Note

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# Create a stationary covariance modelΒΆ

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)
```

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()
```