# FixedStrategy¶

class FixedStrategy(*args)

Fixed truncation strategy.

Available constructors:
FixedStrategy(orthogonalBasis, dimension)
Parameters: orthogonalBasis : OrthogonalBasis An OrthogonalBasis. dimension : positive int Number of terms of the basis.

Notes

The so-called fixed strategy simply consists in retaining the first elements of the PC basis, the latter being ordered according to a given EnumerateFunction (hyperbolic or not). The retained set is built in a single pass. The truncated PC expansion is given by:

In case of a LinearEnumerateFunction, for a given natural integer , a usual choice is to set equals to:

This way the set of retained basis functions gathers all the polynomials with total degree not greater than . The number of terms grows polynomially both in and though, which may lead to difficulties in terms of computational efficiency and memory requirements when dealing with high-dimensional problems.

Examples

>>> import openturns as ot
>>> ot.RandomGenerator.SetSeed(0)
>>> # Define the model
>>> inputDim = 1
>>> model = ot.SymbolicFunction(['x'], ['x*sin(x)'])
>>> # Create the input distribution
>>> distribution = ot.ComposedDistribution([ot.Uniform()]*inputDim)
>>> # Construction of the multivariate orthonormal basis
>>> polyColl = [0.0]*inputDim
>>> for i in range(distribution.getDimension()):
...     polyColl[i] = ot.StandardDistributionPolynomialFactory(distribution.getMarginal(i))
>>> enumerateFunction = ot.LinearEnumerateFunction(inputDim)
>>> productBasis = ot.OrthogonalProductPolynomialFactory(polyColl, enumerateFunction)
>>> # Truncature strategy of the multivariate orthonormal basis
>>> # We choose all the polynomials of degree <= 4
>>> degree = 4
>>> indexMax = enumerateFunction.getStrataCumulatedCardinal(degree)
>>> print(indexMax)
5
>>> # We keep all the polynomials of degree <= 4
>>> # which corresponds to the 5 first ones


Methods

 computeInitialBasis() Compute initial basis for the approximation. getBasis() Accessor to the underlying orthogonal basis. getClassName() Accessor to the object’s name. getId() Accessor to the object’s id. getMaximumDimension() Accessor to the maximum dimension of the orthogonal basis. getName() Accessor to the object’s name. getPsi() Accessor to the orthogonal polynomials of the basis. getShadowedId() Accessor to the object’s shadowed id. getVisibility() Accessor to the object’s visibility state. hasName() Test if the object is named. hasVisibleName() Test if the object has a distinguishable name. setMaximumDimension(maximumDimension) Accessor to the maximum dimension of the orthogonal basis. 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. updateBasis(alpha_k, residual, relativeError) Update the basis for the next iteration of approximation.
__init__(*args)

Initialize self. See help(type(self)) for accurate signature.

computeInitialBasis()

Compute initial basis for the approximation.

getBasis()

Accessor to the underlying orthogonal basis.

Returns: basis : OrthogonalBasis Orthogonal basis of which the adaptive strategy is based.
getClassName()

Accessor to the object’s name.

Returns: class_name : str The object class name (object.__class__.__name__).
getId()

Accessor to the object’s id.

Returns: id : int Internal unique identifier.
getMaximumDimension()

Accessor to the maximum dimension of the orthogonal basis.

Returns: P : integer Maximum dimension of the truncated basis.
getName()

Accessor to the object’s name.

Returns: name : str The name of the object.
getPsi()

Accessor to the orthogonal polynomials of the basis.

Returns: polynomials : list of polynomials Sequence of analytical polynomials.

Notes

The method computeInitialBasis() must be applied first.

Examples

>>> import openturns as ot
>>> productBasis = ot.OrthogonalProductPolynomialFactory([ot.HermiteFactory()])
[1,x0,-0.707107 + 0.707107 * x0^2]

getShadowedId()

Accessor to the object’s shadowed id.

Returns: id : int Internal unique identifier.
getVisibility()

Accessor to the object’s visibility state.

Returns: visible : bool Visibility flag.
hasName()

Test if the object is named.

Returns: hasName : bool True if the name is not empty.
hasVisibleName()

Test if the object has a distinguishable name.

Returns: hasVisibleName : bool True if the name is not empty and not the default one.
setMaximumDimension(maximumDimension)

Accessor to the maximum dimension of the orthogonal basis.

Parameters: P : integer Maximum dimension of the truncated basis.
setName(name)

Accessor to the object’s name.

Parameters: name : str The name of the object.
setShadowedId(id)

Accessor to the object’s shadowed id.

Parameters: id : int Internal unique identifier.
setVisibility(visible)

Accessor to the object’s visibility state.

Parameters: visible : bool Visibility flag.
updateBasis(alpha_k, residual, relativeError)

Update the basis for the next iteration of approximation.

Notes

No changes are made to the basis in the fixed strategy.