inline void subtractMultipleTo(DMatZZpFlint& C,
const DMatZZpFlint& A,
const DMatZZpFlint& B)
{
DMatZZpFlint D(C.ring(), A.numRows(), B.numColumns());
nmod_mat_mul(D.nmod_mat(), A.nmod_mat(), B.nmod_mat());
nmod_mat_sub(C.nmod_mat(), C.nmod_mat(), D.nmod_mat());
}
inline void mult(const DMatZZpFlint& A,
const DMatZZpFlint& B,
DMatZZpFlint& result_product)
{
// DMatZZpFlint& A1 = const_cast<DMatZZpFlint&>(A); // needed because nmod_mat_mul doesn't declare params const
// DMatZZpFlint& B1 = const_cast<DMatZZpFlint&>(B);
// The A1 and B1 on the next line are switched because the memory layout expected
// is the transpose of what we have for DMat.
nmod_mat_mul(result_product.nmod_mat(), A.nmod_mat(), B.nmod_mat());
}
int
main(void)
{
long i;
flint_rand_t state;
flint_randinit(state);
printf("solve_triu_recursive....");
fflush(stdout);
for (i = 0; i < 1000; i++)
{
nmod_mat_t A, X, B, Y;
mp_limb_t m;
long rows, cols;
int unit;
m = n_randtest_prime(state, 0);
rows = n_randint(state, 100);
cols = n_randint(state, 100);
unit = n_randint(state, 2);
nmod_mat_init(A, rows, rows, m);
nmod_mat_init(B, rows, cols, m);
nmod_mat_init(X, rows, cols, m);
nmod_mat_init(Y, rows, cols, m);
nmod_mat_randtriu(A, state, unit);
nmod_mat_randtest(X, state);
nmod_mat_mul(B, A, X);
/* Check Y = A^(-1) * (A * X) = X */
nmod_mat_solve_triu_recursive(Y, A, B, unit);
if (!nmod_mat_equal(Y, X))
{
printf("FAIL!\n");
printf("A:\n");
nmod_mat_print_pretty(A);
printf("X:\n");
nmod_mat_print_pretty(X);
printf("B:\n");
nmod_mat_print_pretty(B);
printf("Y:\n");
nmod_mat_print_pretty(Y);
abort();
}
/* Check aliasing */
nmod_mat_solve_triu_recursive(B, A, B, unit);
if (!nmod_mat_equal(B, X))
{
printf("FAIL!\n");
printf("aliasing test failed");
printf("A:\n");
nmod_mat_print_pretty(A);
printf("B:\n");
nmod_mat_print_pretty(B);
abort();
}
nmod_mat_clear(A);
nmod_mat_clear(B);
nmod_mat_clear(X);
nmod_mat_clear(Y);
}
flint_randclear(state);
printf("PASS\n");
return 0;
}
int
main(void)
{
flint_rand_t state;
long i;
printf("mul_interpolate....");
fflush(stdout);
flint_randinit(state);
/* Check evaluation homomorphism */
for (i = 0; i < 1000; i++)
{
nmod_poly_mat_t A, B, C;
nmod_mat_t a, b, c, d;
mp_limb_t mod, x;
long m, n, k, deg;
mod = n_randtest_prime(state, 0);
m = n_randint(state, 20);
n = n_randint(state, 20);
k = n_randint(state, 20);
deg = 1 + n_randint(state, 10);
nmod_poly_mat_init(A, m, n, mod);
nmod_poly_mat_init(B, n, k, mod);
nmod_poly_mat_init(C, m, k, mod);
nmod_mat_init(a, m, n, mod);
nmod_mat_init(b, n, k, mod);
nmod_mat_init(c, m, k, mod);
nmod_mat_init(d, m, k, mod);
nmod_poly_mat_randtest(A, state, deg);
nmod_poly_mat_randtest(B, state, deg);
nmod_poly_mat_randtest(C, state, deg); /* noise in output */
if (nmod_poly_mat_max_length(A)
+ nmod_poly_mat_max_length(B) - 1 <= mod)
{
nmod_poly_mat_mul_interpolate(C, A, B);
x = n_randint(state, mod);
nmod_poly_mat_evaluate_nmod(a, A, x);
nmod_poly_mat_evaluate_nmod(b, B, x);
nmod_poly_mat_evaluate_nmod(d, C, x);
nmod_mat_mul(c, a, b);
if (!nmod_mat_equal(c, d))
{
printf("FAIL:\n");
printf("A:\n");
nmod_poly_mat_print(A, "x");
printf("B:\n");
nmod_poly_mat_print(B, "x");
printf("C:\n");
nmod_poly_mat_print(C, "x");
printf("\n");
abort();
}
}
nmod_poly_mat_clear(A);
nmod_poly_mat_clear(B);
nmod_poly_mat_clear(C);
nmod_mat_clear(a);
nmod_mat_clear(b);
nmod_mat_clear(c);
nmod_mat_clear(d);
}
/* Check aliasing C and A */
for (i = 0; i < 1000; i++)
{
nmod_poly_mat_t A, B, C;
long m, n, deg;
mp_limb_t mod;
mod = n_randtest_prime(state, 0);
m = n_randint(state, 20);
n = n_randint(state, 20);
deg = 1 + n_randint(state, 10);
nmod_poly_mat_init(A, m, n, mod);
nmod_poly_mat_init(B, n, n, mod);
nmod_poly_mat_init(C, m, n, mod);
nmod_poly_mat_randtest(A, state, deg);
nmod_poly_mat_randtest(B, state, deg);
nmod_poly_mat_randtest(C, state, deg); /* noise in output */
if (nmod_poly_mat_max_length(A)
+ nmod_poly_mat_max_length(B) - 1 <= mod)
{
nmod_poly_mat_mul_interpolate(C, A, B);
nmod_poly_mat_mul_interpolate(A, A, B);
if (!nmod_poly_mat_equal(C, A))
{
printf("FAIL:\n");
printf("A:\n");
nmod_poly_mat_print(A, "x");
printf("B:\n");
nmod_poly_mat_print(B, "x");
printf("C:\n");
nmod_poly_mat_print(C, "x");
printf("\n");
abort();
}
}
nmod_poly_mat_clear(A);
nmod_poly_mat_clear(B);
nmod_poly_mat_clear(C);
}
/* Check aliasing C and B */
for (i = 0; i < 1000; i++)
{
nmod_poly_mat_t A, B, C;
long m, n, deg;
mp_limb_t mod;
mod = n_randtest_prime(state, 0);
m = n_randint(state, 20);
n = n_randint(state, 20);
deg = 1 + n_randint(state, 10);
nmod_poly_mat_init(A, m, m, mod);
nmod_poly_mat_init(B, m, n, mod);
nmod_poly_mat_init(C, m, n, mod);
nmod_poly_mat_randtest(A, state, deg);
nmod_poly_mat_randtest(B, state, deg);
nmod_poly_mat_randtest(C, state, deg); /* noise in output */
if (nmod_poly_mat_max_length(A)
+ nmod_poly_mat_max_length(B) - 1 <= mod)
{
nmod_poly_mat_mul_interpolate(C, A, B);
nmod_poly_mat_mul_interpolate(B, A, B);
if (!nmod_poly_mat_equal(C, B))
{
printf("FAIL:\n");
printf("A:\n");
nmod_poly_mat_print(A, "x");
printf("B:\n");
nmod_poly_mat_print(B, "x");
printf("C:\n");
nmod_poly_mat_print(C, "x");
printf("\n");
abort();
}
}
nmod_poly_mat_clear(A);
nmod_poly_mat_clear(B);
nmod_poly_mat_clear(C);
}
flint_randclear(state);
_fmpz_cleanup();
printf("PASS\n");
return 0;
}
int
main(void)
{
flint_rand_t state;
long i;
printf("sqr....");
fflush(stdout);
flint_randinit(state);
/* Check evaluation homomorphism */
for (i = 0; i < 1000; i++)
{
nmod_poly_mat_t A, C;
nmod_mat_t a, c, d;
mp_limb_t x, mod;
long m, deg;
mod = n_randtest_prime(state, 0);
m = n_randint(state, 20);
deg = 1 + n_randint(state, 10);
nmod_poly_mat_init(A, m, m, mod);
nmod_poly_mat_init(C, m, m, mod);
nmod_mat_init(a, m, m, mod);
nmod_mat_init(c, m, m, mod);
nmod_mat_init(d, m, m, mod);
nmod_poly_mat_randtest(A, state, deg);
nmod_poly_mat_randtest(C, state, deg); /* noise in output */
nmod_poly_mat_sqr(C, A);
x = n_randint(state, 0);
nmod_poly_mat_evaluate_nmod(a, A, x);
nmod_poly_mat_evaluate_nmod(d, C, x);
nmod_mat_mul(c, a, a);
if (!nmod_mat_equal(c, d))
{
printf("FAIL:\n");
printf("A:\n");
nmod_poly_mat_print(A, "x");
printf("C:\n");
nmod_poly_mat_print(C, "x");
printf("\n");
abort();
}
nmod_poly_mat_clear(A);
nmod_poly_mat_clear(C);
nmod_mat_clear(a);
nmod_mat_clear(c);
nmod_mat_clear(d);
}
/* Check aliasing B and A */
for (i = 0; i < 1000; i++)
{
nmod_poly_mat_t A, B;
long m, deg;
mp_limb_t mod;
mod = n_randtest_prime(state, 0);
m = n_randint(state, 20);
deg = 1 + n_randint(state, 10);
nmod_poly_mat_init(A, m, m, mod);
nmod_poly_mat_init(B, m, m, mod);
nmod_poly_mat_randtest(A, state, deg);
nmod_poly_mat_randtest(B, state, deg); /* noise in output */
nmod_poly_mat_sqr(B, A);
nmod_poly_mat_sqr(A, A);
if (!nmod_poly_mat_equal(B, A))
{
printf("FAIL (aliasing):\n");
printf("A:\n");
nmod_poly_mat_print(A, "x");
printf("B:\n");
nmod_poly_mat_print(B, "x");
printf("\n");
abort();
}
nmod_poly_mat_clear(A);
nmod_poly_mat_clear(B);
}
flint_randclear(state);
_fmpz_cleanup();
printf("PASS\n");
return 0;
}
void
_nmod_poly_compose_mod_brent_kung(mp_ptr res, mp_srcptr poly1, long len1,
mp_srcptr poly2,
mp_srcptr poly3, long len3, nmod_t mod)
{
nmod_mat_t A, B, C;
mp_ptr t, h;
long i, n, m;
n = len3 - 1;
if (len3 == 1)
return;
if (len1 == 1)
{
res[0] = poly1[0];
return;
}
if (len3 == 2)
{
res[0] = _nmod_poly_evaluate_nmod(poly1, len1, poly2[0], mod);
return;
}
m = n_sqrt(n) + 1;
nmod_mat_init(A, m, n, mod.n);
nmod_mat_init(B, m, m, mod.n);
nmod_mat_init(C, m, n, mod.n);
h = _nmod_vec_init(n);
t = _nmod_vec_init(n);
/* Set rows of B to the segments of poly1 */
for (i = 0; i < len1 / m; i++)
_nmod_vec_set(B->rows[i], poly1 + i*m, m);
_nmod_vec_set(B->rows[i], poly1 + i*m, len1 % m);
/* Set rows of A to powers of poly2 */
A->rows[0][0] = 1UL;
_nmod_vec_set(A->rows[1], poly2, n);
for (i = 2; i < m; i++)
_nmod_poly_mulmod(A->rows[i], A->rows[i-1],
n, poly2, n, poly3, len3, mod);
nmod_mat_mul(C, B, A);
/* Evaluate block composition using the Horner scheme */
_nmod_vec_set(res, C->rows[m - 1], n);
_nmod_poly_mulmod(h, A->rows[m - 1], n, poly2, n, poly3, len3, mod);
for (i = m - 2; i >= 0; i--)
{
_nmod_poly_mulmod(t, res, n, h, n, poly3, len3, mod);
_nmod_poly_add(res, t, n, C->rows[i], n, mod);
}
_nmod_vec_clear(h);
_nmod_vec_clear(t);
nmod_mat_clear(A);
nmod_mat_clear(B);
nmod_mat_clear(C);
}
int
main(void)
{
flint_rand_t state;
long i;
printf("nullspace....");
fflush(stdout);
flint_randinit(state);
for (i = 0; i < 10000; i++)
{
nmod_mat_t A, B, ker;
mp_limb_t mod;
long m, n, d, r, nullity, nulrank;
m = n_randint(state, 30);
n = n_randint(state, 30);
for (r = 0; r <= FLINT_MIN(m,n); r++)
{
mod = n_randtest_prime(state, 0);
d = n_randint(state, 2*m*n + 1);
nmod_mat_init(A, m, n, mod);
nmod_mat_init(ker, n, n, mod);
nmod_mat_init(B, m, n, mod);
nmod_mat_randrank(A, state, r);
/* Densify */
if (n_randlimb(state) % 2)
nmod_mat_randops(A, d, state);
nullity = nmod_mat_nullspace(ker, A);
nulrank = nmod_mat_rank(ker);
if (nullity != nulrank)
{
printf("FAIL:\n");
printf("rank(ker) != nullity!\n");
nmod_mat_print_pretty(A);
printf("\n");
abort();
}
if (nullity + r != n)
{
printf("FAIL:\n");
printf("nullity + rank != n\n");
nmod_mat_print_pretty(A);
printf("\n");
abort();
}
nmod_mat_mul(B, A, ker);
if (nmod_mat_rank(B) != 0)
{
printf("FAIL:\n");
printf("A * ker != 0\n");
nmod_mat_print_pretty(A);
printf("\n");
abort();
}
nmod_mat_clear(A);
nmod_mat_clear(ker);
nmod_mat_clear(B);
}
}
flint_randclear(state);
printf("PASS\n");
return 0;
}
int
main(void)
{
long i;
flint_rand_t state;
flint_randinit(state);
printf("mul....");
fflush(stdout);
for (i = 0; i < 10000; i++)
{
nmod_mat_t A, B, C, D;
mp_limb_t mod;
long m, k, n;
m = n_randint(state, 50);
k = n_randint(state, 50);
n = n_randint(state, 50);
/* We want to generate matrices with many entries close to half
or full limbs with high probability, to stress overflow handling */
switch (n_randint(state, 3))
{
case 0:
mod = n_randtest_not_zero(state);
break;
case 1:
mod = ULONG_MAX/2 + 1 - n_randbits(state, 4);
break;
case 2:
default:
mod = ULONG_MAX - n_randbits(state, 4);
break;
}
nmod_mat_init(A, m, n, mod);
nmod_mat_init(B, n, k, mod);
nmod_mat_init(C, m, k, mod);
nmod_mat_init(D, m, k, mod);
if (n_randint(state, 2))
nmod_mat_randtest(A, state);
else
nmod_mat_randfull(A, state);
if (n_randint(state, 2))
nmod_mat_randtest(B, state);
else
nmod_mat_randfull(B, state);
nmod_mat_randtest(C, state); /* make sure noise in the output is ok */
nmod_mat_mul(C, A, B);
nmod_mat_mul_check(D, A, B);
if (!nmod_mat_equal(C, D))
{
printf("FAIL: results not equal\n");
nmod_mat_print_pretty(A);
nmod_mat_print_pretty(B);
nmod_mat_print_pretty(C);
nmod_mat_print_pretty(D);
abort();
}
nmod_mat_clear(A);
nmod_mat_clear(B);
nmod_mat_clear(C);
nmod_mat_clear(D);
}
flint_randclear(state);
printf("PASS\n");
return 0;
}
int
main(void)
{
slong i;
FLINT_TEST_INIT(state);
flint_printf("solve_triu....");
fflush(stdout);
for (i = 0; i < 10 * flint_test_multiplier(); i++)
{
nmod_mat_t A, X, B, Y;
mp_limb_t m;
slong rows, cols;
int unit;
m = n_randtest_prime(state, 0);
rows = n_randint(state, 200);
cols = n_randint(state, 200);
unit = n_randint(state, 2);
nmod_mat_init(A, rows, rows, m);
nmod_mat_init(B, rows, cols, m);
nmod_mat_init(X, rows, cols, m);
nmod_mat_init(Y, rows, cols, m);
nmod_mat_randtriu(A, state, unit);
nmod_mat_randtest(X, state);
nmod_mat_mul(B, A, X);
/* Check Y = A^(-1) * (A * X) = X */
nmod_mat_solve_triu(Y, A, B, unit);
if (!nmod_mat_equal(Y, X))
{
flint_printf("FAIL!\n");
flint_printf("A:\n");
nmod_mat_print_pretty(A);
flint_printf("X:\n");
nmod_mat_print_pretty(X);
flint_printf("B:\n");
nmod_mat_print_pretty(B);
flint_printf("Y:\n");
nmod_mat_print_pretty(Y);
abort();
}
/* Check aliasing */
nmod_mat_solve_triu(B, A, B, unit);
if (!nmod_mat_equal(B, X))
{
flint_printf("FAIL!\n");
flint_printf("aliasing test failed");
flint_printf("A:\n");
nmod_mat_print_pretty(A);
flint_printf("B:\n");
nmod_mat_print_pretty(B);
abort();
}
nmod_mat_clear(A);
nmod_mat_clear(B);
nmod_mat_clear(X);
nmod_mat_clear(Y);
}
FLINT_TEST_CLEANUP(state);
flint_printf("PASS\n");
return 0;
}
