/usr/include/openturns/swig/SphericalModel_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 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 | %feature("docstring") OT::SphericalModel
"Spherical covariance function.
Available constructors:
SphericalModel(*spatialDim=1*)
SphericalModel(*scale, amplitude*)
SphericalModel(*scale, amplitude, radius*)
Parameters
----------
spatialDim : int
Spatial dimension :math:`n`.
By default, equal to 1.
scale : sequence of positive 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]`.
radius : float, :math:`a > 0`
Radius of the sphere on which the covariance model is not zero.
By default, equal to 1.
Notes
-----
The *spherical* 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 *spherical* function is defined on the sphere which ray is :math:`a`:
.. math::
C(\\\\vect{s}, \\\\vect{t}) = \\\\sigma^2 \\\\left[1 - \\\\frac{1}{2a} \\\\left\\\\|\\\\dfrac{\\\\vect{s}-\\\\vect{t}}{\\\\vect{\\\\theta}}\\\\right\\\\|_2 \\\\left(3 - \\\\frac{1}{a^2}\\\\left\\\\|\\\\dfrac{\\\\vect{s}-\\\\vect{t}}{\\\\vect{\\\\theta}}\\\\right\\\\|_2^2\\\\right) \\\\right], \\\\quad \\\\forall (\\\\vect{s}, \\\\vect{t}), \\\\left\\\\|\\\\dfrac{\\\\vect{s}-\\\\vect{t}}{\\\\vect{\\\\theta}}\\\\right\\\\|_2 \\\\leq a
The function is equal to zero outside the sphere.
The correlation function :math:`\\\\rho` writes:
.. math::
\\\\rho(\\\\vect{s}, \\\\vect{t}) = 1 - \\\\frac{1}{2a} \\\\left\\\\|\\\\vect{s} - \\\\vect{t}\\\\right\\\\|_2 \\\\left(3 - \\\\frac{1}{a^2}\\\\left\\\\| \\\\vect{s} - \\\\vect{t} \\\\right\\\\|_2^2\\\\right), \\\\quad \\\\forall (\\\\vect{s}, \\\\vect{t}), \\\\left\\\\| \\\\vect{s} - \\\\vect{t} \\\\right\\\\|_2 \\\\leq a
and is equal to zero outside the sphere.
See Also
--------
CovarianceModel
Examples
--------
Create a standard spherical covariance function:
>>> import openturns as ot
>>> covModel = ot.SphericalModel(2)
>>> t = [0.1, 0.3]
>>> s = [0.2, 0.4]
>>> print(covModel(s, t))
[[ 0.789282 ]]
>>> tau = [0.1, 0.3]
>>> print(covModel(tau))
[[ 0.54147 ]]
Create a spherical covariance function specifying the scale, amplitude vectors:
>>> covarianceModel = ot.SphericalModel([0.2, 0.3], [2.5])
Create a squared exponential covariance function specifying the scale vector, the amplitude and radius:
>>> covModel3 = ot.SphericalModel([0.2, 0.3], [2.5], 2.3)"
// ---------------------------------------------------------------------
%feature("docstring") OT::SphericalModel::setRadius
"Radius accessor.
Parameters
----------
radius : float, :math:`a > 0`
Radius of the sphere on which the covariance model is not zero."
// ---------------------------------------------------------------------
%feature("docstring") OT::SphericalModel::getRadius
"Radius accessor.
Returns
-------
radius : float, :math:`a > 0`
Radius of the sphere on which the covariance model is not zero."
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