Note
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Create a functional basis processΒΆ
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)