int is_magic(int N, int *m[])
{
int i, j;
int *sum; /* array to store the sum of lines, columns and diagonals */
if (m == NULL || N <=0)
return 0;
sum = calloc(N+N+2, sizeof(int));
for (i = 0; i < N; i++)
for (j = 0; j < N; j++) {
/* sum of each line */
sum[i] += mat_elem(m, N, i, j);
/* sum of each column */
sum[N+j] += mat_elem(m, N, i, j);
/* sum of main diagonal */
if (i == j)
sum[N+N] += mat_elem(m, N, i, j);
/* sum of secondary diagonal */
if ((i + j + 1) == N)
sum[N+N+1] += mat_elem(m, N, i, j);
}
/* use transitivity to verify the magic property of sums */
for (i = 1; i < N+N+2; i++)
if (sum[i] != sum[i-1])
return 0;
free(sum);
return 1;
}
void swap_row(double *a, double *b, int r1, int r2, int n)
{
double tmp2;
int i;
if (r1 == r2) return;
parallel_for(i(0),n,[&](i i)
{
double tmp, *p1, *p2;
p1 = mat_elem(a, r1, i, n);
p2 = mat_elem(a, r2, i, n);
tmp = *p1, *p1 = *p2, *p2 = tmp;
});
tmp2 = b[r1], b[r1] = b[r2], b[r2] = tmp2;
}
int main(int argc, char** argv) {
char* filename;
FILE *fp;
int m, n, i, info;
double **a;
double det;
int *ipiv;
if (argc < 2) {
fprintf(stderr, "Usage: %s inputfile\n", argv[0]);
exit(1);
}
filename = argv[1];
/* read matrix A from a file */
fp = fopen(filename, "r");
if (fp == NULL) {
fprintf(stderr, "Error: file can not open\n");
exit(1);
}
read_dmatrix(fp, &m, &n, &a);
if (m != n) {
fprintf(stderr, "Error: non-square matrix\n");
exit(1);
}
printf("Matrix A:\n");
fprint_dmatrix(stdout, n, n, a);
/* perform LU decomposition */
ipiv = alloc_ivector(n);
dgetrf_(&n, &n, mat_ptr(a), &n, vec_ptr(ipiv), &info);
if (info != 0) {
fprintf(stderr, "Error: LAPACK::dgetrf failed\n");
exit(1);
}
printf("Result of LU decomposition:\n");
fprint_dmatrix(stdout, n, n, a);
printf("Pivot for LU decomposition:\n");
fprint_ivector(stdout, n, ipiv);
/* calculate determinant */
det = 1.0;
for (i = 0; i < n; ++i) {
det *= mat_elem(a, i, i);
if (ipiv[i] != i+1) det = -det;
}
printf("Determinant of A = %lf\n", det);
free_dmatrix(a);
free_ivector(ipiv);
}
int main(int argc, char** argv) {
char* filename;
FILE *fp;
int m, n;
int i, j, k;
double **a;
double *b;
if (argc < 2) {
fprintf(stderr, "Usage: %s inputfile\n", argv[0]);
exit(1);
}
filename = argv[1];
/* read matrix A and vector B from a file */
fp = fopen(filename, "r");
if (fp == NULL) {
fprintf(stderr, "Error: file can not open\n");
exit(1);
}
read_dmatrix(fp, &m, &n, &a);
if (m != n) {
fprintf(stderr, "Error: inconsistent number of equations\n");
exit(1);
}
read_dvector(fp, &n, &b);
if (m != n) {
fprintf(stderr, "Error: inconsistent number of equations\n");
exit(1);
}
printf("Matrix A:\n");
fprint_dmatrix(stdout, n, n, a);
printf("Vector B (transposed):\n");
fprint_dvector(stdout, n, b);
/* perform Gauss elimination */
for (k = 0; k < n; ++k) {
for (i = k + 1; i < n; ++i) {
for (j = k + 1; j < n; ++j) {
mat_elem(a, i, j) -= mat_elem(a, k, j) * mat_elem(a, i, k) / mat_elem(a, k, k);
}
b[i] -= b[k] * mat_elem(a, i, k) / mat_elem(a, k, k);
}
}
printf("Result of Gauss elimination (only upper triangular has meaning):\n");
fprint_dmatrix(stdout, n, n, a);
printf("Transformed vector B:\n");
fprint_dvector(stdout, n, b);
/* backward substitution */
for (k = n-1; k >= 0; --k) {
for (j = k + 1; j < n; ++j) {
b[k] -= mat_elem(a, k, j) * b[j];
}
b[k] /= mat_elem(a, k, k);
}
printf("Solution X (transposed):\n");
fprint_dvector(stdout, n, b);
free_dmatrix(a);
free_dvector(b);
}
