NormInfEnumerateFunction¶

class NormInfEnumerateFunction(*args)¶

Infinite norm enumerate function.

Parameters

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

See also

EnumerateFunction, LinearEnumerateFunction

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

`__call__`(index)	Call self as a function.
`getBasisSizeFromTotalDegree`(maximumDegree)	Get the basis size corresponding to a total degree.
`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 largest index of the strata of degree lower or equal 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.

__init__(*args)¶

getBasisSizeFromTotalDegree(maximumDegree)¶

Get the basis size corresponding to a total degree.

Parameters

maximumDegreeint: Degree.

Returns

sizeint: Number of members of the basis of degree $max \leq maximumDegree$ .

Examples

>>> import openturns as ot
>>> ef = ot.LinearEnumerateFunction(2)
>>> size = ef.getBasisSizeFromTotalDegree(3)

getClassName()¶

Accessor to the object’s name.

Returns

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

getDimension()¶

Return the dimension of the EnumerateFunction.

Returns

dimint, $dim \geq 0$: Dimension of the EnumerateFunction.

getId()¶

Accessor to the object’s id.

Returns

idint: Internal unique identifier.

getMaximumDegreeCardinal(maximumDegree)¶

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

Parameters

maximumDegreeint: Degree.

Returns

cardinalint: Cardinal of indices of degree $max \leq maximumDegree$ .

Examples

>>> import openturns as 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 largest index of the strata of degree lower or equal to a given value.

Parameters

maximumDegreeint: Degree.

Returns

indexint: Index of the last strata of degree $max \leq maximumDegree$ .

Examples

>>> import openturns as 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

namestr: The name of the object.

getShadowedId()¶

Accessor to the object’s shadowed id.

Returns

idint: Internal unique identifier.

getStrataCardinal(strataIndex)¶

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

Parameters

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

Returns

cardinalint: 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.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

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

Returns

cardinalint: Number of members of the basis associated to the strata of index 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.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

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.

inverse(indices)¶

Get the antecedent of a indices list in the EnumerateFunction.

Parameters

multiIndexsequence of int: List of indices.

Returns

antecedentint: Represents the antecedent of the multiIndex in the EnumerateFunction.

Examples

>>> import openturns as 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

dimint, $dim \geq 0$: Dimension of the EnumerateFunction.

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.

OpenTURNS

An Open source initiative for the Treatment of Uncertainties, Risks'N Statistics

Previous topic

Next topic

This Page

NormInfEnumerateFunction¶