1%feature("docstring") OT::KrigingRandomVector
2"KrigingRandom vector, a conditioned Gaussian process.
3
4Parameters
5----------
6krigingResult : :class:`~openturns.KrigingResult`
7    Structure that contains elements of computation of a kriging algorithm
8points : 1-d or 2-d sequence of float
9    Sequence of values defining a :class:`~openturns.Point` or a :class:`~openturns.Sample`.
10
11Notes
12-----
13KrigingRandomVector helps to create Gaussian random vector, :math:`Y: \Rset^n \mapsto \Rset^d`, with stationary covariance function  :math:`\cC^{stat}: \Rset^n \mapsto \cM_{d \times d}(\Rset)`, conditionally to some observations.
14
15Let :math:`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 :class:`~openturns.KrigingAlgorithm`:
16
17.. math::
18
19    Y(\vect{x}) = \Tr{\vect{f}(\vect{x})} \vect{\beta} + Z(\vect{x})
20
21with :math:`\Tr{\vect{f}(\vect{x})} \vect{\beta}` a general linear model, :math:`Z(\vect{x})` a zero-mean Gaussian process with a stationary autocorrelation function :math:`\cC^{stat}`:
22
23.. math::
24
25    \mathbb{E}[Z(\vect{x}), Z(\vect{\tilde{x}})] = \sigma^2 \cC^{stat}_{\theta}(\vect{x} - \vect{\tilde{x}})
26
27The objective is to generate realizations of the random vector :math:`Y`, on new points :math:`\vect{\tilde{x}}`, conditionally to these observations. For that purpose, :class:`~openturns.KrigingAlgorithm` build such a prior and stores results in a :class:`~openturns.KrigingResult` structure on a first step. This structure is given as input argument.
28
29Then, in a second step, both the prior and the covariance on input points :math:`\vect{\tilde{x}}`, conditionally to the previous observations, are evaluated (respectively :math:`Y(\vect{\tilde{x}})` and :math:`\cC^{stat}_{\theta}(\vect{\tilde{x}})`).
30
31Finally realizations are randomly generated by the Gaussian distribution :math:`\cN ( Y(\vect{\tilde{x}}), \cC^{stat}_{\theta}(\vect{\tilde{x}}) )`
32
33KrigingRandomVector class inherits from :class:`~openturns.UsualRandomVector`. Thus it stores the previous distribution and returns elements thanks to that distribution (realization, mean, covariance, sample...)
34
35Examples
36--------
37Create the model :math:`\cM: \Rset \mapsto \Rset` and the samples:
38
39>>> import openturns as ot
40>>> f = ot.SymbolicFunction(['x'],  ['x * sin(x)'])
41>>> sampleX = [[1.0], [2.0], [3.0], [4.0], [5.0], [6.0], [7.0], [8.0]]
42>>> sampleY = f(sampleX)
43
44Create the algorithm:
45
46>>> basis = ot.Basis([ot.SymbolicFunction(['x'], ['x']), ot.SymbolicFunction(['x'], ['x^2'])])
47>>> covarianceModel = ot.SquaredExponential([1.0])
48>>> covarianceModel.setActiveParameter([])
49>>> algo = ot.KrigingAlgorithm(sampleX, sampleY, covarianceModel, basis)
50>>> algo.run()
51
52Get the results:
53
54>>> result = algo.getResult()
55>>> rvector = ot.KrigingRandomVector(result, [[0.0]])
56
57Get a sample of the random vector:
58
59>>> sample = rvector.getSample(5)"
60
61// ---------------------------------------------------------------------
62
63%feature("docstring") OT::KrigingRandomVector::getRealization
64"Compute a realization of the conditional Gaussian process (conditional on the learning set).
65
66The realization predicts the value on the given input *points*.
67
68Returns
69-------
70realization : :class:`~openturns.Point`
71    Sequence of values of the Gaussian process.
72
73See also
74--------
75getSample"
76
77// ---------------------------------------------------------------------
78
79%feature("docstring") OT::KrigingRandomVector::getSample
80"Compute a sample of realizations of the conditional Gaussian process (conditional on the learning set).
81
82The realization predicts the value on the given input *points*.
83
84Returns
85-------
86realizations : :class:`~openturns.Sample`
87    2-d float sequence of values of the Gaussian process.
88
89See also
90--------
91getRealization"
92
93// ---------------------------------------------------------------------
94
95%feature("docstring") OT::KrigingRandomVector::getKrigingResult
96"Return the kriging result structure.
97
98Returns
99-------
100krigResult : :class:`~openturns.KrigingResult`
101    The structure containing the elements of a KrigingAlgorithm."
102