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

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

funccallable func(x0, *args)

Function whose derivative is to be checked.

gradcallable grad(x0, *args)

Jacobian of func.


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.

seed{None, int, numpy.random.Generator,

If seed is None (or np.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. Specify seed for reproducing the return value from this function. The random numbers generated with this seed affect the random vector along which gradients are computed to check grad. Note that seed is only used when direction argument is set to ‘random’.


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



>>> 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)