# Create a functional basis process¶

The objective of this example is to define a multivariate stochastic process of dimension where , as a linear combination of deterministic functions :

where is a random vector of dimension .

We suppose that is discretized on the mesh which has vertices.

A realization of on consists in generating a realization of the random vector and in evaluating the functions on the mesh .

If we note the realization of , where , we have:

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)


Define the coefficients distribution

mu = [2.0]*2
sigma = [5.0]*2
R = ot.CorrelationMatrix(2)
coefDist = ot.Normal(mu, sigma, R)


Create a basis of functions

phi_1 = ot.SymbolicFunction(['t'], ['sin(t)'])
phi_2 = ot.SymbolicFunction(['t'], ['cos(t)^2'])
myBasis = ot.Basis([phi_1, phi_2])


Create the mesh

myMesh = ot.RegularGrid(0.0, 0.1, 100)


Create the process

process = ot.FunctionalBasisProcess(coefDist, myBasis, myMesh)


Draw a sample

N = 6
sample = process.getSample(N)
graph = sample.drawMarginal(0)
graph.setTitle(str(N)+' realizations of functional basis process')
view = viewer.View(graph)


Total running time of the script: ( 0 minutes 0.075 seconds)

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