1%feature("docstring") OT::GeneralLinearModelResult
2"General linear model result.
3
4Parameters
5----------
6inputSample, outputSample : :class:`~openturns.Sample`
7    The samples :math:`(\vect{x}_k)_{1 \leq k \leq N} \in \Rset^d` and :math:`(\vect{y}_k)_{1 \leq k \leq N}\in \Rset^p`.
8metaModel : :class:`~openturns.Function`
9    The meta model: :math:`\tilde{\cM}: \Rset^d \rightarrow \Rset^p`, defined in :eq:metaModel.
10residuals : :class:`~openturns.Point`
11    The residual errors.
12relativeErrors : :class:`~openturns.Point`
13    The relative errors.
14basis : collection of :class:`~openturns.Basis`
15    Collection of the  :math:`p` functional basis: :math:`(\varphi_j^l: \Rset^d \rightarrow \Rset)_{1 \leq j \leq n_l}` for each :math:`l \in [1, p]`.
16    Its size should be equal to zero if the trend is not estimated.
17trendCoefficients : collection of :class:`~openturns.Point`
18   The trend coefficients vectors :math:`(\vect{\alpha}^1, \dots, \vect{\alpha}^p)`.
19covarianceModel : :class:`~openturns.CovarianceModel`
20    Covariance function of the Gaussian process with its optimized parameters.
21optimalLogLikelihood : float
22    The maximum log-likelihood corresponding to the model.
23
24Notes
25-----
26The structure is usually created by the method *run()* of a :class:`~openturns.GeneralLinearModelAlgorithm`, and obtained thanks to the *getResult()* method.
27
28The meta model :math:`\tilde{\cM}: \Rset^d \rightarrow \Rset^p` is defined by:
29
30.. math::
31    :label: metaModel
32
33    \tilde{\cM}(\vect{x}) = \left(
34      \begin{array}{l}
35        \mu_1(\vect{x}) \\
36        \dots  \\
37        \mu_p(\vect{x})
38       \end{array}
39     \right)
40
41where :math:`\mu_l(\vect{x}) = \sum_{j=1}^{n_l} \alpha_j^l \varphi_j^l(\vect{x})` and :math:`\varphi_j^l: \Rset^d \rightarrow \Rset` are the trend functions.
42
43If a normalizing transformation *T* has been used, the meta model is built on the inputs :math:`\vect{z}_k = T(\vect{x}_k)` and the meta model writes:
44
45.. math::
46    :label: metaModelWithT
47
48    \tilde{\cM}(\vect{x}) = \left(
49      \begin{array}{l}
50        \mu_1\circ T(\vect{x}) \\
51        \dots  \\
52        \mu_p\circ T(\vect{x})
53       \end{array}
54     \right)
55
56Examples
57--------
58Create the model :math:`\cM: \Rset \mapsto \Rset` and the samples:
59
60>>> import openturns as ot
61>>> f = ot.SymbolicFunction(['x'],  ['x * sin(x)'])
62>>> sampleX = [[1.0], [2.0], [3.0], [4.0], [5.0], [6.0]]
63>>> sampleY = f(sampleX)
64
65Create the algorithm:
66
67>>> basis = ot.Basis([ot.SymbolicFunction(['x'], ['x']), ot.SymbolicFunction(['x'], ['x^2'])])
68>>> covarianceModel = ot.GeneralizedExponential([2.0], 2.0)
69>>> algo = ot.GeneralLinearModelAlgorithm(sampleX, sampleY, covarianceModel, basis)
70>>> algo.run()
71
72Get the result:
73
74>>> result = algo.getResult()
75
76Get the meta model:
77
78>>> metaModel = result.getMetaModel()
79>>> graph = metaModel.draw(0.0, 7.0)
80>>> cloud = ot.Cloud(sampleX, sampleY)
81>>> cloud.setPointStyle('fcircle')
82>>> graph = ot.Graph()
83>>> graph.add(cloud)
84>>> graph.add(f.draw(0.0, 7.0))
85>>> graph.setColors(['black', 'blue', 'red'])
86"
87
88// ---------------------------------------------------------------------
89
90%feature("docstring") OT::GeneralLinearModelResult::getTrendCoefficients
91"Accessor to the trend coefficients.
92
93Returns
94-------
95trendCoef : collection of :class:`~openturns.Point`
96    The trend coefficients vectors :math:`(\vect{\alpha}^1, \dots, \vect{\alpha}^p)`
97"
98
99// ---------------------------------------------------------------------
100
101%feature("docstring") OT::GeneralLinearModelResult::getCovarianceModel
102"Accessor to the covariance model.
103
104Returns
105-------
106covModel : :class:`~openturns.CovarianceModel`
107    The covariance model of the Gaussian process *W*.
108"
109
110// ---------------------------------------------------------------------
111
112%feature("docstring") OT::GeneralLinearModelResult::getBasisCollection
113"Accessor to the collection of basis.
114
115Returns
116-------
117basisCollection : collection of :class:`~openturns.Basis`
118    Collection of the :math:`p` function basis: :math:`(\varphi_j^l: \Rset^d \rightarrow \Rset)_{1 \leq j \leq n_l}` for each :math:`l \in [1, p]`.
119
120Notes
121-----
122If the trend is not estimated, the collection is empty.
123"
124
125// ---------------------------------------------------------------------
126
127%feature("docstring") OT::GeneralLinearModelResult::getMetaModel
128"Accessor to the metamodel.
129
130Returns
131-------
132metaModel : :class:`~openturns.Function`
133    The meta model :math:`\tilde{\cM}: \Rset^d \rightarrow \Rset^p`, defined in :eq:'metaModel'.
134"
135
136// ---------------------------------------------------------------------
137
138%feature("docstring") OT::GeneralLinearModelResult::getTransformation
139"Accessor to the normalizing transformation.
140
141Returns
142-------
143transformation : :class:`~openturns.Function`
144    The transformation *T* that normalizes the input sample.
145"
146
147// ---------------------------------------------------------------------
148
149%feature("docstring") OT::GeneralLinearModelResult::setTransformation
150"Set accessor to the normalizing transformation.
151
152Parameters
153----------
154transformation : :class:`~openturns.Function`
155    The transformation *T* that normalizes the input sample.
156"
157
158// ---------------------------------------------------------------------
159
160%feature("docstring") OT::GeneralLinearModelResult::getNoise
161"Accessor to the Gaussian process.
162
163Returns
164-------
165process : :class:`~openturns.Process`
166    Returns the Gaussian process :math:`W` with the optimized parameters.
167"
168
169// ---------------------------------------------------------------------
170
171%feature("docstring") OT::GeneralLinearModelResult::getOptimalLogLikelihood
172"Accessor to the optimal log-likelihood of the model.
173
174Returns
175-------
176optimalLogLikelihood : float
177    The value of the log-likelihood corresponding to the model.
178"
179
180// ---------------------------------------------------------------------
181
182