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:

\[\frac{\partial \mathbf{u}}{\partial \mathbf{m}} = \Bigg [ \frac{\partial \mathbf{u}}{\partial \sigma_0} \;\; \Bigg [ \frac{\partial \mathbf{u}}{\partial \sigma_1} \;\; \Bigg [ \frac{\partial \mathbf{u}}{\partial c_0} \;\; \Bigg [ \frac{\partial \mathbf{u}}{\partial c_1} \;\; \cdots \;\; \Bigg [ \frac{\partial \mathbf{u}}{\partial c_N} \Bigg ]\]

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.