BarycentricOperator#

This module contains the concrete implementations of the barycentric operators classes.

The class BarycentricOperator implements the abstract base class OperatorABC and serves as the parent class for several specialized barycentric transformation operator classes.

These specialized classes differ in how the decomposition of the transformation matrix is performed and how the transformation is applied:

class minterpy.schemes.barycentric.operators.BarycentricOperator(transformation, transformation_data)[source]#

Bases: OperatorABC

Base class for the barycentric transformation operators. Specialized versions (dict, factorised, and piecewise) are derived from this base class.

Properties

`array_repr_full`	Array representation of the global transformation matrix.
`array_repr_sparse`	Array representation of the sub-transformation matrix transforming only the active monomials.
`array_representation`	Reconstructs the global transformation matrix.

Methods

`merging_fct`(*args)	Abstract method for reconstructing the global matrix from the decomposition.
`transformation_fct`(coeffs_in, ...)	Abstract method for executing the potentially decomposed linear transformation.

Parameters:: transformation (TransformationABC)

property array_representation: ndarray#: Reconstructs the global transformation matrix.

abstract static transformation_fct(coeffs_in, coeffs_out_placeholder, *args)[source]#: Abstract method for executing the potentially decomposed linear transformation.

abstract static merging_fct(*args)[source]#: Abstract method for reconstructing the global matrix from the decomposition.

__matmul__(other)[source]#

Applies the transformation operator on the input.

Parameters:: other (OperatorABC | ndarray)
Return type:: MatrixOperator | ndarray

_get_array_repr()[source]#: Reconstructs the global transformation matrix.

__init__(transformation, transformation_data)#

Parameters:: transformation (TransformationABC)

__weakref__#: list of weak references to the object (if defined)

property array_repr_full: ndarray#

Array representation of the global transformation matrix.

Returns:: the matrix representation of the transformation.

Notes

The output transforms the whole basis (not only the active monomials)!

property array_repr_sparse: ndarray#

Array representation of the sub-transformation matrix transforming only the active monomials.

Returns:: the transformation matrix for the active monomials.

Notes

This is an experimental feature which is part of ongoing work.