# ProjectionStrategy¶

class ProjectionStrategy(*args)

Base class for the evaluation strategies of the approximation coefficients.

Available constructors:
ProjectionStrategy(projectionStrategy)
Parameters: projectionStrategy : ProjectionStrategy A projection strategy which is a LeastSquaresStrategy or an IntegrationStrategy.

Notes

Consider with , and with finite variance: .

The functional chaos expansion approximates using an isoprobabilistic transformation T and an orthonormal multivariate basis of . See FunctionalChaosAlgorithm to get more details.

The meta model of , based on the functional chaos decomposition of writes:

where K is a non empty finite set of indices, whose cardinality is denoted by P.

We detail the case where .

The vector is equivalently defined by:

(1)

and:

(2)

where and the mean is evaluated with respect to the measure .

It corresponds to two points of view:

In both cases, the mean is approximated by a linear quadrature formula:

(3)

where f is a function in .

In the approximation (3), the set I, the points and the weights are evaluated from different methods implemented in the WeightedExperiment.

The convergence criterion used to evaluate the coefficients is based on the residual value defined in the FunctionalChaosAlgorithm.

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. getImplementation(*args) Accessor to the underlying implementation. 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. 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.
 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.
getImplementation(*args)

Accessor to the underlying implementation.

Returns: impl : Implementation The implementation class.
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.
getWeights()

Accessor to the weights.

Returns: w : Point Weights of the design of experiments.
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.
setWeights(weights)

Accessor to the weights.

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