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Fixed database typo and removed unnecessary class identifier.

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Batuhan Berk Başoğlu 2020-10-14 10:10:37 -04:00
parent 00ad49a143
commit 45fb349a7d
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venv/Lib/site-packages/scipy/integrate/_ivp/base.py Normal file
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import numpy as np
def check_arguments(fun, y0, support_complex):
"""Helper function for checking arguments common to all solvers."""
y0 = np.asarray(y0)
if np.issubdtype(y0.dtype, np.complexfloating):
if not support_complex:
raise ValueError("`y0` is complex, but the chosen solver does "
"not support integration in a complex domain.")
dtype = complex
else:
dtype = float
y0 = y0.astype(dtype, copy=False)
if y0.ndim != 1:
raise ValueError("`y0` must be 1-dimensional.")
def fun_wrapped(t, y):
return np.asarray(fun(t, y), dtype=dtype)
return fun_wrapped, y0
class OdeSolver(object):
"""Base class for ODE solvers.
In order to implement a new solver you need to follow the guidelines:
1. A constructor must accept parameters presented in the base class
(listed below) along with any other parameters specific to a solver.
2. A constructor must accept arbitrary extraneous arguments
``**extraneous``, but warn that these arguments are irrelevant
using `common.warn_extraneous` function. Do not pass these
arguments to the base class.
3. A solver must implement a private method `_step_impl(self)` which
propagates a solver one step further. It must return tuple
``(success, message)``, where ``success`` is a boolean indicating
whether a step was successful, and ``message`` is a string
containing description of a failure if a step failed or None
otherwise.
4. A solver must implement a private method `_dense_output_impl(self)`,
which returns a `DenseOutput` object covering the last successful
step.
5. A solver must have attributes listed below in Attributes section.
Note that ``t_old`` and ``step_size`` are updated automatically.
6. Use `fun(self, t, y)` method for the system rhs evaluation, this
way the number of function evaluations (`nfev`) will be tracked
automatically.
7. For convenience, a base class provides `fun_single(self, t, y)` and
`fun_vectorized(self, t, y)` for evaluating the rhs in
non-vectorized and vectorized fashions respectively (regardless of
how `fun` from the constructor is implemented). These calls don't
increment `nfev`.
8. If a solver uses a Jacobian matrix and LU decompositions, it should
track the number of Jacobian evaluations (`njev`) and the number of
LU decompositions (`nlu`).
9. By convention, the function evaluations used to compute a finite
difference approximation of the Jacobian should not be counted in
`nfev`, thus use `fun_single(self, t, y)` or
`fun_vectorized(self, t, y)` when computing a finite difference
approximation of the Jacobian.
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 ndarray ``y``.
It can either have shape (n,), then ``fun`` must return array_like with
shape (n,). Or, alternatively, it can have shape (n, n_points), then
``fun`` must return array_like with shape (n, n_points) (each column
corresponds to a single column in ``y``). The choice between the two
options is determined by `vectorized` argument (see below).
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.
vectorized : bool
Whether `fun` is implemented in a vectorized fashion.
support_complex : bool, optional
Whether integration in a complex domain should be supported.
Generally determined by a derived solver class capabilities.
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.
step_size : float
Size of the last successful step. None if no steps were made yet.
nfev : int
Number of the system's rhs evaluations.
njev : int
Number of the Jacobian evaluations.
nlu : int
Number of LU decompositions.
"""
TOO_SMALL_STEP = "Required step size is less than spacing between numbers."
def __init__(self, fun, t0, y0, t_bound, vectorized,
support_complex=False):
self.t_old = None
self.t = t0
self._fun, self.y = check_arguments(fun, y0, support_complex)
self.t_bound = t_bound
self.vectorized = vectorized
if vectorized:
def fun_single(t, y):
return self._fun(t, y[:, None]).ravel()
fun_vectorized = self._fun
else:
fun_single = self._fun
def fun_vectorized(t, y):
f = np.empty_like(y)
for i, yi in enumerate(y.T):
f[:, i] = self._fun(t, yi)
return f
def fun(t, y):
self.nfev += 1
return self.fun_single(t, y)
self.fun = fun
self.fun_single = fun_single
self.fun_vectorized = fun_vectorized
self.direction = np.sign(t_bound - t0) if t_bound != t0 else 1
self.n = self.y.size
self.status = 'running'
self.nfev = 0
self.njev = 0
self.nlu = 0
@property
def step_size(self):
if self.t_old is None:
return None
else:
return np.abs(self.t - self.t_old)
def step(self):
"""Perform one integration step.
Returns
-------
message : string or None
Report from the solver. Typically a reason for a failure if
`self.status` is 'failed' after the step was taken or None
otherwise.
"""
if self.status != 'running':
raise RuntimeError("Attempt to step on a failed or finished "
"solver.")
if self.n == 0 or self.t == self.t_bound:
# Handle corner cases of empty solver or no integration.
self.t_old = self.t
self.t = self.t_bound
message = None
self.status = 'finished'
else:
t = self.t
success, message = self._step_impl()
if not success:
self.status = 'failed'
else:
self.t_old = t
if self.direction * (self.t - self.t_bound) >= 0:
self.status = 'finished'
return message
def dense_output(self):
"""Compute a local interpolant over the last successful step.
Returns
-------
sol : `DenseOutput`
Local interpolant over the last successful step.
"""
if self.t_old is None:
raise RuntimeError("Dense output is available after a successful "
"step was made.")
if self.n == 0 or self.t == self.t_old:
# Handle corner cases of empty solver and no integration.
return ConstantDenseOutput(self.t_old, self.t, self.y)
else:
return self._dense_output_impl()
def _step_impl(self):
raise NotImplementedError
def _dense_output_impl(self):
raise NotImplementedError
class DenseOutput(object):
"""Base class for local interpolant over step made by an ODE solver.
It interpolates between `t_min` and `t_max` (see Attributes below).
Evaluation outside this interval is not forbidden, but the accuracy is not
guaranteed.
Attributes
----------
t_min, t_max : float
Time range of the interpolation.
"""
def __init__(self, t_old, t):
self.t_old = t_old
self.t = t
self.t_min = min(t, t_old)
self.t_max = max(t, t_old)
def __call__(self, t):
"""Evaluate the interpolant.
Parameters
----------
t : float or array_like with shape (n_points,)
Points to evaluate the solution at.
Returns
-------
y : ndarray, shape (n,) or (n, n_points)
Computed values. Shape depends on whether `t` was a scalar or a
1-D array.
"""
t = np.asarray(t)
if t.ndim > 1:
raise ValueError("`t` must be a float or a 1-D array.")
return self._call_impl(t)
def _call_impl(self, t):
raise NotImplementedError
class ConstantDenseOutput(DenseOutput):
"""Constant value interpolator.
This class used for degenerate integration cases: equal integration limits
or a system with 0 equations.
"""
def __init__(self, t_old, t, value):
super(ConstantDenseOutput, self).__init__(t_old, t)
self.value = value
def _call_impl(self, t):
if t.ndim == 0:
return self.value
else:
ret = np.empty((self.value.shape[0], t.shape[0]))
ret[:] = self.value[:, None]
return ret