/usr/include/openturns/swig/AbsoluteExponential_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 | %feature("docstring") OT::AbsoluteExponential
"Absolute exponential covariance function.
Available constructors:
AbsoluteExponential(*spatialDim=1*)
AbsoluteExponential(*scale*)
AbsoluteExponential(*scale, amplitude*)
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 :math:`\\\\vect{\\\\sigma}\\\\in \\\\Rset^d`.
Must be of size equal to 1.
By default, equal to :math:`[1]`.
Notes
-----
The *absolute 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 *absolute exponential* function is defined by:
.. math::
C(\\\\vect{s}, \\\\vect{t}) = \\\\sigma^2 e^{- \\\\left\\\\|\\\\dfrac{\\\\vect{s}-\\\\vect{t}}{\\\\vect{\\\\theta}}\\\\right\\\\|_{1}}, \\\\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\\\\|_{1}}, \\\\quad \\\\forall (\\\\vect{s}, \\\\vect{t}) \\\\in \\\\cD
See Also
--------
CovarianceModel
Examples
--------
Create a standard absolute exponential covariance function:
>>> import openturns as ot
>>> covModel = ot.AbsoluteExponential(2)
>>> t = [0.1, 0.3]
>>> s = [0.2, 0.4]
>>> print(covModel(s, t))
[[ 0.818731 ]]
>>> tau = [0.1, 0.3]
>>> print(covModel(tau))
[[ 0.67032 ]]
Create an absolute exponential covariance function specifying only the scale vector (amplitude is fixed to 1):
>>> covModel2 = ot.AbsoluteExponential([1.5, 2.5])
>>> covModel2bis = ot.AbsoluteExponential([1.5]*3)
Create an absolute exponential covariance function specifying the scale vector and the amplitude :
>>> covModel3 = ot.AbsoluteExponential([1.5, 2.5], [3.5])"
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