/usr/include/openturns/swig/GeneralLinearModelResult_doc.i is in libopenturns-dev 1.9-5.
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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 | %feature("docstring") OT::GeneralLinearModelResult
"Generalized linear model result.
Available constructors:
GeneralLinearModelResult(*inputSample, outputSample, metaModel, residuals, relativeErrors, basis, trendCoefficients, covarianceModel, optimalLogLikelihood*)
GeneralLinearModelResult(*inputSample, outputSample, metaModel, residuals, relativeErrors, basis, trendCoefficients, covarianceModel, covarianceCholeskyFactor, covarianceHMatrix, optimalLogLikelihood*)
Parameters
----------
inputSample, outputSample : :class:`~openturns.Sample`
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`.
metaModel : :class:`~openturns.Function`
The meta model: :math:`\\\\tilde{\\\\cM}: \\\\Rset^d \\\\rightarrow \\\\Rset^p`, defined in :eq:'metaModel'.
residuals : :class:`~openturns.Point`
The residual errors.
relativeErrors : :class:`~openturns.Point`
The relative errors.
basis : collection of :class:`~openturns.Basis`
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]`.
Its size should be equal to zero if the trend is not estimated.
trendCoefficients : collection of :class:`~openturns.Point`
The trend coefficients vectors :math:`(\\\\vect{\\\\alpha}^1, \\\\dots, \\\\vect{\\\\alpha}^p)`.
covarianceModel : :class:`~openturns.CovarianceModel`
Covariance function of the normal process with its optimized parameters.
covarianceCholeskyFactor : :class:`~openturns.TriangularMatrix`
The Cholesky factor :math:`\\\\mat{L}` of :math:`\\\\mat{C}`.
covarianceHMatrix : :class:`~openturns.HMatrix`
The *hmat* implementation of :math:`\\\\mat{L}`.
optimalLogLikelihood : float
The maximum log-likelihood corresponding to the model.
Notes
-----
The structure is usually created by the method *run()* of a :class:`~openturns.GeneralLinearModelAlgorithm`, and obtained thanks to the *getResult()* method.
The meta model :math:`\\\\tilde{\\\\cM}: \\\\Rset^d \\\\rightarrow \\\\Rset^p` is defined by:
.. math::
:label: metaModel
\\\\tilde{\\\\cM}(\\\\vect{x}) = \\\\left(
\\\\begin{array}{l}
\\\\mu_1(\\\\vect{x}) \\\\\\\\
\\\\dots \\\\\\\\
\\\\mu_p(\\\\vect{x})
\\\\end{array}
\\\\right)
where :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.
If 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:
.. math::
:label: metaModelWithT
\\\\tilde{\\\\cM}(\\\\vect{x}) = \\\\left(
\\\\begin{array}{l}
\\\\mu_1\\\\circ T(\\\\vect{x}) \\\\\\\\
\\\\dots \\\\\\\\
\\\\mu_p\\\\circ T(\\\\vect{x})
\\\\end{array}
\\\\right)
Examples
--------
Create the model :math:`\\\\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]]
>>> sampleY = f(sampleX)
Create the algorithm:
>>> basis = ot.Basis([ot.SymbolicFunction(['x'], ['x']), ot.SymbolicFunction(['x'], ['x^2'])])
>>> covarianceModel = ot.GeneralizedExponential([2.0], 2.0)
>>> algo = ot.GeneralLinearModelAlgorithm(sampleX, sampleY, covarianceModel, basis)
>>> algo.run()
Get the result:
>>> result = algo.getResult()
Get the meta model:
>>> metaModel = result.getMetaModel()
>>> graph = metaModel.draw(0.0, 7.0)
>>> cloud = ot.Cloud(sampleX, sampleY)
>>> cloud.setPointStyle('fcircle')
>>> graph = ot.Graph()
>>> graph.add(cloud)
>>> graph.add(f.draw(0.0, 7.0))
>>> graph.setColors(['black', 'blue', 'red'])
"
// ---------------------------------------------------------------------
%feature("docstring") OT::GeneralLinearModelResult::getTrendCoefficients
"Accessor to the trend coefficients.
Returns
-------
trendCoef : collection of :class:`~openturns.Point`
The trend coefficients vectors :math:`(\\\\vect{\\\\alpha}^1, \\\\dots, \\\\vect{\\\\alpha}^p)`
"
// ---------------------------------------------------------------------
%feature("docstring") OT::GeneralLinearModelResult::getCovarianceModel
"Accessor to the covariance model.
Returns
-------
covModel : :class:`~openturns.CovarianceModel`
The covariance model of the Normal process *W*.
"
// ---------------------------------------------------------------------
%feature("docstring") OT::GeneralLinearModelResult::getBasisCollection
"Accessor to the collection of basis.
Returns
-------
basisCollection : collection of :class:`~openturns.Basis`
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]`.
Notes
-----
If the trend is not estimated, the collection is empty.
"
// ---------------------------------------------------------------------
%feature("docstring") OT::GeneralLinearModelResult::getMetaModel
"Accessor to the metamodel.
Returns
-------
metaModel : :class:`~openturns.Function`
The meta model :math:`\\\\tilde{\\\\cM}: \\\\Rset^d \\\\rightarrow \\\\Rset^p`, defined in :eq:'metaModel'.
"
// ---------------------------------------------------------------------
%feature("docstring") OT::GeneralLinearModelResult::getTransformation
"Accessor to the normalizing transformation.
Returns
-------
transformation : :class:`~openturns.Function`
The transformation *T* that normalizes the input sample.
"
// ---------------------------------------------------------------------
%feature("docstring") OT::GeneralLinearModelResult::setTransformation
"Set accessor to the normalizing transformation.
Parameters
----------
transformation : :class:`~openturns.Function`
The transformation *T* that normalizes the input sample.
"
// ---------------------------------------------------------------------
%feature("docstring") OT::GeneralLinearModelResult::getNoise
"Accessor to the normal process.
Returns
-------
process : :class:`~openturns.Process`
Returns the normal process :math:`W` with the optimized parameters.
"
// ---------------------------------------------------------------------
%feature("docstring") OT::GeneralLinearModelResult::getOptimalLogLikelihood
"Accessor to the optimal log-likelihood of the model.
Returns
-------
optimalLogLikelihood : float
The value of the log-likelihood corresponding to the model.
"
// ---------------------------------------------------------------------
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