173 lines
4.5 KiB
C
173 lines
4.5 KiB
C
/*=============================================================================
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This file is part of FLINT.
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FLINT is free software; you can redistribute it and/or modify
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it under the terms of the GNU General Public License as published by
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the Free Software Foundation; either version 2 of the License, or
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(at your option) any later version.
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FLINT is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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GNU General Public License for more details.
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You should have received a copy of the GNU General Public License
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along with FLINT; if not, write to the Free Software
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Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
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=============================================================================*/
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/******************************************************************************
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Copyright (C) 2010 Fredrik Johansson
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******************************************************************************/
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#include "fmpz_mat.h"
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#define AA(i,j) fmpz_mat_entry(A, i, j)
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#define BB(i,j) fmpz_mat_entry(B, i, j)
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#define XX(i,j) fmpz_mat_entry(X, i, j)
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int
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_fmpz_mat_solve_cramer_3x3(fmpz_mat_t X, fmpz_t den,
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const fmpz_mat_t A, const fmpz_mat_t B)
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{
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fmpz_t t15, t16, t17;
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int success;
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fmpz_init(t15);
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fmpz_init(t16);
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fmpz_init(t17);
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fmpz_mul(t17, AA(1,0), AA(2,1));
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fmpz_submul(t17, AA(1,1), AA(2,0));
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fmpz_mul(t16, AA(1,2), AA(2,0));
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fmpz_submul(t16, AA(1,0), AA(2,2));
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fmpz_mul(t15, AA(1,1), AA(2,2));
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fmpz_submul(t15, AA(1,2), AA(2,1));
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fmpz_mul (den, t15, AA(0,0));
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fmpz_addmul(den, t16, AA(0,1));
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fmpz_addmul(den, t17, AA(0,2));
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success = !fmpz_is_zero(den);
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if (success)
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{
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fmpz_t t12, t13, t14, x0, x1, x2;
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slong i, n = fmpz_mat_ncols(B);
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fmpz_init(t12);
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fmpz_init(t13);
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fmpz_init(t14);
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fmpz_init(x0);
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fmpz_init(x1);
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fmpz_init(x2);
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for (i = 0; i < n; i++)
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{
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fmpz_mul(t14, AA(2,0), BB(1,i));
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fmpz_submul(t14, AA(1,0), BB(2,i));
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fmpz_mul(t13, AA(2,1), BB(1,i));
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fmpz_submul(t13, AA(1,1), BB(2,i));
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fmpz_mul(t12, AA(2,2), BB(1,i));
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fmpz_submul(t12, AA(1,2), BB(2,i));
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fmpz_mul (x0, t15, BB(0,i));
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fmpz_addmul(x0, t13, AA(0,2));
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fmpz_submul(x0, t12, AA(0,1));
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fmpz_mul (x1, t16, BB(0,i));
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fmpz_addmul(x1, t12, AA(0,0));
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fmpz_submul(x1, t14, AA(0,2));
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fmpz_mul (x2, t17, BB(0,i));
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fmpz_addmul(x2, t14, AA(0,1));
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fmpz_submul(x2, t13, AA(0,0));
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fmpz_swap(XX(0,i), x0);
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fmpz_swap(XX(1,i), x1);
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fmpz_swap(XX(2,i), x2);
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}
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fmpz_clear(t12);
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fmpz_clear(t13);
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fmpz_clear(t14);
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fmpz_clear(x0);
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fmpz_clear(x1);
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fmpz_clear(x2);
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}
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fmpz_clear(t15);
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fmpz_clear(t16);
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fmpz_clear(t17);
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return success;
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}
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int
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fmpz_mat_solve_cramer(fmpz_mat_t X, fmpz_t den,
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const fmpz_mat_t A, const fmpz_mat_t B)
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{
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slong i, dim = fmpz_mat_nrows(A);
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if (dim == 0 || fmpz_mat_ncols(B) == 0)
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{
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fmpz_one(den);
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return 1;
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}
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else if (dim == 1)
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{
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fmpz_set(den, fmpz_mat_entry(A, 0, 0));
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if (fmpz_is_zero(den))
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return 0;
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if (!fmpz_mat_is_empty(B))
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_fmpz_vec_set(X->rows[0], B->rows[0], fmpz_mat_ncols(B));
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return 1;
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}
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else if (dim == 2)
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{
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fmpz_t t, u;
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_fmpz_mat_det_cofactor_2x2(den, A->rows);
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if (fmpz_is_zero(den))
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return 0;
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fmpz_init(t);
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fmpz_init(u);
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for (i = 0; i < fmpz_mat_ncols(B); i++)
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{
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fmpz_mul (t, fmpz_mat_entry(A, 1, 1), fmpz_mat_entry(B, 0, i));
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fmpz_submul(t, fmpz_mat_entry(A, 0, 1), fmpz_mat_entry(B, 1, i));
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fmpz_mul (u, fmpz_mat_entry(A, 0, 0), fmpz_mat_entry(B, 1, i));
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fmpz_submul(u, fmpz_mat_entry(A, 1, 0), fmpz_mat_entry(B, 0, i));
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fmpz_swap(fmpz_mat_entry(X, 0, i), t);
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fmpz_swap(fmpz_mat_entry(X, 1, i), u);
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}
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fmpz_clear(t);
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fmpz_clear(u);
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return 1;
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}
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else if (dim == 3)
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{
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return _fmpz_mat_solve_cramer_3x3(X, den, A, B);
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}
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else
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{
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flint_printf("Exception (fmpz_mat_solve_cramer). dim > 3 not implemented.");
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abort();
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}
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}
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