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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 | %feature("docstring") OT::MaternModel
"Matern covariance model.
Available constructors:
MaternModel(*dim=1*)
MaternModel(*dim, theta, nu*)
MaternModel(*scale, nu*)
MaternModel(*scale, sigma, nu*)
Parameters
----------
dim : int, :math:`dim \\\\geq 0`
Input dimension.
theta : float
Scale coefficient :math:`\\\\theta` of the covariance function.
nu : float
Coefficient :math:`\\\\nu` of the covariance function.
scale : sequence of floats
Scale coefficients :math:`\\\\theta`.
The spatial dimension is the size of vector.
sigma : sequence of floats
Amplitude coefficients :math:`\\\\sigma`.
Should be of size 1
Notes
-----
The covariance function of input dimension *dim* is:
.. math::
C(s, t) = \\\\sigma^2 \\\\frac{1}{\\\\Gamma(\\\\nu) 2^{\\\\nu-1}} \\\\left(\\\\sqrt{2 \\\\nu} ||\\\\frac{s-t}{\\\\theta}||\\\\right)^{\\\\nu} K_{\\\\nu} \\\\left(\\\\sqrt{2 \\\\nu} ||\\\\frac{s-t}{\\\\theta}||\\\\right)
where the division is vectorial, :math:`\\\\sigma` is the amplitude (default value is 1.0). Note that the model is unidimensional.
See Also
--------
CovarianceModel, SquaredExponential, AbsoluteExponential, GeneralizedExponential
Examples
--------
>>> import openturns as ot
>>> covarianceModel = ot.MaternModel(2)
>>> t = [0.1, 0.3]
>>> s = [0.2, 0.4]
>>> print(covarianceModel(s, t))
[[ 0.999705 ]]
>>> tau = [0.1, 0.3]
>>> print(covarianceModel(tau))
[[ 0.998554 ]]"
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