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:
from __future__ import print_function import openturns as ot import math as m
# 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') graph