flint-sys 0.9.0

Bindings to the FLINT C library
Documentation 
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
134
135
136
137
138
139
140
141
142
143
144

/*
    Copyright (C) 2018 arbguest

    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 "arb.h"
#include "arb_mat.h"

static int
_arb_mat_solve_c(arb_mat_t X, const arb_mat_t A, const arb_mat_t B, slong prec)
{
    int result;
    slong m, n;
    arb_mat_t I, R;

    n = arb_mat_nrows(A);
    m = arb_mat_ncols(X);

    if (n == 0 || m == 0)
        return 1;

    arb_mat_init(I, n, n);
    arb_mat_init(R, n, n);

    arb_mat_one(I);
    result = arb_mat_approx_solve(R, A, I, prec);
    if (result)
    {
        arb_mat_t RA, RB;

        arb_mat_init(RA, n, n);
        arb_mat_init(RB, n, m);

        arb_mat_mul(RA, R, A, prec);
        arb_mat_mul(RB, R, B, prec);

        result = arb_mat_solve_lu(X, RA, RB, prec);

        arb_mat_clear(RA);
        arb_mat_clear(RB);
    }

    arb_mat_clear(I);
    arb_mat_clear(R);

    return result;
}

static int
_arb_mat_solve_d(arb_mat_t X, const arb_mat_t A, const arb_mat_t B, slong prec)
{
    int result;
    slong m, n;
    arb_mat_t I, R;

    n = arb_mat_nrows(A);
    m = arb_mat_ncols(X);

    if (n == 0 || m == 0)
        return 1;

    arb_mat_init(I, n, n);
    arb_mat_init(R, n, n);

    arb_mat_one(I);
    result = arb_mat_approx_solve(R, A, I, prec);
    if (result)
    {
        arb_mat_t RA, RB, E;
        mag_t d;

        arb_mat_init(RA, n, n);
        arb_mat_init(RB, n, m);
        arb_mat_init(E, n, n);
        mag_init(d);

        arb_mat_mul(RA, R, A, prec);
        arb_mat_mul(RB, R, B, prec);
        arb_mat_sub(E, I, RA, prec);
        arb_mat_bound_inf_norm(d, E);

        if (mag_cmp_2exp_si(d, 0) < 0)
        {
            slong i, j;
            mag_t e, err;

            mag_init(e);
            mag_init(err);

            mag_geom_series(d, d, 1);
            arb_mat_set(X, RB);

            for (j = 0; j < m; j++)
            {
                mag_zero(err);
                for (i = 0; i < n; i++)
                {
                    arb_get_mag(e, arb_mat_entry(RB, i, j));
                    mag_max(err, err, e);
                }
                mag_mul(err, err, d);
                for (i = 0; i < n; i++)
                {
                    arb_add_error_mag(arb_mat_entry(X, i, j), err);
                }
            }

            mag_clear(e);
            mag_clear(err);
        }
        else
        {
            result = arb_mat_solve_lu(X, RA, RB, prec);
        }

        arb_mat_clear(RA);
        arb_mat_clear(RB);
        arb_mat_clear(E);
        mag_clear(d);
    }

    arb_mat_clear(I);
    arb_mat_clear(R);

    return result;
}

int
arb_mat_solve_precond(arb_mat_t X, const arb_mat_t A, const arb_mat_t B, slong prec)
{
    slong n = arb_mat_nrows(A);
    slong m = arb_mat_ncols(B);

    if (m < 0.1 * n + 1)
        return _arb_mat_solve_c(X, A, B, prec);
    else
        return _arb_mat_solve_d(X, A, B, prec);
}