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
145
146
147
148
149
150
151

/*
    Copyright (C) 2016 Arb authors

    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 void
_arb_sqr(arb_t dest, const arb_t src, slong prec)
{
    arb_mul(dest, src, src, prec);
}

int
_arb_mat_ldl_inplace(arb_mat_t A, slong prec)
{
    slong n, i, j, k;
    arb_t tmp;
    int result;

    n = arb_mat_nrows(A);
    arb_init(tmp);

    result = 1;
    for (i = 0; i < n && result; i++)
    {
        for (j = 0; j < i; j++)
        {
            for (k = 0; k < j; k++)
            {
                arb_mul(tmp,
                        arb_mat_entry(A, i, k),
                        arb_mat_entry(A, j, k), prec);
                arb_submul(arb_mat_entry(A, i, j),
                           arb_mat_entry(A, k, k), tmp, prec);
            }
            arb_div(arb_mat_entry(A, i, j),
                    arb_mat_entry(A, i, j),
                    arb_mat_entry(A, j, j), prec);
        }
        for (k = 0; k < i; k++)
        {
            _arb_sqr(tmp, arb_mat_entry(A, i, k), prec);
            arb_submul(arb_mat_entry(A, i, i),
                       arb_mat_entry(A, k, k), tmp, prec);
        }
        if (!arb_is_positive(arb_mat_entry(A, i, i)))
            result = 0;
    }

    arb_clear(tmp);

    return result;
}

int
_arb_mat_ldl_golub_and_van_loan(arb_mat_t A, slong prec)
{
    slong n, i, j, k;
    arb_struct *v;
    int result;

    n = arb_mat_nrows(A);
    v = _arb_vec_init(n);

    result = 1;
    for (j = 0; j < n; j++)
    {
        for (i = 0; i < j; i++)
        {
            arb_mul(v + i,
                    arb_mat_entry(A, j, i),
                    arb_mat_entry(A, i, i), prec);
        }

        arb_set(v + j, arb_mat_entry(A, j, j));
        for (i = 0; i < j; i++)
        {
            arb_submul(v + j, arb_mat_entry(A, j, i), v + i, prec);
        }

        if (!arb_is_positive(v + j))
        {
            result = 0;
            break;
        }

        arb_set(arb_mat_entry(A, j, j), v + j);
        for (i = j + 1; i < n; i++)
        {
            for (k = 0; k < j; k++)
            {
                arb_submul(arb_mat_entry(A, i, j),
                           arb_mat_entry(A, i, k), v + k, prec);
            }
            arb_div(arb_mat_entry(A, i, j),
                    arb_mat_entry(A, i, j), v + j, prec);
        }
    }

    _arb_vec_clear(v, n);

    return result;
}

int
arb_mat_ldl(arb_mat_t L, const arb_mat_t A, slong prec)
{
    slong n;
    int result;

    if (!arb_mat_is_square(A))
    {
        flint_throw(FLINT_ERROR, "arb_mat_ldl: a square matrix is required\n");
    }

    if (arb_mat_nrows(L) != arb_mat_nrows(A) ||
        arb_mat_ncols(L) != arb_mat_ncols(A))
    {
        flint_throw(FLINT_ERROR, "arb_mat_ldl: incompatible dimensions\n");
    }

    if (arb_mat_is_empty(A))
        return 1;

    n = arb_mat_nrows(A);

    arb_mat_set(L, A);

    if (n == 1)
        return arb_is_positive(arb_mat_entry(L, 0, 0));

    result = _arb_mat_ldl_golub_and_van_loan(L, prec);

    /* set the strictly upper triangular region of L to zero */
    {
        slong i, j;
        for (i = 0; i < n; i++)
            for (j = i+1; j < n; j++)
                arb_zero(arb_mat_entry(L, i, j));
    }

    return result;
}