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:

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

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.