/usr/include/openturns/swig/SecondOrderModelImplementation_doc.i is in libopenturns-dev 1.9-5.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
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 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 | %define OT_SecondOrderModel_doc
"Second order model.
Notes
-----
We consider :math:`X: \\\\Omega \\\\times\\\\cD \\\\mapsto \\\\Rset^d` a multivariate
stochastic process of dimension :math:`d`, where :math:`\\\\omega \\\\in \\\\Omega`
is an event, :math:`\\\\cD` is a domain of :math:`\\\\Rset^n`,
:math:`\\\\vect{t}\\\\in \\\\cD` is a multivariate index and
:math:`X(\\\\omega, \\\\vect{t}) \\\\in \\\\Rset^d`.
We note :math:`X_{\\\\vect{t}}: \\\\Omega \\\\rightarrow \\\\Rset^d` the random variable at
index :math:`\\\\vect{t} \\\\in \\\\cD` defined by
:math:`X_{\\\\vect{t}}(\\\\omega)=X(\\\\omega, \\\\vect{t})` and
:math:`X(\\\\omega): \\\\cD \\\\mapsto \\\\Rset^d` a realization of the process
:math:`X`, for a given :math:`\\\\omega \\\\in \\\\Omega` defined by
:math:`X(\\\\omega)(\\\\vect{t})=X(\\\\omega, \\\\vect{t})`.
The *SecondOrderModel* class enable to get both spectral information of such process thanks to the :class:`SpectralModel` class and spatial/temporal information using the :class:`CovarianceModel` information.
A SecondOrderModel object can be created only through its derived classes:
:class:`~openturns.ExponentialCauchy`"
%enddef
%feature("docstring") OT::SecondOrderModelImplementation
OT_SecondOrderModel_doc
// ---------------------------------------------------------------------
%define OT_SecondOrderModel_compute_covariance_doc
"Evaluate the covariance function.
Available usages:
computeCovariance(s, t)
computeCovariance(tau)
Parameters
----------
s, t : floats or sequence of floats.
Inputs.
tau : float or sequence of floats.
Input.
Returns
-------
covariance : CovarianceMatrix
The evaluation of the covariance function.
Notes
-----
*computeCovariance* evaluates the covariance model
:math:`C : \\\\cD \\\\times \\\\cD \\\\mapsto \\\\cM_{d \\\\times d}(\\\\Rset)` at
:math:`(s,t)\\\\in \\\\Rset^n`:
.. math::
C(\\\\vect{s}, \\\\vect{t})=\\\\Expect{(X_{\\\\vect{s}}-m(\\\\vect{s}))\\\\Tr{(X_{\\\\vect{t}}-m(\\\\vect{t}))}}
We note that the first usage calls the second as model is stationary. Thus,
:math:`C(\\\\vect{s}, \\\\vect{t})` = :math:`C^{stat}(\\\\vect{\\\\tau})` with
:math:`\\\\vect{\\\\tau}=\\\\vect{s}-\\\\vect{t}`. "
%enddef
%feature("docstring") OT::SecondOrderModelImplementation::computeCovariance
OT_SecondOrderModel_compute_covariance_doc
// ---------------------------------------------------------------------
%define OT_SecondOrderModel_compute_spectral_density_doc
"Evaluate the spectral density function for a specific frequency.
Parameters
----------
f : float
Frequency value.
Returns
-------
spd : HermitianMatrixs
The evaluation of spectral density function at frequency f.
Notes
-----
*computeSpectralDensity* evaluates the spectral model :math:`S : \\\\Rset^n \\\\mapsto \\\\cH^+_{d}` at :math:`f\\\\in \\\\Rset^n`:
.. math::
\\\\forall \\\\vect{f} \\\\in \\\\Rset^n, \\\\cS(\\\\vect{f}) = \\\\prod_{k=1}^{n} \\\\vect{\\\\theta}_k \\\\mat{\\\\Sigma} \\\\rho(\\\\vect{f} \\\\odot \\\\vect{\\\\theta})
where :math:`\\\\mat{\\\\Sigma}` is a covariance matrix that explains the covariance structure and
:math:`(\\\\vect{f} \\\\odot \\\\vect{\\\\theta})_k = \\\\vect{f}_k \\\\vect{\\\\theta}_k`"
%enddef
%feature("docstring") OT::SecondOrderModelImplementation::computeSpectralDensity
OT_SecondOrderModel_compute_spectral_density_doc
// ---------------------------------------------------------------------
%define OT_SecondOrderModel_discretize_doc
"Discretize the second order on a given RegularGrid/Mesh model using its covariance function.
Parameters
----------
meshOrGrid : :class:`~openturns.Mesh` or :class:`~openturns.RegularGrid`
Mesh or time grid of size :math:`N` associated with the process.
Returns
-------
covarianceMatrix : :class:`~openturns.CovarianceMatrix`
Covariance matrix :math:`\\\\in\\\\cM_{nd\\\\times nd}(\\\\Rset)` (if the process is of
dimension :math:`d`).
Notes
-----
This method makes a discretization of the covariance model on *meshOrGrid* composed of
the vertices :math:`(\\\\vect{t}_1, \\\\dots, \\\\vect{t}_{N-1})` and returns the
covariance matrix:
.. math ::
\\\\mat{C}_{1,\\\\dots,k} = \\\\left(
\\\\begin{array}{cccc}
C(\\\\vect{t}_1, \\\\vect{t}_1) &C(\\\\vect{t}_1, \\\\vect{t}_2) & \\\\dots & C(\\\\vect{t}_1, \\\\vect{t}_{k}) \\\\\\\\
\\\\dots & C(\\\\vect{t}_2, \\\\vect{t}_2) & \\\\dots & C(\\\\vect{t}_2, \\\\vect{t}_{k}) \\\\\\\\
\\\\dots & \\\\dots & \\\\dots & \\\\dots \\\\\\\\
\\\\dots & \\\\dots & \\\\dots & C(\\\\vect{t}_{k}, \\\\vect{t}_{k})
\\\\end{array} \\\\right)"
%enddef
%feature("docstring") OT::SecondOrderModelImplementation::discretize
OT_SecondOrderModel_discretize_doc
// ---------------------------------------------------------------------
%define OT_SecondOrderModel_get_covariance_model_doc
"Return the covariance model.
Returns
-------
covarianceModel : :class:`~openturns.CovarianceModel`
The covariance model of the second order model."
%enddef
%feature("docstring") OT::SecondOrderModelImplementation::getCovarianceModel
OT_SecondOrderModel_get_covariance_model_doc
// ---------------------------------------------------------------------
%define OT_SecondOrderModel_getDimension_doc
"Get the dimension of the *SecondOrderModel*.
Returns
-------
dimension : int
Dimension of the *SecondOrderModel*."
%enddef
%feature("docstring") OT::SecondOrderModelImplementation::getDimension
OT_SecondOrderModel_getDimension_doc
// ---------------------------------------------------------------------
%define OT_SecondOrderModel_get_spatial_dimension_doc
"Get the spatial dimension of the spectral density function.
Returns
-------
spatialDimension : int
SpatialDimension of the *SecondOrderModel*."
%enddef
%feature("docstring") OT::SecondOrderModelImplementation::getSpatialDimension
OT_SecondOrderModel_get_spatial_dimension_doc
// ---------------------------------------------------------------------
%define OT_SecondOrderModel_get_spectral_model_doc
"Return the spectral model.
Returns
-------
spectralModel : :class:`~openturns.SpectralModel`
The spectral model of the second order model."
%enddef
%feature("docstring") OT::SecondOrderModelImplementation::getSpectralModel
OT_SecondOrderModel_get_spectral_model_doc
// ---------------------------------------------------------------------
%define OT_SecondOrderModel_set_models_doc
"Set both the covariance and spectral models of a second order model.
Parameters
----------
covarianceModel : :class:`~openturns.CovarianceModel`
The covariance model of the second order model.
spectralModel : :class:`~openturns.SpectralModel`
The spectral model of the second order model."
%enddef
%feature("docstring") OT::SecondOrderModelImplementation::setModels
OT_SecondOrderModel_set_models_doc
// ---------------------------------------------------------------------
|