simpeg.maps.LogMap.deriv#
- LogMap.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 logarithm for each parameter in the model \(\mathbf{m}\), i.e.:
\[\mathbf{u}(\mathbf{m}) = log(\mathbf{m})\]the derivative of the mapping with respect to the model is a diagonal matrix of the form:
\[\frac{\partial \mathbf{u}}{\partial \mathbf{m}} = \textrm{diag} \big ( \mathbf{m}^{-1} \big )\]- 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
- m(
- Returns:
scipy.sparse.csr_matrixDerivative 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.