# Create a custom covariance modelΒΆ

This example illustrates how the user can define his own covariance model.

```from __future__ import print_function
import openturns as ot
import openturns.viewer as viewer
from matplotlib import pylab as plt
import math as m
ot.Log.Show(ot.Log.NONE)
```

Create the time grid

```N = 32
a = 4.0
mesh = ot.IntervalMesher([N]).build(ot.Interval(-a, a))
```

Create the covariance function at (s,t)

```def C(s, t):
return m.exp( -4.0 * abs(s - t) / (1 + (s * s + t * t)))
```

Create the large covariance matrix

```covariance = ot.CovarianceMatrix(mesh.getVerticesNumber())
for k in range(mesh.getVerticesNumber()):
t = mesh.getVertices()[k]
for l in range(k + 1):
s = mesh.getVertices()[l]
covariance[k, l] = C(s[0], t[0])
```

Create the covariance model

```covmodel = ot.UserDefinedCovarianceModel(mesh, covariance)
```

Draw the covariance model

```def f(x):
return [covmodel([x[0]], [x[1]])[0, 0]]

func = ot.PythonFunction(2, 1, f)
func.setDescription(['\$s\$', '\$t\$', '\$cov\$'])
cov_graph = func.draw([-a] * 2, [a] * 2, [512] * 2)
cov_graph.setLegendPosition('')
view = viewer.View(cov_graph)
plt.show()
```

Total running time of the script: ( 0 minutes 1.617 seconds)

Gallery generated by Sphinx-Gallery