int check_rref_form(slong * perm, nmod_mat_t A, slong rank)
{
slong i, j, k, prev_pivot;
/* bottom should be zero */
for (i = rank; i < A->r; i++)
for (j = 0; j < A->c; j++)
if (nmod_mat_entry(A, i, j) != 0)
return 0;
prev_pivot = -1;
for (i = 0; i < rank; i++)
{
for (j = 0; j < A->c; j++)
{
if (nmod_mat_entry(A, i, j) != 0)
{
/* pivot should have a higher column index than previous */
if (j <= prev_pivot)
return 0;
/* column should be 0 ... 0 1 0 ... 0 */
for (k = 0; k < rank; k++)
if (nmod_mat_entry(A, k, j) != (i == k))
return 0;
prev_pivot = j;
break;
}
}
}
return 1;
}
void
nmod_mat_scalar_mul(nmod_mat_t B, const nmod_mat_t A, mp_limb_t c)
{
if (c == 0UL)
{
nmod_mat_zero(B);
}
else if (c == 1UL)
{
nmod_mat_set(B, A);
}
else if (c == A->mod.n - 1UL)
{
nmod_mat_neg(B, A);
}
else
{
long i, j;
for (i = 0; i < A->r; i++)
for (j = 0; j < A->c; j++)
nmod_mat_entry(B, i, j) = n_mulmod2_preinv(
nmod_mat_entry(A, i, j), c, A->mod.n, A->mod.ninv);
}
}
void
nmod_mat_solve_tril_classical(nmod_mat_t X, const nmod_mat_t L,
const nmod_mat_t B, int unit)
{
int nlimbs;
long i, j, n, m;
nmod_t mod;
mp_ptr inv, tmp;
n = L->r;
m = B->c;
mod = L->mod;
if (!unit)
{
inv = _nmod_vec_init(n);
for (i = 0; i < n; i++)
inv[i] = n_invmod(nmod_mat_entry(L, i, i), mod.n);
}
else
inv = NULL;
nlimbs = _nmod_vec_dot_bound_limbs(n, mod);
tmp = _nmod_vec_init(n);
for (i = 0; i < m; i++)
{
for (j = 0; j < n; j++)
tmp[j] = nmod_mat_entry(X, j, i);
for (j = 0; j < n; j++)
{
mp_limb_t s;
s = _nmod_vec_dot(L->rows[j], tmp, j, mod, nlimbs);
s = nmod_sub(nmod_mat_entry(B, j, i), s, mod);
if (!unit)
s = n_mulmod2_preinv(s, inv[j], mod.n, mod.ninv);
tmp[j] = s;
}
for (j = 0; j < n; j++)
nmod_mat_entry(X, j, i) = tmp[j];
}
_nmod_vec_clear(tmp);
if (!unit)
_nmod_vec_clear(inv);
}
void
fmpz_mat_CRT_ui(fmpz_mat_t res, const fmpz_mat_t mat1,
const fmpz_t m1, const nmod_mat_t mat2, int sign)
{
long i, j;
mp_limb_t c;
mp_limb_t m2 = mat2->mod.n;
mp_limb_t m2inv = mat2->mod.ninv;
fmpz_t m1m2;
c = fmpz_fdiv_ui(m1, m2);
c = n_invmod(c, m2);
if (c == 0)
{
printf("Exception in fmpz_mat_CRT_ui: m1 not invertible modulo m2!\n");
abort();
}
fmpz_init(m1m2);
fmpz_mul_ui(m1m2, m1, m2);
for (i = 0; i < mat1->r; i++)
{
for (j = 0; j < mat1->c; j++)
_fmpz_CRT_ui_precomp(fmpz_mat_entry(res, i, j),
fmpz_mat_entry(mat1, i, j), m1,
nmod_mat_entry(mat2, i, j), m2, m2inv, m1m2, c, sign);
}
fmpz_clear(m1m2);
}
mp_limb_t
_nmod_mat_det(nmod_mat_t A)
{
mp_limb_t det;
long * P;
long m = A->r;
long rank;
long i;
P = flint_malloc(sizeof(long) * m);
rank = nmod_mat_lu(P, A, 1);
det = 0UL;
if (rank == m)
{
det = 1UL;
for (i = 0; i < m; i++)
det = n_mulmod2_preinv(det, nmod_mat_entry(A, i, i),
A->mod.n, A->mod.ninv);
}
if (_perm_parity(P, m) == 1)
det = nmod_neg(det, A->mod);
flint_free(P);
return det;
}
mp_limb_t
nmod_mat_trace(const nmod_mat_t mat)
{
mp_limb_t t;
slong i, n = nmod_mat_nrows(mat);
if (n == 0)
return 0;
t = nmod_mat_entry(mat, 0, 0);
for (i = 1; i < n; i++)
t = nmod_add(t, nmod_mat_entry(mat, i, i), mat->mod);
return t;
}
void
nmod_poly_mat_evaluate_nmod(nmod_mat_t B, const nmod_poly_mat_t A, mp_limb_t x)
{
slong i, j;
for (i = 0; i < A->r; i++)
for (j = 0; j < A->c; j++)
nmod_mat_entry(B, i, j) = nmod_poly_evaluate_nmod(
nmod_poly_mat_entry(A, i, j), x);
}
void
fmpz_mat_scalar_addmul_nmod_mat_fmpz(fmpz_mat_t B,
const nmod_mat_t A, const fmpz_t c)
{
long i, j;
for (i = 0; i < A->r; i++)
for (j = 0; j < A->c; j++)
fmpz_addmul_ui(fmpz_mat_entry(B,i,j), c, nmod_mat_entry(A,i,j));
}
int nmod_mat_inv(nmod_mat_t B, const nmod_mat_t A)
{
nmod_mat_t I;
long i, dim;
int result;
dim = A->r;
switch (dim)
{
case 0:
result = 1;
break;
case 1:
if (nmod_mat_entry(A, 0, 0) == 0UL)
{
result = 0;
}
else
{
nmod_mat_entry(B, 0, 0) =
n_invmod(nmod_mat_entry(A, 0, 0), B->mod.n);
result = 1;
}
break;
default:
nmod_mat_init(I, dim, dim, B->mod.n);
for (i = 0; i < dim; i++)
nmod_mat_entry(I, i, i) = 1UL;
result = nmod_mat_solve(B, A, I);
nmod_mat_clear(I);
}
return result;
}
mp_limb_t
nmod_mat_det(const nmod_mat_t A)
{
nmod_mat_t tmp;
mp_limb_t det;
long dim = A->r;
if (dim != A->c)
{
printf("nmod_mat_det: nonsquare matrix");
abort();
}
if (dim == 0) return 1UL;
if (dim == 1) return nmod_mat_entry(A, 0, 0);
nmod_mat_init_set(tmp, A);
det = _nmod_mat_det(tmp);
nmod_mat_clear(tmp);
return det;
}
void
fmpz_mat_multi_CRT_ui_precomp(fmpz_mat_t mat,
nmod_mat_t * const residues, long nres,
fmpz_comb_t comb, fmpz_comb_temp_t temp, int sign)
{
long i, j, k;
mp_ptr r;
r = _nmod_vec_init(nres);
for (i = 0; i < fmpz_mat_nrows(mat); i++)
{
for (j = 0; j < fmpz_mat_ncols(mat); j++)
{
for (k = 0; k < nres; k++)
r[k] = nmod_mat_entry(residues[k], i, j);
fmpz_multi_CRT_ui(fmpz_mat_entry(mat, i, j), r, comb, temp, sign);
}
}
_nmod_vec_clear(r);
}
int
nmod_mat_randpermdiag(nmod_mat_t mat, flint_rand_t state,
mp_srcptr diag, long n)
{
int parity;
long i;
long * rows;
long * cols;
rows = _perm_init(mat->r);
cols = _perm_init(mat->c);
parity = _perm_randtest(rows, mat->r, state);
parity ^= _perm_randtest(cols, mat->c, state);
nmod_mat_zero(mat);
for (i = 0; i < n; i++)
nmod_mat_entry(mat, rows[i], cols[i]) = diag[i];
_perm_clear(rows);
_perm_clear(cols);
return parity;
}
int
main(void)
{
slong i;
FLINT_TEST_INIT(state);
flint_printf("rref....");
fflush(stdout);
for (i = 0; i < 1000 * flint_test_multiplier(); i++)
{
nmod_mat_t A, B, C, D;
mp_limb_t mod;
slong j, k, m, n, rank1, rank2;
slong *perm;
int equal;
mp_limb_t c;
mod = n_randtest_prime(state, 0);
m = n_randint(state, 20);
n = n_randint(state, 20);
perm = _perm_init(2*m);
nmod_mat_init(A, m, n, mod);
nmod_mat_init(D, 2*m, n, mod);
nmod_mat_randtest(A, state);
nmod_mat_init_set(B, A);
nmod_mat_init_set(C, A);
rank1 = nmod_mat_rref(B);
if (!check_rref_form(perm, B, rank1))
{
flint_printf("FAIL (malformed rref)\n");
nmod_mat_print_pretty(A); flint_printf("\n\n");
nmod_mat_print_pretty(B); flint_printf("\n\n");
abort();
}
/* Concatenate the original matrix with the rref, scramble the rows,
and check that the rref is the same */
_perm_randtest(perm, 2 * m, state);
for (j = 0; j < m; j++)
{
do { c = n_randint(state, mod); } while (c == 0);
for (k = 0; k < n; k++)
nmod_mat_entry(D, perm[j], k) =
nmod_mul(nmod_mat_entry(A, j, k), c, A->mod);
}
for (j = 0; j < m; j++)
{
do { c = n_randint(state, mod); } while (c == 0);
for (k = 0; k < n; k++)
nmod_mat_entry(D, perm[m + j], k) =
nmod_mul(nmod_mat_entry(B, j, k), c, A->mod);
}
rank2 = nmod_mat_rref(D);
equal = (rank1 == rank2);
if (equal)
{
for (j = 0; j < rank2; j++)
for (k = 0; k < n; k++)
equal = equal && (nmod_mat_entry(B, j, k) ==
nmod_mat_entry(D, j, k));
for (j = rank2; j < 2 * rank2; j++)
for (k = 0; k < n; k++)
equal = equal && (nmod_mat_entry(D, j, k) == 0);
}
if (!equal)
{
flint_printf("FAIL (rank1 = %wd, rank2 = %wd)!\n", rank1, rank2);
nmod_mat_print_pretty(A); flint_printf("\n\n");
nmod_mat_print_pretty(B); flint_printf("\n\n");
nmod_mat_print_pretty(D); flint_printf("\n\n");
abort();
}
_perm_clear(perm);
nmod_mat_clear(A);
nmod_mat_clear(B);
nmod_mat_clear(C);
nmod_mat_clear(D);
}
FLINT_TEST_CLEANUP(state);
flint_printf("PASS\n");
return 0;
}
