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

Derivative of the mapping with respect to the input parameters.

Let \(m\) be the single parameter that the mapping acts on. The SurjectFull class constructs a mapping that can be defined as a projection matrix \(\mathbf{P}\); i.e.:

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

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 the original operator \(\mathbf{P}\); a (mesh.nC , 1) numpy.ndarray of 1s.

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