/usr/include/openturns/swig/GeneralizedExponential_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 | %feature("docstring") OT::GeneralizedExponential
"Absolute exponential covariance function.
Available constructors:
GeneralizedExponential(*spatialDim=1*)
GeneralizedExponential(*scale, p*)
GeneralizedExponential(*scale, amplitude, p*)
Parameters
----------
spatialDim : int
Spatial dimension :math:`n`.
When not fulfilled, the spatial dimension is equal to the size of the parameter :math:`\\\\vect{\\\\theta}`.
By default, equal to 1.
scale : sequence of floats
Scale coefficient :math:`\\\\vect{\\\\theta}\\\\in \\\\Rset^n`.
The size of :math:`\\\\vect{\\\\theta}` is the spatial dimension.
amplitude : sequence of positive floats
Amplitude of the process :math:`\\\\vect{\\\\sigma}\\\\in \\\\Rset^d`.
Must be of size equal to 1.
By default, equal to :math:`[1]`.
p : float, :math:`0<p \\\\leq 2`
Define the exponent of the euclidean norm that is used within the model.
Notes
-----
The *generalized exponential function* is a stationary covariance function whith dimension :math:`d=1`.
We consider the scalar stochastic process :math:`X: \\\\Omega \\\\times\\\\cD \\\\mapsto \\\\Rset`, where :math:`\\\\omega \\\\in \\\\Omega` is an event, :math:`\\\\cD` is a domain of :math:`\\\\Rset^n`.
The *generalized exponential* function is defined by:
.. math::
C(\\\\vect{s}, \\\\vect{t}) = \\\\sigma^2 e^{-\\\\left|\\\\left|\\\\dfrac{\\\\vect{s}-\\\\vect{t}}{\\\\vect{\\\\theta}}\\\\right|\\\\right|_{2}^p}, \\\\quad \\\\forall (\\\\vect{s}, \\\\vect{t}) \\\\in \\\\cD
The correlation function :math:`\\\\rho` writes:
.. math::
\\\\rho(\\\\vect{s}, \\\\vect{t}) = e^{-\\\\left\\\\| \\\\vect{s}-\\\\vect{t} \\\\right\\\\||_{2}^p}, \\\\quad \\\\forall (\\\\vect{s}, \\\\vect{t}) \\\\in \\\\cD
See Also
--------
CovarianceModel
Examples
--------
Create a standard generalized exponential covariance function:
>>> import openturns as ot
>>> covModel = ot.GeneralizedExponential(2)
>>> t = [0.1, 0.3]
>>> s = [0.2, 0.4]
>>> print(covModel(s, t))
[[ 0.868123 ]]
>>> tau = [0.1, 0.3]
>>> print(covModel(tau))
[[ 0.728893 ]]
Create a generalized exponential covariance function specifying the scale vector and p:
>>> covModel2 = ot.GeneralizedExponential([1.5, 2.5], 1.5)
>>> covModel2bis = ot.GeneralizedExponential([1.5] * 2, 1.5)
Create a generalized exponential covariance function specifying the scale vector, the amplitude and p:
>>> covModel3 = ot.GeneralizedExponential([1.5, 2.5], [3.5], 1.5)"
// ---------------------------------------------------------------------
%feature("docstring") OT::GeneralizedExponential::setP
"P accessor.
Parameters
----------
p : int, :math:`p \\\\geq 1`
Define the norm that is used within the model."
// ---------------------------------------------------------------------
%feature("docstring") OT::GeneralizedExponential::getP
"P accessor.
Returns
-------
p : int, :math:`p \\\\geq 1`
Define the norm that is used within the model."
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