Create a custom covariance model

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

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()