How to plot this in MATLAB

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S. David
S. David 2011-4-5
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
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Andrew Newell
Andrew Newell 2011-4-5
How many dimensions are involved? It's very hard to visualize greater than 3 dimensions.
S. David
S. David 2011-4-5
Let us say 2D or 3D, not more. How can we do that?

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回答（3 个）

the cyclist
the cyclist 2011-4-5
A clever way to do this might be to use the "convhull" command, if you can generate a dataset that obeys that relationship.
Sean de Wolski
Sean de Wolski 2011-4-5
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S. David
S. David 2011-4-5
Thanks you, the code is not very much understandable. Can you comment on it, please?

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the cyclist
the cyclist 2011-4-6
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.
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S. David
S. David 2011-4-7
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

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