Exemple #1
0
int main()
{
    long iter;
    flint_rand_t state;

    printf("theta....");
    fflush(stdout);

    flint_randinit(state);

    /* Test consistency with/without transform */
    for (iter = 0; iter < 10000; iter++)
    {
        acb_t t1, t2, t3, t4, t1b, t2b, t3b, t4b, z, tau;
        long prec0, prec1, prec2, e0;

        acb_init(t1); acb_init(t2); acb_init(t3); acb_init(t4);
        acb_init(t1b); acb_init(t2b); acb_init(t3b); acb_init(t4b);
        acb_init(z);
        acb_init(tau);

        prec0 = 2 + n_randint(state, 2000);
        prec1 = 2 + n_randint(state, 2000);
        prec2 = 2 + n_randint(state, 2000);
        e0 = 1 + n_randint(state, 100);

        acb_randtest(tau, state, prec0, e0);
        acb_randtest(z, state, prec0, e0);

        acb_modular_theta(t1, t2, t3, t4, z, tau, prec1);
        acb_modular_theta_notransform(t1b, t2b, t3b, t4b, z, tau, prec2);

        if (!acb_overlaps(t1, t1b) || !acb_overlaps(t2, t2b) ||
            !acb_overlaps(t3, t3b) || !acb_overlaps(t4, t4b))
        {
            printf("FAIL (overlap)\n");
            printf("z = "); acb_printd(z, 25); printf("\n\n");
            printf("tau = "); acb_printd(tau, 25); printf("\n\n");

            printf("t1  = "); acb_printd(t1, 15); printf("\n\n");
            printf("t1b = "); acb_printd(t1b, 15); printf("\n\n");

            printf("t2  = "); acb_printd(t2, 15); printf("\n\n");
            printf("t2b = "); acb_printd(t2b, 15); printf("\n\n");

            printf("t3  = "); acb_printd(t3, 15); printf("\n\n");
            printf("t3b = "); acb_printd(t3b, 15); printf("\n\n");

            printf("t4  = "); acb_printd(t4, 15); printf("\n\n");
            printf("t4b = "); acb_printd(t4b, 15); printf("\n\n");

            abort();
        }

        acb_clear(t1); acb_clear(t2); acb_clear(t3); acb_clear(t4);
        acb_clear(t1b); acb_clear(t2b); acb_clear(t3b); acb_clear(t4b);
        acb_clear(z);
        acb_clear(tau);
    }

    flint_randclear(state);
    flint_cleanup();
    printf("PASS\n");
    return EXIT_SUCCESS;
}
Exemple #2
0
void
acb_elliptic_p_jet(acb_ptr r, const acb_t z, const acb_t tau, slong len, slong prec)
{
    acb_t t01, t02, t03, t04;
    acb_ptr tz1, tz2, tz3, tz4;
    acb_t t;
    int real;
    slong k;

    if (len < 1)
        return;

    if (len == 1)
    {
        acb_elliptic_p(r, z, tau, prec);
        return;
    }

    real = acb_is_real(z) && arb_is_int_2exp_si(acb_realref(tau), -1) &&
                arb_is_positive(acb_imagref(tau));

    acb_init(t);

    acb_init(t01);
    acb_init(t02);
    acb_init(t03);
    acb_init(t04);

    tz1 = _acb_vec_init(len);
    tz2 = _acb_vec_init(len);
    tz3 = _acb_vec_init(len);
    tz4 = _acb_vec_init(len);

    acb_modular_theta_jet(tz1, tz2, tz3, tz4, z, tau, len, prec);

    /* [theta_4(z) / theta_1(z)]^2 */
    _acb_poly_div_series(tz2, tz4, len, tz1, len, len, prec);
    _acb_poly_mullow(tz1, tz2, len, tz2, len, len, prec);

    acb_zero(t);
    acb_modular_theta(t01, t02, t03, t04, t, tau, prec);

    /* [theta_2(0) * theta_3(0)] ^2 */
    acb_mul(t, t02, t03, prec);
    acb_mul(t, t, t, prec);
    _acb_vec_scalar_mul(tz1, tz1, len, t, prec);

    /* - [theta_2(0)^4 + theta_3(0)^4] / 3 */
    acb_pow_ui(t02, t02, 4, prec);
    acb_pow_ui(t03, t03, 4, prec);
    acb_add(t, t02, t03, prec);
    acb_div_ui(t, t, 3, prec);
    acb_sub(tz1, tz1, t, prec);

    /* times pi^2 */
    acb_const_pi(t, prec);
    acb_mul(t, t, t, prec);
    _acb_vec_scalar_mul(r, tz1, len, t, prec);

    if (real)
    {
        for (k = 0; k < len; k++)
            arb_zero(acb_imagref(r + k));
    }

    acb_clear(t);

    acb_clear(t01);
    acb_clear(t02);
    acb_clear(t03);
    acb_clear(t04);

    _acb_vec_clear(tz1, len);
    _acb_vec_clear(tz2, len);
    _acb_vec_clear(tz3, len);
    _acb_vec_clear(tz4, len);
}