Gaussian Elimination in C
This is a simple implementation of the Gaussian Elimination algorithm for solving n linear equations with n unknowns.
Further explanation is given here.
Further explanation is given here.
1 2 #include <stdio.h> 3 4 int n; 5 float a[10][11]; 6 7 void forwardSubstitution() { 8 int i, j, k, max; 9 float t; 10 for (i = 0; i < n; ++i) { 11 max = i; 12 for (j = i + 1; j < n; ++j) 13 if (a[j][i] > a[max][i]) 14 max = j; 15 16 for (j = 0; j < n + 1; ++j) { 17 t = a[max][j]; 18 a[max][j] = a[i][j]; 19 a[i][j] = t; 20 } 21 22 for (j = n; j >= i; --j) 23 for (k = i + 1; k < n; ++k) 24 a[k][j] -= a[k][i]/a[i][i] * a[i][j]; 25 26 /* for (k = 0; k < n; ++k) { 27 for (j = 0; j < n + 1; ++j) 28 printf("%.2f\t", a[k][j]); 29 printf("\n"); 30 }*/ 31 } 32 } 33 34 void reverseElimination() { 35 int i, j; 36 for (i = n - 1; i >= 0; --i) { 37 a[i][n] = a[i][n] / a[i][i]; 38 a[i][i] = 1; 39 for (j = i - 1; j >= 0; --j) { 40 a[j][n] -= a[j][i] * a[i][n]; 41 a[j][i] = 0; 42 } 43 } 44 } 45 46 void gauss() { 47 int i, j; 48 49 forwardSubstitution(); 50 reverseElimination(); 51 52 for (i = 0; i < n; ++i) { 53 for (j = 0; j < n + 1; ++j) 54 printf("%.2f\t", a[i][j]); 55 printf("\n"); 56 } 57 } 58 59 int main(int argc, char *argv[]) { 60 int i, j; 61 62 FILE *fin = fopen("gauss.in", "r"); 63 fscanf(fin, "%d", &n); 64 for (i = 0; i < n; ++i) 65 for (j = 0; j < n + 1; ++j) 66 fscanf(fin, "%f", &a[i][j]); 67 fclose(fin); 68 69 gauss(); 70 71 return 0; 72 } 73
