/usr/include/openturns/swig/DiracCovarianceModel_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 | %feature("docstring") OT::DiracCovarianceModel
"Dirac covariance function.
Available constructors:
DiracCovarianceModel(*spatialDim=1*)
DiracCovarianceModel(*spatialDim, amplitude*)
DiracCovarianceModel(*spatialDim, amplitude, spatialCorrelation*)
DiracCovarianceModel(*spatialDim, spatialCovariance*)
Parameters
----------
spatialDim : int
Spatial dimension :math:`n`.
By default, equal to 1.
amplitude : sequence of positive floats
Amplitude of the process :math:`\\\\vect{\\\\sigma}\\\\in \\\\Rset^d`.
Its size is the dimension :math:`d` of the process.
By default, equal to :math:`[1]`.
spatialCorrelation : :class:`~openturns.CorrelationMatrix`
Correlation matrix :math:`\\\\mat{R} \\\\in \\\\cS^+_d([-1, 1])`.
By default, Identity matrix.
spatialCovariance : :class:`~openturns.CovarianceMatrix`
Covariance matrix :math:`\\\\mat{C}^{stat} \\\\in \\\\cS_d^+(\\\\Rset)`.
By default, Identity matrix.
Notes
-----
The *Dirac* covariance function is a stationary covariance function whith dimension :math:`d \\\\geq 1`.
We consider the stochastic process :math:`X: \\\\Omega \\\\times\\\\cD \\\\mapsto \\\\Rset^d`, where :math:`\\\\omega \\\\in \\\\Omega` is an event, :math:`\\\\cD` is a domain of :math:`\\\\Rset^n`.
The *Dirac* covariance function is defined by:
.. math::
C(\\\\vect{s}, \\\\vect{t}) = 1_{\\\\{\\\\vect{s}=\\\\vect{t}\\\\}} \\\\, \\\\mbox{Diag}(\\\\vect{\\\\sigma}) \\\\, \\\\mat{R}\\\\, \\\\mbox{Diag}(\\\\vect{\\\\sigma}), \\\\quad \\\\forall (\\\\vect{s}, \\\\vect{t}) \\\\in \\\\cD
where :math:`\\\\mat{R} \\\\in \\\\cS_d^+([-1,1])` is the spatial correlation matrix. We can define the spatial covariance matrix :math:`\\\\mat{C}^{stat}` as:
.. math::
\\\\mat{C}^{stat} = \\\\mbox{Diag}(\\\\vect{\\\\sigma}) \\\\, mat{R}\\\\, \\\\mbox{Diag}(\\\\vect{\\\\sigma})
The correlation function :math:`\\\\rho` writes:
.. math::
\\\\rho(\\\\vect{s}, \\\\vect{t}) = 1_{\\\\{\\\\vect{s}=\\\\vect{t}\\\\}}
See Also
--------
CovarianceModel
Examples
--------
Create a standard Dirac covariance function:
>>> import openturns as ot
>>> covModel = ot.DiracCovarianceModel(2)
>>> t = [0.1, 0.3]
>>> s = [0.1, 0.3]
>>> print(covModel(s, t))
[[ 1 ]]
>>> tau = [0.1, 0.3]
>>> print(covModel(tau))
[[ 0 ]]
Create a Dirac covariance function specifying the amplitude vector:
>>> covModel2 = ot.DiracCovarianceModel(2, [1.5, 2.5])
Create a Dirac covariance function specifying the amplitude vector and the correlation matrix:
>>> corrMat = ot.CorrelationMatrix(2)
>>> corrMat[1,0] = 0.1
>>> covModel3 = ot.DiracCovarianceModel(2, [1.5, 2.5], corrMat)"
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