How to plot this in MATLAB

Hi,

How to plot the following inequality in MATLAB in 3D:

Ax<=b

where A is an m-by-n matrix, x is an n-by-1 vector, and b is an m-by-1 vector??

Thanks in advance

[Andrew Newell]

What variables do you want on the axes?

[S. David]

Actually, I am not sure. I just know that this inequality plots a polyhedron, and I want to see this using MATLAB.

[Andrew Newell]

Oh, so you really want to plot the surface of the polyhedron?

[Walter Roberson]

What exactly is to be plotted? In how many dimensions?

[Andrew Newell]

How many dimensions are involved? It's very hard to visualize greater than 3 dimensions.

[S. David]

Let us say 2D or 3D, not more. How can we do that?

Answer 1

[the cyclist]

A clever way to do this might be to use the "convhull" command, if you can generate a dataset that obeys that relationship.

[S. David]

Suppose all are given. How to plot it?

Answer 2

[Sean de Wolski]

http://www.mathworks.com/matlabcentral/fileexchange/?term=vert2con

Some useful reading for you.

[S. David]

Thanks you, the code is not very much understandable. Can you comment on it, please?

Answer 3

[the cyclist]

I sat down and thought about this more carefully, and I think the question is a little ambiguous, in a couple different ways.

Let's look at the simplest possible example:

A = eye(2);
b = ones(2,1);

First, it is not perfectly clear what is meant by Ax<=b, because that is the comparison of two vectors, and there is no less than or greater than relationship between them. For example, if Ax = [2; 3] and b=[3; 2], then does the inequality hold?

Maybe it means, though, that every element of Ax must be less than b. If that is the case, then I guess we want to find the boundary. This is solution to A*x=b. (Note that this is now a strict equality now.) I have not done real matrix algebra in a while, but I believe the best way to do this in MATLAB is

 x_boundary = A\b

which means in our simple case that x_boundary = [1;1].

So, it seems you want a plot of the region where x <= x_boundary. That's a semi-infinite region, methinks. Not sure how you want to plot that.

Hope that helps a little. It's been a while since I've thought about this type of math, so be sure to do your own thinking on this and see if it makes sense.

[S. David]

Basically, Ax<=b is a polyhedron, and it is bounded, you just have to get the correct matrix A and vector b. As an example, let us say:

A=[1 1 1;1 1 -1; 1 -1 1; 1 -1 -1;-1 1 1;-1 1 -1;-1 -1 1;-1 -1 -1;];

b=[1;1;1;1;1;1;1;1]

These A and b, assures that the polyhedron is convex. The question now, given these A and b, how to plot the bounded polyhedron?

Thanks in advance