# 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

A vector representing a set of model parameters

v

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.