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:

from __future__ import print_function
import openturns as ot
import openturns.viewer as viewer
from matplotlib import pylab as plt
import math as m
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]

	t	X0	X1	y0
0	0	0.3093648	0.6666518	0.5401311
1	1	1.250061	0.9036111	3.379164
2	2	-0.6796922	0.397775	2.620206
3	3	0.5303686	0.1043219	3.292174
4	4	-1.047571	-0.747914	5.656781
5	5	-0.4927935	0.2471667	5.303937
6	6	1.950947	0.7535556	10.37404
7	7	-1.762565	0.9172875	10.94805
8	8	0.3132281	-1.260281	9.686419
9	9	1.156489	-1.275325	11.96392