simpeg.regularization.JointTotalVariation.deriv#
- JointTotalVariation.deriv(model)[source]#
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 multiple physical properties \(\mathbf{m_1}, \; \mathbf{m_2}, \; ...\) such that:
\[\begin{split}\mathbf{m} = \begin{bmatrix} \mathbf{m_1} \\ \mathbf{m_2} \\ \vdots \end{bmatrix}\end{split}\]The gradient has the form:
\[\begin{split}\frac{\partial \phi}{\partial \mathbf{m}} = \begin{bmatrix} \dfrac{\partial \phi}{\partial \mathbf{m_1}} \\ \dfrac{\partial \phi}{\partial \mathbf{m_2}} \\ \vdots \end{bmatrix}\end{split}\]- Parameters:
- model(
n_param, )numpy.ndarray The model; a vector array containing all physical properties.
- model(
- Returns:
- (
n_param, )numpy.ndarray Gradient of the regularization function evaluated for the model provided.
- (