simpeg.maps.MuRelative.deriv#

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

Derivative of mapping with respect to the input parameters.

For a mapping that transforms a set of relative permeabilities ${\mathit{\mu }}_{\mathit{r}}$ to their corresponding magnetic permeabilities, i.e.:

$$\mathit{\mu }({\mathit{\mu }}_{\mathit{r}})={\mu }_0{\mathit{\mu }}_{\mathit{r}},$$

the derivative of the mapping with respect to the model is the identity matrix scaled by the permeability of free-space. Thus:

$$\frac{\partial \mathit{\mu }}{\partial {\mathit{\mu }}_{\mathit{r}}}={\mu }_0\mathbf{I}$$

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.