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scipy.optimize.

# check_grad

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

  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.

      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:
    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

  `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