SimPEG.objective_function.ComboObjectiveFunction.W

property ComboObjectiveFunction.W

Full weighting matrix for the combo objective function.

Consider a composite objective function :math`phi` that is a weighted sum of objective functions \(\phi_i\) with multipliers \(c_i\) such that

\[\phi = \sum_{i = 1}^N c_i \phi_i = \sum_{i = 1}^N \frac{c_i}{2} \big \| \mathbf{W}_i \, f_i (\mathbf{m}) \big \|^2_2\]

Where each objective function \(\phi_i\) has a weighting matrix \(W_i\), this method returns the full weighting matrix for the composite objective function:

\[\begin{split}\mathbf{W} = \begin{bmatrix} \sqrt{c_1} W_i \\ \vdots \\ \sqrt{c_N} W_N \end{bmatrix}\end{split}\]

Returns:

scipy.sparse.csr_matrix

Full weighting matrix for the combo objective function.