1 /*
2     Copyright (C) 2010 Fredrik Johansson
3 
4     This file is part of FLINT.
5 
6     FLINT is free software: you can redistribute it and/or modify it under
7     the terms of the GNU Lesser General Public License (LGPL) as published
8     by the Free Software Foundation; either version 2.1 of the License, or
9     (at your option) any later version.  See <https://www.gnu.org/licenses/>.
10 */
11 
12 #include <stdio.h>
13 #include <stdlib.h>
14 #include <gmp.h>
15 #include "flint.h"
16 #include "fmpz.h"
17 #include "fmpz_vec.h"
18 #include "fmpz_mat.h"
19 #include "ulong_extras.h"
20 
21 
22 int
main(void)23 main(void)
24 {
25     fmpz_mat_t A, X, B, AX;
26     fmpz_t den;
27     slong i, m, n, r;
28     int success;
29 
30     FLINT_TEST_INIT(state);
31 
32     flint_printf("solve....");
33     fflush(stdout);
34 
35     for (i = 0; i < 1000 * flint_test_multiplier(); i++)
36     {
37         m = n_randint(state, 10);
38         n = n_randint(state, 10);
39 
40         fmpz_mat_init(A, m, m);
41         fmpz_mat_init(B, m, n);
42         fmpz_mat_init(X, m, n);
43         fmpz_mat_init(AX, m, n);
44         fmpz_init(den);
45 
46         fmpz_mat_randrank(A, state, m, 1+n_randint(state, 2)*n_randint(state, 100));
47         fmpz_mat_randtest(B, state, 1+n_randint(state, 2)*n_randint(state, 100));
48 
49         /* Dense */
50         if (n_randint(state, 2))
51             fmpz_mat_randops(A, state, 1+n_randint(state, 1 + m*m));
52 
53         success = fmpz_mat_solve(X, den, A, B);
54 
55         fmpz_mat_mul(AX, A, X);
56         fmpz_mat_scalar_divexact_fmpz(AX, AX, den);
57 
58         if (!fmpz_mat_equal(AX, B) || !success)
59         {
60             flint_printf("FAIL:\n");
61             flint_printf("AX != B!\n");
62             flint_printf("A:\n"),      fmpz_mat_print_pretty(A),  flint_printf("\n");
63             flint_printf("B:\n"),      fmpz_mat_print_pretty(B),  flint_printf("\n");
64             flint_printf("X:\n"),      fmpz_mat_print_pretty(X),  flint_printf("\n");
65             flint_printf("den(X) = "), fmpz_print(den),           flint_printf("\n");
66             flint_printf("AX:\n"),     fmpz_mat_print_pretty(AX), flint_printf("\n");
67             abort();
68         }
69 
70         fmpz_mat_clear(A);
71         fmpz_mat_clear(B);
72         fmpz_mat_clear(X);
73         fmpz_mat_clear(AX);
74         fmpz_clear(den);
75     }
76 
77     /* Test singular systems */
78     for (i = 0; i < 1000 * flint_test_multiplier(); i++)
79     {
80         m = 1 + n_randint(state, 10);
81         n = 1 + n_randint(state, 10);
82         r = n_randint(state, m);
83 
84         fmpz_mat_init(A, m, m);
85         fmpz_mat_init(B, m, n);
86         fmpz_mat_init(X, m, n);
87         fmpz_mat_init(AX, m, n);
88         fmpz_init(den);
89 
90         fmpz_mat_randrank(A, state, r, 1+n_randint(state, 2)*n_randint(state, 100));
91         fmpz_mat_randtest(B, state, 1+n_randint(state, 2)*n_randint(state, 100));
92 
93         /* Dense */
94         if (n_randint(state, 2))
95             fmpz_mat_randops(A, state, 1+n_randint(state, 1 + m*m));
96 
97         success = fmpz_mat_solve(X, den, A, B);
98 
99         if (!fmpz_is_zero(den) || success)
100         {
101             flint_printf("FAIL:\n");
102             flint_printf("singular system gave nonzero determinant\n");
103             abort();
104         }
105 
106         fmpz_mat_clear(A);
107         fmpz_mat_clear(B);
108         fmpz_mat_clear(X);
109         fmpz_mat_clear(AX);
110         fmpz_clear(den);
111     }
112 
113     FLINT_TEST_CLEANUP(state);
114 
115     flint_printf("PASS\n");
116     return 0;
117 }
118