OrthogonalProductFunctionFactory¶

class OrthogonalProductFunctionFactory(*args)¶

Base class for orthogonal multivariate functions.

Available constructors:

OrthogonalProductFunctionFactory(functions)

OrthogonalProductFunctionFactory(functions, enumerateFunction)

Parameters:

functionslist of OrthogonalUniVariateFunctionFamily: List of orthogonal univariate function factories with the same dimension as the orthogonal basis.
enumerateFunctionEnumerateFunction: Associates to an integer its multi-index image in the $\Nset^d$ dimension, which is the dimension of the basis. This multi-index represents the collection of degrees of the univariate polynomials.

See also

OrthogonalProductPolynomialFactory

Notes

OrthogonalProductFunctionFactory is a particular case of implementation of the OrthogonalBasis in the case of polynomial chaos expansion. It provides to the OrthogonalBasis the persistent types of the univariate orthogonal polynomials (e.g. Hermite, Legendre, Laguerre and Jacobi) needed to determine the distribution measure of projection of the input variable. Let’s note that the exact hessian and gradient have been implemented for the product of polynomials. To facilitate the construction of the basis it is recommended to use the class StandardDistributionPolynomialFactory.

Examples

>>> import openturns as ot
>>> from math import pi
>>> funcColl = [ot.HaarWaveletFactory(), ot.FourierSeriesFactory()]
>>> dim = len(funcColl)
>>> enumerateFunction = ot.LinearEnumerateFunction(dim)
>>> productBasis = ot.OrthogonalProductFunctionFactory(funcColl, enumerateFunction)

Methods

`build`(index)	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.
`getFunctionFamilyCollection`()	Get the collection of univariate orthogonal function families.
`getId`()	Accessor to the object's id.
`getInputDimension`()	Get the input dimension of the Basis.
`getMeasure`()	Get the measure upon which the basis is orthogonal.
`getName`()	Accessor to the object's name.
`getOutputDimension`()	Get the output dimension of the Basis.
`getShadowedId`()	Accessor to the object's shadowed id.
`getSize`()	Get the size of the Basis.
`getSubBasis`(indices)	Get a sub-basis of the Basis.
`getVisibility`()	Accessor to the object's visibility state.
`hasName`()	Test if the object is named.
`hasVisibleName`()	Test if the object has a distinguishable name.
`isFinite`()	Tell whether the basis is finite.
`isOrthogonal`()	Tell whether the basis is orthogonal.
`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.

add
getDimension

__init__(*args)¶

build(index)¶

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 $\Nset$ to $\Nset^d$ (with $d$ 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 $\Nset^d$ to $\Nset$ (with $d$ 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.

getFunctionFamilyCollection()¶

Get the collection of univariate orthogonal function families.

Returns:

polynomialFamilylist of OrthogonalUniVariateFunctionFamily: List of orthogonal univariate function families.

getId()¶

Accessor to the object’s id.

Returns:

idint: Internal unique identifier.

getInputDimension()¶

Get the input dimension of the Basis.

Returns:

inDimint: Input dimension of the Basis.

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.

getOutputDimension()¶

Get the output dimension of the Basis.

Returns:

outDimint: Output dimension of the Basis.

getShadowedId()¶

Accessor to the object’s shadowed id.

Returns:

idint: Internal unique identifier.

getSize()¶

Get the size of the Basis.

Returns:

sizeint: Size of the Basis.

getSubBasis(indices)¶

Get a sub-basis of the Basis.

Parameters:

indiceslist of int: Indices of the terms of the Basis put in the sub-basis.

Returns:

subBasislist of Function: Functions defining a sub-basis.

Examples

>>> import openturns as ot
>>> dimension = 3
>>> input = ['x0', 'x1', 'x2']
>>> functions = []
>>> for i in range(dimension):
...     functions.append(ot.SymbolicFunction(input, [input[i]]))
>>> basis = ot.Basis(functions)
>>> subbasis = basis.getSubBasis([1])
>>> print(subbasis[0].getEvaluation())
[x0,x1,x2]->[x1]

getVisibility()¶

Accessor to the object’s visibility state.

Returns:

visiblebool: Visibility flag.

hasName()¶

Test if the object is named.

Returns:

hasNamebool: True if the name is not empty.

hasVisibleName()¶

Test if the object has a distinguishable name.

Returns:

hasVisibleNamebool: True if the name is not empty and not the default one.

isFinite()¶

Tell whether the basis is finite.

Returns:

isFinitebool: True if the basis is finite.

isOrthogonal()¶

Tell whether the basis is orthogonal.

Returns:

isOrthogonalbool: True if the basis is orthogonal.

setName(name)¶

Accessor to the object’s name.

Parameters:

namestr: The name of the object.

setShadowedId(id)¶

Accessor to the object’s shadowed id.

Parameters:

idint: Internal unique identifier.

setVisibility(visible)¶

Accessor to the object’s visibility state.

Parameters:

visiblebool: Visibility flag.

Examples using the class¶

Create multivariate functions

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Examples using the class¶