OpInfOperator

class OpInfOperator(entries=None)

Template for nonparametric operators that can be calibrated through Operator Inference, i.e., \(\Ophat_{\ell}(\qhat, \u) = \Ohat_{\ell}\d(\qhat, \u)\).

In this package, an “operator” is a function \(\Ophat_{\ell}: \RR^r \times \RR^m \to \RR^r\) that acts on a state vector \(\qhat\in\RR^r\) and (optionally) an input vector \(\u\in\RR^m\).

Models are defined as the sum of several operators, for example, an opinf.models.ContinuousModel object represents a system of ordinary differential equations:

\[\ddt\qhat(t) = \sum_{\ell=1}^{n_\textrm{terms}}\Ophat_{\ell}(\qhat(t),\u(t)).\]

Operator Inference calibrates operators that can be written as the product of a matrix and some known (possibly nonlinear) function of the state and/or input:

\[\Ophat_{\ell}(\qhat, \u) = \Ohat_{\ell}\d(\qhat, \u),\]

where \(\Ohat_{\ell}\in\RR^{r\times d}\) is a constant matrix, called the operator entries, and \(\d_{\ell}:\RR^r\times\RR^m\to\RR^d\).

Notes

• To define operators with a more general structure than \(\Ohat_{\ell}\d(\qhat, \u),\) see OperatorTemplate.

• If the operator entries \(\Ohat_{\ell}\) depend on one or more external parameters, it is called a parametric operator. See ParametricOpInfOperator.

Properties:

entries

Discrete representation of the operator, the matrix \(\Ohat\).

shape

Shape of the operator matrix.

state_dimension

Dimension \(r\) of the state \(\qhat\) that the operator acts on.

Methods:

apply	Apply the operator mapping to the given state / input.
copy	Return a copy of the operator.
datablock	Construct the data matrix block corresponding to the operator.
galerkin	Get the (Petrov-)Galerkin projection of this operator.
jacobian	Construct the state Jacobian of the operator.
load	Load an operator from an HDF5 file.
operator_dimension	Column dimension of the operator entries.
save	Save the operator to an HDF5 file.
set_entries	Set the entries attribute.
verify	Verify consistency between dimension properties and required methods.