GeneralLinearModelResult

class GeneralLinearModelResult(*args)

General linear model result.

Parameters:
inputSample, outputSampleSample

The samples (\vect{x}_k)_{1 \leq k \leq N} \in \Rset^d and (\vect{y}_k)_{1 \leq k \leq N}\in \Rset^p.

metaModelFunction

The meta model: \tilde{\cM}: \Rset^d \rightarrow \Rset^p, defined in :eq:metaModel.

basisBasis

Functional basis of size b : (\varphi^l: \Rset^d \rightarrow \Rset^p) for each l \in [1, b]. Its size should be equal to zero if the trend is not estimated.

trendCoefsequence of float

The trend coefficients vectors (\vect{\alpha}^1, \dots, \vect{\alpha}^p) stored as a Point.

covarianceModelCovarianceModel

Covariance function of the Gaussian process with its optimized parameters.

optimalLogLikelihoodfloat

The maximum log-likelihood corresponding to the model.

Methods

getBasis()

Accessor to the functional basis.

getClassName()

Accessor to the object's name.

getCovarianceModel()

Accessor to the covariance model.

getInputSample()

Accessor to the input sample.

getMetaModel()

Accessor to the metamodel.

getName()

Accessor to the object's name.

getNoise()

Accessor to the Gaussian process.

getOptimalLogLikelihood()

Accessor to the optimal log-likelihood of the model.

getOutputSample()

Accessor to the output sample.

getTrendCoefficients()

Accessor to the trend coefficients.

hasName()

Test if the object is named.

setInputSample(sampleX)

Accessor to the input sample.

setMetaModel(metaModel)

Accessor to the metamodel.

setName(name)

Accessor to the object's name.

setOutputSample(sampleY)

Accessor to the output sample.

getRelativeErrors

getResiduals

setRelativeErrors

setResiduals

Notes

The structure is usually created by the method run() of a GeneralLinearModelAlgorithm, and obtained thanks to the getResult() method.

The meta model \tilde{\cM}: \Rset^d \rightarrow \Rset^p is defined by:

(1)\tilde{\cM}(\vect{x}) = \left( \begin{array}{l} \mu_1(\vect{x}) \\ \dots \\ \mu_p(\vect{x}) \end{array} \right)

where \mu_l(\vect{x}) = \sum_{j=1}^{b} \alpha_j^l \varphi_j^l(\vect{x}) and \varphi_j^l: \Rset^d \rightarrow \Rset are the trend functions (the l-th marginal of varphi(x)).

(2)\tilde{\cM}(\vect{x}) = \left( \begin{array}{l} \mu_1\circ T(\vect{x}) \\ \dots \\ \mu_p\circ T(\vect{x}) \end{array} \right)

Examples

Create the model \cM: \Rset \mapsto \Rset and the samples:

>>> import openturns as ot
>>> f = ot.SymbolicFunction(['x'],  ['x * sin(x)'])
>>> sampleX = [[1.0], [2.0], [3.0], [4.0], [5.0], [6.0]]
>>> sampleY = f(sampleX)

Create the algorithm:

>>> basis = ot.Basis([ot.SymbolicFunction(['x'], ['x']), ot.SymbolicFunction(['x'], ['x^2'])])
>>> covarianceModel = ot.GeneralizedExponential([2.0], 2.0)
>>> algo = ot.GeneralLinearModelAlgorithm(sampleX, sampleY, covarianceModel, basis)
>>> algo.run()

Get the result:

>>> result = algo.getResult()

Get the meta model:

>>> metaModel = result.getMetaModel()
>>> graph = metaModel.draw(0.0, 7.0)
>>> cloud = ot.Cloud(sampleX, sampleY)
>>> cloud.setPointStyle('fcircle')
>>> graph = ot.Graph()
>>> graph.add(cloud)
>>> graph.add(f.draw(0.0, 7.0))
__init__(*args)
getBasis()

Accessor to the functional basis.

Returns:
basisBasis

Functional basis of size b : (\varphi^l: \Rset^d \rightarrow \Rset^p) for each l \in [1, b].

Notes

If the trend is not estimated, the collection is empty.

getClassName()

Accessor to the object’s name.

Returns:
class_namestr

The object class name (object.__class__.__name__).

getCovarianceModel()

Accessor to the covariance model.

Returns:
covModelCovarianceModel

The covariance model of the Gaussian process W.

getInputSample()

Accessor to the input sample.

Returns:
inputSampleSample

The input sample.

getMetaModel()

Accessor to the metamodel.

Returns:
metaModelFunction

Metamodel.

getName()

Accessor to the object’s name.

Returns:
namestr

The name of the object.

getNoise()

Accessor to the Gaussian process.

Returns:
processProcess

Returns the Gaussian process W with the optimized parameters.

getOptimalLogLikelihood()

Accessor to the optimal log-likelihood of the model.

Returns:
optimalLogLikelihoodfloat

The value of the log-likelihood corresponding to the model.

getOutputSample()

Accessor to the output sample.

Returns:
outputSampleSample

The output sample.

getTrendCoefficients()

Accessor to the trend coefficients.

Returns:
trendCoefPoint

The trend coefficients vectors (\vect{\alpha}^1, \dots, \vect{\alpha}^p) stored as a Point.

hasName()

Test if the object is named.

Returns:
hasNamebool

True if the name is not empty.

setInputSample(sampleX)

Accessor to the input sample.

Parameters:
inputSampleSample

The input sample.

setMetaModel(metaModel)

Accessor to the metamodel.

Parameters:
metaModelFunction

Metamodel.

setName(name)

Accessor to the object’s name.

Parameters:
namestr

The name of the object.

setOutputSample(sampleY)

Accessor to the output sample.

Parameters:
outputSampleSample

The output sample.