Create a stationary covariance model

This use case illustrates how the user can define his own stationary covariance model thanks to the object UserDefinedStationaryCovarianceModel defined from:

• a mesh of dimension defined by the vertices and the associated simplices,

• a collection of covariance matrices stored in the object CovarianceMatrixCollection noted where for

Then we build a stationary covariance function which is a piecewise constant function on defined by:

where is such that is the vertex of the nearest to

import openturns as ot
import openturns.viewer as viewer
from matplotlib import pylab as plt
ot.Log.Show(ot.Log.NONE)

We detail the example described in the documentation Create the time grid

t0 = 0.0
dt = 0.5
N = int((20.0 - t0) / dt)
mesh = ot.RegularGrid(t0, dt, N)

# Create the covariance function


def gamma(tau):
    return 1.0 / (1.0 + tau * tau)


# Create the collection of HermitianMatrix
coll = ot.SquareMatrixCollection()
for k in range(N):
    t = mesh.getValue(k)
    matrix = ot.SquareMatrix([[gamma(t)]])
    coll.add(matrix)

Create the covariance model

covmodel = ot.UserDefinedStationaryCovarianceModel(mesh, coll)

# One vertex of the mesh
tau = 1.5

# Get the covariance function computed at the vertex tau
covmodel(tau)

[[ 0.307692 ]]

Graph of the spectral function

x = ot.Sample(N, 2)
for k in range(N):
    t = mesh.getValue(k)
    x[k, 0] = t
    value = covmodel(t)
    x[k, 1] = value[0, 0]

# Create the curve of the spectral function
curve = ot.Curve(x, 'User Model')

# Create the graph
myGraph = ot.Graph('User covariance model', 'Time',
                   'Covariance function', True)
myGraph.add(curve)
myGraph.setLegendPosition('topright')
view = viewer.View(myGraph)
plt.show()