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. approxAlgoImpFactApproximationAlgorithmImplementationFactory
The factory that builds the desired
ApproximationAlgorithm
. By default the classPenalizedLeastSquaresAlgorithmFactory
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, outputSample2d sequence of float
The input random variables and the output samples that describe the model.
 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 . 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
.Attributes: thisown
The membership flag
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_namestr
The object class name (object.__class__.__name__).

getExperiment
()¶ Accessor to the experiments.
Returns:  exp
WeightedExperiment
Weighted experiment used to evaluate the coefficients.
 exp

getId
()¶ Accessor to the object’s id.
Returns:  idint
Internal unique identifier.

getMeasure
()¶ Accessor to the measure.
Returns:  muDistribution
Measure defining the scalar product.

getName
()¶ Accessor to the object’s name.
Returns:  namestr
The name of the object.

getRelativeError
()¶ Accessor to the relative error.
Returns:  efloat
Relative error.

getResidual
()¶ Accessor to the residual.
Returns:  erfloat
Residual error.

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.

setExperiment
(weightedExperiment)¶ Accessor to the design of experiment.
Parameters:  exp
WeightedExperiment
Weighted design of experiment.
 exp

setMeasure
(measure)¶ Accessor to the measure.
Parameters:  mDistribution
Measure defining the scalar product.

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.

setWeights
(weights)¶ Accessor to the weights.
Parameters:  w
Point
Weights of the design of experiments.
 w

thisown
¶ The membership flag