# LeastSquaresStrategy¶

class LeastSquaresStrategy(*args)

Least squares strategy for the approximation coefficients.

Available constructors:

LeastSquaresStrategy(weightedExp)

LeastSquaresStrategy(weightedExp, approxAlgoImpFact)

LeastSquaresStrategy(measure, approxAlgoImpFact)

LeastSquaresStrategy(measure, weightedExp, approxAlgoImpFact)

LeastSquaresStrategy(inputSample, outputSample, approxAlgoImpFact)

LeastSquaresStrategy(inputSample, weights, outputSample, approxAlgoImpFact)

Parameters: weightedExp : WeightedExperiment Experimental design used for the transformed input data. By default the class MonteCarloExperiment is used. approxAlgoImpFact : ApproximationAlgorithmImplementationFactory The factory that builds the desired ApproximationAlgorithm. By default the class PenalizedLeastSquaresAlgorithmFactory is used. measure : Distribution Distribution with respect to which the basis is orthonormal. By default, the limit measure defined within the class WeightedExperiment is used. inputSample, outputSample : 2-d sequence of float The input random variables and the output samples that describe the model. weights : sequence 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 . If not precised, all weights are equals to , where is the size of the sample.

Notes

This class is not usable because it has sense only within the FunctionalChaosAlgorithm : the least squares strategy evaluates the coefficients of the polynomials decomposition as follows:

where .

The mean expectation is approximated by a relation of type:

where is a function defined as:

In the approximation of the mean expectation, the set I, the points and the weights are evaluated from methods implemented in the WeightedExperiment.

Methods

 getClassName() Accessor to the object’s name. getCoefficients() Accessor to the coefficients. getExperiment() Accessor to the experiments. getId() Accessor to the object’s id. 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. getShadowedId() Accessor to the object’s shadowed id. getVisibility() Accessor to the object’s visibility state. getWeights() Accessor to the weights. hasName() Test if the object is named. hasVisibleName() Test if the object has a distinguishable name. 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. setShadowedId(id) Accessor to the object’s shadowed id. setVisibility(visible) Accessor to the object’s visibility state. setWeights(weights) Accessor to the weights.
 computeCoefficients
__init__(*args)

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

getClassName()

Accessor to the object’s name.

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

Accessor to the coefficients.

Returns: coef : Point Coefficients .
getExperiment()

Accessor to the experiments.

Returns: exp : WeightedExperiment Weighted experiment used to evaluate the coefficients.
getId()

Accessor to the object’s id.

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

Accessor to the input sample.

Returns: X : Sample Input Sample.
getMeasure()

Accessor to the measure.

Returns: mu : Distribution Measure defining the scalar product.
getName()

Accessor to the object’s name.

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

Accessor to the output sample.

Returns: Y : Sample Output Sample.
getRelativeError()

Accessor to the relative error.

Returns: e : float Relative error.
getResidual()

Accessor to the residual.

Returns: er : float Residual error.
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.
getWeights()

Accessor to the weights.

Returns: w : Point Weights of the design of experiments.
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.
setExperiment(weightedExperiment)

Accessor to the design of experiment.

Parameters: exp : WeightedExperiment Weighted design of experiment.
setInputSample(inputSample)

Accessor to the input sample.

Parameters: X : Sample Input Sample.
setMeasure(measure)

Accessor to the measure.

Parameters: m : Distribution Measure defining the scalar product.
setName(name)

Accessor to the object’s name.

Parameters: name : str The name of the object.
setOutputSample(outputSample)

Accessor to the output sample.

Parameters: Y : Sample Output Sample.
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.
setWeights(weights)

Accessor to the weights.

Parameters: w : Point Weights of the design of experiments.