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)
```