flint3-sys 3.2.3

Rust bindings to the FLINT C library
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133

/*
    Copyright (C) 2014 Abhinav Baid

    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 <gmp.h>
#include "fmpz_mat.h"
#include "fmpq.h"
#include "fmpq_vec.h"
#include "fmpq_mat.h"

int
fmpz_mat_is_reduced_with_removal(const fmpz_mat_t A, double delta, double eta,
                                 const fmpz_t gs_B, int newd)
{
    int res;
    slong i, j, k, d = A->r, n = A->c;
    fmpq_mat_t Aq, Bq, mu;
    mpq_t deltax, etax;
    fmpq_t deltaq, etaq, tmp, gs_Bq;

    if (d == 0 || d == 1)
        return 1;

    fmpq_mat_init(Aq, d, n);
    fmpq_mat_init(Bq, d, n);
    fmpq_mat_init(mu, d, d);

    mpq_init(deltax);
    mpq_init(etax);

    fmpq_init(deltaq);
    fmpq_init(etaq);
    fmpq_init(tmp);
    fmpq_init(gs_Bq);

    mpq_set_d(deltax, delta);
    mpq_set_d(etax, eta);
    fmpq_set_mpq(deltaq, deltax);
    fmpq_set_mpq(etaq, etax);
    mpq_clears(deltax, etax, NULL);

    fmpq_mat_set_fmpz_mat(Aq, A);

    fmpz_set(fmpq_numref(gs_Bq), gs_B);
    fmpz_one(fmpq_denref(gs_Bq));

    for (j = 0; j < n; j++)
    {
        fmpq_set(fmpq_mat_entry(Bq, 0, j), fmpq_mat_entry(Aq, 0, j));
    }
    /* diagonal of mu stores the squared GS norms */
    _fmpq_vec_dot(fmpq_mat_entry(mu, 0, 0), Bq->rows[0], Bq->rows[0], n);
    if (newd == 0 && fmpq_cmp(fmpq_mat_entry(mu, 0, 0), gs_Bq) < 0)
    {
        res = 0;
        goto cleanup;
    }

    for (i = 1; i < d; i++)
    {
        for (j = 0; j < n; j++)
        {
            fmpq_set(fmpq_mat_entry(Bq, i, j), fmpq_mat_entry(Aq, i, j));
        }

        for (j = 0; j < i; j++)
        {
            _fmpq_vec_dot(tmp, Aq->rows[i], Bq->rows[j], n);

            /* avoid division by zero */
            if (fmpq_is_zero(fmpq_mat_entry(mu, j, j)))
            {
                res = 0;
                goto cleanup;
            }

            fmpq_div(fmpq_mat_entry(mu, i, j), tmp, fmpq_mat_entry(mu, j, j));

            for (k = 0; k < n; k++)
            {
                fmpq_submul(fmpq_mat_entry(Bq, i, k),
                            fmpq_mat_entry(mu, i, j), fmpq_mat_entry(Bq, j, k));
            }
            if (i < newd)
            {
                fmpq_abs(tmp, fmpq_mat_entry(mu, i, j));
                if (fmpq_cmp(tmp, etaq) > 0)    /* check size reduction */
                {
                    res = 0;
                    goto cleanup;
                }
            }
        }
        _fmpq_vec_dot(fmpq_mat_entry(mu, i, i), Bq->rows[i], Bq->rows[i], n);
        if (i >= newd && fmpq_cmp(fmpq_mat_entry(mu, i, i), gs_Bq) < 0) /* check removals */
        {
            res = 0;
            goto cleanup;
        }
        if (i < newd)
        {
            fmpq_set(tmp, deltaq);
            fmpq_submul(tmp, fmpq_mat_entry(mu, i, i - 1),
                             fmpq_mat_entry(mu, i, i - 1));
            fmpq_mul(tmp, tmp, fmpq_mat_entry(mu, i - 1, i - 1));
            if (fmpq_cmp(tmp, fmpq_mat_entry(mu, i, i)) > 0)    /* check Lovasz condition */
            {
                res = 0;
                goto cleanup;
            }
        }
    }

    res = 1;

cleanup:

    fmpq_mat_clear(Aq);
    fmpq_mat_clear(Bq);
    fmpq_mat_clear(mu);
    fmpq_clear(deltaq);
    fmpq_clear(etaq);
    fmpq_clear(tmp);
    fmpq_clear(gs_Bq);
    return res;
}