simpeg.regularization.SmoothnessFullGradient.deriv2#

SmoothnessFullGradient.deriv2(m, v=None)[source]#

Hessian of the regularization function evaluated for the model provided.

Where ϕ(m) is the discrete regularization function (objective function), this method returns the second-derivative (Hessian) with respect to the model parameters:

2ϕm2

or the second-derivative (Hessian) multiplied by a vector (v):

2ϕm2v
Parameters:
m(n_param, ) numpy.ndarray

The model for which the Hessian is evaluated.

vNone, (n_param, ) numpy.ndarray (optional)

A vector.

Returns:
(n_param, n_param) scipy.sparse.csr_matrix | (n_param, ) numpy.ndarray

If the input argument v is None, the Hessian of the regularization function for the model provided is returned. If v is not None, the Hessian multiplied by the vector provided is returned.