NormInfEnumerateFunction

class NormInfEnumerateFunction(*args)

Infinite norm enumerate function.

Parameters:
dim : integer

Dimension of the EnumerateFunction. dim must be equal to the dimension of the OrthogonalBasis.

Notes

One defines the infinity norm of a multi-index a by:

\| \vect{a} \|_{\infty} = max_i a_i

This would lead to first select the basis polynomials depending on a specific subset of input variables.

Examples

>>> import openturns as ot
>>> # 2-dimensional case
>>> enumerateFunction = ot.NormInfEnumerateFunction(2)
>>> for i in range(10):
...     print(enumerateFunction(i))
[0,0]
[1,0]
[0,1]
[1,1]
[2,0]
[2,1]
[0,2]
[1,2]
[2,2]
[3,0]

Methods

getClassName() Accessor to the object’s name.
getDimension() Return the dimension of the EnumerateFunction.
getId() Accessor to the object’s id.
getMaximumDegreeCardinal(maximumDegree) Get the cardinal of indices of degree inferior or equal to a given value.
getMaximumDegreeStrataIndex(maximumDegree) Get the index of the strata of degree inferior to a given value.
getName() Accessor to the object’s name.
getShadowedId() Accessor to the object’s shadowed id.
getStrataCardinal(strataIndex) Get the number of members of the basis associated to a given strata.
getStrataCumulatedCardinal(strataIndex) Get the cardinal of the cumulated strata above or equal to the given strata.
getVisibility() Accessor to the object’s visibility state.
hasName() Test if the object is named.
hasVisibleName() Test if the object has a distinguishable name.
inverse(indices) Get the antecedent of a indices list in the EnumerateFunction.
setDimension(dimension) Set the dimension of the EnumerateFunction.
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.
__call__  
__init__(*args)

Initialize self. See help(type(self)) for accurate signature.

getClassName()

Accessor to the object’s name.

Returns:
class_name : str

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

getDimension()

Return the dimension of the EnumerateFunction.

Returns:
dim : int, dim \geq 0

Dimension of the EnumerateFunction.

getId()

Accessor to the object’s id.

Returns:
id : int

Internal unique identifier.

getMaximumDegreeCardinal(maximumDegree)

Get the cardinal of indices of degree inferior or equal to a given value.

Parameters:
maximumDegree : int

Number of polynoms of the basis.

Returns:
cardinal : int

Cardinal of indices of degree max \leq maximumDegree.

Examples

>>> import openturns as ot
>>> enumerateFunction = ot.EnumerateFunction(ot.LinearEnumerateFunction(2))
>>> for i in range(6):
...     indices = enumerateFunction(i)
...     degree = sum(indices)
...     print(str(int(degree))+' '+str(indices))
0 [0,0]
1 [1,0]
1 [0,1]
2 [2,0]
2 [1,1]
2 [0,2]
>>> print(enumerateFunction.getMaximumDegreeCardinal(2))
6
getMaximumDegreeStrataIndex(maximumDegree)

Get the index of the strata of degree inferior to a given value.

Parameters:
maximumDegree : int

Degree.

Returns:
index : int

Index of the strata of degree max \leq maximumDegree.

Examples

>>> import openturns as ot
>>> enumerateFunction = ot.EnumerateFunction(ot.LinearEnumerateFunction(2))
>>> for i in [1, 2]:
...     indices = enumerateFunction(i)
...     strataIndex = sum(indices) + 1
...     print(str(int(strataIndex))+' '+str(indices))
2 [1,0]
2 [0,1]
>>> print(enumerateFunction.getMaximumDegreeStrataIndex(2))
2
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.

getStrataCardinal(strataIndex)

Get the number of members of the basis associated to a given strata.

Parameters:
strataIndex : int

Index of the strata in the hierarchical basis. In the context of product of polynomial basis, this is the total polynom degree.

Returns:
cardinal : int

Number of members of the basis associated to the strata strataIndex. In the context of product of polynomial basis, this is the number of polynoms of the basis which total degree is strataIndex.

Examples

>>> import openturns as ot
>>> enumerateFunction = ot.EnumerateFunction(ot.LinearEnumerateFunction(2))
>>> for i in [3, 4, 5]:
...     indices = enumerateFunction(i)
...     degree = sum(indices)
...     print(str(int(degree))+' '+str(indices))
2 [2,0]
2 [1,1]
2 [0,2]
>>> print(enumerateFunction.getStrataCardinal(2))
3
getStrataCumulatedCardinal(strataIndex)

Get the cardinal of the cumulated strata above or equal to the given strata.

Parameters:
strataIndex : int

Index of the strata in the hierarchical basis. In the context of product of polynomial basis, this is the total polynomial degree.

Returns:
cardinal : int

Number of members of the basis associated to the strates inferior or equal to strataIndex. In the context of product of polynomial basis, this is the number of polynomials of the basis which total degree is inferior or equal to strataIndex.

Examples

>>> import openturns as ot
>>> enumerateFunction = ot.EnumerateFunction(ot.LinearEnumerateFunction(2))
>>> for i in range(6):
...     indices = enumerateFunction(i)
...     degree = sum(indices)
...     print(str(int(degree))+' '+str(indices))
0 [0,0]
1 [1,0]
1 [0,1]
2 [2,0]
2 [1,1]
2 [0,2]
>>> print(enumerateFunction.getStrataCumulatedCardinal(2))
6
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.

inverse(indices)

Get the antecedent of a indices list in the EnumerateFunction.

Parameters:
multiIndex : sequence of int

List of indices.

Returns:
antecedent : int

Represents the antecedent of the multiIndex in the EnumerateFunction.

Examples

>>> import openturns as ot
>>> enumerateFunction = ot.EnumerateFunction(ot.LinearEnumerateFunction(2))
>>> for i in range(6):
...     print(str(i)+' '+str(enumerateFunction(i)))
0 [0,0]
1 [1,0]
2 [0,1]
3 [2,0]
4 [1,1]
5 [0,2]
>>> print(enumerateFunction.inverse([1,1]))
4
setDimension(dimension)

Set the dimension of the EnumerateFunction.

Parameters:
dim : int, dim \geq 0

Dimension of the EnumerateFunction.

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.