simpeg.maps.LinearMap.deriv#

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

Derivative of the mapping with respect to the input parameters.

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 or numpy.ndarray: Derivative of the mapping with respect to the model parameters. For an identity mapping, this is just a sparse identity matrix. If the input argument v is not None, the method returns the derivative times the vector v; which in this case is just v.

Notes

Let \(\mathbf{m}\) be a set of model parameters and let \(\mathbf{I}\) denote the identity map. Where the identity mapping acting on the model parameters can be expressed as:

\[\mathbf{u} = \mathbf{I m},\]

the deriv method returns the derivative of \(\mathbf{u}\) with respect to the model parameters; i.e.:

\[\frac{\partial \mathbf{u}}{\partial \mathbf{m}} = \mathbf{I}\]

For the Identity map deriv simply returns a sparse identity matrix.