# 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 wich 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:

[40]:

from __future__ import print_function
import openturns as ot
import math as m

[41]:

# Define the coefficients distribution
mu = [2.0]*2
sigma = [5.0]*2
R = ot.CorrelationMatrix(2)
coefDist = ot.Normal(mu, sigma, R)

[42]:

# 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])

[43]:

# Create the mesh
myMesh = ot.RegularGrid(0.0, 0.1, 100)

[44]:

# Create the process
process = ot.FunctionalBasisProcess(coefDist, myBasis, myMesh)

[45]:

# Draw a sample
N = 6
sample = process.getSample(N)
graph = sample.drawMarginal(0)
graph.setTitle(str(N)+' realizations of functional basis process')
graph

[45]: