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 $ϕ_{i}$ with multipliers $c_{i}$ such that

ϕ = \sum_{i = 1}^{N} c_{i} ϕ_{i} = \sum_{i = 1}^{N} \frac{c_{i}}{2} ‖ W_{i} f_{i} (m) ‖_{2}^{2}

Where each objective function $ϕ_{i}$ has a weighting matrix $W_{i}$ , this method returns the full weighting matrix for the composite objective function:

\begin{array}{r} W = [\begin{array}{c} \sqrt{c_{1}} W_{i} \\ ⋮ \\ \sqrt{c_{N}} W_{N} \end{array}] \end{array}

Returns:

scipy.sparse.csr_matrix: Full weighting matrix for the combo objective function.