simpeg.maps.LogisticSigmoidMap.deriv#

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

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:

$$\frac{\partial \mathbf{u}}{\partial \mathbf{m}}=\text{diag}((b-a)\cdot sigmoid(\mathbf{m})\cdot (1-sigmoid(\mathbf{m})))$$

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.