|
||||
Number of evaluations of the right-hand side.
|
||||
njev : int
|
||||
Number of evaluations of the Jacobian.
|
||||
|
||||
References
|
||||
----------
|
||||
.. [1] A. C. Hindmarsh, "ODEPACK, A Systematized Collection of ODE
|
||||
Solvers," IMACS Transactions on Scientific Computation, Vol 1.,
|
||||
pp. 55-64, 1983.
|
||||
.. [2] L. Petzold, "Automatic selection of methods for solving stiff and
|
||||
nonstiff systems of ordinary differential equations", SIAM Journal
|
||||
on Scientific and Statistical Computing, Vol. 4, No. 1, pp. 136-148,
|
||||
1983.
|
||||
"""
|
||||
def __init__(self, fun, t0, y0, t_bound, first_step=None, min_step=0.0,
|
||||
max_step=np.inf, rtol=1e-3, atol=1e-6, jac=None, lband=None,
|
||||
uband=None, vectorized=False, **extraneous):
|
||||
warn_extraneous(extraneous)
|
||||
super().__init__(fun, t0, y0, t_bound, vectorized)
|
||||
|
||||
if first_step is None:
|
||||
first_step = 0 # LSODA value for automatic selection.
|
||||
else:
|
||||
first_step = validate_first_step(first_step, t0, t_bound)
|
||||
|
||||
first_step *= self.direction
|
||||
|
||||
if max_step == np.inf:
|
||||
max_step = 0 # LSODA value for infinity.
|
||||
elif max_step <= 0:
|
||||
raise ValueError("`max_step` must be positive.")
|
||||
|
||||
if min_step < 0:
|
||||
raise ValueError("`min_step` must be nonnegative.")
|
||||
|
||||
rtol, atol = validate_tol(rtol, atol, self.n)
|
||||
|
||||
solver = ode(self.fun, jac)
|
||||
solver.set_integrator('lsoda', rtol=rtol, atol=atol, max_step=max_step,
|
||||
min_step=min_step, first_step=first_step,
|
||||
lband=lband, uband=uband)
|
||||
solver.set_initial_value(y0, t0)
|
||||
|
||||
# Inject t_bound into rwork array as needed for itask=5.
|
||||
solver._integrator.rwork[0] = self.t_bound
|
||||
solver._integrator.call_args[4] = solver._integrator.rwork
|
||||
|
||||
self._lsoda_solver = solver
|
||||
|
||||
def _step_impl(self):
|
||||
solver = self._lsoda_solver
|
||||
integrator = solver._integrator
|
||||
|
||||
# From lsoda.step and lsoda.integrate itask=5 means take a single
|
||||
# step and do not go past t_bound.
|
||||
itask = integrator.call_args[2]
|
||||
integrator.call_args[2] = 5
|
||||
solver._y, solver.t = integrator.run(
|
||||
solver.f, solver.jac or (lambda: None), solver._y, solver.t,
|
||||
self.t_bound, solver.f_params, solver.jac_params)
|
||||
integrator.call_args[2] = itask
|
||||
|
||||
if solver.successful():
|
||||
self.t = solver.t
|
||||
self.y = solver._y
|
||||
# From LSODA Fortran source njev is equal to nlu.
|
||||
self.njev = integrator.iwork[12]
|
||||
self.nlu = integrator.iwork[12]
|
||||
return True, None
|
||||
else:
|
||||
return False, 'Unexpected istate in LSODA.'
|
||||
|
||||
def _dense_output_impl(self):
|
||||
iwork = self._lsoda_solver._integrator.iwork
|
||||
rwork = self._lsoda_solver._integrator.rwork
|
||||
|
||||
order = iwork[14]
|
||||
h = rwork[11]
|
||||
yh = np.reshape(rwork[20:20 + (order + 1) * self.n],
|
||||
(self.n, order + 1), order='F').copy()
|
||||
|
||||
return LsodaDenseOutput(self.t_old, self.t, h, order, yh)
|
||||
|
||||
|
||||
class LsodaDenseOutput(DenseOutput):
|
||||
def __init__(self, t_old, t, h, order, yh):
|
||||
super().__init__(t_old, t)
|
||||
self.h = h
|
||||
self.yh = yh
|
||||
self.p = np.arange(order + 1)
|
||||
|
||||
def _call_impl(self, t):
|
||||
if t.ndim == 0:
|
||||
x = ((t - self.t) / self.h) ** self.p
|
||||
else:
|
||||
x = ((t - self.t) / self.h) ** self.p[:, None]
|
||||
|
||||
return np.dot(self.yh, x)
|
||||
Reference in New Issue
Block a user