/*
    Copyright (C) 2010 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 2.1 of the License, or
    (at your option) any later version.  See <https://www.gnu.org/licenses/>.
*/

#include <stdio.h>
#include <stdlib.h>
#include <gmp.h>
#include "flint.h"
#include "nmod_vec.h"
#include "nmod_mat.h"
#include "ulong_extras.h"


int
main(void)
{
    nmod_mat_t A, X, B, AX;
    slong i, m, n, r;
    mp_limb_t mod;
    int solved;
    FLINT_TEST_INIT(state);
    

    flint_printf("solve....");
    fflush(stdout);

    for (i = 0; i < 1000 * flint_test_multiplier(); i++)
    {
        m = n_randint(state, 20);
        n = n_randint(state, 20);
        mod = n_randtest_prime(state, 0);

        nmod_mat_init(A, m, m, mod);
        nmod_mat_init(B, m, n, mod);
        nmod_mat_init(X, m, n, mod);
        nmod_mat_init(AX, m, n, mod);

        nmod_mat_randrank(A, state, m);
        nmod_mat_randtest(B, state);

        /* Dense */
        if (n_randint(state, 2))
            nmod_mat_randops(A, 1+n_randint(state, 1+m*m), state);

        solved = nmod_mat_solve(X, A, B);

        nmod_mat_mul(AX, A, X);

        if (!nmod_mat_equal(AX, B) || !solved)
        {
            flint_printf("FAIL:\n");
            flint_printf("AX != B!\n");
            flint_printf("A:\n");
            nmod_mat_print_pretty(A);
            flint_printf("B:\n");
            nmod_mat_print_pretty(B);
            flint_printf("X:\n");
            nmod_mat_print_pretty(X);
            flint_printf("AX:\n");
            nmod_mat_print_pretty(AX);
            flint_printf("\n");
            abort();
        }

        nmod_mat_clear(A);
        nmod_mat_clear(B);
        nmod_mat_clear(X);
        nmod_mat_clear(AX);
    }

    /* Test singular systems */
    for (i = 0; i < 1000 * flint_test_multiplier(); i++)
    {
        m = 1 + n_randint(state, 20);
        n = 1 + n_randint(state, 20);
        r = n_randint(state, m);
        mod = n_randtest_prime(state, 0);

        nmod_mat_init(A, m, m, mod);
        nmod_mat_init(B, m, n, mod);
        nmod_mat_init(X, m, n, mod);
        nmod_mat_init(AX, m, n, mod);

        nmod_mat_randrank(A, state, r);
        nmod_mat_randtest(B, state);

        /* Dense */
        if (n_randint(state, 2))
            nmod_mat_randops(A, 1+n_randint(state, 1+m*m), state);

        solved = nmod_mat_solve(X, A, B);

        if (solved)
        {
            flint_printf("FAIL:\n");
            flint_printf("singular system was 'solved'\n");
            nmod_mat_print_pretty(A);
            nmod_mat_print_pretty(X);
            nmod_mat_print_pretty(B);
            abort();
        }

        nmod_mat_clear(A);
        nmod_mat_clear(B);
        nmod_mat_clear(X);
        nmod_mat_clear(AX);
    }

    FLINT_TEST_CLEANUP(state);
    
    flint_printf("PASS\n");
    return 0;
}