# 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

A vector representing a set of model parameters

v

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.