/usr/include/openturns/swig/SphericalModel_doc.i is in libopenturns-dev 1.7-3.
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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 | %feature("docstring") OT::SphericalModel
"Spherical covariance model.
Available constructors:
SphericalModel(*dim=1*)
SphericalModel(*dim=1, amplitude, scale, a*)
Parameters
----------
dim : int, :math:`dim \\\\geq 0`
Input dimension (spatial dimension).
amplitude : sequence of float
Vector :math:`\\\\vect{a}` of dimension :math:`d`.
Amplitude of the covariance model
scale : sequence of float
Vector :math:`\\\\vect{\\\\lambda}` of dimension :math:`spatialDim`.
Scale parameter
a : float
Positive. Ray of the sphere on which the covariance model is not zero
Default is 1.
Notes
-----
The covariance function of input dimension *dim* is defined on a sphere of ray :math:`a` (for :math:`||\\\\frac{s-t}{\\\\theta}|| \\\\leq a`) as follows:
.. math::
C(s, t) = \\\\sigma^2 * (1 - \\\\frac{1}{2a} ||\\\\frac{s-t}{\\\\theta}|| ) * (3 - ||\\\\frac{s-t}{\\\\theta}||^2)
where the division is vectorial, :math:`\\\\theta` is the scale parameter, :math:`\\\\sigma` is the amplitude (default value is 1.0). Note that the model is unidimensional. and equals 0 outside the sphere.
See Also
--------
CovarianceModel, SquaredExponential, GeneralizedExponential, MaternModel
Examples
--------
>>> import openturns as ot
>>> covarianceModel = ot.SphericalModel(2, [1.0], [0.2, 0.3])
>>> t = [0.1, 0.3]
>>> s = [0.2, 0.4]
>>> print(covarianceModel(s, t))
[[ 0.0393519 ]]
>>> tau = [0.1, 0.3]
>>> print(covarianceModel(tau))
[[ 0 ]]"
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