IntegrationStrategy

class IntegrationStrategy(*args)

Integration strategy for the approximation coefficients.

Available constructors:

IntegrationStrategy(measure)

IntegrationStrategy(weightedExp)

IntegrationStrategy(measure, weightedExp)

IntegrationStrategy(inputSample, outputSample)

IntegrationStrategy(inputSample, weights, outputSample)

Parameters:
weightedExpWeightedExperiment

Experimental design used for the transformed input data.

By default the class MonteCarloExperiment is used.

measureDistribution

The input distribution \mu_{\inputRV} with respect to which the basis is orthonormal.

By default, the limit measure defined within the class WeightedExperiment is used.

inputSample2-d sequence of float

The input sample of size \sampleSize.

outputSample2-d sequence of float

The output sample of size \sampleSize.

weightssequence of float

Numerical point that are the weights associated to the input sample points such that the corresponding weighted experiment is a good approximation of \mu_{\inputRV}.

By default, all weights are equal to \omega_i = \frac{1}{\sampleSize}.

Methods

getClassName()

Accessor to the object's name.

getCoefficients()

Accessor to the coefficients.

getDesignProxy()

Accessor to the design proxy.

getExperiment()

Accessor to the experiments.

getInputSample()

Accessor to the input sample.

getMeasure()

Accessor to the measure.

getName()

Accessor to the object's name.

getOutputSample()

Accessor to the output sample.

getRelativeError()

Accessor to the relative error.

getResidual()

Accessor to the residual.

getWeights()

Accessor to the weights.

hasName()

Test if the object is named.

involvesModelSelection()

Get the model selection flag.

isLeastSquares()

Get the least squares flag.

setExperiment(weightedExperiment)

Accessor to the design of experiment.

setInputSample(inputSample)

Accessor to the input sample.

setMeasure(measure)

Accessor to the measure.

setName(name)

Accessor to the object's name.

setOutputSample(outputSample)

Accessor to the output sample.

setWeights(weights)

Accessor to the weights.

See also

FunctionalChaosAlgorithm, ProjectionStrategy, LeastSquaresStrategy

Notes

This class is used in the functional chaos expansion context implemented in the class FunctionalChaosAlgorithm. It is not usable outside this context.

The model is approximated by the meta model defined in Functional Chaos Expansion by equation (5) and the coefficients a_k)_{k \in I_n} are computed with the inner product defined in Functional Chaos Expansion by equation (7). This computation makes sense if and only if the basis is orthonormal with respect to the distribution \mu_{\inputRV}.

__init__(*args)
getClassName()

Accessor to the object’s name.

Returns:
class_namestr

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

getCoefficients()

Accessor to the coefficients.

Returns:
coefPoint

Coefficients (\alpha_k)_{k \in I_n}.

getDesignProxy()

Accessor to the design proxy.

Parameters:
designProxyDesignProxy

The design matrix.

getExperiment()

Accessor to the experiments.

Returns:
expWeightedExperiment

Weighted experiment used to evaluate the coefficients.

getInputSample()

Accessor to the input sample.

Returns:
XSample

Input Sample.

getMeasure()

Accessor to the measure.

Returns:
muDistribution

Measure \mu_{\inputRV} defining the inner product.

getName()

Accessor to the object’s name.

Returns:
namestr

The name of the object.

getOutputSample()

Accessor to the output sample.

Returns:
YSample

Output Sample.

getRelativeError()

Accessor to the relative error.

Returns:
efloat

Relative error.

getResidual()

Accessor to the residual.

Returns:
erfloat

Residual error.

getWeights()

Accessor to the weights.

Returns:
wPoint

Weights of the design of experiments.

hasName()

Test if the object is named.

Returns:
hasNamebool

True if the name is not empty.

involvesModelSelection()

Get the model selection flag.

A model selection method can be used to select the coefficients of the decomposition which enable to best predict the output. Model selection can lead to a sparse functional chaos expansion.

Returns:
involvesModelSelectionbool

True if the method involves a model selection method.

isLeastSquares()

Get the least squares flag.

There are two methods to compute the coefficients: integration or least squares.

Returns:
isLeastSquaresbool

True if the coefficients are estimated from least squares.

setExperiment(weightedExperiment)

Accessor to the design of experiment.

Parameters:
expWeightedExperiment

Weighted design of experiment.

setInputSample(inputSample)

Accessor to the input sample.

Parameters:
XSample

Input Sample.

setMeasure(measure)

Accessor to the measure.

Parameters:
mDistribution

Measure \mu_{\inputRV} defining the scalar product.

setName(name)

Accessor to the object’s name.

Parameters:
namestr

The name of the object.

setOutputSample(outputSample)

Accessor to the output sample.

Parameters:
YSample

Output Sample.

setWeights(weights)

Accessor to the weights.

Parameters:
wPoint

Weights of the design of experiments.

Examples using the class

Create a PCE by integration on the cantilever beam

Create a PCE by integration on the cantilever beam

Create a sparse chaos by integration

Create a sparse chaos by integration

Use advanced features for PCE

Use advanced features for PCE