SimPEG.maps.Projection.deriv

Projection.deriv(m, v=None)

Derivative of the mapping with respect to the input parameters.

Let \(\mathbf{m}\) be a set of model parameters and let \(\mathbf{P}\) be a matrix denoting the projection mapping. Where the projection mapping acting on the model parameters can be expressed as:

\[\mathbf{u} = \mathbf{P m},\]

the deriv method returns the derivative of \(\mathbf{u}\) with respect to the model parameters; i.e.:

\[\frac{\partial \mathbf{u}}{\partial \mathbf{m}} = \mathbf{P}\]

Note that in this case, deriv simply returns a sparse projection matrix.

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.