get_operator_regularizer()

classmethod TikhonovDecoupledSolver.get_operator_regularizer(operators: list, regularization_parameters: list, state_dimension: int, input_dimension: int = 0)

Construct a regularizer so that each operator is regularized separately.

The regularization term for this solver is

\[\|\bfGamma\Ohat\trp\|_F^2\]

where \(\Ohat\in\RR^{r\times d}\) is the unknown and \(\bfGamma\in\RR^{d \times d}\) is a given regularization matrix. This method constructs \(\bfGamma\) such that each operator represented in \(\Ohat\) is regularized separately. For example, if \(\Ohat = [~\chat~~\Ahat~~\Hhat~~\Bhat~]\), then \(\bfGamma\) may be designed so that

\[\|\bfGamma\Ohat\trp\|_F^2 = \gamma_1^2\|\chat\|_F^2 + \gamma_2^2\|\Ahat\|_F^2 + \gamma_3^2\|\Hhat\|_F^2 + \gamma_4^2\|\Bhat\|_F^2.\]

Parameters:

operatorslist of opinf.operators objects

Collection of operators comprising the operator matrix.

regularization_parameterslist of floats or ndarrays

Regularization hyperparameters for each operator, i.e., regularization_parameters[i] corresponds to operators[i].

state_dimensionint

Dimension of the (reduced) state.

input_dimensionint

Dimension of the input. If there is no input, this should be 0 (default).

Returns:

regularizer(d,) ndarray

Diagonals of the regularization matrix so that operators[i] is regularized with constant regularization_parameters[i].

Raises:

ValueError

If a different number of operators and ‘ regularization_parameters are provided, or if the input_dimension is not provided but at least one of the operators acts on inputs.

TypeError

If an entry operators has an unsupported type.

Warns:

OpInfWarning

If only one operator is provided (use L2Solver instead), or if the input_dimension is provided but none of the operators act on inputs.