SolverTemplate

class SolverTemplate

Template for solvers for the Operator Inference regression \(\Z \approx \Ohat\D\trp\) (or \(\D\Ohat\trp \approx \Z\trp\)) for the operator matrix \(\Ohat\).

Child classes formulate the regression, which may include regularization terms and/or optimization constraints. Hyperparameters should be set in the constructor (regularization terms, etc.).

Properties:

d

Number of unknowns in each row of the operator matrix (number of columns of \(\D\) and \(\Ohat\)).

data_matrix

\(k \times d\) data matrix \(\D\).

k

Number of equations in the least-squares problem (number of rows of \(\D\) and number of columns of \(\Z\)).

lhs_matrix

\(r \times k\) left-hand side data \(\Z\).

r

Number of operator matrix rows to learn (number of rows of \(\Z\) and \(\Ohat\))

Methods:

cond	Compute the \(2\)-norm condition number of the data matrix \(\D\).
copy	Make a copy of the solver.
fit	Verify dimensions and save the data matrices.
load	Load a serialized solver from an HDF5 file, created previously from the save() method.
residual	Compute the residual of the \(2\)-norm regression objective for each row of the given operator matrix.
save	Serialize the solver, saving it in HDF5 format.
solve	Solve the Operator Inference regression.
verify	Verify the solver.