> Hi,

It's been so long since I sent this that I guess some of you will have

>

> I hope this doesn't constitute what Gregoire calls a very stupid

> problem!

>

> 1) Does anyone know a free/cheap plotting tool for vector fields. (At

> each point x of a 3d (or 2d) array, I have a vector v(x). Thus my plot

> will be lots of little arrow)

>

> 2) Has anyone done any work or heard of any work on Random Tensor

> fields. I've made a start and got somewhere (for what it's worth) but I

> don't want to reinvent the wheel.

>

> Colin

>

retired and your children will be reading my final response. So for those

who replied - sorry it took me so long to get back!

Anyhow - I had a good number of replies and some people wanted to get

replies forwarded so here they are

1) Pat Lapcevic has a homemade (fortran) program which I'm going to try

and get hold of. He also suggests GRIDBUILDER - a finite element grid

builder from Rob McLaren (email mclaren@...). He doesn't

know the cost and I've not yet got a reply from Rob.

2) Med Bennett suggests some IDL commercial software (@:$1500). Check it at

http://www.rsinc.com

Another commercial suggestion was from C TECH Development

http://www.ctech.com

3) Denis Marcotte informs us that Matlab has Quiver and Quiver3 for 2 and 3d

respectively.

... while GillesG@... suggests a SCI-LAB solution. Sci-Lab being a

Matlab type solution. Information at

http://www-rocq.inria.fr/scilab/scilab.html

Download from ftp://ftp.inria.fr/INRIA/Projects/Meta2/Scilab

4) Denis Allard and Katherine Campbell tell us that (at least) in 2d there

is an Splus solution to plotting vectors and Katherine provides us with some

code

plot(lrange$x,lrange$y,type="n",axes=F,xlab="",ylab="")

draw.vectors(slope[1:2,,])

draw.vectors <- function(z) {

# Assume z is 2 x n x m

n <- dim(z)[2]

m <- dim(z)[3]

zmax <- max(sqrt(z[1,,]^2+z[2,,]^2))

tz <- 0.5*z/zmax

for (i in 1:n) {

for (j in 1:m) {

arrows(i-tz[1,i,j],j-tz[1,i,j],

i+tz[1,i,j],j+tz[2,i,j],

size=.02,open=T,rel=F)

}

}

}

Thanks for that Katherine

5) alistair@... has seen some stuff in SAS which he believes to be

usefull.

6) Dan Cornford suggests the NEUROSAT page for some work on wind field

models for random vector fields and asks when or where we might meet random

tensor fields.

Well a quick reply is to note that Permeability, Stress, Strain etc. etc.

are 2nd order tensors - their covariances need to expressed fully with a 4th

order tensor. They tend to occur quite often when modelling Petroleum

reservoirs - although in practice there is usually no need to consider the

general case and the tensor is treated as diagonal.

As we know, the class of isotropic covariance functions in 3d is a subclass

of the 1d covariance functions (eg the 1d spherical (or triangular model) is

not +ve definite in 3d). From here, you can ask yourself what are the

conditions for isotropy of a random vector field (eg. Yaglom 1986) - that

is when the covariance is independent of the choice of orthogonal co-ord

system. It turns out that this imposes some restrictions on the form of

covariance function (Yaglom). I was just looking at how this generalises to

tensors. (The real purpose for me was to check the functional form of a

covariance tensor that was provided by a third party - as it's behavior

seemed a bit odd)

Anyhow - many thanks to all who replied. I'll check things out in a bit

more detail and if anything blows me away I'll be sure to pass it on.

Colin

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