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:
import openturns as ot import openturns.viewer as viewer 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)