flint-sys 0.9.0

Bindings to the FLINT C library
Documentation 
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/*
    Copyright (C) 2023 Jean Kieffer

    This file is part of FLINT.

    FLINT is free software: you can redistribute it and/or modify it under
    the terms of the GNU Lesser General Public License (LGPL) as published
    by the Free Software Foundation; either version 3 of the License, or
    (at your option) any later version.  See <https://www.gnu.org/licenses/>.
*/

#include "test_helpers.h"
#include "acb.h"
#include "acb_mat.h"
#include "acb_theta.h"

TEST_FUNCTION_START(acb_theta_ql_jet_error, state)
{
    slong iter;

    /* Test: compute theta values at two points in a common ball */
    for (iter = 0; iter < 10 * flint_test_multiplier(); iter++)
    {
        slong g = 1 + n_randint(state, 3);
        slong n = 1 << (2 * g);
        slong ord = n_randint(state, 2);
        slong bits = 2;
        slong nb = acb_theta_jet_nb(ord, g);
        slong nb_der = acb_theta_jet_nb(ord + 2, g);
        slong lprec = ACB_THETA_LOW_PREC;
        slong mprec = ACB_THETA_LOW_PREC + n_randint(state, 50);
        slong hprec = mprec + n_randint(state, 50);
        acb_mat_t tau1, tau2, tau3;
        acb_ptr z1, z2, z3, dth;
        acb_theta_ctx_tau_t ctx_tau;
        acb_theta_ctx_z_t ctx_z;
        arb_ptr err;
        acb_ptr d1, d2, test;
        acb_t x;
        slong j, k;

        acb_mat_init(tau1, g, g);
        acb_mat_init(tau2, g, g);
        acb_mat_init(tau3, g, g);
        z1 = _acb_vec_init(g);
        z2 = _acb_vec_init(g);
        z3 = _acb_vec_init(g);
        acb_theta_ctx_tau_init(ctx_tau, 0, g);
        acb_theta_ctx_z_init(ctx_z, g);
        dth = _acb_vec_init(n * nb_der);
        err = _arb_vec_init(n * nb);
        d1 = _acb_vec_init(n * nb);
        d2 = _acb_vec_init(n * nb);
        test = _acb_vec_init(n * nb);
        acb_init(x);

        acb_siegel_randtest_reduced(tau1, state, hprec, bits);
        acb_siegel_randtest_vec_reduced(z1, state, 1, tau1, 0, hprec);

        for (j = 0; j < g; j++)
        {
            for (k = j; k < g; k++)
            {
                acb_set(acb_mat_entry(tau1, k, j), acb_mat_entry(tau1, j, k));
                acb_urandom(x, state, hprec);
                acb_mul_2exp_si(x, x, -mprec);
                acb_add(acb_mat_entry(tau2, j, k), acb_mat_entry(tau1, j, k), x, hprec);
                acb_set(acb_mat_entry(tau2, k, j), acb_mat_entry(tau2, j, k));
                acb_union(acb_mat_entry(tau3, j, k), acb_mat_entry(tau1, j, k),
                    acb_mat_entry(tau2, j, k), hprec);
                acb_set(acb_mat_entry(tau3, k, j), acb_mat_entry(tau3, j, k));
            }
            acb_urandom(x, state, hprec);
            acb_mul_2exp_si(x, x, -mprec);
            acb_add(&z2[j], &z1[j], x, hprec);
            acb_union(&z3[j], &z1[j], &z2[j], hprec);
        }

        if (!acb_mat_contains(tau3, tau2) || !acb_mat_contains(tau3, tau1)
            || !_acb_vec_contains(z3, z1, g) || !_acb_vec_contains(z3, z1, g))
        {
            flint_printf("FAIL (input)\n");
            flint_printf("mprec = %wd, hprec = %wd\n", mprec, hprec);
            acb_mat_printd(tau1, 5);
            acb_mat_printd(tau2, 5);
            acb_mat_printd(tau3, 5);
            _acb_vec_printd(z1, g, 5);
            _acb_vec_printd(z2, g, 5);
            _acb_vec_printd(z3, g, 5);
            flint_abort();
        }

        acb_theta_ctx_tau_set(ctx_tau, tau1, hprec);
        acb_theta_ctx_z_set(ctx_z, z1, ctx_tau, hprec);
        acb_theta_sum_jet(d1, ctx_z, 1, ctx_tau, ord, 1, 1, hprec);

        acb_theta_ctx_tau_set(ctx_tau, tau2, hprec);
        acb_theta_ctx_z_set(ctx_z, z2, ctx_tau, hprec);
        acb_theta_sum_jet(d2, ctx_z, 1, ctx_tau, ord, 1, 1, hprec);

        acb_theta_ctx_tau_set(ctx_tau, tau3, lprec);
        acb_theta_ctx_z_set(ctx_z, z3, ctx_tau, lprec);
        acb_theta_sum_jet(dth, ctx_z, 1, ctx_tau, ord + 2, 1, 1, lprec);

        for (k = 0; k < n; k++)
        {
            acb_theta_ql_jet_error(err + k * nb, z3, tau3, dth + k * nb_der, ord, lprec);
        }
         /* Errors are wrt midpoint, so multiply by 2 */
        _arb_vec_scalar_mul_2exp_si(err, err, n * nb, 1);

        _acb_vec_set(test, d1, n * nb);
        for (k = 0; k < n * nb; k++)
        {
            acb_add_error_arb(&test[k], &err[k]);
        }

        if (!_acb_vec_overlaps(test, d2, n * nb)
            || !_acb_vec_is_finite(test, n * nb)
            || !_acb_vec_is_finite(d2, n * nb))
        {
            flint_printf("FAIL (bounds)\n");
            flint_printf("values:\n");
            _acb_vec_printd(d1, n * nb, 5);
            _acb_vec_printd(d2, n * nb, 5);
            flint_printf("bounds:\n");
            _arb_vec_printd(err, n * nb, 5);
            flint_printf("difference:\n");
            _acb_vec_sub(d1, d1, d2, n * nb, hprec);
            _acb_vec_printd(d1, n * nb, 5);
            flint_abort();
        }

        acb_mat_clear(tau1);
        acb_mat_clear(tau2);
        acb_mat_clear(tau3);
        _acb_vec_clear(z1, g);
        _acb_vec_clear(z2, g);
        _acb_vec_clear(z3, g);
        acb_theta_ctx_tau_clear(ctx_tau);
        acb_theta_ctx_z_clear(ctx_z);
        _acb_vec_clear(dth, n * nb_der);
        _arb_vec_clear(err, n * nb);
        _acb_vec_clear(d1, n * nb);
        _acb_vec_clear(d2, n * nb);
        _acb_vec_clear(test, n * nb);
        acb_clear(x);
    }

    TEST_FUNCTION_END(state);
}