NormInfEnumerateFunction¶

class NormInfEnumerateFunction(*args)¶

Infinite norm enumerate function.

Parameters:

diminteger, default=1: 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:

$\| \vect{\alpha} \|_{\infty} = \max_{i=1} \; \alpha_i$

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 number of multi-indices of total degree lower or equal to a threshold.
`getMaximumDegreeStrataIndex`(maximumDegree)	Get the largest index of the strata containing multi-indices lower or equal to the given maximum degree.
`getName`()	Accessor to the object's name.
`getShadowedId`()	Accessor to the object's shadowed id.
`getStrataCardinal`(strataIndex)	Get the number of multi-indices in the basis inside a given strata.
`getStrataCumulatedCardinal`(strataIndex)	Get the number of multi-indices in the basis inside a range of stratas.
`getUpperBound`()	Accessor to the upper bound.
`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.
`setUpperBound`(upperBound)	Accessor to the upper bound.
`setVisibility`(visible)	Accessor to the object's visibility state.

__init__(*args)¶

getBasisSizeFromTotalDegree(maximumDegree)¶

Get the basis size corresponding to a total degree.

Parameters:

max_degint: Maximum total degree.

Returns:

sizeint: Number of multi-indices in the basis of total degree $\leq \max_{deg}$ .

Notes

In the specific context of a linear enumeration (LinearEnumerateFunction) this is also the cumulated cardinal of stratas up to max_deg.

Examples

>>> import openturns as ot
>>> dim = 2
>>> enum_func = ot.LinearEnumerateFunction(dim)
>>> enum_func.getBasisSizeFromTotalDegree(3)
10
>>> enum_func.getStrataCumulatedCardinal(3)
10

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 number of multi-indices of total degree lower or equal to a threshold.

Parameters:

max_degint: Maximum total degree.

Returns:

cardinalint: Number of multi-indices in the basis of total degree $\leq \max_{deg}$ .

Notes

In the specific context of a linear enumeration (LinearEnumerateFunction) this is also the cumulated cardinal of stratas of index $\leq \max_{deg}$ .

Examples

>>> import openturns as ot
>>> dim = 2
>>> enum_func = ot.LinearEnumerateFunction(dim)
>>> enum_func.getMaximumDegreeCardinal(2)
6

getMaximumDegreeStrataIndex(maximumDegree)¶

Get the largest index of the strata containing multi-indices lower or equal to the given maximum degree.

Parameters:

max_degint: Maximum total degree.

Returns:

indexint: Index of the last strata that contains multi-indices of total degree $\leq \max_{deg}$ .

Notes

In the specific context of a linear enumeration (LinearEnumerateFunction) this is the strata of index max_deg.

Examples

>>> import openturns as ot
>>> dim = 2
>>> enum_func = ot.LinearEnumerateFunction(dim)
>>> enum_func.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 multi-indices in the basis inside a given strata.

Parameters:

strataIndexint: Index of the strata of the tensorized basis.

Returns:

cardinalint: Number of multi-indices in the basis inside the strata strataIndex.

Notes

In the specific context of a linear enumeration (LinearEnumerateFunction) the strata strataIndex consists of a hyperplane of all the multi-indices of total degree strataIndex, and its cardinal is strataIndex + 1.

Examples

>>> import openturns as ot
>>> dim = 2
>>> enum_func = ot.LinearEnumerateFunction(dim)
>>> enum_func.getStrataCardinal(2)
3

getStrataCumulatedCardinal(strataIndex)¶

Get the number of multi-indices in the basis inside a range of stratas.

Parameters:

strataIndexint: Index of the strata of the tensorized basis.

Returns:

cardinalint: Number of multi-indices in the basis inside the stratas of index lower or equal to strataIndex.

Notes

The number of multi-indices is the total of multi-indices inside the stratas. In the specific context of a linear enumeration (LinearEnumerateFunction) this returns the number of multi-indices of maximal total degree strataIndex.

Examples

>>> import openturns as ot
>>> dim = 2
>>> enum_func = ot.LinearEnumerateFunction(dim)
>>> enum_func.getStrataCumulatedCardinal(2)
6
>>> sum([enum_func.getStrataCardinal(i) for i in range(3)])
6

getUpperBound()¶

Accessor to the upper bound.

Returns:

ubsequence of int: Upper bound of the indices (inclusive).

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
>>> dim = 2
>>> enum_func = ot.LinearEnumerateFunction(dim)
>>> for i in range(6):
...     print(str(i)+' '+str(enum_func(i)))
0 [0,0]
1 [1,0]
2 [0,1]
3 [2,0]
4 [1,1]
5 [0,2]
>>> print(enum_func.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.

setUpperBound(upperBound)¶

Accessor to the upper bound.

Parameters:

ubsequence of int: Upper bound of the indices (inclusive).

setVisibility(visible)¶

Accessor to the object’s visibility state.

Parameters:

visiblebool: Visibility flag.

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