InterpInputOperator

class InterpInputOperator(training_parameters=None, entries=None, InterpolatorClass: type = None, fromblock=False)

Parametric input operator \(\Ophat_{\ell}(\qhat,\u;\bfmu) = \Bhat(\bfmu)\u\) where \(\Bhat(\bfmu) \in \RR^{r \times m}\) and the parametric dependence is handled with elementwise interpolation.

\[\Bhat(\bfmu) = \textrm{interpolate}( (\bfmu_0,\Bhat^{(0)}),\ldots,(\bfmu_{s-1},\Bhat^{(s-1)}); \bfmu)\]

Here,

• \(\bfmu_0,\ldots,\bfmu_{s-1}\in\RR^p\) are the (fixed) training parameter values, and

• \(\Bhat^{(i)} = \Bhat(\bfmu_i) \in \RR^{r \times m}\) are the operator entries evaluated at the training parameter values.

See opinf.operators.InputOperator.

Parameters:

training_parameterslist of s scalars or (p,) 1D ndarrays

Parameter values for which the operator entries are known or will be inferred from data. If not provided in the constructor, use set_training_parameters() later.

entrieslist of s ndarrays, or None

Operator entries corresponding to the training_parameters. If not provided in the constructor, use set_entries() later.

InterpolatorClasstype or None

Class for the elementwise interpolation. Must obey the syntax

>>> interpolator = InterpolatorClass(data_points, data_values)
>>> interpolator_evaluation = interpolator(new_data_point)

This can be, e.g., a class from scipy.interpolate. If None (default), use scipy.interpolate.CubicSpline for one-dimensional parameters and scipy.interpolate.LinearNDInterpolator otherwise. If not provided in the constructor, use set_interpolator() later.

fromblockbool

If True, interpret entries as a horizontal concatenation of arrays; if False (default), interpret entries as a list of arrays.

Properties:

entries

Operator matrices corresponding to the training parameters values, i.e., entries[i] is the operator matrix corresponding to the parameter value training_parameters[i].

input_dimension

Dimension of the input \(\u\) that the operator acts on.

interpolator

Interpolator object for evaluating the operator at specified parameter values.

parameter_dimension

Dimension \(p\) of the parameter vector \(\bfmu\) that the operator matrix depends on.

shape

Shape of the operator matrix when evaluated at a parameter value.

state_dimension

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

training_parameters

Parameter values where the operator matrix is known or will be inferred from data.

Methods:

apply	Apply the operator to the given state and input at the specified parameter value, \(\Ophat_\ell(\qhat,\u;\bfmu)\).
copy	Return a copy of the operator.
datablock	Return the data matrix block corresponding to the operator.
evaluate	Evaluate the operator at the given parameter value.
galerkin	Project this operator to a low-dimensional linear space.
jacobian	Construct the state Jacobian of the operator, \(\ddqhat\Ophat_\ell(\qhat,\u;\bfmu)\).
load	Load a parametric operator from an HDF5 file.
operator_dimension	Number of columns in the concatenated operator matrix.
save	Save the operator to an HDF5 file.
set_entries	Set the operator matrices at the training parameter values.
set_interpolator	Construct the interpolator for the operator matrix.
set_training_parameters	Set the training parameter values.
verify	Verify dimension attributes and evaluate().