NormInfEnumerateFunction¶
- class NormInfEnumerateFunction(*args)¶
Infinite norm enumerate function.
- Parameters:
- dimint, default=1
Dimension of the
EnumerateFunction
. dim must be equal to the dimension of theOrthogonalBasis
.
See also
Notes
One defines the infinity norm of a multi-index by:
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.
Accessor to the object's name.
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.
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 .
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,
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 .
Notes
In the specific context of a linear enumeration (
LinearEnumerateFunction
) this is also the cumulated cardinal of stratas of index .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 .
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,
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).