/usr/include/openturns/swig/DiracCovarianceModel_doc.i is in libopenturns-dev 1.7-3.
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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 | %feature("docstring") OT::DiracCovarianceModel
"Dirac covariance function.
Available constructors:
DiracCovarianceModel(*spatialDim, amplitude*)
DiracCovarianceModel(*spatialDim, amplitude, spatialCorrelation*)
DiracCovarianceModel(*spatialDim, spatialCovariance*)
Parameters
----------
spatialDim : int
Dimension of the domain :math:`\\\\cD`.
amplitude : sequence of float
Vector :math:`\\\\vect{\\\\sigma}` of dimension :math:`d`.
spatialCorrelation : :class:`~openturns.CorrelationMatrix`
Correlation matrix :math:`\\\\mat{R} \\\\in \\\\mathcal{M}_{d \\\\times d}([-1, 1])`.
spatialCovariance : :class:`~openturns.CovarianceMatrix`
Covariance matrix :math:`C^{stat} \\\\in \\\\mathcal{M}^{+}_{d \\\\times d}(\\\\Rset)`.
Notes
-----
The Dirac model defines a stationary covariance function
:math:`C^{stat}(\\\\vect{\\\\tau}) = C(\\\\vect{s}, \\\\vect{s}+\\\\vect{\\\\tau}) \\\\forall (\\\\vect{s},\\\\vect{\\\\tau}) \\\\in \\\\cD`
such that :
.. math::
\\\\forall \\\\vect{\\\\tau} \\\\in \\\\cD,\\\\quad
C^{stat}( \\\\vect{\\\\tau} )= 1_{\\\\tau=0} \\\\times \\\\left[\\\\vect{\\\\Sigma}\\\\right] \\\\,\\\\mat{R}\\\\, \\\\left[ \\\\mat{\\\\Sigma}\\\\right]
where :math:`\\\\mat{R} \\\\in \\\\mathcal{M}_{d \\\\times d}([-1, 1])` is a correlation
matrix, :math:`\\\\mat{\\\\Sigma} \\\\in \\\\mathcal{M}_{d \\\\times d}(\\\\Rset)` is defined by:
.. math::
\\\\mat{\\\\Sigma}= \\\\mbox{Diag}(\\\\sigma_1, \\\\dots, \\\\sigma_d)
with :math:`\\\\sigma_i>0` for any :math:`i`. :math:`\\\\vect{\\\\sigma}` is the amplitude vector.
The model is used for example in linear regression. Indeed, in that context, error is considered to be gaussian with `homoscedasticitc` variance
(same variance distribution, independent spatial correlation)
Examples
--------
Create two *DiracCovarianceModel* of dimension 2:
>>> import openturns as ot
>>> spatialDimension = 3
>>> amplitude = [1., 2.]
>>> correlation = ot.CorrelationMatrix(2)
>>> correlation[1,0] = 0.1
>>> covarianceModel = ot.DiracCovarianceModel(spatialDimension, amplitude)
>>> covarianceModelCorr = ot.DiracCovarianceModel(spatialDimension, amplitude, correlation)
"
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