KrigingRandomVector

class KrigingRandomVector(*args)

KrigingRandom vector, a conditioned Gaussian process.

Available constructors:
KrigingRandomVector(krigingResult, points)
Parameters:

krigingResult : KrigingResult

Structure that contains elements of computation of a kriging algorithm

points : 1-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…)

Methods

getAntecedent() Accessor to the antecedent RandomVector in case of a composite RandomVector.
getClassName() Accessor to the object’s name.
getCovariance() Accessor to the covariance of the RandomVector.
getDescription() Accessor to the description of the RandomVector.
getDimension() Accessor to the dimension of the RandomVector.
getDistribution() Accessor to the distribution of the RandomVector.
getDomain() Accessor to the domain of the Event.
getFunction() Accessor to the Function in case of a composite RandomVector.
getId() Accessor to the object’s id.
getKrigingResult() Return the kriging result structure.
getMarginal(*args) Get the random vector corresponding to the i^{th} marginal component(s).
getMean() Accessor to the mean of the RandomVector.
getName() Accessor to the object’s name.
getOperator() Accessor to the comparaison operator of the Event.
getProcess() Get the stochastic process.
getRealization() Compute a realization of the conditional Gaussian process (conditional on the learning set).
getSample(*args) Compute a sample of realizations of the conditional Gaussian process (conditional on the learning set).
getShadowedId() Accessor to the object’s shadowed id.
getThreshold() Accessor to the threshold of the Event.
getVisibility() Accessor to the object’s visibility state.
hasName() Test if the object is named.
hasVisibleName() Test if the object has a distinguishable name.
isComposite() Accessor to know if the RandomVector is a composite one.
setDescription(description) Accessor to the description of the RandomVector.
setName(name) Accessor to the object’s name.
setShadowedId(id) Accessor to the object’s shadowed id.
setVisibility(visible) Accessor to the object’s visibility state.
__init__(*args)

x.__init__(…) initializes x; see help(type(x)) for signature

getAntecedent()

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

Returns:

antecedent : RandomVector

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

getClassName()

Accessor to the object’s name.

Returns:

class_name : str

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

getCovariance()

Accessor to the covariance of the RandomVector.

Returns:

covariance : CovarianceMatrix

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()

Accessor to the description of the RandomVector.

Returns:

description : Description

Describes the components of the RandomVector.

getDimension()

Accessor to the dimension of the RandomVector.

Returns:

dimension : positive int

Dimension of the RandomVector.

getDistribution()

Accessor to the distribution of the RandomVector.

Returns:

distribution : Distribution

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()

Accessor to the domain of the Event.

Returns:

domain : Domain

Describes the domain of an event.

getFunction()

Accessor to the Function in case of a composite RandomVector.

Returns:

function : Function

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

getId()

Accessor to the object’s id.

Returns:

id : int

Internal unique identifier.

getKrigingResult()

Return the kriging result structure.

Returns:

krigResult : KrigingResult

The structure containing the elements of a KrigingAlgorithm.

Examples

>>> import openturns as ot
>>> ot.RandomGenerator.SetSeed(0)
>>> sampleSize = 6
>>> dimension = 1
>>> f = ot.SymbolicFunction(['x0'], ['x0 * sin(x0)'])
>>> X = ot.Sample(sampleSize, dimension)
>>> for i in range(sampleSize):
...    X[i, 0] = 3.0 + i
>>> X[0, 0] = 1.0
>>> X[1, 0] = 3.0
>>> Y = f(X)
>>> # create algorithm
>>> basis = ot.ConstantBasisFactory(dimension).build()
>>> covarianceModel = ot.SquaredExponential([2.23606797749979])
>>> algo = ot.KrigingAlgorithm(X, Y, covarianceModel, basis)
>>> algo.run()
>>> # get the results
>>> result = algo.getResult()
>>> # Random vector evaluation
>>> rvector = ot.KrigingRandomVector(result, [[0.0]])
>>> # Get the kriging result
>>> krigResult = rvector.getKrigingResult()
getMarginal(*args)

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

Parameters:

i : int or list of ints, 0\leq i < dim

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

Returns:

vector : RandomVector

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()

Accessor to the mean of the RandomVector.

Returns:

mean : Point

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()

Accessor to the object’s name.

Returns:

name : str

The name of the object.

getOperator()

Accessor to the comparaison operator of the Event.

Returns:

operator : ComparisonOperator

Comparaison operator used to define the Event.

getProcess()

Get the stochastic process.

Returns:

process : Process

Stochastic process used to define the Event.

getRealization()

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

The realization predicts the value on the given input points.

Returns:

realization : Point

Sequence of values of the Gaussian process.

See also

getSample

Examples

>>> import openturns as ot
>>> ot.RandomGenerator.SetSeed(0)
>>> sampleSize = 6
>>> dimension = 1
>>> f = ot.SymbolicFunction(['x0'], ['x0 * sin(x0)'])
>>> X = ot.Sample(sampleSize, dimension)
>>> for i in range(sampleSize):
...     X[i, 0] = 3.0 + i
>>> X[0, 0] = 1.0
>>> X[1, 0] = 3.0
>>> Y = f(X)
>>> # create algorithm
>>> basis = ot.ConstantBasisFactory(dimension).build()
>>> covarianceModel = ot.SquaredExponential([2.23606797749979])
>>> algo = ot.KrigingAlgorithm(X, Y, covarianceModel, basis)
>>> algo.run()
>>> # get the results
>>> result = algo.getResult()
>>> # Random vector evaluation
>>> rvector = ot.KrigingRandomVector(result, [[0]])
>>> # Realization of the random vector
>>> realization = rvector.getRealization()
getSample(*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:

realizations : Sample

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

See also

getRealization

Examples

>>> import openturns as ot
>>> ot.RandomGenerator.SetSeed(0)
>>> sampleSize = 6
>>> dimension = 1
>>> f = ot.SymbolicFunction(['x0'], ['x0 * sin(x0)'])
>>> X = ot.Sample(sampleSize, dimension)
>>> for i in range(sampleSize):
...    X[i, 0] = 3.0 + i
>>> X[0, 0] = 1.0
>>> X[1, 0] = 3.0
>>> Y = f(X)
>>> # create algorithm
>>> basis = ot.ConstantBasisFactory(dimension).build()
>>> covarianceModel = ot.SquaredExponential([2.23606797749979])
>>> algo = ot.KrigingAlgorithm(X, Y, covarianceModel, basis)
>>> algo.run()
>>> # get the results
>>> result = algo.getResult()
>>> # Random vector evaluation
>>> rvector = ot.KrigingRandomVector(result, [[0.0]])
>>> # Realization of the random vector
>>> realizations = rvector.getSample(5)
getShadowedId()

Accessor to the object’s shadowed id.

Returns:

id : int

Internal unique identifier.

getThreshold()

Accessor to the threshold of the Event.

Returns:

threshold : float

Threshold of the Event.

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.

isComposite()

Accessor to know if the RandomVector is a composite one.

Returns:

isComposite : bool

Indicates if the RandomVector is of type Composite or not.

setDescription(description)

Accessor to the description of the RandomVector.

Parameters:

description : str or sequence of str

Describes the components of the RandomVector.

setName(name)

Accessor to the object’s name.

Parameters:

name : str

The name of the object.

setShadowedId(id)

Accessor to the object’s shadowed id.

Parameters:

id : int

Internal unique identifier.

setVisibility(visible)

Accessor to the object’s visibility state.

Parameters:

visible : bool

Visibility flag.