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

A copy of the underlying implementation object.

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.

Examples using the class

Polynomial chaos exploitation

Polynomial chaos exploitation

Create a polynomial chaos for the Ishigami function: a quick start guide to polynomial chaos

Create a polynomial chaos for the Ishigami function: a quick start guide to polynomial chaos