/usr/include/openturns/swig/MaternModel_doc.i is in libopenturns-dev 1.9-5.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
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 | %feature("docstring") OT::MaternModel
"Matern covariance function.
Available constructors:
MaternModel(*spatialDim=1*)
MaternModel(*scale, nu*)
MaternModel(*scale, amplitude, nu*)
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]`.
nu : float, :math:`\\\\nu \\\\geq 0`
Coefficient :math:`\\\\nu`.
Notes
-----
The *Matern* 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 *Matern* function is defined by:
.. math::
C(\\\\vect{s}, \\\\vect{t}) = \\\\sigma^2 \\\\dfrac{ 2^{1-\\\\nu} }{\\\\Gamma(\\\\nu) } \\\\left(\\\\sqrt{2 \\\\nu} \\\\left\\\\|\\\\dfrac{\\\\vect{s}-\\\\vect{t}}{\\\\vect{\\\\theta}}\\\\right\\\\|_2\\\\right)^{\\\\nu} \\\\mathrm{K}_{\\\\nu} \\\\left(\\\\sqrt{2 \\\\nu} \\\\left\\\\|\\\\dfrac{\\\\vect{s}-\\\\vect{t}}{\\\\vect{\\\\theta}}\\\\right\\\\|_2\\\\right), \\\\quad \\\\forall (\\\\vect{s}, \\\\vect{t}) \\\\in \\\\cD \\\\times \\\\cD
The correlation function :math:`\\\\rho` writes:
.. math::
\\\\rho(\\\\vect{s}, \\\\vect{t}) = \\\\dfrac{ 2^{1-\\\\nu} }{\\\\Gamma(\\\\nu) } \\\\left(\\\\sqrt{2 \\\\nu} \\\\left\\\\| \\\\vect{s}- \\\\vect{t} \\\\right\\\\|_2\\\\right)^{\\\\nu} \\\\mathrm{K}_{\\\\nu} \\\\left(\\\\sqrt{2 \\\\nu} \\\\left\\\\| \\\\vect{s}- \\\\vect{t} \\\\right\\\\|_2\\\\right), \\\\quad \\\\forall (\\\\vect{s}, \\\\vect{t}) \\\\in \\\\cD \\\\times \\\\cD
See Also
--------
CovarianceModel
Examples
--------
Create a standard Matern covariance function:
>>> import openturns as ot
>>> covModel = ot.MaternModel(2)
>>> t = [0.1, 0.3]
>>> s = [0.2, 0.4]
>>> print(covModel(s, t))
[[ 0.974477 ]]
>>> tau = [0.1, 0.3]
>>> print(covModel(tau))
[[ 0.894994 ]]
Create a Matern covariance function specifying the scale vector and :math:`\\\\nu`:
>>> covModel2 = ot.MaternModel([1.5, 2.5], 2.3)
>>> covModel2bis = ot.MaternModel([1.5]*3, 2.3)
Create a Matern covariance function specifying the scale vector, the amplitude and :math:`\\\\nu`:
>>> covModel3 = ot.MaternModel([1.5, 2.5], [3.5], 4.5)"
// ---------------------------------------------------------------------
%feature("docstring") OT::MaternModel::setNu
"Nu accessor.
Parameters
----------
nu : float, :math:`\\\\nu \\\\geq 0`
Coefficient :math:`\\\\nu`."
// ---------------------------------------------------------------------
%feature("docstring") OT::MaternModel::getNu
"Nu accessor.
Returns
-------
nu : float, :math:`\\\\nu \\\\geq 0`
Coefficient :math:`\\\\nu`."
|