SoizeGhanemFactory

class SoizeGhanemFactory(*args)

SoizeGhanem orthonormal multivariate functional family.

For the any multivariate distribution with continuous copula.

Available constructor:

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.

Methods

add(elt)

Add a function.

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.

getInputDimension()

Get the input dimension of the Basis.

getMarginal(indices)

Get the marginal orthogonal functions.

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.

getSize()

Get the size of the Basis.

getSubBasis(indices)

Get a sub-basis of the Basis.

hasName()

Test if the object is named.

isFinite()

Tell whether the basis is finite.

isOrthogonal()

Tell whether the basis is orthogonal.

isTensorProduct()

Tell whether the basis is a tensor product

setName(name)

Accessor to the object's name.

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.JointDistribution(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]
__init__(*args)
add(elt)

Add a function.

Parameters:
functiona Function

Function to be added.

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.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.

getInputDimension()

Get the input dimension of the Basis.

Returns:
inDimint

Input dimension of the functions.

getMarginal(indices)

Get the marginal orthogonal functions.

Parameters:
indicessequence of int, 0 \leq i < \inputDim

List of marginal indices of the input variables.

Returns:
functionFamilylistlist of OrthogonalBasis

The marginal orthogonal functions.

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.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 functions.

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]
hasName()

Test if the object is named.

Returns:
hasNamebool

True if the name is not empty.

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.

isTensorProduct()

Tell whether the basis is a tensor product

Returns:
isTensorProductbool

True if the basis is a tensor product.

setName(name)

Accessor to the object’s name.

Parameters:
namestr

The name of the object.