int main() { slong iter; flint_rand_t state; flint_printf("trace...."); fflush(stdout); flint_randinit(state); /* check that the acb trace contains the fmpq trace */ for (iter = 0; iter < 10000; iter++) { fmpq_mat_t Q; fmpq_t Qtrace; acb_mat_t A; acb_t Atrace; slong n, qbits, prec; n = n_randint(state, 8); qbits = 1 + n_randint(state, 100); prec = 2 + n_randint(state, 200); fmpq_mat_init(Q, n, n); fmpq_init(Qtrace); acb_mat_init(A, n, n); acb_init(Atrace); fmpq_mat_randtest(Q, state, qbits); fmpq_mat_trace(Qtrace, Q); acb_mat_set_fmpq_mat(A, Q, prec); acb_mat_trace(Atrace, A, prec); if (!acb_contains_fmpq(Atrace, Qtrace)) { 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("Qtrace = \n"); fmpq_print(Qtrace); flint_printf("\n\n"); flint_printf("A = \n"); acb_mat_printd(A, 15); flint_printf("\n\n"); flint_printf("Atrace = \n"); acb_printd(Atrace, 15); flint_printf("\n\n"); flint_printf("Atrace = \n"); acb_print(Atrace); flint_printf("\n\n"); abort(); } fmpq_mat_clear(Q); fmpq_clear(Qtrace); acb_mat_clear(A); acb_clear(Atrace); } /* check trace(A*B) = trace(B*A) */ for (iter = 0; iter < 10000; iter++) { slong m, n, prec; acb_mat_t a, b, ab, ba; acb_t trab, trba; prec = 2 + n_randint(state, 200); m = n_randint(state, 10); n = n_randint(state, 10); acb_mat_init(a, m, n); acb_mat_init(b, n, m); acb_mat_init(ab, m, m); acb_mat_init(ba, n, n); acb_init(trab); acb_init(trba); acb_mat_randtest(a, state, 2 + n_randint(state, 100), 10); acb_mat_randtest(b, state, 2 + n_randint(state, 100), 10); acb_mat_mul(ab, a, b, prec); acb_mat_mul(ba, b, a, prec); acb_mat_trace(trab, ab, prec); acb_mat_trace(trba, ba, prec); if (!acb_overlaps(trab, trba)) { flint_printf("FAIL (overlap, iter = %wd)\n", iter); flint_printf("m = %wd, n = %wd, prec = %wd\n", m, n, prec); flint_printf("\n"); flint_printf("a = \n"); acb_mat_printd(a, 15); flint_printf("\n\n"); flint_printf("b = \n"); acb_mat_printd(b, 15); flint_printf("\n\n"); flint_printf("ab = \n"); acb_mat_printd(ab, 15); flint_printf("\n\n"); flint_printf("ba = \n"); acb_mat_printd(ba, 15); flint_printf("\n\n"); flint_printf("trace(ab) = \n"); acb_printd(trab, 15); flint_printf("\n\n"); flint_printf("trace(ba) = \n"); acb_printd(trba, 15); flint_printf("\n\n"); } acb_clear(trab); acb_clear(trba); acb_mat_clear(a); acb_mat_clear(b); acb_mat_clear(ab); acb_mat_clear(ba); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; }
int main(void) { long i; flint_rand_t state; printf("trace...."); fflush(stdout); flint_randinit(state); /* Test trace(AB) = trace(BA) */ for (i = 0; i < 1000; i++) { fmpq_mat_t A, B, AB, BA; fmpq_t trab, trba; long m, n; m = n_randint(state, 10); n = n_randint(state, 10); fmpq_mat_init(A, m, n); fmpq_mat_init(B, n, m); fmpq_mat_init(AB, m, m); fmpq_mat_init(BA, n, n); fmpq_init(trab); fmpq_init(trba); fmpq_mat_randtest(A, state, 1 + n_randint(state, 100)); fmpq_mat_randtest(B, state, 1 + n_randint(state, 100)); fmpq_mat_mul(AB, A, B); fmpq_mat_mul(BA, B, A); fmpq_mat_trace(trab, AB); fmpq_mat_trace(trba, BA); if (!fmpq_equal(trab, trba)) { printf("FAIL:\n"); fmpq_mat_print(A), printf("\n"); fmpq_mat_print(B), printf("\n"); fmpq_mat_print(AB), printf("\n"); fmpq_mat_print(BA), printf("\n"); printf("tr(AB): "), fmpq_print(trab), printf("\n"); printf("tr(BA): "), fmpq_print(trba), printf("\n"); abort(); } fmpq_mat_clear(A); fmpq_mat_clear(B); fmpq_mat_clear(AB); fmpq_mat_clear(BA); fmpq_clear(trab); fmpq_clear(trba); } flint_randclear(state); _fmpz_cleanup(); printf("PASS\n"); return 0; }