simpeg.maps.ParametricPolyMap.deriv#

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

Derivative of the mapping with respect to the model.

For a model $\mathbf{m}=[{\sigma }_1,{\sigma }_2,\mathbf{c}]$, the derivative of the mapping with respect to the model parameters is a numpy.ndarray of shape (mesh.nC, nP) of the form:

$$\frac{\partial \mathbf{u}}{\partial \mathbf{m}}=[\frac{\partial \mathbf{u}}{\partial {\sigma }_0}[\frac{\partial \mathbf{u}}{\partial {\sigma }_1}[\frac{\partial \mathbf{u}}{\partial c_0}[\frac{\partial \mathbf{u}}{\partial c_1}\cdots [\frac{\partial \mathbf{u}}{\partial c_N}]$$

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.