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
|
/*
Copyright (C) 2012 Fredrik Johansson
This file is part of Arb.
Arb 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 2.1 of the License, or
(at your option) any later version. See <http://www.gnu.org/licenses/>.
*/
#include "acb_mat.h"
int main()
{
slong iter;
flint_rand_t state;
flint_printf("solve....");
fflush(stdout);
flint_randinit(state);
for (iter = 0; iter < 10000 * arb_test_multiplier(); iter++)
{
fmpq_mat_t Q, QX, QB;
acb_mat_t A, X, B;
slong n, m, qbits, prec;
int q_invertible, r_invertible, r_invertible2;
n = n_randint(state, 10);
m = n_randint(state, 10);
qbits = 1 + n_randint(state, 30);
prec = 2 + n_randint(state, 200);
fmpq_mat_init(Q, n, n);
fmpq_mat_init(QX, n, m);
fmpq_mat_init(QB, n, m);
acb_mat_init(A, n, n);
acb_mat_init(X, n, m);
acb_mat_init(B, n, m);
fmpq_mat_randtest(Q, state, qbits);
fmpq_mat_randtest(QB, state, qbits);
q_invertible = fmpq_mat_solve_fraction_free(QX, Q, QB);
if (!q_invertible)
{
acb_mat_set_fmpq_mat(A, Q, prec);
r_invertible = acb_mat_solve(X, A, B, prec);
if (r_invertible)
{
flint_printf("FAIL: matrix is singular over Q but not over R\n");
flint_printf("n = %wd, prec = %wd\n", n, prec);
flint_printf("\n");
flint_printf("Q = \n"); fmpq_mat_print(Q); flint_printf("\n\n");
flint_printf("QX = \n"); fmpq_mat_print(QX); flint_printf("\n\n");
flint_printf("QB = \n"); fmpq_mat_print(QB); flint_printf("\n\n");
flint_printf("A = \n"); acb_mat_printd(A, 15); flint_printf("\n\n");
flint_abort();
}
}
else
{
/* now this must converge */
while (1)
{
acb_mat_set_fmpq_mat(A, Q, prec);
acb_mat_set_fmpq_mat(B, QB, prec);
r_invertible = acb_mat_solve(X, A, B, prec);
if (r_invertible)
{
break;
}
else
{
if (prec > 10000)
{
flint_printf("FAIL: failed to converge at 10000 bits\n");
flint_printf("Q = \n"); fmpq_mat_print(Q); flint_printf("\n\n");
flint_printf("QX = \n"); fmpq_mat_print(QX); flint_printf("\n\n");
flint_printf("QB = \n"); fmpq_mat_print(QB); flint_printf("\n\n");
flint_printf("A = \n"); acb_mat_printd(A, 15); flint_printf("\n\n");
flint_abort();
}
prec *= 2;
}
}
if (!acb_mat_contains_fmpq_mat(X, QX))
{
flint_printf("FAIL (containment, iter = %wd)\n", iter);
flint_printf("n = %wd, prec = %wd\n", n, prec);
flint_printf("\n");
flint_printf("Q = \n"); fmpq_mat_print(Q); flint_printf("\n\n");
flint_printf("QB = \n"); fmpq_mat_print(QB); flint_printf("\n\n");
flint_printf("QX = \n"); fmpq_mat_print(QX); flint_printf("\n\n");
flint_printf("A = \n"); acb_mat_printd(A, 15); flint_printf("\n\n");
flint_printf("B = \n"); acb_mat_printd(B, 15); flint_printf("\n\n");
flint_printf("X = \n"); acb_mat_printd(X, 15); flint_printf("\n\n");
flint_abort();
}
/* test aliasing */
r_invertible2 = acb_mat_solve(B, A, B, prec);
if (!acb_mat_equal(X, B) || r_invertible != r_invertible2)
{
flint_printf("FAIL (aliasing)\n");
flint_printf("A = \n"); acb_mat_printd(A, 15); flint_printf("\n\n");
flint_printf("B = \n"); acb_mat_printd(B, 15); flint_printf("\n\n");
flint_printf("X = \n"); acb_mat_printd(X, 15); flint_printf("\n\n");
flint_abort();
}
}
fmpq_mat_clear(Q);
fmpq_mat_clear(QB);
fmpq_mat_clear(QX);
acb_mat_clear(A);
acb_mat_clear(B);
acb_mat_clear(X);
}
flint_randclear(state);
flint_cleanup();
flint_printf("PASS\n");
return EXIT_SUCCESS;
}
|
