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

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.
__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: index : int 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. indices : sequence 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. function : Function 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_name : str The object class name (object.__class__.__name__).
getDimension()

Get the dimension of the Basis.

Returns: dimension : int Dimension of the Basis.
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.
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.
getShadowedId()

Accessor to the object’s shadowed id.

Returns: id : int Internal unique identifier.
getSize()

Get the size of the Basis.

Returns: size : int Size of the Basis.
getSubBasis(indices)

Get a sub-basis of the Basis.

Parameters: indices : list of int Indices of the terms of the Basis put in the sub-basis. subBasis : list 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: visible : bool Visibility flag.
hasName()

Test if the object is named.

Returns: hasName : bool True if the name is not empty.
hasVisibleName()

Test if the object has a distinguishable name.

Returns: hasVisibleName : bool True if the name is not empty and not the default one.
isFinite()

Tell whether the basis is finite.

Returns: isFinite : bool True if the basis is finite.
isOrthogonal()

Tell whether the basis is orthogonal.

Returns: isOrthogonal : bool True if the basis is orthogonal.
setName(name)

Accessor to the object’s name.

Parameters: name : str The name of the object.
setShadowedId(id)

Accessor to the object’s shadowed id.

Parameters: id : int Internal unique identifier.
setVisibility(visible)

Accessor to the object’s visibility state.

Parameters: visible : bool Visibility flag.