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(
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
- m(
- Returns:
scipy.sparse.csr_matrixDerivative 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.