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.

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.

getMarginal(*args)

Get the marginal enumerate function.

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.

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]
__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.

getMarginal(*args)

Get the marginal enumerate function.

Parameters:
indicesint or sequence of int, 0 \leq i < n

List of marginal indices.

Returns:
enumerateFunctionEnumerateFunction

The marginal enumerate function.

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).