simpeg.maps.Projection.deriv#

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

Derivative of the mapping with respect to the input parameters.

Let $\mathbf{m}$ be a set of model parameters and let $\mathbf{P}$ be a matrix denoting the projection mapping. Where the projection mapping acting on the model parameters can be expressed as:

$$\mathbf{u}=\mathbf{P}\mathbf{m},$$

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

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.