simpeg.maps.ExpMap.deriv#

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

Derivative of mapping with respect to the input parameters.

For a mapping $\mathbf{u}(\mathbf{m})$ that computes the natural exponential function for each parameter in the model $\mathbf{m}$, i.e.:

$$\mathbf{u}(\mathbf{m})=exp(\mathbf{m}),$$

the derivative of the mapping with respect to the model is a diagonal matrix of the form:

$$\frac{\partial \mathbf{u}}{\partial \mathbf{m}}=\text{diag}(exp(\mathbf{m}))$$

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.