# Create a custom 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

[1]:

from __future__ import print_function
import openturns as ot

[2]:

# 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.CovarianceMatrixCollection()
for k in range(N):
t = mesh.getValue(k)
matrix = ot.CovarianceMatrix([[gamma(t)]])

[6]:

# 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)

[6]:


[[ 0.307692 ]]

[7]:

# 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)

[7]: