LeastSquaresStrategy¶
- class LeastSquaresStrategy(*args)¶
Least squares strategy for the approximation coefficients.
- Available constructors:
LeastSquaresStrategy(weightedExp)
LeastSquaresStrategy(weightedExp, approxAlgoImpFact)
LeastSquaresStrategy(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.- inputSample2-d sequence of float
The input random observations where is the input of the physical model, is the input dimension and is the sample size.
- outputSample2-d sequence of float
The output random observations where is the output of the physical model, is the output dimension and is the sample size.
- 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.
- weightedExp
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
Accessor to the object's name.
Accessor to the coefficients.
Accessor to the design proxy.
Accessor to the experiments.
Accessor to the input sample.
Accessor to the measure.
getName
()Accessor to the object's name.
Accessor to the output sample.
Accessor to the relative error.
Accessor to the residual.
Accessor to the weights.
hasName
()Test if the object is named.
Get the model selection flag.
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.
- __init__(*args)¶
- getClassName()¶
Accessor to the object’s name.
- Returns:
- class_namestr
The object class name (object.__class__.__name__).
- getDesignProxy()¶
Accessor to the design proxy.
- Parameters:
- designProxy
DesignProxy
The design matrix.
- designProxy
- getExperiment()¶
Accessor to the experiments.
- Returns:
- exp
WeightedExperiment
Weighted experiment used to evaluate the coefficients.
- exp
- 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.
- 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:
- involvesModelSelection: bool
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:
- isLeastSquares: bool
True if the coefficients are estimated from least squares.
- 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.
Examples using the class¶
Compute grouped indices for the Ishigami function
Create a full or sparse polynomial chaos expansion
Advanced polynomial chaos construction
Create a polynomial chaos for the Ishigami function: a quick start guide to polynomial chaos
Polynomial chaos expansion cross-validation
Polynomial chaos is sensitive to the degree
Compute Sobol’ indices confidence intervals
Compute leave-one-out error of a polynomial chaos expansion