TensorizedUniVariateFunctionFactory

class TensorizedUniVariateFunctionFactory(*args)

Base class for tensorized multivariate functions.

Available constructors:

TensorizedUniVariateFunctionFactory(functions)

TensorizedUniVariateFunctionFactory(functions, enumerateFunction)

Parameters:

functions : list of UniVariateFunctionFamily

List of univariate function factories.

enumerateFunction : EnumerateFunction

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 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

add(elt) Add an element in the Basis.
build(index) Build the element of the given index.
getClassName() Accessor to the object’s name.
getDimension() Get the dimension of the Basis.
getEnumerateFunction()
getFunctionFamilyCollection()
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.
isFunctional() Tell whether the basis is functional.
isOrthogonal() Tell whether the basis is orthogonal.
setEnumerateFunction(phi)
setFunctionFamilyCollection(coll)
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)

x.__init__(…) initializes x; see help(type(x)) for signature

add(elt)

Add an element in the Basis.

Parameters:

function : Function

Function added in the Basis.

Examples

>>> import openturns as ot
>>> dimension = 3
>>> input = ['x0', 'x1', 'x2']
>>> functions = []
>>> for i in range(2):
...     functions.append(ot.SymbolicFunction(input, [input[i]]))
>>> basis = ot.Basis(functions)
>>> basis.add(ot.SymbolicFunction(input, [input[2]]))
build(index)

Build the element of the given index.

Parameters:

index : int, index \geq 0

Index of an element of the Basis.

Returns:

function : Function

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_name : str

The object class name (object.__class__.__name__).

getDimension()

Get the dimension of the Basis.

Returns:

dimension : int

Dimension of the Basis.

getId()

Accessor to the object’s id.

Returns:

id : int

Internal unique identifier.

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.

Returns:

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.

isFunctional()

Tell whether the basis is functional.

Returns:

isOrthogonal : bool

True if the basis is functional i.e. if its terms are a solution to an equation (e.g. a basis made up of Legendre functions).

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.