/usr/include/openturns/swig/ExponentialModel_doc.i is in libopenturns-dev 1.9-5.
This file is owned by root:root, with mode 0o644.
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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 | %feature("docstring") OT::ExponentialModel
"Multivariate stationary exponential covariance function.
Available constructors:
ExponentialModel(*spatialDim=1*)
ExponentialModel(*scale, amplitude*)
ExponentialModel(*scale, amplitude, spatialCorrelation*)
ExponentialModel(*scale, spatialCovariance*)
Parameters
----------
spatialDim : int
Spatial dimension :math:`n`.
By default, the spatial dimension is deduced from the :math:`\\\\vect{\\\\theta}` parameter. If this one is not specified, then :math:`n=1`.
scale : sequence of floats
Scale coefficient :math:`\\\\vect{\\\\theta}\\\\in \\\\Rset^n`.
amplitude : sequence of positive floats
Amplitude of the process :math:`\\\\vect{\\\\sigma}\\\\in \\\\Rset^d`.
spatialCorrelation : :class:`~openturns.CorrelationMatrix`
Correlation matrix :math:`\\\\mat{R} \\\\in \\\\cS_d^+([-1, 1])`
By default, :math:`\\\\mat{R}= \\\\mat{I}_d` where the dimension :math:`d` is deduced from the amplitude :math:`\\\\vect{\\\\sigma}`.
spatialCovariance : :class:`~openturns.CovarianceMatrix`
Covariance matrix :math:`C^{stat} \\\\in \\\\cS_d^+(\\\\Rset)`.
Notes
-----
The *exponential* function is a stationary covariance function whith dimension :math:`d\\\\geq1`.
We consider the scalar stochastic process :math:`X: \\\\Omega \\\\times\\\\cD \\\\rightarrow \\\\Rset^d`, where :math:`\\\\omega \\\\in \\\\Omega` is an event, :math:`\\\\cD` is a domain of :math:`\\\\Rset^n`.
The *exponential* function is defined by:
.. math::
C(\\\\vect{s}, \\\\vect{t}) = \\\\rho\\\\left(\\\\dfrac{\\\\vect{s}}{\\\\theta}, \\\\dfrac{\\\\vect{t}}{\\\\theta}\\\\right)\\\\, \\\\mbox{Diag}(\\\\vect{\\\\sigma}) \\\\, \\\\mat{R} \\\\, \\\\mbox{Diag}(\\\\vect{\\\\sigma}), \\\\quad \\\\forall (\\\\vect{s}, \\\\vect{t}) \\\\in \\\\cD
where the spatial covariance function :math:`\\\\rho` writes:
.. math::
\\\\rho(\\\\vect{s}, \\\\vect{t} ) = e^{-\\\\left\\\\| \\\\vect{s}- \\\\vect{t} \\\\right\\\\|_2} \\\\quad \\\\forall (\\\\vect{s}, \\\\vect{t}) \\\\in \\\\cD
The spatial covariance matrix writes:
.. math::
C^{stat}(\\\\vect{s}, \\\\vect{t})= \\\\mbox{Diag}(\\\\vect{\\\\sigma}) \\\\, \\\\mat{R} \\\\, \\\\mbox{Diag}(\\\\vect{\\\\sigma})
Examples
--------
Create an exponential model from the amplitude :math:`\\\\vect{\\\\sigma}` and the scale :math:`\\\\vect{\\\\theta}`:
>>> import openturns as ot
>>> amplitude = [1.0, 2.0]
>>> scale = [4.0, 5.0]
>>> myCovarianceModel = ot.ExponentialModel(scale, amplitude)
Create an exponential model from the amplitude, scale and the correlation matrix:
>>> amplitude = [1.0, 2.0]
>>> scale = [4.0, 5.0]
>>> spatialCorrelation = ot.CorrelationMatrix(2)
>>> spatialCorrelation[0,1] = 0.8
>>> myCovarianceModel = ot.ExponentialModel(scale, amplitude, spatialCorrelation)
Create an exponential model from the scale and covariance matrix:
>>> amplitude = [1.0, 2.0]
>>> scale = [4.0, 5.0]
>>> spatialCovariance = ot.CovarianceMatrix(2)
>>> spatialCovariance[0,0] = 4.0
>>> spatialCovariance[1,1] = 5.0
>>> spatialCovariance[0,1] = 1.2
>>> spatialDimension = 2
>>> myCovarianceModel = ot.ExponentialModel(scale, spatialCovariance)"
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