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Asked by Scott Jones
on 20 Nov 2012

function [x] = IntegerGaussrevised(A,b) n = size(A,1); %getting n A = [A,b]; %produces the augmented matrix

%elimination process starts

for i = 1:n-1 p = i; %comparison to select the pivot

for j = i+1:n if abs(A(j,i)) > abs(A(i,i)) U = A(i,:); A(i,:) = A(j,:); A(j,:) = U; end end %cheking for nullity of the pivots

while A(p,i)== 0 && p <= n p = p+1; end if p == n+1 disp('No unique solution'); break else if p ~= i T = A(i,:); A(i,:) = A(p,:); A(p,:) = T; end end

for j = i+1:n m = A(j,i)/A(i,i); for k = i+1:n+1 A(j,k) = A(j,k) - m*A(i,k); end end end

%checking for nonzero of last entry

if A(n,n) == 0 disp('No unique solution'); return end

%backward substitution

x(n) = A(n,n+1)/A(n,n); for i = n - 1:-1:1 sumax = 0; for j = i+1:n sumax = sumax + A(i,j)*x(j); end x(i) = (A(i,n+1) - sumax)/A(i,i); end

end end

Answer by Jan Simon
on 21 Nov 2012

Edited by Jan Simon
on 21 Nov 2012

Please follow Matt J's advice to format the code properly.

Does "integer only" mean, that all occurring values are integers? Then the modifications concern one line only:

m = A(j,i) / A(i,i);

Here fractional parts can be introduced. So check at first, if the result is an integer: `m ~= floor(m)`. If this is not the case, multiply theother lines of the augm,ented Matrix by `A(i,i)`.

**But** this will fail when there is an overflow: Numbers greater than 2^52 cannot be represented exactly with double precision. Therefore my suggestion has severe limits. Even for tiny matrices (< 10 rows) this can fail, if the elements are in the magnitude of 1000.

So perhaps you are looking for something completely different.

Scott Jones
on 8 Dec 2012

Hey, sorry it took me so long to sort the code out. My question is poorly worded as well. What I meant by integer only Gaussian elimination Integer was a way for to do it that involves ensuring that at each stage in the elimination process the augmented matrix for the system must contain only integers. (inputs are also integers). Thanks for all of your help so far really appreciate you taking the time to try and help.

## 2 Comments

## Matt J

Direct link to this comment:http://www.mathworks.com/matlabcentral/answers/54297#comment_112251

The code is really hard to read. Please format it.

## Walter Roberson

Direct link to this comment:http://www.mathworks.com/matlabcentral/answers/54297#comment_112289

http://www.mathworks.com/matlabcentral/answers/13205-tutorial-how-to-format-your-question-with-markup