SimPEG.regularization.AmplitudeSmoothnessFirstOrder.f_m_deriv#
- AmplitudeSmoothnessFirstOrder.f_m_deriv(m) csr_matrix[source]#
Derivative of the regularization kernel function.
For first-order smoothness regularization in the x-direction, the derivative of the regularization kernel function with respect to the model is given by:
\[\begin{split}\frac{\partial \mathbf{f_m}}{\partial \mathbf{m}} = \begin{bmatrix} \mathbf{G_x} & \mathbf{0} \\ \mathbf{0} & \mathbf{G_x} \end{bmatrix}\end{split}\]where \(\mathbf{G_x}\) is the partial cell gradient operator along x (i.e. the x-derivative).
- Parameters:
- m
numpy.ndarray The model.
- m
- Returns:
scipy.sparse.csr_matrixThe derivative of the regularization kernel function.