flint-sys 0.9.0

Bindings to the FLINT C library
Documentation 
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/*
    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 3 of the License, or
    (at your option) any later version.  See <https://www.gnu.org/licenses/>.
*/

#include "test_helpers.h"
#include "ulong_extras.h"
#include "nmod_mat.h"

TEST_FUNCTION_START(nmod_mat_inv, state)
{
    nmod_mat_t A, B, C, I;
    slong i, m, r;
    ulong mod;
    int result;

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

        nmod_mat_init(A, m, m, mod);
        nmod_mat_init(B, m, m, mod);
        nmod_mat_init(C, m, m, mod);
        nmod_mat_init(I, m, m, mod);

        nmod_mat_one(I);

        /* Verify that A * A^-1 = I for random matrices */

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

        result = nmod_mat_inv(B, A);
        nmod_mat_mul(C, A, B);

        if (!nmod_mat_equal(C, I) || !result)
            TEST_FUNCTION_FAIL(
                    "A * A^-1 != I\n"
                    "A = %{nmod_mat}\n"
                    "A^-1 = %{nmod_mat}\n"
                    "A * A^-1 = %{nmod_mat}\n",
                    A, B, C);

        /* Test aliasing */
        nmod_mat_set(C, A);
        nmod_mat_inv(A, A);
        nmod_mat_mul(B, A, C);

        if (!nmod_mat_equal(B, I))
            TEST_FUNCTION_FAIL(
                    "Aliasing failed\n"
                    "A = %{nmod_mat}\n",
                    C);

        nmod_mat_clear(A);
        nmod_mat_clear(B);
        nmod_mat_clear(C);
        nmod_mat_clear(I);
    }

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

        nmod_mat_init(A, m, m, mod);
        nmod_mat_init(B, m, m, mod);

        nmod_mat_randrank(A, state, r);

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

        result = nmod_mat_inv(B, A);

        if (result)
            TEST_FUNCTION_FAIL("singular matrix reported as invertible\n");

        /* Aliasing */
        result = nmod_mat_inv(A, A);
        if (result)
            TEST_FUNCTION_FAIL("singular matrix reported as invertible\n");

        nmod_mat_clear(A);
        nmod_mat_clear(B);
    }

    TEST_FUNCTION_END(state);
}