OrthonormalizationAlgorithm

class OrthonormalizationAlgorithm(*args)

Algorithm used to build the orthonormal basis.

With respect to a specific distribution.

Available constructors:

OrthonormalizationAlgorithm(orthoAlgoImp)

OrthonormalizationAlgorithm(measure)

Parameters:

orthoAlgoImp : OrthonormalizationAlgorithmImplementation

An orthonormalization algorithm implementation which is the GramSchmidtAlgorithm or the ChebychevAlgorithm.

measure : Distribution

A distribution for which the orthonormal polynomial basis is built.

Notes

It enables to build the orthonormal polynomial basis with respect to the given distribution.

In the first usage, the algorithm orthoAlgoImp is used (that specifies the associated distribution). In the second usage, the Gram-Schmidt algorithm is used by default. Only the distribution measure is specified.

Methods

getClassName() Accessor to the object’s name.
getId() Accessor to the object’s id.
getImplementation(*args) Accessor to the underlying implementation.
getMeasure() Accessor to the measure.
getName() Accessor to the object’s name.
getRecurrenceCoefficients(n) Accessor to the recurrence coefficients.
setMeasure(measure) Accessor to the measure.
setName(name) Accessor to the object’s name.
__init__(*args)
getClassName()

Accessor to the object’s name.

Returns:

class_name : str

The object class name (object.__class__.__name__).

getId()

Accessor to the object’s id.

Returns:

id : int

Internal unique identifier.

getImplementation(*args)

Accessor to the underlying implementation.

Returns:

impl : Implementation

The implementation class.

getMeasure()

Accessor to the measure.

Returns:

m : Distribution

The measure for which the orthonormal polynomial basis is built.

getName()

Accessor to the object’s name.

Returns:

name : str

The name of the object.

getRecurrenceCoefficients(n)

Accessor to the recurrence coefficients.

Parameters:

n : integer

Index ot the recurrence step.

Returns:

coef : sequence of float

Calculate the coefficients of recurrence a_0, a_1, a_2 such that P_{n+1}(x) = (a_0 \times x + a_1) \times P_n(x) + a_2 \times P_{n-1}(x).

setMeasure(measure)

Accessor to the measure.

Parameters:

m : Distribution

The measure for which the orthonormal polynomial basis is built.

setName(name)

Accessor to the object’s name.

Parameters:

name : str

The name of the object.