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Vertex value function

A vertex value function f_{vertexvalue}: \mathcal{D} \times \mathbb{R}^d \rightarrow \mathcal{D} \times \mathbb{R}^q is a particular field function that lets invariant the mesh of a field and defined by a function h : \mathbb{R}^n \times \mathbb{R}^d \rightarrow \mathbb{R}^q such that:

\begin{aligned} f_{vertexvalue}(\underline{t}, \underline{x})=(\underline{t}, h(\underline{t},\underline{x}))\end{aligned}

Let’s note that the input dimension of f_{vertexvalue} still design the dimension of \underline{x} : d. Its output dimension is equal to q.

The creation of the VertexValueFunction object requires the function h and the integer n: the dimension of the vertices of the mesh \mathcal{M}.

This example illustrates the creation of a field from the function h:\mathbb{R}\times\mathbb{R}^2 such as:

\begin{aligned} h(\underline{t}, \underline{x})=(t+x_1^2+x_2^2) \end{aligned}

import openturns as ot

ot.Log.Show(ot.Log.NONE)

Create a mesh

N = 100
mesh = ot.RegularGrid(0.0, 1.0, N)

Create the function that acts the values of the mesh

h = ot.SymbolicFunction(["t", "x1", "x2"], ["t+x1^2+x2^2"])

Create the field function

f = ot.VertexValueFunction(h, mesh)

Evaluate f

inF = ot.Normal(2).getSample(N)
outF = f(inF)

# print input/output at first 10 mesh nodes
txy = mesh.getVertices()
txy.stack(inF)
txy.stack(outF)
txy[:10]
tX0X1y0
000.027720260.16977820.02959305
11-0.730191-0.055132651.536219
22-0.40832130.62514462.557532
33-0.03512366-1.5516345.408803
440.061064030.54564374.301456
551.0127430.34162576.142357
661.01481.86168110.49568
77-1.895510.6808911.05657
880.5093272-0.38839128.410262
99-0.8785590.14739019.79359


Total running time of the script: ( 0 minutes 0.002 seconds)