OrthogonalBasis

class OrthogonalBasis(*args)

Orthogonal basis.

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(index) Get the term of the basis collection at a given index.
getClassName() Accessor to the object’s name.
getEnumerateFunction() Return the enumerate function.
getId() Accessor to the object’s id.
getImplementation(*args) 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(index)

Get the term of the basis collection at a given index.

Parameters:

index : int

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

Returns:

function : Function

The term of the basis collection at the index index.

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)
getClassName()

Accessor to the object’s name.

Returns:

class_name : str

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

getEnumerateFunction()

Return the enumerate function.

Returns:

enumerateFunction : EnumerateFunction

Enumerate function that translates unidimensional indices into multidimensional indices.

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()

Get the measure upon which the basis is orthogonal.

Returns:

measure : Distribution

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:

name : str

The name of the object.

setName(name)

Accessor to the object’s name.

Parameters:

name : str

The name of the object.