GaussianProcessRegressionResult¶

class GaussianProcessRegressionResult(*args)¶

Gaussian process regression (aka kriging) result.

Warning

This class is experimental and likely to be modified in future releases. To use it, import the openturns.experimental submodule.

Refer to Gaussian process regression.

Parameters:

gpfitResultGaussianProcessFitterResult: Structure result of a gaussian process fitter.
covarianceCoefficients2-d sequence of float: The $\vect{\gamma}$ defined in (3).

Methods

`getBasis`()	Accessor to the collection of basis.
`getClassName`()	Accessor to the object's name.
`getCovarianceCoefficients`()	Accessor to the covariance coefficients.
`getCovarianceModel`()	Accessor to the covariance model.
`getInputSample`()	Accessor to the input sample.
`getLinearAlgebraMethod`()	Accessor to the linear algebra method used to fit.
`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.
`getRegressionMatrix`()	Accessor to the regression matrix.
`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(), and obtained thanks to the getResult() method.

Refer to the documentation of GaussianProcessRegression to get details on the notations.

Examples

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

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

Create the algorithm:

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

Create the interpolating Gaussian process approximation:

>>> algo = otexp.GaussianProcessRegression(fit_algo.getResult())
>>> algo.run()

Get the resulting interpolating metamodel $\metaModel$ :

>>> result = algo.getResult()
>>> metaModel = result.getMetaModel()

__init__(*args)¶

getBasis()¶

Accessor to the collection of basis.

Returns:

basisBasis: Functional basis to estimate the trend: $(\varphi_j)_{1 \leq j \leq b}: \Rset^\inputDim \rightarrow \Rset$ .

Notes

If the trend is not estimated, the basis is empty. The same basis is used for each marginal output.

getClassName()¶

Accessor to the object’s name.

Returns:

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

getCovarianceCoefficients()¶

Accessor to the covariance coefficients.

Returns:

covCoeffSample: The $\vect{\gamma}$ defined in (3).

getCovarianceModel()¶

Accessor to the covariance model.

Returns:

covModelCovarianceModel: The covariance model of the Gaussian process $\vect{W}$ .

getInputSample()¶

Accessor to the input sample.

Returns:

inputSampleSample: The input sample.

getLinearAlgebraMethod()¶

Accessor to the linear algebra method used to fit.

Returns:

linAlgMethodint

The used linear algebra method to fit the model:

otexp.GaussianProcessFitterResult.LAPACK or 0: using LAPACK to fit the model,
otexp.GaussianProcessFitterResult.HMAT or 1: using HMAT to fit the model.

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: The Gaussian process $\vect{W}$ its 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.

getRegressionMatrix()¶

Accessor to the regression matrix.

Returns:

processMatrix: Returns the regression matrix.

Notes

The regression matrix, e.g the evaluation of the basis function upon the input design sample. It contains $\sampleSize \times \outputDim$ lines and as many column as the size of the functional basis. The column $k$ is defined as:

$\left(\varphi_k(\vect{x}_1), \dots,\varphi_k(\vect{x}_\sampleSize) \right).$

getTrendCoefficients()¶

Accessor to the trend coefficients.

Returns: