# SimPEG.maps.ChiMap.deriv#

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

Derivative of mapping with respect to the input parameters.

For a mapping $$\boldsymbol{\mu}(\boldsymbol{\chi})$$ that transforms a set of magnetic susceptibilities $$\boldsymbol{\chi}$$ to their corresponding magnetic permeabilities, i.e.:

$\boldsymbol{\mu}(\boldsymbol{\chi}) = \mu_0 \big (1 + \boldsymbol{\chi} \big ),$

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

$\frac{\partial \boldsymbol{\mu}}{\partial \boldsymbol{\chi}} = \mu_0 \mathbf{I}$
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.