simpeg.regularization.CrossGradient.deriv

CrossGradient.deriv(model)

Gradient of the regularization function evaluated for the model provided.

Where \(\phi (\mathbf{m})\) is the discrete regularization function (objective function), this method evaluates and returns the derivative with respect to the model parameters; i.e. the gradient. For a model \(\mathbf{m}\) consisting of two physical properties such that:

\[\begin{split}\mathbf{m} = \begin{bmatrix} \mathbf{m_1} \\ \mathbf{m_2} \end{bmatrix}\end{split}\]

The gradient has the form:

\[\begin{split}2 \frac{\partial \phi}{\partial \mathbf{m}} = \begin{bmatrix} \dfrac{\partial \phi}{\partial \mathbf{m_1}} \\ \dfrac{\partial \phi}{\partial \mathbf{m_2}} \end{bmatrix}\end{split}\]

Parameters:

model(n_param, ) numpy.ndarray

The model; a vector array containing all physical properties.

Returns:

(n_param, ) numpy.ndarray

Gradient of the regularization function evaluated for the model provided.