SequentialStrategy

class SequentialStrategy(*args)

Sequential truncation strategy.

Available constructors:

SequentialStrategy(orthogonalBasis, maximumDimension)

Parameters
orthogonalBasisOrthogonalBasis

An OrthogonalBasis.

maximumDimensionpositive int

Maximum number of terms of the basis.

See also

AdaptiveStrategy, SequentialStrategy, CleaningStrategy

Notes

The sequential strategy consists in constructing the basis of the truncated PC iteratively. Precisely, one begins with the first term \Psi_0, that is K_0 = \{0\}, and one complements the current basis as follows: K_{k+1} = K_k \cup \{\Psi_{k+1}\}. The construction process is stopped when a given accuracy criterion, defined in the ProjectionStrategy, is reached, or when k is equal to a prescribed maximum basis size P.

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 = 20 first polynomials of the
>>> # multivariate basis those verifying the convergence criterion.
>>> maximumDimension = 20
>>> adaptiveStrategy = ot.SequentialStrategy(productBasis, maximumDimension)

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)
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__).

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.

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.

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.

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.

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.