SoizeGhanemFactory¶

class SoizeGhanemFactory(*args)¶

SoizeGhanem orthonormal multivariate functional family.

For the any multivariate distribution with continuous copula.

Available constructor:

SoizeGhanemFactory()

SoizeGhanemFactory(measure, useCopula)

SoizeGhanemFactory(measure, phi, useCopula)

Parameters

measureDistribution: The measure defining the inner product of the factory.
phiEnumerateFunction: The function mapping the index of the multivariate basis function to the multi-index of the marginal variables. Default is to use the LinearEnumerateFunction.
useCopulabool: Flag to tell if the copula density has to be used directly or indirectly through the joint PDF of the measure. Default is True.

See also

StandardDistributionPolynomialFactory, OrthogonalProductPolynomialFactory

Notes

This class implements the multivariate orthonormal basis associated with an arbitrary multidimensional distribution with continuous copula and marginals with well-defined orthonormal polyomials of arbitrary order. The details are in [soizeghanem2004].

Examples

>>> import openturns as ot
>>> marginals = [ot.Uniform(-1.0, 1.0), ot.Normal(0.0, 1.0)]
>>> copula = ot.ClaytonCopula(1.0)
>>> distribution = ot.ComposedDistribution(marginals, copula)
>>> factory = ot.SoizeGhanemFactory(distribution)
>>> point = [0.5]*2
>>> for i in range(3):
...     value = factory.build(i)(point)
...     print('SoizeGhanem_' + str(i) + '(' + str(point) + ')=' + str(value))
SoizeGhanem_0([0.5, 0.5])=[0.870518]
SoizeGhanem_1([0.5, 0.5])=[0.753891]
SoizeGhanem_2([0.5, 0.5])=[0.435259]

Methods

`build`(*args)	Get the term of the basis collection at a given index or multi-indices.
`getClassName`()	Accessor to the object’s name.
`getDimension`()	Get the dimension of the Basis.
`getEnumerateFunction`()	Return the enumerate function.
`getId`()	Accessor to the object’s id.
`getMeasure`()	Get the measure upon which the basis is orthogonal.
`getName`()	Accessor to the object’s name.
`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

__init__(*args)¶: Initialize self. See help(type(self)) for accurate signature.

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 $\Nset$ 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__).

getDimension()¶

Get the dimension of the Basis.

Returns

dimensionint: Dimension of the Basis.

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.

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.

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.

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