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, SequentialStrategy

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.

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