OrthogonalBasis

class OrthogonalBasis(*args)

Orthogonal basis.

See also

StandardDistributionPolynomialFactory

Notes

OrthogonalBasis is the interface class of the OrthogonalFunctionFactory implementation, which is an OrthogonalProductPolynomialFactory in the particular case of polynomial chaos expansion.

Examples

>>> import openturns as ot
>>> # Create an orthogonal basis
>>> polynomialCollection = [ot.LegendreFactory(), ot.LaguerreFactory(), ot.HermiteFactory()]
>>> productBasis = ot.OrthogonalBasis(ot.OrthogonalProductPolynomialFactory(polynomialCollection))

Methods

build(*args)	Get the term of the basis collection at a given index or multi-indices.
getClassName()	Accessor to the object's name.
getEnumerateFunction()	Return the enumerate function.
getId()	Accessor to the object's id.
getImplementation()	Accessor to the underlying implementation.
getMeasure()	Get the measure upon which the basis is orthogonal.
getName()	Accessor to the object's name.
setName(name)	Accessor to the object's name.

__init__(*args)

build(*args)

Get the term of the basis collection at a given index or multi-indices.

Parameters

indexint

Indicates the term of the basis which must be constructed. In other words, index is used by a bijection from to (with the dimension of the basis). The bijection is detailed in EnumerateFunction.

indicessequence of int

Indicates the term of the basis which must be constructed. In other words, indices is used by a bijection from to (with the dimension of the basis). The bijection is the inverse of EnumerateFunction.

Returns

functionFunction

The term of the basis collection at the index index or the inverse of indices.

Examples

>>> import openturns as ot
>>> # Create an orthogonal basis
>>> polynomialCollection = [ot.LegendreFactory(), ot.LaguerreFactory(), ot.HermiteFactory()]
>>> productBasis = ot.OrthogonalBasis(ot.OrthogonalProductPolynomialFactory(polynomialCollection))
>>> termBasis = productBasis.build(4)
>>> print(termBasis.getEvaluation())
-1.11803 + 3.3541 * x0^2
>>> termBasis = productBasis.build(5)
>>> print(termBasis.getEvaluation())
(1.73205 * x0) * (-1 + x1)
>>> termBasis2 = productBasis.build([1,1,0])
>>> print(termBasis2.getEvaluation())
(1.73205 * x0) * (-1 + x1)

getClassName()

Accessor to the object’s name.

Returns

class_namestr

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

getEnumerateFunction()

Return the enumerate function.

Returns

enumerateFunctionEnumerateFunction

Enumerate function that translates unidimensional indices into multidimensional indices.

getId()

Accessor to the object’s id.

Returns

idint

Internal unique identifier.

getImplementation()

Accessor to the underlying implementation.

Returns

implImplementation

The implementation class.

getMeasure()

Get the measure upon which the basis is orthogonal.

Returns

measureDistribution

Measure upon which the basis is orthogonal.

Examples

>>> import openturns as ot
>>> # Create an orthogonal basis
>>> polynomialCollection = [ot.LegendreFactory(), ot.LaguerreFactory(), ot.HermiteFactory()]
>>> productBasis = ot.OrthogonalBasis(ot.OrthogonalProductPolynomialFactory(polynomialCollection))
>>> measure = productBasis.getMeasure()
>>> print(measure.getMarginal(0))
Uniform(a = -1, b = 1)
>>> print(measure.getMarginal(1))
Gamma(k = 1, lambda = 1, gamma = 0)
>>> print(measure.getMarginal(2))
Normal(mu = 0, sigma = 1)

getName()

Accessor to the object’s name.

Returns

namestr

The name of the object.

setName(name)

Accessor to the object’s name.

Parameters

namestr

The name of the object.