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.

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.

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.

__init__(*args)
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

A copy of the underlying implementation object.

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:
nint

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).

setMeasure(measure)

Accessor to the measure.

Parameters:
mDistribution

The measure for which the orthonormal polynomial basis is built.

setName(name)

Accessor to the object’s name.

Parameters:
namestr

The name of the object.