CleaningStrategy¶

class CleaningStrategy(*args)¶

Cleaning truncation strategy.

Available constructors:

CleaningStrategy(orthogonalBasis, maximumDimension)

CleaningStrategy(orthogonalBasis, maximumDimension, verbose)

CleaningStrategy(orthogonalBasis, maximumDimension, maximumSize, significanceFactor)

CleaningStrategy(orthogonalBasis, maximumDimension, maximumSize, significanceFactor, verbose)

Parameters:

orthogonalBasisOrthogonalBasis: An OrthogonalBasis.
maximumDimensionpositive int: Maximum index that can be used by the EnumerateFunction to determine the last term of the basis.
maximumSizepositve int: Parameter that characterizes the cleaning strategy. It represents the number of efficient coefficients of the basis. Its default value is set to 20.
significanceFactorfloat: Parameter used as a threshold for selecting the efficient coefficients of the basis. The real threshold represents the multiplication of the significanceFactor with the maximum magnitude of the current determined coefficients. Its default value is equal to $1e^{-4}$ .
verbosebool: Used for the online monitoring of the current basis updates (removed or added coefficients).

See also

AdaptiveStrategy, FixedStrategy

Notes

The cleaning strategy aims at building a PC expansion containing at most $P$ significant coefficients, i.e. at most $P$ significant basis functions. It proceeds as follows:

Generate an initial PC basis made of the $P$ first polynomials (according to the adopted EnumerateFunction), or equivalently an initial set of indices $K = \{0, \ldots, P-1\}$ .
Discard from the basis all those polynomials $\Psi_j$ associated with insignificance coefficients, i.e. the coefficients that satisfy:

$|a_j| \leq \epsilon \times \max_{ k \in K, k \neq 0 } |a_k|$

where $\epsilon$ is the significance factor, default is $\epsilon = 10^{-4}$ .

Add the next basis term $\Psi_{k+1}$ to the current basis $K$ .
Reiterate the procedure until either $P$ terms have been retained or if the given maximum index $P_{max}$ has been reached.

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 want to select, among the maximumDimension = 100 first polynomials of
>>> # the multivariate basis, those which have the maximumSize = 20 most 
>>> # significant contribution (greatest coefficients), with respect to the 
>>> # significance factor = 10^-4.
>>> maximumDimension = 100
>>> maximumSize = 20
>>> significanceFactor = 1e-4
>>> adaptiveStrategy = ot.CleaningStrategy(productBasis, maximumDimension,
...                                          maximumSize, significanceFactor)

Methods

`computeInitialBasis`()	Compute initial basis for the approximation.
`getBasis`()	Accessor to the underlying orthogonal basis.
`getClassName`()	Accessor to the object's name.
`getCurrentVectorIndex`()	Accessor to the current vector index.
`getId`()	Accessor to the object's id.
`getMaximumDimension`()	Accessor to the maximum dimension of the orthogonal basis.
`getMaximumSize`()	Accessor to the maximum size 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.
`getSignificanceFactor`()	Accessor to the significance factor.
`getVerbose`()	Accessor to the verbose.
`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.
`setMaximumSize`(maximumSize)	Accessor to the maximum size of the orthogonal basis.
`setName`(name)	Accessor to the object's name.
`setShadowedId`(id)	Accessor to the object's shadowed id.
`setSignificanceFactor`(significanceFactor)	Accessor to the significance factor.
`setVerbose`(verbose)	Accessor to the verbose.
`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)¶

computeInitialBasis()¶

Compute initial basis for the approximation.

See also

getPsi

getBasis()¶

Accessor to the underlying orthogonal basis.

Returns:

basisOrthogonalBasis: Orthogonal basis of which the adaptive strategy is based.

getClassName()¶

Accessor to the object’s name.

Returns:

class_namestr: The object class name (object.__class__.__name__).

getCurrentVectorIndex()¶

Accessor to the current vector index.

Returns:

indexinteger: Current index of the basis term.

getId()¶

Accessor to the object’s id.

Returns:

idint: Internal unique identifier.

getMaximumDimension()¶

Accessor to the maximum dimension of the orthogonal basis.

Returns:

Pinteger: Maximum dimension of the truncated basis.

getMaximumSize()¶

Accessor to the maximum size of the orthogonal basis.

Returns:

sizeinteger: Maximum number of significant terms of the basis.

See also

setMaximumSize

getName()¶

Accessor to the object’s name.

Returns:

namestr: The name of the object.

getPsi()¶

Accessor to the orthogonal polynomials of the basis.

Returns:

polynomialslist of polynomials: Sequence of $P$ analytical polynomials.

Notes

The method computeInitialBasis() must be applied first.

Examples

>>> import openturns as ot
>>> productBasis = ot.OrthogonalProductPolynomialFactory([ot.HermiteFactory()])
>>> adaptiveStrategy = ot.FixedStrategy(productBasis, 3)
>>> adaptiveStrategy.computeInitialBasis()
>>> print(adaptiveStrategy.getPsi())
[1,x0,-0.707107 + 0.707107 * x0^2]

getShadowedId()¶

Accessor to the object’s shadowed id.

Returns:

idint: Internal unique identifier.

getSignificanceFactor()¶

Accessor to the significance factor.

Returns:

factorfloat: Value of the significance factor.

See also

setSignificanceFactor

getVerbose()¶

Accessor to the verbose.

Returns:

verbosebool: Return if the online monitoring of the current basis updates is enabled or not.

See also

setVerbose

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.

setMaximumDimension(maximumDimension)¶

Accessor to the maximum dimension of the orthogonal basis.

Parameters:

Pinteger: Maximum dimension of the truncated basis.

setMaximumSize(maximumSize)¶

Accessor to the maximum size of the orthogonal basis.

Parameters:

sizeinteger: Maximum number of significant terms of the basis.

See also

getMaximumSize

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.

setSignificanceFactor(significanceFactor)¶

Accessor to the significance factor.

Parameters:

factorfloat: Value of the significance factor.

See also

getSignificanceFactor

setVerbose(verbose)¶

Accessor to the verbose.

Parameters:

verbosebool: Enable the online monitoring of the current basis updates or not.

See also

getVerbose

setVisibility(visible)¶

Accessor to the object’s visibility state.

Parameters:

visiblebool: 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.

Examples using the class¶

Advanced polynomial chaos construction

Create a sparse chaos by integration

OpenTURNS

An Open source initiative for the Treatment of Uncertainties, Risks'N Statistics

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CleaningStrategy¶

Examples using the class¶