# SimPEG.maps.SurjectUnits.deriv#

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

Derivative of the mapping with respect to the input parameters.

Let $$\mathbf{m}$$ be a set of model parameters. The surjective mapping can be defined as a sparse projection matrix $$\mathbf{P}$$. Therefore we can define the surjective mapping acting on the model parameters as:

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

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 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.