simpeg.maps.InjectActiveCells.deriv#

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

Derivative of the mapping with respect to the input parameters.

For a discrete set of model parameters $\mathbf{m}$ defined on a set of active cells, the mapping $\mathbf{u}(\mathbf{m})$ is defined as:

$$\mathbf{u}(\mathbf{m})=\mathbf{Pm}+\mathbf{d}{m}_{\perp }$$

where $\mathbf{P}$ is a (nC , nP) projection matrix from active cells to all mesh cells, and $\mathbf{d}$ is a (nC , 1) matrix that projects the inactive cell value $m_{\perp }$ to all inactive mesh cells.

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.