OrthonormalizationAlgorithm¶

class OrthonormalizationAlgorithm(*args)¶

Algorithm used to build the orthonormal basis.

With respect to a specific distribution.

Available constructors:

OrthonormalizationAlgorithm(orthoAlgoImp)

OrthonormalizationAlgorithm(measure)

Parameters

orthoAlgoImpOrthonormalizationAlgorithmImplementation: An orthonormalization algorithm implementation.
measureDistribution: A distribution for which the orthonormal polynomial basis is built.

See also

AdaptiveStieltjesAlgorithm

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`()	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)¶: Initialize self. See help(type(self)) for accurate signature.

getClassName()¶

Accessor to the object’s name.

Returns

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

getId()¶

Accessor to the object’s id.

Returns

idint: Internal unique identifier.

getImplementation()¶

Accessor to the underlying implementation.

Returns

implImplementation: The implementation class.

getMeasure()¶

Accessor to the measure.

Returns

mDistribution: The measure for which the orthonormal polynomial basis is built.

getName()¶

Accessor to the object’s name.

Returns

namestr: The name of the object.

getRecurrenceCoefficients(n)¶

Accessor to the recurrence coefficients.

Parameters

ninteger: Index ot the recurrence step.

Returns

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