scipy.optimize.

check_grad#

scipy.optimize.check_grad(func, grad, x0, *args, epsilon=np.float64(1.4901161193847656e-08), direction='all', rng=None)[source]#

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

Parameters:
funccallable func(x0, *args)

Function whose derivative is to be checked.

gradcallable grad(x0, *args)

Jacobian of func.

x0ndarray

Points to check grad against forward difference approximation of grad using func.

args\*args, optional

Extra arguments passed to func and grad.

epsilonfloat, optional

Step size used for the finite difference approximation. It defaults to sqrt(np.finfo(float).eps), which is approximately 1.49e-08.

directionstr, 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.

Changed in version 1.15.0: As part of the SPEC-007 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:
errfloat

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

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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