PenalizedLeastSquaresAlgorithm¶
- class PenalizedLeastSquaresAlgorithm(*args)¶
Penalized least squares algorithm.
Refer to Least squares problems numerical methods.
- Available constructors:
PenalizedLeastSquaresAlgorithm(x, y, psi, indices, penalizationFactor=0, useNormal=False)
PenalizedLeastSquaresAlgorithm(x, y, weight, psi, indices, penalizationFactor=0, useNormal=False)
PenalizedLeastSquaresAlgorithm(x, y, weight, psi, indices, penalizationFactor=0, penalizationMatrix, useNormal=False)
- Parameters:
- x2-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.
- y2-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.
- weightsequence of float
Output weights
- psisequence of
Function
Basis
- indicessequence of int
Indices allowed in the basis
- penalizationFactorfloat, optional
Penalization factor
- penalizationMatrix2-d sequence of float
Penalization matrix
- useNormalbool, optional
Solve the normal equation
Notes
For each output marginal , solve the least-squares problem:
where is the -th marginal of the sample of output observations, is the number of coefficients, is the design matrix computed from the input sample x and is the vector of coefficients.
Methods
Accessor to the object's name.
Accessor to the coefficients.
getName
()Accessor to the object's name.
getPsi
()Accessor to the basis.
Accessor to the coefficients.
Accessor to the coefficients.
Accessor to the weights.
getX
()Accessor to the input sample.
getY
()Accessor to the output sample.
hasName
()Test if the object is named.
Get the model selection flag.
run
()Run the algorithm.
setName
(name)Accessor to the object's name.
- __init__(*args)¶
- getClassName()¶
Accessor to the object’s name.
- Returns:
- class_namestr
The object class name (object.__class__.__name__).
- getName()¶
Accessor to the object’s name.
- Returns:
- namestr
The name of the object.
- getRelativeError()¶
Accessor to the coefficients.
- Returns:
- relativeErrorfloat
The relative error
- getResidual()¶
Accessor to the coefficients.
- Returns:
- coefficientsfloat
The residual
- 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.
- run()¶
Run the algorithm.
- setName(name)¶
Accessor to the object’s name.
- Parameters:
- namestr
The name of the object.