As part of an assigment i am needed to write a C++ Program to solve a system of equations using Gaussian elimination with scaled partial pivoting method.
Now our prof has told us to simple use the pseudocode found in the book. I did my best to finish it however, the answer the program is outputting is not the same as the one i have calculated by hand. Any help would be greatly appreciated

 * Developer : Rioch D'lyma
 * Class : 3MN3
 * Due
 * Purpose :
 * Created on January 20, 2011, 12:23 AM
#include <stdlib.h>
#include <cstdlib>
#include <iostream>
#include <math.h>
using namespace std;

int main(int argc, char** argv) {

    float x[4];
    float sum;
    float temp;
    int i,j,k,n;
    float r,rmax,smax,xmult;
    float a[5][5] = {
    float b[5] = {4,0,3,1};
    int l[5] = {1,2,3,4};
    float s[5] = {0,0,0,0};
    n = 3;

    for(i=1; i<=n;i++){
        l[i] = i;
        s[i] = 0;

            if(a[i][j] > s[i]){
                s[i] =a[i][j];

        s[i] = smax;

 //   cout << s[0] << endl;
   // cout << s[1] << endl;
  //  cout << s[2] << endl;
   // cout << s[3] << endl;

        rmax = 0;
        for (i=k;i<=n;i++){
           // cout << a[l[i]][k] << " / " << s[l[i]] << endl;
            r = fabs(a[l[i]][k]/s[l[i]]);
                rmax = r;
        temp = l[j];
        l[j] = l[k];
        l[k] = temp;

           // cout << "K = " << k << endl;
            //cout << "I = " << i << endl;
            //cout << a[l[i]][k] << " / " << a[l[k]][k] << endl;
            xmult = a[l[i]][k]/a[l[k]][k];
            a[l[i]][k] = xmult;
            //cout << xmult << endl;
                a[l[i]][j] = a[l[i]][j] - (xmult*a[l[k]][k]);



        for(i=k; i<=n;i++){
            b[l[i]] = b[l[i]] - (a[l[i]][k]*b[l[k]]);

    x[n] = b[l[n]]/a[l[n]][n];

        sum = b[l[i]];
        for (j=i+1;j<=n;j++){
            sum = sum - (a[l[i]][j]*x[j]);
        x[i] = sum/a[l[i]][j];
    for(int r = 0; r <= n;r++){
        cout << "x" << r+1 << " = " << x[r] << endl;

    return 0;


procedure Gauss(n, (ai j ), (li )) integer i, j, k, n;	real r, rmax, smax, xmult real array (ai j )1:n×1:n , (li )1:n ;	real array allocate (si )1:n for i = 1 to n do
li ←i smax ← 0 for j = 1 to n do
smax ← max(smax, |ai j |) end for
si ← smax end for
for k = 1 to n − 1 do rmax ← 0
for i = k to n do r ← |ali ,k /sli |
if (r > rmax) then rmax ← r
j←i end if
end for
lj ↔lk for i = k + 1 to n do
xmult ← ali ,k /alk ,k ali,k ←xmult for j = k + 1 to n do
ali,j ← ali,j −(xmult)alk,j end for
end for end for
deallocate array (si ) end procedure Gauss

procedure Solve(n, (ai j ), (li ), (bi ), (xi )) integer i, k, n;	real sum real array (ai j )1:n×1:n , (li )1:n , (bi )1:n , (xi )1:n for k = 1 to n − 1 do
for i = k + 1 to n do
bli ←bli −ali,kblk end for
end for
xn ←bln/aln,n fori =n−1to1 step−1do
sum ← bli for j = i + 1 to n do
sum ← sum − ali , j x j end for
xi ←sum/ali,i

I have included both my code and the Pseudocode given to us. Array a is the coefficient's and b is the constants.


I suggest you come up with a simple example problem, and then do the problem step by step by hand. Then step through the code with a debugger and ensure that it is doing every step the same as you did by hand. This will let you find the bug, then you just need to fix it!

Then step through the code with a debugger and ensure that it is doing every step the same as you did by hand. This will let you find the bug, then you just need to fix it!

I second that, definitely use a debugger to check the values that are being calculated at each step.

Also, you have done some strange things in your code. You have used #include <stdlib.h> and #include <cstdlib> , which (I think) are the same thing, except that the first is deprecated in C++. You should also use <cmath> instead of math.h .

Thanks for the reply guys!

I have not learnt how to use a debugger but will look it up. However if you notice i have a number of outputs commented out, i have been using that to keep track of what the calculations are doing.

And the problem i have been using has been solved by hand already, as we had to do it by hand and then code.

Ravenous about the


statements. I primarily use netbeans on my mac to write the programs and test it on windows using visual express before handing it in, so i just put both in and clean it up later based on what is required on the windows. In theory that shouldnt happen but netbeans ask i put diff statements than visual.

As for the


i shall start using


Thanks :)

I ended up figuring it out. My input was in wrong and a few '+1' and "<' were not used correctly :)

You should really really learn to use a debugger. Almost every IDE has one built in.

Also, if your problem is solved please mark the thread as 'solved'.