simpeg.maps.SurjectUnits.deriv#
- SurjectUnits.deriv(m, v=None)[source]#
Derivative of the mapping with respect to the input parameters.
Let \(\mathbf{m}\) be a set of model parameters. The surjective mapping can be defined as a sparse projection matrix \(\mathbf{P}\). Therefore we can define the surjective mapping acting on the model parameters as:
\[\mathbf{u} = \mathbf{P m},\]the deriv method returns the derivative of \(\mathbf{u}\) with respect to the model parameters; i.e.:
\[\frac{\partial \mathbf{u}}{\partial \mathbf{m}} = \mathbf{P}\]Note that in this case, deriv simply returns a sparse projection matrix.
- 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_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.