# GeneralLinearModelResult¶

class GeneralLinearModelResult(*args)

General linear model result.

Available constructors:

GeneralLinearModelResult(inputSample, outputSample, metaModel, residuals, relativeErrors, basis, trendCoefficients, covarianceModel, optimalLogLikelihood)

GeneralLinearModelResult(inputSample, outputSample, metaModel, residuals, relativeErrors, basis, trendCoefficients, covarianceModel, covarianceCholeskyFactor, covarianceHMatrix, optimalLogLikelihood)

Parameters: inputSample, outputSample : Sample The samples and . metaModel : Function The meta model: , defined in :eq:’metaModel’. residuals : Point The residual errors. relativeErrors : Point The relative errors. basis : collection of Basis Collection of the functional basis: for each . Its size should be equal to zero if the trend is not estimated. trendCoefficients : collection of Point The trend coefficients vectors . covarianceModel : CovarianceModel Covariance function of the Gaussian process with its optimized parameters. covarianceCholeskyFactor : TriangularMatrix The Cholesky factor of . covarianceHMatrix : HMatrix The hmat implementation of . optimalLogLikelihood : float The maximum log-likelihood corresponding to the model.

Notes

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

The meta model is defined by:

(1)

where and are the trend functions.

If a normalizing transformation T has been used, the meta model is built on the inputs and the meta model writes:

(2)

Examples

Create the model 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.setColors(['black', 'blue', 'red'])


Methods

 getBasisCollection() Accessor to the collection of basis. getClassName() Accessor to the object’s name. getCovarianceModel() Accessor to the covariance model. getId() Accessor to the object’s id. getMetaModel() Accessor to the metamodel. getModel() Accessor to the model. getName() Accessor to the object’s name. getNoise() Accessor to the Gaussian process. getOptimalLogLikelihood() Accessor to the optimal log-likelihood of the model. getRelativeErrors() Accessor to the relative errors. getResiduals() Accessor to the residuals. getShadowedId() Accessor to the object’s shadowed id. getTransformation() Accessor to the normalizing transformation. getTrendCoefficients() Accessor to the trend coefficients. getVisibility() Accessor to the object’s visibility state. hasName() Test if the object is named. hasVisibleName() Test if the object has a distinguishable name. setMetaModel(metaModel) Accessor to the metamodel. setModel(model) Accessor to the model. setName(name) Accessor to the object’s name. setRelativeErrors(relativeErrors) Accessor to the relative errors. setResiduals(residuals) Accessor to the residuals. setShadowedId(id) Accessor to the object’s shadowed id. setTransformation(transformation) Set accessor to the normalizing transformation. setVisibility(visible) Accessor to the object’s visibility state.
__init__(*args)

Initialize self. See help(type(self)) for accurate signature.

getBasisCollection()

Accessor to the collection of basis.

Returns: basisCollection : collection of Basis Collection of the function basis: for each .

Notes

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

getClassName()

Accessor to the object’s name.

Returns: class_name : str The object class name (object.__class__.__name__).
getCovarianceModel()

Accessor to the covariance model.

Returns: covModel : CovarianceModel The covariance model of the Gaussian process W.
getId()

Accessor to the object’s id.

Returns: id : int Internal unique identifier.
getMetaModel()

Accessor to the metamodel.

Returns: metaModel : Function Metamodel.
getModel()

Accessor to the model.

Returns: model : Function Physical model approximated by a metamodel.
getName()

Accessor to the object’s name.

Returns: name : str The name of the object.
getNoise()

Accessor to the Gaussian process.

Returns: process : Process Returns the Gaussian process with the optimized parameters.
getOptimalLogLikelihood()

Accessor to the optimal log-likelihood of the model.

Returns: optimalLogLikelihood : float The value of the log-likelihood corresponding to the model.
getRelativeErrors()

Accessor to the relative errors.

Returns: relativeErrors : Point The relative errors defined as follows for each output of the model: with the vector of the model’s values and the metamodel’s values.
getResiduals()

Accessor to the residuals.

Returns: residuals : Point The residual values defined as follows for each output of the model: with the model’s values and the metamodel’s values.
getShadowedId()

Accessor to the object’s shadowed id.

Returns: id : int Internal unique identifier.
getTransformation()

Accessor to the normalizing transformation.

Returns: transformation : Function The transformation T that normalizes the input sample.
getTrendCoefficients()

Accessor to the trend coefficients.

Returns: trendCoef : collection of Point The trend coefficients vectors
getVisibility()

Accessor to the object’s visibility state.

Returns: visible : bool Visibility flag.
hasName()

Test if the object is named.

Returns: hasName : bool True if the name is not empty.
hasVisibleName()

Test if the object has a distinguishable name.

Returns: hasVisibleName : bool True if the name is not empty and not the default one.
setMetaModel(metaModel)

Accessor to the metamodel.

Parameters: metaModel : Function Metamodel.
setModel(model)

Accessor to the model.

Parameters: model : Function Physical model approximated by a metamodel.
setName(name)

Accessor to the object’s name.

Parameters: name : str The name of the object.
setRelativeErrors(relativeErrors)

Accessor to the relative errors.

Parameters: relativeErrors : sequence of float The relative errors defined as follows for each output of the model: with the vector of the model’s values and the metamodel’s values.
setResiduals(residuals)

Accessor to the residuals.

Parameters: residuals : sequence of float The residual values defined as follows for each output of the model: with the model’s values and the metamodel’s values.
setShadowedId(id)

Accessor to the object’s shadowed id.

Parameters: id : int Internal unique identifier.
setTransformation(transformation)

Set accessor to the normalizing transformation.

Parameters: transformation : Function The transformation T that normalizes the input sample.
setVisibility(visible)

Accessor to the object’s visibility state.

Parameters: visible : bool Visibility flag.