identity#

Concrete implementation of Identity transformation when there is no basis change.

Notes

This class is needed for completeness reasons and also to enable the high-level helper functions for polynomial basis transformations to handle transformations between identical basis.

class minterpy.transformations.identity.Identity(origin_poly)[source]#

Bases: TransformationABC

Transformation between same basis.

Properties

`grid`	The grid of the origin polynomial.
`multi_index`	The multi index set of the origin polynomial (and also the target polynomial).
`transformation_operator`	The polynomial basis transformation operator.

Parameters:: origin_poly (MultivariatePolynomialSingleABC)

origin_type#: alias of MultivariatePolynomialABC

target_type#: alias of MultivariatePolynomialABC

_get_transformation_operator()#

Abstract container for storing the transformation operator.

This is a placeholder of the ABC, which is overwritten by the concrete implementation.

_apply_transformation(origin_poly)[source]#

Transforms the polynomial to the target type of the transformation.

Parameters:: origin_poly – instance of the polynomial to be transformed
Returns:: an instance of the transformed polynomial in the target basis

__call__(origin_poly=None)#

Transformation of polynomial.

This function is called when an instance of transformation is called T() or T(x). If called without any arguments, the transformation is applied on the origin_poly used to construct the transformation. If an argument is passed, the transformation is applied on the instance passed.

Parameters:: origin_poly (MultivariatePolynomialSingleABC | None) – (optional) an instance of the polynomial to be transformed.
Returns:: an instance of the polynomial in the target basis.

__init__(origin_poly)#

Parameters:: origin_poly (MultivariatePolynomialSingleABC)

classmethod __init_subclass__(**kwargs)#: Add a concrete implementation to the registry of available transformations

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

property _target_indices: MultiIndexSet#

The MultiIndexSet of the target_poly.

Returns:: the indices the target polynomial will have

property grid: Grid#: The grid of the origin polynomial.

property multi_index: MultiIndexSet#: The multi index set of the origin polynomial (and also the target polynomial).

property transformation_operator: OperatorABC#

The polynomial basis transformation operator.

Returns:: instance of the transformation operator

Notes

The transformation operator once constructed can be reused for transforming other polynomial instance of the origin_poly type, which have the same basis (and grid) as the origin_poly, to the target_poly type.