simpeg.flow.richards.SimulationNDCellCentered.Jtvec_approx

SimulationNDCellCentered.Jtvec_approx(m, v, f=None)

Approximation of the Jacobian transpose times a vector for the model provided.

The Jacobian defines the derivative of the predicted data vector with respect to the model parameters. For a data vector \(\mathbf{d}\) predicted for a set of model parameters \(\mathbf{m}\), the Jacobian is an (n_data, n_param) matrix whose elements are given by:

\[J_{ij} = \frac{\partial d_i}{\partial m_j}\]

For a model m and vector v, the Jtvec_approx method approximates the matrix-vector product:

\[\mathbf{u} = \mathbf{J^T \, v}\]

Parameters:

m(n_param, ) numpy.ndarray

The model parameters.

v(n_data, ) numpy.ndarray

Vector we are multiplying.

fsimpeg.field.Fields, optional

If provided, fields will not need to be recomputed for the current model to compute Jtvec.

Returns:

(n_param, ) numpy.ndarray

Approximation of the Jacobian transpose times a vector for the model provided.