int
fmpz_mat_solve_fflu(fmpz_mat_t X, fmpz_t den,
const fmpz_mat_t A, const fmpz_mat_t B)
{
fmpz_mat_t LU;
slong dim, *perm;
int result;
if (fmpz_mat_is_empty(A) || fmpz_mat_is_empty(B))
{
fmpz_one(den);
return 1;
}
dim = fmpz_mat_nrows(A);
perm = _perm_init(dim);
fmpz_mat_init_set(LU, A);
result = (fmpz_mat_fflu(LU, den, perm, LU, 1) == dim);
if (result)
fmpz_mat_solve_fflu_precomp(X, perm, LU, B);
else
fmpz_zero(den);
_perm_clear(perm);
fmpz_mat_clear(LU);
return result;
}
void
_fmpz_mat_det_bareiss(fmpz_t det, fmpz_mat_t tmp)
{
long *perm, n = fmpz_mat_nrows(tmp);
perm = _perm_init(n);
fmpz_mat_fflu(tmp, det, perm, tmp, 1);
if (_perm_parity(perm, n) == 1)
fmpz_neg(det, det);
_perm_clear(perm);
}
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()
{
slong iter;
flint_rand_t state;
flint_printf("lu....");
fflush(stdout);
flint_randinit(state);
for (iter = 0; iter < 10000; iter++)
{
fmpq_mat_t Q;
acb_mat_t A, LU, P, L, U, T;
slong i, j, n, qbits, prec, *perm;
int q_invertible, r_invertible;
n = n_randint(state, 8);
qbits = 1 + n_randint(state, 100);
prec = 2 + n_randint(state, 202);
fmpq_mat_init(Q, n, n);
acb_mat_init(A, n, n);
acb_mat_init(LU, n, n);
acb_mat_init(P, n, n);
acb_mat_init(L, n, n);
acb_mat_init(U, n, n);
acb_mat_init(T, n, n);
perm = _perm_init(n);
fmpq_mat_randtest(Q, state, qbits);
q_invertible = fmpq_mat_is_invertible(Q);
if (!q_invertible)
{
acb_mat_set_fmpq_mat(A, Q, prec);
r_invertible = acb_mat_lu(perm, LU, A, prec);
if (r_invertible)
{
flint_printf("FAIL: matrix is singular over Q but not over R\n");
flint_printf("n = %wd, prec = %wd\n", n, prec);
flint_printf("\n");
flint_printf("Q = \n"); fmpq_mat_print(Q); flint_printf("\n\n");
flint_printf("A = \n"); acb_mat_printd(A, 15); flint_printf("\n\n");
flint_printf("LU = \n"); acb_mat_printd(LU, 15); flint_printf("\n\n");
}
}
else
{
/* now this must converge */
while (1)
{
acb_mat_set_fmpq_mat(A, Q, prec);
r_invertible = acb_mat_lu(perm, LU, A, prec);
if (r_invertible)
{
break;
}
else
{
if (prec > 10000)
{
flint_printf("FAIL: failed to converge at 10000 bits\n");
abort();
}
prec *= 2;
}
}
acb_mat_one(L);
for (i = 0; i < n; i++)
for (j = 0; j < i; j++)
acb_set(acb_mat_entry(L, i, j),
acb_mat_entry(LU, i, j));
for (i = 0; i < n; i++)
for (j = i; j < n; j++)
acb_set(acb_mat_entry(U, i, j),
acb_mat_entry(LU, i, j));
for (i = 0; i < n; i++)
acb_one(acb_mat_entry(P, perm[i], i));
acb_mat_mul(T, P, L, prec);
acb_mat_mul(T, T, U, prec);
if (!acb_mat_contains_fmpq_mat(T, Q))
{
flint_printf("FAIL (containment, iter = %wd)\n", iter);
flint_printf("n = %wd, prec = %wd\n", n, prec);
flint_printf("\n");
flint_printf("Q = \n"); fmpq_mat_print(Q); flint_printf("\n\n");
flint_printf("A = \n"); acb_mat_printd(A, 15); flint_printf("\n\n");
flint_printf("LU = \n"); acb_mat_printd(LU, 15); flint_printf("\n\n");
flint_printf("L = \n"); acb_mat_printd(L, 15); flint_printf("\n\n");
flint_printf("U = \n"); acb_mat_printd(U, 15); flint_printf("\n\n");
flint_printf("P*L*U = \n"); acb_mat_printd(T, 15); flint_printf("\n\n");
abort();
}
}
fmpq_mat_clear(Q);
acb_mat_clear(A);
acb_mat_clear(LU);
acb_mat_clear(P);
acb_mat_clear(L);
acb_mat_clear(U);
acb_mat_clear(T);
_perm_clear(perm);
}
flint_randclear(state);
flint_cleanup();
flint_printf("PASS\n");
return EXIT_SUCCESS;
}
int
fmpz_poly_mat_inv(fmpz_poly_mat_t Ainv, fmpz_poly_t den,
const fmpz_poly_mat_t A)
{
long n = fmpz_poly_mat_nrows(A);
if (n == 0)
{
fmpz_poly_one(den);
return 1;
}
else if (n == 1)
{
fmpz_poly_set(den, E(A, 0, 0));
fmpz_poly_one(E(Ainv, 0, 0));
return !fmpz_poly_is_zero(den);
}
else if (n == 2)
{
fmpz_poly_mat_det(den, A);
if (fmpz_poly_is_zero(den))
{
return 0;
}
else if (Ainv == A)
{
fmpz_poly_swap(E(A, 0, 0), E(A, 1, 1));
fmpz_poly_neg(E(A, 0, 1), E(A, 0, 1));
fmpz_poly_neg(E(A, 1, 0), E(A, 1, 0));
return 1;
}
else
{
fmpz_poly_set(E(Ainv, 0, 0), E(A, 1, 1));
fmpz_poly_set(E(Ainv, 1, 1), E(A, 0, 0));
fmpz_poly_neg(E(Ainv, 0, 1), E(A, 0, 1));
fmpz_poly_neg(E(Ainv, 1, 0), E(A, 1, 0));
return 1;
}
}
else
{
fmpz_poly_mat_t LU, I;
long * perm;
int result;
perm = _perm_init(n);
fmpz_poly_mat_init_set(LU, A);
result = (fmpz_poly_mat_fflu(LU, den, perm, LU, 1) == n);
if (result)
{
fmpz_poly_mat_init(I, n, n);
fmpz_poly_mat_one(I);
fmpz_poly_mat_solve_fflu_precomp(Ainv, perm, LU, I);
fmpz_poly_mat_clear(I);
}
else
fmpz_poly_zero(den);
if (_perm_parity(perm, n))
{
fmpz_poly_mat_neg(Ainv, Ainv);
fmpz_poly_neg(den, den);
}
_perm_clear(perm);
fmpz_poly_mat_clear(LU);
return result;
}
}
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;
}
int main(void)
{
int i;
FLINT_TEST_INIT(state);
flint_printf("inv....");
fflush(stdout);
/* check inv(inv(a)) == a */
for (i = 0; i < 10000; i++)
{
slong n, *a, *b, *c;
n = n_randint(state, 100);
a = _perm_init(n);
b = _perm_init(n);
c = _perm_init(n);
_perm_randtest(a, n, state);
_perm_inv(b, a, n);
_perm_inv(c, b, n);
if (!_perm_equal(a, c, n))
{
flint_printf("FAIL:\n");
flint_printf("a: "); _perm_print(a, n); flint_printf("\n\n");
flint_printf("b: "); _perm_print(b, n); flint_printf("\n\n");
flint_printf("c: "); _perm_print(c, n); flint_printf("\n\n");
abort();
}
_perm_clear(a);
_perm_clear(b);
_perm_clear(c);
}
/* check aliasing */
for (i = 0; i < 10000; i++)
{
slong n, *a, *b;
n = n_randint(state, 100);
a = _perm_init(n);
b = _perm_init(n);
_perm_randtest(a, n, state);
_perm_inv(b, a, n);
_perm_inv(a, a, n);
if (!_perm_equal(a, b, n))
{
flint_printf("FAIL:\n");
flint_printf("a: "); _perm_print(a, n); flint_printf("\n\n");
flint_printf("b: "); _perm_print(b, n); flint_printf("\n\n");
abort();
}
_perm_clear(a);
_perm_clear(b);
}
FLINT_TEST_CLEANUP(state);
flint_printf("PASS\n");
return 0;
}