/usr/include/openturns/swig/UserDefinedStationaryCovarianceModel_doc.i is in libopenturns-dev 1.7-3.
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 | %feature("docstring") OT::UserDefinedStationaryCovarianceModel
"Stationary covariance model defined by the User.
Parameters
----------
mesh : :class:`~openturns.Mesh`
A mesh that contains `N` vertices.
sample : :class:`~openturns.CovarianceMatrixCollection`
A collection of *N* covariance matrices.
Notes
-----
The covariance model is built as follows.
We consider a process :math:`X: \\\\Omega \\\\times\\\\cD \\\\mapsto \\\\Rset^d` with :math:`\\\\cD \\\\in \\\\Rset^n`.
We note :math:`(\\\\vect{t}_0,\\\\dots, \\\\vect{t}_{N-1})` the vertices of :math:`\\\\cM \\\\in \\\\cD` and :math:`(\\\\mat{C}_{k})_{0 \\\\leq k \\\\leq N-1}` where :math:`\\\\mat{C}_{k} \\\\in \\\\mathcal{M}_{d \\\\times d}(\\\\Rset)` the collection of covariance matrices fixed by the User.
Then we build a stationary covariance function :math:`C^{stat}` which is a piecewise constant function defined on :math:`\\\\cD \\\\times \\\\cD` by:
.. math::
\\\\forall \\\\vect{\\\\tau} \\\\in \\\\cD, \\\\, \\\\quad C^{stat}(\\\\vect{\\\\tau}) = \\\\mat{C}_k
where *k* is such that :math:`\\\\vect{t}_k` is the vertex of :math:`\\\\cM` the nearest to :math:`\\\\vect{\\\\tau}`.
Examples
--------
Create a mesh:
>>> import openturns as ot
>>> # Create the time grid
>>> t0 = 0.0
>>> dt = 0.5
>>> N = int((20.0 - t0)/ dt)
>>> myShiftMesh = ot.RegularGrid(t0, dt, N)
Create the stationary covariance function:
>>> def gamma(tau):
... return 1.0 / (1.0 + tau * tau)
Create the collection of N covariance matrices:
>>> myCovarianceCollection = ot.CovarianceMatrixCollection()
>>> for k in range(N):
... t = myShiftMesh.getValue(k)
... matrix = ot.CovarianceMatrix(1)
... matrix[0, 0] = gamma(t)
... myCovarianceCollection.add(matrix)
Create the User defined stationary covariance model:
>>> myCovarianceModel = ot.UserDefinedStationaryCovarianceModel(myShiftMesh,myCovarianceCollection)
Compute the covariance function at the vertex tau:
>>> tau = 1.5
>>> myCovModelMatrix = myCovarianceModel(tau)
"
// ---------------------------------------------------------------------
%feature("docstring") OT::UserDefinedStationaryCovarianceModel::getMesh
"Accessor to the mesh.
Returns
-------
mesh : :class:`~openturns.Mesh`
The mesh associated to the collection of covariance matrices.
"
// ---------------------------------------------------------------------
%feature("docstring") OT::UserDefinedStationaryCovarianceModel::getTimeGrid
"Accessor to the time grid.
Returns
-------
mesh : :class:`~openturns.RegularGrid`
The time grid associated to the collection of covariance matrices when the mesh can be interpreted as a reglar time grid.
"
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