SimPEG.maps.ExpMap.deriv#

ExpMap.deriv(m, v=None)[source]#

Derivative of mapping with respect to the input parameters.

For a mapping \(\mathbf{u}(\mathbf{m})\) that computes the natural exponential function for each parameter in the model \(\mathbf{m}\), i.e.:

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

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

\[\frac{\partial \mathbf{u}}{\partial \mathbf{m}} = \textrm{diag} \big ( exp(\mathbf{m}) \big )\]
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.