int main()
{
slong iter;
flint_rand_t state;
flint_printf("dft....");
fflush(stdout);
flint_randinit(state);
for (iter = 0; iter < 100 * arb_test_multiplier(); iter++)
{
acb_mat_t A, Ainv, AT;
slong n, prec;
n = n_randint(state, 10);
prec = 53 + n_randint(state, 30);
acb_mat_init(A, n, n);
acb_mat_init(Ainv, n, n);
acb_mat_init(AT, n, n);
acb_mat_randtest(A, state, 100, 10);
acb_mat_dft(A, 0, prec);
if (!acb_mat_inv(Ainv, A, prec))
{
flint_printf("FAIL: small DFT matrix (n = %wd) not invertible\n", n);
flint_abort();
}
acb_mat_conjugate_transpose(AT, A);
if (!acb_mat_overlaps(AT, Ainv))
{
flint_printf("FAIL: overlap (n = %wd)\n", n);
flint_printf("A = \n"); acb_mat_printd(A, 15); flint_printf("\n\n");
flint_printf("Ainv = \n"); acb_mat_printd(Ainv, 15); flint_printf("\n\n");
flint_printf("AT = \n"); acb_mat_printd(AT, 15); flint_printf("\n\n");
flint_abort();
}
acb_mat_clear(A);
acb_mat_clear(Ainv);
acb_mat_clear(AT);
}
flint_randclear(state);
flint_cleanup();
flint_printf("PASS\n");
return EXIT_SUCCESS;
}
int main()
{
slong iter;
flint_rand_t state;
flint_printf("mul....");
fflush(stdout);
flint_randinit(state);
for (iter = 0; iter < 10000 * arb_test_multiplier(); iter++)
{
slong m, n, k, qbits1, qbits2, rbits1, rbits2, rbits3;
fmpq_mat_t A, B, C;
acb_mat_t a, b, c, d;
qbits1 = 2 + n_randint(state, 200);
qbits2 = 2 + n_randint(state, 200);
rbits1 = 2 + n_randint(state, 200);
rbits2 = 2 + n_randint(state, 200);
rbits3 = 2 + n_randint(state, 200);
m = n_randint(state, 10);
n = n_randint(state, 10);
k = n_randint(state, 10);
fmpq_mat_init(A, m, n);
fmpq_mat_init(B, n, k);
fmpq_mat_init(C, m, k);
acb_mat_init(a, m, n);
acb_mat_init(b, n, k);
acb_mat_init(c, m, k);
acb_mat_init(d, m, k);
fmpq_mat_randtest(A, state, qbits1);
fmpq_mat_randtest(B, state, qbits2);
fmpq_mat_mul(C, A, B);
acb_mat_set_fmpq_mat(a, A, rbits1);
acb_mat_set_fmpq_mat(b, B, rbits2);
acb_mat_mul(c, a, b, rbits3);
if (!acb_mat_contains_fmpq_mat(c, C))
{
flint_printf("FAIL\n\n");
flint_printf("m = %wd, n = %wd, k = %wd, bits3 = %wd\n", m, n, k, rbits3);
flint_printf("A = "); fmpq_mat_print(A); flint_printf("\n\n");
flint_printf("B = "); fmpq_mat_print(B); flint_printf("\n\n");
flint_printf("C = "); fmpq_mat_print(C); flint_printf("\n\n");
flint_printf("a = "); acb_mat_printd(a, 15); flint_printf("\n\n");
flint_printf("b = "); acb_mat_printd(b, 15); flint_printf("\n\n");
flint_printf("c = "); acb_mat_printd(c, 15); flint_printf("\n\n");
abort();
}
/* test aliasing with a */
if (acb_mat_nrows(a) == acb_mat_nrows(c) &&
acb_mat_ncols(a) == acb_mat_ncols(c))
{
acb_mat_set(d, a);
acb_mat_mul(d, d, b, rbits3);
if (!acb_mat_equal(d, c))
{
flint_printf("FAIL (aliasing 1)\n\n");
abort();
}
}
/* test aliasing with b */
if (acb_mat_nrows(b) == acb_mat_nrows(c) &&
acb_mat_ncols(b) == acb_mat_ncols(c))
{
acb_mat_set(d, b);
acb_mat_mul(d, a, d, rbits3);
if (!acb_mat_equal(d, c))
{
flint_printf("FAIL (aliasing 2)\n\n");
abort();
}
}
fmpq_mat_clear(A);
fmpq_mat_clear(B);
fmpq_mat_clear(C);
acb_mat_clear(a);
acb_mat_clear(b);
acb_mat_clear(c);
acb_mat_clear(d);
}
/* check algebraic properties like associativity and distributivity */
for (iter = 0; iter < 1000 * arb_test_multiplier(); iter++)
{
slong m, n, k, l;
slong rbits;
acb_mat_t a, b, c, d, ab, ac, bd, cd, s;
rbits = 2 + n_randint(state, 200);
m = n_randint(state, 10);
n = n_randint(state, 10);
k = n_randint(state, 10);
l = n_randint(state, 10);
_acb_mat_init_randtest(a, m, n, state);
_acb_mat_init_randtest(b, n, k, state);
_acb_mat_init_randtest(c, n, k, state);
_acb_mat_init_randtest(d, k, l, state);
acb_mat_init(ab, m, k);
acb_mat_init(ac, m, k);
acb_mat_init(bd, n, l);
acb_mat_init(cd, n, l);
acb_mat_init(s, n, k);
acb_mat_mul(ab, a, b, rbits);
acb_mat_mul(ac, a, c, rbits);
acb_mat_mul(bd, b, d, rbits);
acb_mat_mul(cd, c, d, rbits);
acb_mat_add(s, b, c, rbits);
/* check associativity of multiplication */
/* (A*B)*D = A*(B*D) */
{
acb_mat_t lhs, rhs;
acb_mat_init(lhs, m, l);
acb_mat_init(rhs, m, l);
acb_mat_mul(lhs, ab, d, rbits);
acb_mat_mul(rhs, a, bd, rbits);
if (!acb_mat_overlaps(lhs, rhs))
{
flint_printf("FAIL\n\n");
flint_printf("m, n, k, l = %wd, %wd, %wd, %wd\n", m, n, k, l);
flint_printf("rbits = %wd\n", rbits);
_acb_mat_nprintd("a", a);
_acb_mat_nprintd("b", b);
_acb_mat_nprintd("d", d);
_acb_mat_nprintd("(a*b)*d", lhs);
_acb_mat_nprintd("a*(b*d)", rhs);
abort();
}
acb_mat_clear(lhs);
acb_mat_clear(rhs);
}
/* check left distributivity of multiplication over addition */
/* A*(B + C) = A*B + A*C */
{
acb_mat_t lhs, rhs;
acb_mat_init(lhs, m, k);
acb_mat_init(rhs, m, k);
acb_mat_mul(lhs, a, s, rbits);
acb_mat_add(rhs, ab, ac, rbits);
if (!acb_mat_overlaps(lhs, rhs))
{
flint_printf("FAIL\n\n");
flint_printf("m, n, k, l = %wd, %wd, %wd, %wd\n", m, n, k, l);
flint_printf("rbits = %wd\n", rbits);
_acb_mat_nprintd("a", a);
_acb_mat_nprintd("b", b);
_acb_mat_nprintd("c", c);
_acb_mat_nprintd("a*(b + c)", lhs);
_acb_mat_nprintd("a*b + b*c", rhs);
abort();
}
acb_mat_clear(lhs);
acb_mat_clear(rhs);
}
/* check right distributivity of multiplication over addition */
/* (B + C)*D = B*D + C*D */
{
acb_mat_t lhs, rhs;
acb_mat_init(lhs, n, l);
acb_mat_init(rhs, n, l);
acb_mat_mul(lhs, s, d, rbits);
acb_mat_add(rhs, bd, cd, rbits);
if (!acb_mat_overlaps(lhs, rhs))
{
flint_printf("FAIL\n\n");
flint_printf("m, n, k, l = %wd, %wd, %wd, %wd\n", m, n, k, l);
flint_printf("rbits = %wd\n", rbits);
_acb_mat_nprintd("b", b);
_acb_mat_nprintd("c", c);
_acb_mat_nprintd("d", d);
_acb_mat_nprintd("(b + c)*d", lhs);
_acb_mat_nprintd("b*d + c*d", rhs);
abort();
}
acb_mat_clear(lhs);
acb_mat_clear(rhs);
}
/* check left multiplicative identity I*D = D */
{
acb_mat_t one, lhs;
acb_mat_init(one, k, k);
acb_mat_init(lhs, k, l);
acb_mat_one(one);
acb_mat_mul(lhs, one, d, rbits);
if (!acb_mat_contains(lhs, d))
{
flint_printf("FAIL\n\n");
flint_printf("k = %wd, l = %wd\n", k, l);
flint_printf("rbits = %wd\n", rbits);
_acb_mat_nprintd("identity * d", lhs);
_acb_mat_nprintd("d", d);
abort();
}
acb_mat_clear(one);
acb_mat_clear(lhs);
}
/* check right multiplicative identity A*I = A */
{
acb_mat_t one, lhs;
acb_mat_init(one, n, n);
acb_mat_init(lhs, m, n);
acb_mat_one(one);
acb_mat_mul(lhs, a, one, rbits);
if (!acb_mat_contains(lhs, a))
{
flint_printf("FAIL\n\n");
flint_printf("m = %wd, n = %wd\n", m, n);
flint_printf("rbits = %wd\n", rbits);
_acb_mat_nprintd("a * identity", lhs);
_acb_mat_nprintd("a", a);
abort();
}
acb_mat_clear(one);
acb_mat_clear(lhs);
}
acb_mat_clear(a);
acb_mat_clear(b);
acb_mat_clear(c);
acb_mat_clear(d);
acb_mat_clear(ab);
acb_mat_clear(ac);
acb_mat_clear(bd);
acb_mat_clear(cd);
acb_mat_clear(s);
}
flint_randclear(state);
flint_cleanup();
flint_printf("PASS\n");
return EXIT_SUCCESS;
}
int main()
{
slong iter;
flint_rand_t state;
flint_printf("exp....");
fflush(stdout);
flint_randinit(state);
/* check exp(A)*exp(c*A) = exp((1+c)*A) */
for (iter = 0; iter < 500 * arb_test_multiplier(); iter++)
{
acb_mat_t A, E, F, EF, G;
fmpq_mat_t Q;
acb_t c, d;
slong n, qbits, prec;
n = n_randint(state, 5);
qbits = 2 + n_randint(state, 300);
prec = 2 + n_randint(state, 300);
acb_init(c);
acb_init(d);
fmpq_mat_init(Q, n, n);
acb_mat_init(A, n, n);
acb_mat_init(E, n, n);
acb_mat_init(F, n, n);
acb_mat_init(EF, n, n);
acb_mat_init(G, n, n);
_fmpq_mat_randtest_for_exp(Q, state, qbits);
acb_mat_set_fmpq_mat(A, Q, prec);
acb_mat_exp(E, A, prec);
acb_randtest(c, state, prec, 10);
acb_mat_scalar_mul_acb(F, A, c, prec);
acb_mat_exp(F, F, prec);
acb_add_ui(d, c, 1, prec);
acb_mat_scalar_mul_acb(G, A, d, prec);
acb_mat_exp(G, G, prec);
acb_mat_mul(EF, E, F, prec);
if (!acb_mat_overlaps(EF, G))
{
flint_printf("FAIL\n\n");
flint_printf("n = %wd, prec = %wd\n", n, prec);
flint_printf("c = \n"); acb_printd(c, 15); flint_printf("\n\n");
flint_printf("A = \n"); acb_mat_printd(A, 15); flint_printf("\n\n");
flint_printf("E = \n"); acb_mat_printd(E, 15); flint_printf("\n\n");
flint_printf("F = \n"); acb_mat_printd(F, 15); flint_printf("\n\n");
flint_printf("E*F = \n"); acb_mat_printd(EF, 15); flint_printf("\n\n");
flint_printf("G = \n"); acb_mat_printd(G, 15); flint_printf("\n\n");
flint_abort();
}
acb_clear(c);
acb_clear(d);
fmpq_mat_clear(Q);
acb_mat_clear(A);
acb_mat_clear(E);
acb_mat_clear(F);
acb_mat_clear(EF);
acb_mat_clear(G);
}
flint_randclear(state);
flint_cleanup();
flint_printf("PASS\n");
return EXIT_SUCCESS;
}
