simpeg.maps.LogisticSigmoidMap.deriv

LogisticSigmoidMap.deriv(m, v=None)

Derivative of mapping with respect to the input parameters.

For a mapping \(\mathbf{u}(\mathbf{m})\) the derivative of the mapping with respect to the model is a diagonal matrix of the form:

\[\frac{\partial \mathbf{u}}{\partial \mathbf{m}} = \textrm{diag} \big ( (b-a)\cdot sigmoid(\mathbf{m})\cdot(1-sigmoid(\mathbf{m})) \big )\]

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:

numpy.ndarray or 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.