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

/*
    Copyright (C) 2013 Fredrik Johansson

    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 "fmpq.h"
#include "fmpq_mat.h"
#include "arb_mat.h"

void
_fmpq_mat_randtest_for_exp(fmpq_mat_t mat, flint_rand_t state, flint_bitcnt_t bits)
{
    slong i, j;
    slong d, l, u;
    d = n_randint(state, 5);
    l = n_randint(state, 5);
    u = n_randint(state, 5);
    fmpq_mat_zero(mat);
    for (i = 0; i < fmpq_mat_nrows(mat); i++)
    {
        for (j = 0; j < fmpq_mat_ncols(mat); j++)
        {
            if ((i == j && d) || (i < j && u) || (i > j && l))
            {
                fmpq_randtest(fmpq_mat_entry(mat, i, j), state, bits);
            }
        }
    }
}

TEST_FUNCTION_START(arb_mat_exp, state)
{
    slong iter;

    /* check exp(A)*exp(c*A) = exp((1+c)*A) */
    for (iter = 0; iter < 1000 * 0.1 * flint_test_multiplier(); iter++)
    {
        arb_mat_t A, E, F, EF, G;
        fmpq_mat_t Q;
        arb_t c, d;
        slong n, qbits, prec;

        n = n_randint(state, 5);
        qbits = 2 + n_randint(state, 300);
        prec = 2 + n_randint(state, 300);

        arb_init(c);
        arb_init(d);
        fmpq_mat_init(Q, n, n);
        arb_mat_init(A, n, n);
        arb_mat_init(E, n, n);
        arb_mat_init(F, n, n);
        arb_mat_init(EF, n, n);
        arb_mat_init(G, n, n);

        _fmpq_mat_randtest_for_exp(Q, state, qbits);
        arb_mat_set_fmpq_mat(A, Q, prec);

        arb_mat_exp(E, A, prec);

        arb_randtest(c, state, prec, 10);
        arb_mat_scalar_mul_arb(F, A, c, prec);
        arb_mat_exp(F, F, prec);

        arb_add_ui(d, c, 1, prec);
        arb_mat_scalar_mul_arb(G, A, d, prec);
        arb_mat_exp(G, G, prec);

        arb_mat_mul(EF, E, F, prec);

        if (!arb_mat_overlaps(EF, G))
        {
            flint_printf("FAIL\n\n");
            flint_printf("n = %wd, prec = %wd\n", n, prec);

            flint_printf("c = \n"); arb_printd(c, 15); flint_printf("\n\n");

            flint_printf("A = \n"); arb_mat_printd(A, 15); flint_printf("\n\n");
            flint_printf("E   = \n"); arb_mat_printd(E, 15); flint_printf("\n\n");
            flint_printf("F   = \n"); arb_mat_printd(F, 15); flint_printf("\n\n");
            flint_printf("E*F = \n"); arb_mat_printd(EF, 15); flint_printf("\n\n");
            flint_printf("G   = \n"); arb_mat_printd(G, 15); flint_printf("\n\n");

            flint_abort();
        }

        arb_clear(c);
        arb_clear(d);
        fmpq_mat_clear(Q);
        arb_mat_clear(A);
        arb_mat_clear(E);
        arb_mat_clear(F);
        arb_mat_clear(EF);
        arb_mat_clear(G);
    }

    TEST_FUNCTION_END(state);
}