class AdaptiveStieltjesAlgorithm(*args)

AdaptiveStieltjes algorithm used to build the orthonormal basis.

The algorithm builds a polynomial basis orthonormal with respect to a specific distribution.

Parameters: measure : Distribution A measure for which the orthonormal polynomial basis is built.

Notes

It implements an adaptive Stieltjes algorithm that builds the polynomial family orthonormal with respect to the distribution measure, using the GaussKronrod adaptive integration method to compute the following dot-products: and where is the monic polynomial associated to the orthonormal polynomial , needed to compute the coefficients of the three-terms recurrence relation that defines (see OrthogonalUnivariatePolynomialFamily):

where and .

Methods

 getClassName() Accessor to the object’s name. getId() Accessor to the object’s id. getMeasure() Accessor to the measure. getName() Accessor to the object’s name. getRecurrenceCoefficients(n) Accessor to the recurrence coefficients. getShadowedId() Accessor to the object’s shadowed id. getVisibility() Accessor to the object’s visibility state. hasName() Test if the object is named. hasVisibleName() Test if the object has a distinguishable name. setMeasure(measure) Accessor to the measure. setName(name) Accessor to the object’s name. setShadowedId(id) Accessor to the object’s shadowed id. setVisibility(visible) Accessor to the object’s visibility state.
__init__(*args)

Initialize self. See help(type(self)) for accurate signature.

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.
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. coef : sequence of float Calculate the coefficients of recurrence , , such that .
getShadowedId()

Accessor to the object’s shadowed id.

Returns: id : int Internal unique identifier.
getVisibility()

Accessor to the object’s visibility state.

Returns: visible : bool Visibility flag.
hasName()

Test if the object is named.

Returns: hasName : bool True if the name is not empty.
hasVisibleName()

Test if the object has a distinguishable name.

Returns: hasVisibleName : bool True if the name is not empty and not the default one.
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.
setShadowedId(id)

Accessor to the object’s shadowed id.

Parameters: id : int Internal unique identifier.
setVisibility(visible)

Accessor to the object’s visibility state.

Parameters: visible : bool Visibility flag.