NormInfEnumerateFunction

class NormInfEnumerateFunction(*args)

Infinite norm enumerate function.

Parameters:
dimint, 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

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.

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.

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.

hasName()

Test if the object is named.

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.

setUpperBound(upperBound)

Accessor to the upper bound.
__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.

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.

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).

hasName()

Test if the object is named.

Returns:
hasNamebool

True if the name is not empty.

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.

setUpperBound(upperBound)

Accessor to the upper bound.

Parameters:
ubsequence of int

Upper bound of the indices (inclusive).