Create a parametric spectral density function

This example illustrates how the User can create a density spectral function from parametric models.

The library implements the Cauchy spectral model as a parametric model for the spectral density function .

The library defines this model thanks to the object CauchyModel.

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

1. Define a spectral density function from correlation matrix

amplitude = [1.0, 2.0, 3.0]
scale = [4.0, 5.0, 6.0]
spatialCorrelation = ot.CorrelationMatrix(3)
spatialCorrelation[0, 1] = 0.8
spatialCorrelation[0, 2] = 0.6
spatialCorrelation[1, 2] = 0.1
spectralModel_Corr = ot.CauchyModel(amplitude, scale, spatialCorrelation)
spectralModel_Corr

class=CauchyModel amplitude=[4,5,6] scale=[1,2,3] spatial correlation=
[[ 1 0.8 0.6 ]
[ 0.8 1 0.1 ]
[ 0.6 0.1 1 ]]

2. Define a spectral density function from a covariance matrix

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
spectralModel_Cov = ot.CauchyModel(scale, spatialCovariance)
spectralModel_Cov

class=CauchyModel amplitude=[2,2.23607,2.44949] scale=[4,5,6] spatial correlation=
[[ 1 0.268328 0.183712 ]
[ 0.268328 1 -0.0365148 ]
[ 0.183712 -0.0365148 1 ]]