SimPEG.regularization.SmoothnessFirstOrder.deriv

SmoothnessFirstOrder.deriv(m) → numpy.ndarray

The regularization is:

$$R(m)=\frac{1}{2}\mathbf{(}\mathbf{m}\mathbf{-}{\mathbf{m}}_{\mathbf{\text{ref}}}{\mathbf{)}}^{\mathrm{\top }}{\mathbf{W}}^{\mathrm{\top }}\mathbf{W}\mathbf{(}\mathbf{m}\mathbf{-}{\mathbf{m}}_{\mathbf{\text{ref}}}\mathbf{)}$$

So the derivative is straight forward:

$$R(m)={\mathbf{W}}^{\mathrm{\top }}\mathbf{W}\mathbf{(}\mathbf{m}\mathbf{-}{\mathbf{m}}_{\mathbf{\text{ref}}}\mathbf{)}$$