KrigingRandomVector

class KrigingRandomVector(*args)

KrigingRandom vector, a conditioned Gaussian process.

Parameters
krigingResultKrigingResult

Structure that contains elements of computation of a kriging algorithm

points1-d or 2-d sequence of float

Sequence of values defining a Point or a Sample.

Notes

KrigingRandomVector helps to create Gaussian random vector, Y: \Rset^n \mapsto \Rset^d, with stationary covariance function \cC^{stat}: \Rset^n \mapsto \cM_{d \times d}(\Rset), conditionally to some observations.

Let Y(x=x_1)=y_1,\cdots,Y(x=x_n)=y_n be the observations of the Gaussian process. We assume the same Gaussian prior as in the KrigingAlgorithm:

Y(\vect{x}) = \Tr{\vect{f}(\vect{x})} \vect{\beta} + Z(\vect{x})

with \Tr{\vect{f}(\vect{x})} \vect{\beta} a general linear model, Z(\vect{x}) a zero-mean Gaussian process with a stationary autocorrelation function \cC^{stat}:

\mathbb{E}[Z(\vect{x}), Z(\vect{\tilde{x}})] = \sigma^2 \cC^{stat}_{\theta}(\vect{x} - \vect{\tilde{x}})

The objective is to generate realizations of the random vector Y, on new points \vect{\tilde{x}}, conditionally to these observations. For that purpose, KrigingAlgorithm build such a prior and stores results in a KrigingResult structure on a first step. This structure is given as input argument.

Then, in a second step, both the prior and the covariance on input points \vect{\tilde{x}}, conditionally to the previous observations, are evaluated (respectively Y(\vect{\tilde{x}}) and \cC^{stat}_{\theta}(\vect{\tilde{x}})).

Finally realizations are randomly generated by the Gaussian distribution \cN ( Y(\vect{\tilde{x}}), \cC^{stat}_{\theta}(\vect{\tilde{x}}) )

KrigingRandomVector class inherits from UsualRandomVector. Thus it stores the previous distribution and returns elements thanks to that distribution (realization, mean, covariance, sample…)

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], [7.0], [8.0]]
>>> sampleY = f(sampleX)

Create the algorithm:

>>> basis = ot.Basis([ot.SymbolicFunction(['x'], ['x']), ot.SymbolicFunction(['x'], ['x^2'])])
>>> covarianceModel = ot.SquaredExponential([1.0])
>>> covarianceModel.setActiveParameter([])
>>> algo = ot.KrigingAlgorithm(sampleX, sampleY, covarianceModel, basis)
>>> algo.run()

Get the results:

>>> result = algo.getResult()
>>> rvector = ot.KrigingRandomVector(result, [[0.0]])

Get a sample of the random vector:

>>> sample = rvector.getSample(5)

Methods

getAntecedent(self)

Accessor to the antecedent RandomVector in case of a composite RandomVector.

getClassName(self)

Accessor to the object’s name.

getCovariance(self)

Accessor to the covariance of the RandomVector.

getDescription(self)

Accessor to the description of the RandomVector.

getDimension(self)

Accessor to the dimension of the RandomVector.

getDistribution(self)

Accessor to the distribution of the RandomVector.

getDomain(self)

Accessor to the domain of the Event.

getFunction(self)

Accessor to the Function in case of a composite RandomVector.

getId(self)

Accessor to the object’s id.

getKrigingResult(self)

Return the kriging result structure.

getMarginal(self, \*args)

Get the random vector corresponding to the i^{th} marginal component(s).

getMean(self)

Accessor to the mean of the RandomVector.

getName(self)

Accessor to the object’s name.

getOperator(self)

Accessor to the comparaison operator of the Event.

getParameter(self)

Accessor to the parameter of the distribution.

getParameterDescription(self)

Accessor to the parameter description of the distribution.

getProcess(self)

Get the stochastic process.

getRealization(self)

Compute a realization of the conditional Gaussian process (conditional on the learning set).

getSample(self, \*args)

Compute a sample of realizations of the conditional Gaussian process (conditional on the learning set).

getShadowedId(self)

Accessor to the object’s shadowed id.

getThreshold(self)

Accessor to the threshold of the Event.

getVisibility(self)

Accessor to the object’s visibility state.

hasName(self)

Test if the object is named.

hasVisibleName(self)

Test if the object has a distinguishable name.

isComposite(self)

Accessor to know if the RandomVector is a composite one.

setDescription(self, description)

Accessor to the description of the RandomVector.

setName(self, name)

Accessor to the object’s name.

setParameter(self, parameters)

Accessor to the parameter of the distribution.

setShadowedId(self, id)

Accessor to the object’s shadowed id.

setVisibility(self, visible)

Accessor to the object’s visibility state.

__init__(self, *args)

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

getAntecedent(self)

Accessor to the antecedent RandomVector in case of a composite RandomVector.

Returns
antecedentRandomVector

Antecedent RandomVector \vect{X} in case of a CompositeRandomVector such as: \vect{Y}=f(\vect{X}).

getClassName(self)

Accessor to the object’s name.

Returns
class_namestr

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

getCovariance(self)

Accessor to the covariance of the RandomVector.

Returns
covarianceCovarianceMatrix

Covariance of the considered UsualRandomVector.

Examples

>>> import openturns as ot
>>> distribution = ot.Normal([0.0, 0.5], [1.0, 1.5], ot.CorrelationMatrix(2))
>>> randomVector = ot.RandomVector(distribution)
>>> ot.RandomGenerator.SetSeed(0)
>>> print(randomVector.getCovariance())
[[ 1    0    ]
 [ 0    2.25 ]]
getDescription(self)

Accessor to the description of the RandomVector.

Returns
descriptionDescription

Describes the components of the RandomVector.

getDimension(self)

Accessor to the dimension of the RandomVector.

Returns
dimensionpositive int

Dimension of the RandomVector.

getDistribution(self)

Accessor to the distribution of the RandomVector.

Returns
distributionDistribution

Distribution of the considered UsualRandomVector.

Examples

>>> import openturns as ot
>>> distribution = ot.Normal([0.0, 0.0], [1.0, 1.0], ot.CorrelationMatrix(2))
>>> randomVector = ot.RandomVector(distribution)
>>> ot.RandomGenerator.SetSeed(0)
>>> print(randomVector.getDistribution())
Normal(mu = [0,0], sigma = [1,1], R = [[ 1 0 ]
 [ 0 1 ]])
getDomain(self)

Accessor to the domain of the Event.

Returns
domainDomain

Describes the domain of an event.

getFunction(self)

Accessor to the Function in case of a composite RandomVector.

Returns
functionFunction

Function used to define a CompositeRandomVector as the image through this function of the antecedent \vect{X}: \vect{Y}=f(\vect{X}).

getId(self)

Accessor to the object’s id.

Returns
idint

Internal unique identifier.

getKrigingResult(self)

Return the kriging result structure.

Returns
krigResultKrigingResult

The structure containing the elements of a KrigingAlgorithm.

getMarginal(self, *args)

Get the random vector corresponding to the i^{th} marginal component(s).

Parameters
iint or list of ints, 0\leq i < dim

Indicates the component(s) concerned. dim is the dimension of the RandomVector.

Returns
vectorRandomVector

RandomVector restricted to the concerned components.

Notes

Let’s note \vect{Y}=\Tr{(Y_1,\dots,Y_n)} a random vector and I \in [1,n] a set of indices. If \vect{Y} is a UsualRandomVector, the subvector is defined by \tilde{\vect{Y}}=\Tr{(Y_i)}_{i \in I}. If \vect{Y} is a CompositeRandomVector, defined by \vect{Y}=f(\vect{X}) with f=(f_1,\dots,f_n), f_i some scalar functions, the subvector is \tilde{\vect{Y}}=(f_i(\vect{X}))_{i \in I}.

Examples

>>> import openturns as ot
>>> distribution = ot.Normal([0.0, 0.0], [1.0, 1.0], ot.CorrelationMatrix(2))
>>> randomVector = ot.RandomVector(distribution)
>>> ot.RandomGenerator.SetSeed(0)
>>> print(randomVector.getMarginal(1).getRealization())
[0.608202]
>>> print(randomVector.getMarginal(1).getDistribution())
Normal(mu = 0, sigma = 1)
getMean(self)

Accessor to the mean of the RandomVector.

Returns
meanPoint

Mean of the considered UsualRandomVector.

Examples

>>> import openturns as ot
>>> distribution = ot.Normal([0.0, 0.5], [1.0, 1.5], ot.CorrelationMatrix(2))
>>> randomVector = ot.RandomVector(distribution)
>>> ot.RandomGenerator.SetSeed(0)
>>> print(randomVector.getMean())
[0,0.5]
getName(self)

Accessor to the object’s name.

Returns
namestr

The name of the object.

getOperator(self)

Accessor to the comparaison operator of the Event.

Returns
operatorComparisonOperator

Comparaison operator used to define the Event.

getParameter(self)

Accessor to the parameter of the distribution.

Returns
parameterPoint

Parameter values.

getParameterDescription(self)

Accessor to the parameter description of the distribution.

Returns
descriptionDescription

Parameter names.

getProcess(self)

Get the stochastic process.

Returns
processProcess

Stochastic process used to define the Event.

getRealization(self)

Compute a realization of the conditional Gaussian process (conditional on the learning set).

The realization predicts the value on the given input points.

Returns
realizationPoint

Sequence of values of the Gaussian process.

See also

getSample
getSample(self, *args)

Compute a sample of realizations of the conditional Gaussian process (conditional on the learning set).

The realization predicts the value on the given input points.

Returns
realizationsSample

2-d float sequence of values of the Gaussian process.

See also

getRealization
getShadowedId(self)

Accessor to the object’s shadowed id.

Returns
idint

Internal unique identifier.

getThreshold(self)

Accessor to the threshold of the Event.

Returns
thresholdfloat

Threshold of the Event.

getVisibility(self)

Accessor to the object’s visibility state.

Returns
visiblebool

Visibility flag.

hasName(self)

Test if the object is named.

Returns
hasNamebool

True if the name is not empty.

hasVisibleName(self)

Test if the object has a distinguishable name.

Returns
hasVisibleNamebool

True if the name is not empty and not the default one.

isComposite(self)

Accessor to know if the RandomVector is a composite one.

Returns
isCompositebool

Indicates if the RandomVector is of type Composite or not.

setDescription(self, description)

Accessor to the description of the RandomVector.

Parameters
descriptionstr or sequence of str

Describes the components of the RandomVector.

setName(self, name)

Accessor to the object’s name.

Parameters
namestr

The name of the object.

setParameter(self, parameters)

Accessor to the parameter of the distribution.

Parameters
parametersequence of float

Parameter values.

setShadowedId(self, id)

Accessor to the object’s shadowed id.

Parameters
idint

Internal unique identifier.

setVisibility(self, visible)

Accessor to the object’s visibility state.

Parameters
visiblebool

Visibility flag.