simpeg.regularization.CrossGradient.deriv#

CrossGradient.deriv(model)[source]#

Gradient of the regularization function evaluated for the model provided.

Where $\varphi (\mathbf{m})$ 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:

$$\begin{array}{r}\mathbf{m}=\left[\begin{array}{c}{\mathbf{m}}_{\mathbf{1}}\\ {\mathbf{m}}_{\mathbf{2}}\end{array}\right]\end{array}$$

The gradient has the form:

$$\begin{array}{r}2\frac{\partial \varphi }{\partial \mathbf{m}}=\left[\begin{array}{c}{\displaystyle \frac{\partial \varphi }{\partial {\mathbf{m}}_{\mathbf{1}}}}\\ {\displaystyle \frac{\partial \varphi }{\partial {\mathbf{m}}_{\mathbf{2}}}}\end{array}\right]\end{array}$$

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.