# Vertex value function¶

A vertex value function is a particular field function that lets invariant the mesh of a field and defined by a function such that:

Let’s note that the input dimension of still design the dimension of : . Its output dimension is equal to .

The creation of the VertexValueFunction object requires the function and the integer : the dimension of the vertices of the mesh .

This example illustrates the creation of a field from the function such as:

[30]:

from __future__ import print_function
import openturns as ot
import math as m

[31]:

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

[32]:

# Create the function that acts the values of the mesh
h = ot.SymbolicFunction(['t', 'x1', 'x2'],  ['t+x1^2+x2^2'])

[33]:

# Create the field function
f = ot.VertexValueFunction(h, mesh)

[35]:

# 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]

[35]:

 t X0 X1 y0 0 0.0 -0.2123086987944725 -0.7893040071601587 0.6680757993028859 1 1.0 1.5290373341626469 -1.304449412588666 5.039543439266129 2 2.0 0.3736086588719189 -0.6418723437038079 2.551583535595893 3 3.0 0.7298081558085032 -0.9832478695352569 4.4993963172302305 4 4.0 0.9660822714813948 0.1490416675117666 4.955528373925339 5 5.0 0.04030023504666454 1.3174179103602734 6.737214059482846 6 6.0 -0.2949152511221915 0.6153272637397903 6.465602646845962 7 7.0 0.5106266891413226 -0.5369799682760767 7.549087101993205 8 8.0 0.9674464251994424 -0.25673537559122184 9.001865638711145 9 9.0 -1.0063128915366755 -1.2324330184244943 11.531556780575814