Calculate matrix determinant with partial pivoting Gauss in C - c

Question

I'm trying to make a simple console application in C which will calculate the determinant of a Matrix using the Gauss partial pivoting elimination method. The 2 problems that I have are :
- someone told me that there are certain matrix-es that don't work with this method ( mathematically speaking ), after reading articles on google, i could not find what is that special case
- after a lot of tests I found out that my program is not working for some matrix-es, after 2 days of "wasting" time editing and undoing, i could not find the problem.
Any type of improvements are more than welcomed. I'm just starting with C.
#include<stdio.h>
#include<cstdlib>
#include<math.h>
#include<conio.h>
#include<windows.h>
// calculate biggest element on column
int indice_max(int dim, int col, float coloana[20][20]) {
float max = 0;
int indice;
for(int i = 1; i <= dim; i++)
if(fabs(max) < fabs(coloana[i][col])) {
max = coloana[i][col];
indice = i;
}
return indice;
}
// permute 2 lines
void permutare_linie(int linie1, int linie2, int dim, float matrice[20][20]) {
float aux;
for(int i = 1; i <= dim; i++) {
aux = matrice[linie1][i];
matrice[linie1][i] = matrice[linie2][i];
matrice[linie2][i] = aux;
}
}
// print matrix
void afisare_matrice(int dimensiune, float matrice[20][20], int lpiv) {
for(int i = 1; i<= dimensiune; i++) {
for(int j = 1; j <= dimensiune; j++) {
if(i == lpiv)
SetConsoleTextAttribute(GetStdHandle(STD_OUTPUT_HANDLE), BACKGROUND_GREEN);
else
SetConsoleTextAttribute(GetStdHandle(STD_OUTPUT_HANDLE), FOREGROUND_RED | FOREGROUND_GREEN | FOREGROUND_BLUE );
printf("%4.2f ", matrice[i][j]);
}
printf("\n");
}
}
void main(void) {
float matrice[20][20];
int dimensiune ;
float rezultat = 1;
float pivot;
int lpiv;
int cpiv;
int optiune;
while(1) {
// MENU
printf("ALEGET OPTIUNEA:\n");
printf("1) Calculate matrix determinant\n");
printf("2) Exit\n");
scanf("%d", &optiune);
if(optiune == 1) {
// Read determinant dimension
printf("Matrix dimension:");
scanf("%d", &dimensiune);
// Read determinant
for(int i = 1; i <= dimensiune; i++)
for(int j = 1; j <= dimensiune; j++) {
printf("M[%d][%d]=", i, j);
scanf("%f", &matrice[i][j]);
}
// pivot initial coords
lpiv = 1;
cpiv = 1;
printf("\n----- Entered Matrix -----\n\n");
afisare_matrice(dimensiune, matrice, 0);
printf("\n");
for(int pas = 1; pas <= dimensiune - 1; pas++) {
if(fabs(matrice[lpiv][cpiv]) > fabs(matrice[indice_max(dimensiune, cpiv, matrice)][cpiv])) {
permutare_linie(lpiv, indice_max(dimensiune, cpiv, matrice), dimensiune, matrice);
rezultat = -(rezultat);
}
pivot = matrice[lpiv][cpiv];
for(int inm = 1; inm <= dimensiune; inm++) {
matrice[lpiv][inm] = matrice[lpiv][inm] / pivot;
}
rezultat *= fabs(pivot);
// transform matrix to a superior triangular
for(int l = lpiv+1; l <= dimensiune; l++)
for(int c=cpiv+1; c <= dimensiune; c++) {
matrice[l][c] -= matrice[l][cpiv] * matrice[lpiv][c] / matrice[lpiv][cpiv];
}
for(int i = lpiv + 1; i <= dimensiune; i++)
matrice[i][cpiv] = 0;
// afisam rezultat / pas
printf("----- Step %d -----\n\n", pas);
afisare_matrice(dimensiune, matrice, lpiv);
printf("\nResult after step %d : %4.2f\n\n", pas, rezultat);
lpiv++;
cpiv++;
}
// final result
rezultat = rezultat * matrice[dimensiune][dimensiune];
printf("----- REZULTAT FINAL -----\n\n");
SetConsoleTextAttribute(GetStdHandle(STD_OUTPUT_HANDLE), FOREGROUND_RED | FOREGROUND_INTENSITY);
printf("Rezultat = %4.2f\nRezultat rotunjit:%4.0f\n\n", rezultat, floorf(rezultat * 100 + 0.5) / 100);
SetConsoleTextAttribute(GetStdHandle(STD_OUTPUT_HANDLE), FOREGROUND_RED | FOREGROUND_GREEN | FOREGROUND_BLUE );
}
else {
exit(0);
}
}
}

Answer 1

Your code does some division:
matrice[lpiv][inm] = matrice[lpiv][inm] / pivot;
If it happens to divide by zero, an error will occur. I guess this will happen for the zero matrix.
It seems that your code is actually trying to invert the matrix, not just calculate the determinant.