Linear programming code not showing the solution

I extracted the following code from an online pdf that solves basic feasible solution of linear programming problems.

function vert = feassol(A, b)
% Basic feasible solutions vert to the system of constraints
% Ax = b, x >= 0.
% They are stored in columns of the matrix vert.

[m, n] = size(A);
warning off
b = b(:);
vert = [];
if (n >= m)
t = nchoosek(1:n,m);
nv = nchoosek(n,m);
for i = 1:nv
    y = zeros(n,1);
    x = A(:,t(i,:))\b;
    if all(x >= 0 & (x ~= inf & x ~= -inf))
        y(t (i, :)) = x;
    end
end
else
    error('Nuber of equations is greater than th neumber of variables.')
end
if ~isempty(vert)
    vert = delcols(vert);
else
    vert = [];
end
end

To test the code, the author used the system

A = [1 1 1 0; 0 1 0 1];
b = [6; 3];

and obtain the results

vert = feassol(A, b)
vert =
0 0 3 6
0 3 3 0
6 3 0 0
3 0 0 3

But whenever I run the code, I get

>> vert = feassol(A,b)
vert =
     []

What am I not doing right with the code? Any help will be much appreciated. Thanks in advance!

Answer 1

[Walter Roberson]

Where do you assign something nonempty to vert?

Why do you calculate y since you never use it?

[Hmm!]

You are right. But as I said the author just used the code to illustate the example I gave. The author never made mention of y. The question is a LP program in the form Ax = b, x>=0

Could you help fix this for me?

[Walter Roberson]

vert(:, end+1) = y;

[Hmm!]

>> vert = feassol(A,b)
Unrecognized function or variable 'y'.
Error in feassol (line 27)
    vert(:, end+1) = y; 
    
    %this error showed up after I pasted vert(:, end+1)=y; after "vert = [];"
    
    %where do I paste vert(:, end+1) = y;?

[Walter Roberson]

function vert = feassol(A, b)
% Basic feasible solutions vert to the system of constraints
% Ax = b, x >= 0.
% They are stored in columns of the matrix vert.

[m, n] = size(A);
warning off
b = b(:);
vert = [];
if (n >= m)
t = nchoosek(1:n,m);
nv = nchoosek(n,m);
for i = 1:nv
  y = zeros(n,1);
  x = A(:,t(i,:))\b;
  if all(x >= 0 & (x ~= inf & x ~= -inf))
      y(t (i, :)) = x;
      vert(:, end+1) = y;
  end
end
else
  error('Nuber of equations is greater than th neumber of variables.')
end
if ~isempty(vert)
  vert = delcols(vert);
else
  vert = [];
end
end

[Walter Roberson]

note that you test x>=0 but you also test about negative infinity. A nonnegative value cannot be negative infinity.

[Walter Roberson]

Also if you got that error message then you passed in an array with more rows than columns.

[Hmm!]

Another heckle...

>> feassol
Unrecognized function or variable 'delcols'.

Error in feassol (line 27)
  vert = delcols(vert);
  
  % How to do with delcols?

[Walter Roberson]

I do not know. You called decols in the code you supplied; no documentation has been supplied as to its purpose or its implementation.

But if I were to guess... I would guess it probably isn't needed.

[Hmm!]

Sorry. It is another written function that I had to called. I have just figure it out.

Answer 2

[Matt J]

As long as your feasible set is bounded, you can use this FEX submission instead,

https://www.mathworks.com/matlabcentral/fileexchange/30892-analyze-n-dimensional-polyhedra-in-terms-of-vertices-or-in-equalities

A = [1 1 1 0; 0 1 0 1];
b = [6; 3];

[args{1:4}]=addBounds([],[],A,b,[0;0;0;0]);
vert=lcon2vert(args{:}).'

for which I get the result,

vert =

    6.0000    3.0000   -0.0000   -0.0000
    0.0000    3.0000    3.0000   -0.0000
   -0.0000         0    3.0000    6.0000
    3.0000         0         0    3.0000