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Module « scipy.optimize »

Fonction check_grad - module scipy.optimize

Signature de la fonction check_grad

def check_grad(func, grad, x0, *args, epsilon=np.float64(1.4901161193847656e-08), direction='all', rng=None) 

Description

help(scipy.optimize.check_grad)

    


Check the correctness of a gradient function by comparing it against a
(forward) finite-difference approximation of the gradient.

Parameters
----------
func : callable ``func(x0, *args)``
    Function whose derivative is to be checked.
grad : callable ``grad(x0, *args)``
    Jacobian of `func`.
x0 : ndarray
    Points to check `grad` against forward difference approximation of grad
    using `func`.
args : \\*args, optional
    Extra arguments passed to `func` and `grad`.
epsilon : float, optional
    Step size used for the finite difference approximation. It defaults to
    ``sqrt(np.finfo(float).eps)``, which is approximately 1.49e-08.
direction : str, optional
    If set to ``'random'``, then gradients along a random vector
    are used to check `grad` against forward difference approximation
    using `func`. By default it is ``'all'``, in which case, all
    the one hot direction vectors are considered to check `grad`.
    If `func` is a vector valued function then only ``'all'`` can be used.
rng : {None, int, `numpy.random.Generator`}, optional
    If `rng` is passed by keyword, types other than `numpy.random.Generator` are
    passed to `numpy.random.default_rng` to instantiate a ``Generator``.
    If `rng` is already a ``Generator`` instance, then the provided instance is
    used. Specify `rng` for repeatable function behavior.

    If this argument is passed by position or `seed` is passed by keyword,
    legacy behavior for the argument `seed` applies:

    - If `seed` is None (or `numpy.random`), the `numpy.random.RandomState`
      singleton is used.
    - If `seed` is an int, a new ``RandomState`` instance is used,
      seeded with `seed`.
    - If `seed` is already a ``Generator`` or ``RandomState`` instance then
      that instance is used.

    .. versionchanged:: 1.15.0
        As part of the `SPEC-007 <https://scientific-python.org/specs/spec-0007/>`_
        transition from use of `numpy.random.RandomState` to
        `numpy.random.Generator`, this keyword was changed from `seed` to `rng`.
        For an interim period, both keywords will continue to work, although only one
        may be specified at a time. After the interim period, function calls using the
        `seed` keyword will emit warnings. The behavior of both `seed` and
        `rng` are outlined above, but only the `rng` keyword should be used in new code.
        
    The random numbers generated affect the random vector along which gradients
    are computed to check ``grad``. Note that `rng` is only used when `direction`
    argument is set to `'random'`.

Returns
-------
err : float
    The square root of the sum of squares (i.e., the 2-norm) of the
    difference between ``grad(x0, *args)`` and the finite difference
    approximation of `grad` using func at the points `x0`.

See Also
--------

:func:`approx_fprime`
    ..

Examples
--------
>>> import numpy as np
>>> def func(x):
...     return x[0]**2 - 0.5 * x[1]**3
>>> def grad(x):
...     return [2 * x[0], -1.5 * x[1]**2]
>>> from scipy.optimize import check_grad
>>> check_grad(func, grad, [1.5, -1.5])
2.9802322387695312e-08  # may vary
>>> rng = np.random.default_rng()
>>> check_grad(func, grad, [1.5, -1.5],
...             direction='random', seed=rng)
2.9802322387695312e-08

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