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 \(\boldsymbol{\mu_r}\) to their corresponding magnetic permeabilities, i.e.:
\[\boldsymbol{\mu}(\boldsymbol{\mu_r}) = \mu_0 \boldsymbol{\mu_r},\]the derivative of the mapping with respect to the model is the identity matrix scaled by the permeability of free-space. Thus:
\[\frac{\partial \boldsymbol{\mu}}{\partial \boldsymbol{\mu_r}} = \mu_0 \mathbf{I}\]- 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
- 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.