simpeg.maps.IdentityMap.deriv#

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

Derivative of the mapping with respect to the input parameters.

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 or numpy.ndarray

Derivative of the mapping with respect to the model parameters. For an identity mapping, this is just a sparse identity matrix. If the input argument v is not None, the method returns the derivative times the vector v; which in this case is just v.

Notes

Let $\mathbf{m}$ be a set of model parameters and let $\mathbf{I}$ denote the identity map. Where the identity mapping acting on the model parameters can be expressed as:

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

the deriv method returns the derivative of $\mathbf{u}$ with respect to the model parameters; i.e.:

$$\frac{\partial \mathbf{u}}{\partial \mathbf{m}}=\mathbf{I}$$

For the Identity map deriv simply returns a sparse identity matrix.