TensorizedUniVariateFunctionFactory

class TensorizedUniVariateFunctionFactory(*args)

Base class for tensorized multivariate functions.

Available constructors:

TensorizedUniVariateFunctionFactory(functions)

TensorizedUniVariateFunctionFactory(functions, enumerateFunction)

Parameters
functionslist of UniVariateFunctionFamily

List of univariate function factories.

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.

Notes

TensorizedUniVariateFunctionFactory allows one to create multidimensional functions as the tensor product of univariate functions created by their respective factories (i.e. UniVariateFunctionFamily):

\Phi_n(x_1,\dots,x_d)=\prod_{i=1}^d \phi^i_{enum(n)_i}(x_i)

where \phi^i_k is the univariate basis of degree k associated to the component x_i and enum(n)_i is the ith component of the multi-index enum(n)

Let’s note that the exact hessian and gradient have been implemented for the product of polynomials.

Examples

>>> import openturns as ot
>>> funcColl = [ot.HaarWaveletFactory(), ot.FourierSeriesFactory(), ot.MonomialFunctionFactory()]
>>> dim = len(funcColl)
>>> enumerateFunction = ot.LinearEnumerateFunction(dim)
>>> productBasis = ot.TensorizedUniVariateFunctionFactory(funcColl, enumerateFunction)

Methods

build(index)

Build the element of the given index.

getClassName()

Accessor to the object's name.

getDimension()

Get the dimension of the Basis.

getId()

Accessor to the object's id.

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

getEnumerateFunction

getFunctionFamilyCollection

setEnumerateFunction

setFunctionFamilyCollection
__init__(*args)
build(index)

Build the element of the given index.

Parameters
indexint, index \geq 0

Index of an element of the Basis.

Returns
functionFunction

The function at the index index of the 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)
>>> print(basis.build(0).getEvaluation())
[x0,x1,x2]->[x0]
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.

getId()

Accessor to the object’s id.

Returns
idint

Internal unique identifier.

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.