SimPEG.potential_fields.magnetics.Simulation3DIntegral.getJ

Simulation3DIntegral.getJ(m, f=None)

Returns the full Jacobian.

The general definition of the linear forward simulation is:

\[\mathbf{d} = \mathbf{G \, f}(\mathbf{m})\]

where \(\mathbf{f}\) is a mapping operator (optional) from the model space to a user-defined parameter space, and \(\mathbf{G}\) is an (n_data, n_param) linear operator. The getJ method forms and returns the full Jacobian:

\[\mathbf{J}(\mathbf{m}) = \mathbf{G} \frac{\partial \mathbf{f}}{\partial \mathbf{m}}\]

for the model \(\mathbf{m}\) provided. When \(\mathbf{f}\) is the identity map (default), the Jacobian is no longer model-dependent and reduces to:

\[\mathbf{J} = \mathbf{G}\]

Parameters:

mnumpy.ndarray

The model vector.

fNone

Precomputed fields are not used to speed up the computation of the Jacobian for linear problems.

Returns:

J(n_data, n_param) numpy.ndarray

\(J = G\frac{\partial f}{\partial\mathbf{m}}\). Where \(f\) is model_map.