# SimPEG.maps.IdentityMap.deriv#

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

Derivative of the mapping with respect to the input parameters.

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 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:

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

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.