Note

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# Create a stationary covariance modelΒΆ

This use case illustrates how the User can create a covariance function from parametric models. The library implements the *multivariate Exponential model* as a parametric model for the covariance function where the spatial covariance function writes:

It is possible to define the exponential model from the spatial covariance matrix rather than the correlation matrix :

with:

We call the amplitude vector and the scale vector.

The library implements the multivariate exponential model thanks to the object *ExponentialModel* which is created from:

the scale and amplitude vectors : in that case, by default ;

the scale and amplitude vectors and the spatial correlation matrix ;

the scale and amplitude vectors and the spatial covariance matrix ; Then is mapped into the associated correlation matrix and the previous constructor is used.

```
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 amplitude vector (output dimension 3)

```
amplitude = [1.0, 2.0, 3.0]
# Scale vector (input dimension 1)
scale = [4.0]
# spatialCorrelation
spatialCorrelation = ot.CorrelationMatrix(3)
spatialCorrelation[0, 1] = 0.8
spatialCorrelation[0, 2] = 0.6
spatialCorrelation[1, 2] = 0.1
# spatialCovariance
spatialCovariance = ot.CovarianceMatrix(3)
spatialCovariance[0, 0] = 4.0
spatialCovariance[1, 1] = 5.0
spatialCovariance[2, 2] = 6.0
spatialCovariance[0, 1] = 1.2
spatialCovariance[0, 2] = 0.9
spatialCovariance[1, 2] = -0.2
```

Create the covariance model from the amplitude and scale, no spatial correlation

```
ot.ExponentialModel(scale, amplitude)
```

ExponentialModel(scale=[4], amplitude=[1,2,3], no spatial correlation)

or from the amplitude, scale and spatialCovariance

```
ot.ExponentialModel(scale, amplitude, spatialCorrelation)
```

ExponentialModel(scale=[4], amplitude=[1,2,3], spatial correlation=

[[ 1 0.8 0.6 ]

[ 0.8 1 0.1 ]

[ 0.6 0.1 1 ]])

or from the scale and spatialCovariance

```
ot.ExponentialModel(scale, spatialCovariance)
```

ExponentialModel(scale=[4], amplitude=[2,2.23607,2.44949], no spatial correlation)

**Total running time of the script:** ( 0 minutes 0.002 seconds)