Hey all,

I'm trying to write this exceedingly simple-looking naive Gaussian elimination program, but it isn't working. I got the algorithm right out of the math book. It even looks a lot like other working examples I've seen.

It appears that it gives me the the correct values in the upper-right triangle, but it doesn't give me the zeros in the lower-left. I've even tried a couple of other algorithms and still had trouble. Oh, and I know that the line for operation on the vector B is missing. Just trying to get one step at a time.

Can anyone give me any idea what I'm doing wrong?

thanks!

Code:
```/* Naive Gaussian Elimination */

/* includes */

#include<math.h>

#include<stdlib.h>

#include<stdio.h>

/* ********************* */

/* global variables */

// I know, global variables are bad :/

// two-dimensional array for the default 'A' array
// zeros make array indexes match up w/matrix ones
double A[8][8] = { { 0, 0, 0, 0, 0, 0, 0 },
{ 0, 0.1897, 0.3784, 0.6449, 0.7271, 0.4449, 0.1730, 0.0118 },
{ 0, 0.1934, 0.8600, 0.8180, 0.3093, 0.6946, 0.9797, 0.8939 },
{ 0, 0.6822, 0.8537, 0.6602, 0.8385, 0.6213, 0.2714, 0.1991 },
{ 0, 0.3028, 0.5936, 0.3420, 0.5681, 0.7948, 0.2523, 0.2987 },
{ 0, 0.5417, 0.4966, 0.2897, 0.3704, 0.9568, 0.8757, 0.6614 },
{ 0, 0.1509, 0.8998, 0.3412, 0.7027, 0.5226, 0.7373, 0.2844 },
{ 0, 0.6979, 0.8216, 0.5341, 0.5466, 0.8801, 0.1365, 0.4692 } };

/* another known problem for debugging */
// zeros make array indexes match up w/matrix ones
/* double A[8][8] = { { 0, 0, 0, 0, 0, 0, 0 },
{ 0, 6, -2, 2, 4, 0, 0, 0 },
{ 0, 12, -8, 6, 10, 0, 0, 0 },
{ 0, 3, -13, 9, 3, 0, 0, 0 },
{ 0, -6, 4, 1, -18, 0, 0, 0},
{ 0, 0, 0, 0, 0, 0, 0 },
{ 0, 0, 0, 0, 0, 0, 0  },
{ 0, 0, 0, 0, 0, 0, 0  } }; */

// one-dimensional array for default vector 'b'
double b[8] = { 0, 0.5000, -0.3000, -0.2000, 0.7000, -0.9000, 0.3000, -0.1000 };

/* ********************* */

/* Main */
int main(){

/* variables */
char overwrite;

/* prototypes */
void printArray();
void printVector();
void performGaussianElimination();

/* Say hello */

printf("\n\n\nThis program will solve a system of equations with Naive Gaussian Elimination. \n\n");

printf("The default matrix used will be: ");
printArray();

printf("\n\nThe default vector used will be: ");
printVector();

performGaussianElimination();

printf("\nThe matrix after forward elimination is:");
printArray();

return 0;
}

/* ********************* */
/* Print Array Function (working correctly) */

void printArray(){
int i,j;

printf("\n");

// loop through rows
for(i=1; i <=7; i++){

// output column values
for(j=1; j<=7; j++) {
printf("%lf   ", A[i][j]);
} // end inner 'for'

printf("\n");
} // end outer 'for'

return;
}

/* ********************* */
/* Print Vector Function */
void printVector(){
int j;

printf("\n");

// output column values
for(j=1; j<=7-1; j++) {
printf("%lf   ", b[j]);
} // end inner 'for'

printf("\n");

return;
}

/* ********************* */
/* Perform Gaussian Elimination Function */

void performGaussianElimination(){
int i,j,k,m;
double xmult;

// forward elimination

for(k=1; k<7; k++)
{
for(i=k+1; i<=7; i++){
if(A[k][k]!=0){
xmult = A[i][k]/A[k][k];
}
A[i][k] = xmult;
for(j=k+1; j<=7; j++){
A[i][j] = A[i][j] - xmult * A[k][j];
}
}
}

// do backward substitution, not done yet

return;
}```