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
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
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.