simpeg.maps.Weighting.deriv

Weighting.deriv(m, v=None)

Derivative of mapping with respect to the input parameters.

For a weighting mapping \(\mathbf{u}(\mathbf{m})\) that scales the input parameters in the model \(\mathbf{m}\) by their corresponding weights \(\mathbf{w}\); i.e.:

\[\mathbf{u}(\mathbf{m}) = \mathbf{w} \dot \mathbf{m},\]

the derivative of the mapping with respect to the model is a diagonal matrix of the form:

\[\frac{\partial \mathbf{u}}{\partial \mathbf{m}} = diag (\mathbf{w})\]

Parameters:

m(nP) numpy.ndarray

A vector representing a set of model parameters

v(nP) numpy.ndarray

If not None, the method returns the derivative times the vector v

Returns:

scipy.sparse.csr_matrix

Derivative of the mapping with respect to the model parameters. If the input argument v is not None, the method returns the derivative times the vector v.