A simple gaussian elimination implemented in C.

To simplify, I hard coded the linear system

10 x_{1} |
+ 2 x_{2} |
+ 3 x_{3} |
+ 4 x_{4} |
= 5 | |

6 x_{1} |
+ 17 x_{2} |
+ 8 x_{3} |
+ 9 x_{4} |
= 10 | |

11 x_{1} |
+ 12 x_{2} |
+ 23 x_{3} |
+ 14 x_{4} |
= 15 | |

16 x_{1} |
+ 17 x_{2} |
+ 18 x_{3} |
+ 29 x_{4} |
= 20 |

into the AB float matrix.

```
/*
* Description: Solve a hard coded linear system by gaussian elimination
* Author: Silveira Neto
* License: Public Domain
*/
#include
```
#include
#define ROWS 4
#define COLS 5
/**
* Linear System, Ax = B
*
* 10*x1 + 2*x2 + 3*x3 + 4*x4 = 5
* 6*x1 + 17*x2 + 8*x3 + 9*x4 = 10
* 11*x1 + 12*x2 + 23*x3 + 14*x4 = 15
* 16*x1 + 17*x2 + 18*x3 + 29*x4 = 20
*/
float AB[ROWS][COLS] = {
{10, 2, 3, 4, 5},
{ 6, 17, 8, 9, 10},
{11, 12, 23, 14, 15},
{16, 17, 18, 29, 20}
};
/* Answer x from Ax=B */
float X[ROWS] = {0,0,0,0};
int main(int argc, char** argv) {
int row, col, i;
/* gaussian elimination */
for (col=0; col
Before the gaugassian elimination, AB is

10 2 3 4 5
6 17 8 9 10
11 12 23 14 15
16 17 18 29 20

and after it is

10.00000 0.00000 0.00000 0.00000 2.82486
0.00000 15.80000 0.00000 0.00000 3.92768
0.00000 0.00000 15.85443 0.00000 3.85164
0.00000 0.00000 0.00000 14.13174 3.35329

that corresponds to

10 *x*_{1}
= 2.82486
15.80000 *x*_{2}
= 3.92768
15.85443 *x*_{3}
= 3.85164
14.13174 *x*_{4}
= 3.35329

The solution vector is X = (*x*_{1}, *x*_{2}, *x*_{3}, *x*_{4}). We get it by X=B/A.

The program output, X, is

0.28249 0.24859 0.24294 0.23729

**Benchmarking:**

I'm this serial implementation over one node of our cluster, a machine with 4 processors (Intel Xeon 1.8 Ghz) and 1Gb RAM memory. I tried random systems from 1000 to 5000 variables and got the average time.