317 lines
10 KiB
C
317 lines
10 KiB
C
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/*=============================================================================
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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 William Hart
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Copyright (C) 2010 Fredrik Johansson
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******************************************************************************/
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#ifndef FMPZ_MAT_H
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#define FMPZ_MAT_H
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#undef ulong
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#define ulong ulongxx /* interferes with system includes */
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#include <stdio.h>
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#undef ulong
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#include <gmp.h>
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#define ulong mp_limb_t
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#include "flint.h"
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#include "fmpz.h"
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#include "nmod_mat.h"
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#include "fmpz_poly.h"
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#ifdef __cplusplus
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extern "C" {
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#endif
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typedef struct
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{
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fmpz * entries;
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slong r;
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slong c;
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fmpz ** rows;
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} fmpz_mat_struct;
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typedef fmpz_mat_struct fmpz_mat_t[1];
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/* Memory management ********************************************************/
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#define fmpz_mat_entry(mat,i,j) ((mat)->rows[i] + (j))
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#define fmpz_mat_nrows(mat) ((mat)->r)
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#define fmpz_mat_ncols(mat) ((mat)->c)
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void fmpz_mat_init(fmpz_mat_t mat, slong rows, slong cols);
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void fmpz_mat_init_set(fmpz_mat_t mat, const fmpz_mat_t src);
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void fmpz_mat_swap(fmpz_mat_t mat1, fmpz_mat_t mat2);
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void fmpz_mat_set(fmpz_mat_t mat1, const fmpz_mat_t mat2);
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void fmpz_mat_clear(fmpz_mat_t mat);
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int fmpz_mat_equal(const fmpz_mat_t mat1, const fmpz_mat_t mat2);
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int fmpz_mat_is_zero(const fmpz_mat_t mat);
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static __inline__ int
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fmpz_mat_is_empty(const fmpz_mat_t mat)
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{
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return (mat->r == 0) || (mat->c == 0);
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}
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static __inline__ int
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fmpz_mat_is_square(const fmpz_mat_t mat)
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{
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return (mat->r == mat->c);
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}
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void fmpz_mat_zero(fmpz_mat_t mat);
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void fmpz_mat_one(fmpz_mat_t mat);
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/* Input and output *********************************************************/
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int fmpz_mat_fprint(FILE * file, const fmpz_mat_t mat);
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int fmpz_mat_fprint_pretty(FILE * file, const fmpz_mat_t mat);
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static __inline__
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int fmpz_mat_print(const fmpz_mat_t mat)
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{
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return fmpz_mat_fprint(stdout, mat);
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}
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static __inline__
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int fmpz_mat_print_pretty(const fmpz_mat_t mat)
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{
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return fmpz_mat_fprint_pretty(stdout, mat);
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}
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int fmpz_mat_fread(FILE* file, fmpz_mat_t mat);
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static __inline__
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int fmpz_mat_read(fmpz_mat_t mat)
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{
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return fmpz_mat_fread(stdin, mat);
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}
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/* Random matrix generation *************************************************/
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void fmpz_mat_randbits(fmpz_mat_t mat, flint_rand_t state, mp_bitcnt_t bits);
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void fmpz_mat_randtest(fmpz_mat_t mat, flint_rand_t state, mp_bitcnt_t bits);
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void fmpz_mat_randtest_unsigned(fmpz_mat_t mat, flint_rand_t state, mp_bitcnt_t bits);
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void fmpz_mat_randintrel(fmpz_mat_t mat, flint_rand_t state, mp_bitcnt_t bits);
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void fmpz_mat_randsimdioph(fmpz_mat_t mat, flint_rand_t state, mp_bitcnt_t bits, mp_bitcnt_t bits2);
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void fmpz_mat_randntrulike(fmpz_mat_t mat, flint_rand_t state, mp_bitcnt_t bits, ulong q);
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void fmpz_mat_randntrulike2(fmpz_mat_t mat, flint_rand_t state, mp_bitcnt_t bits, ulong q);
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void fmpz_mat_randajtai(fmpz_mat_t mat, flint_rand_t state, double alpha);
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void fmpz_mat_randrank(fmpz_mat_t mat, flint_rand_t state, slong rank, mp_bitcnt_t bits);
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void fmpz_mat_randdet(fmpz_mat_t mat, flint_rand_t state, const fmpz_t det);
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void fmpz_mat_randops(fmpz_mat_t mat, flint_rand_t state, slong count);
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int fmpz_mat_randpermdiag(fmpz_mat_t mat, flint_rand_t state, const fmpz * diag, slong n);
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/* Norms */
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slong fmpz_mat_max_bits(const fmpz_mat_t mat);
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/* Transpose */
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void fmpz_mat_transpose(fmpz_mat_t B, const fmpz_mat_t A);
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/* Addition and subtraction */
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void fmpz_mat_add(fmpz_mat_t C, const fmpz_mat_t A, const fmpz_mat_t B);
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void fmpz_mat_sub(fmpz_mat_t C, const fmpz_mat_t A, const fmpz_mat_t B);
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void fmpz_mat_neg(fmpz_mat_t B, const fmpz_mat_t A);
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/* Scalar operations */
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void fmpz_mat_scalar_mul_fmpz(fmpz_mat_t B, const fmpz_mat_t A, const fmpz_t c);
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void fmpz_mat_scalar_mul_si(fmpz_mat_t B, const fmpz_mat_t A, slong c);
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void fmpz_mat_scalar_mul_ui(fmpz_mat_t B, const fmpz_mat_t A, ulong c);
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void fmpz_mat_scalar_addmul_fmpz(fmpz_mat_t B, const fmpz_mat_t A, const fmpz_t c);
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void fmpz_mat_scalar_addmul_si(fmpz_mat_t B, const fmpz_mat_t A, slong c);
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void fmpz_mat_scalar_addmul_ui(fmpz_mat_t B, const fmpz_mat_t A, ulong c);
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void fmpz_mat_scalar_submul_fmpz(fmpz_mat_t B, const fmpz_mat_t A, const fmpz_t c);
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void fmpz_mat_scalar_submul_si(fmpz_mat_t B, const fmpz_mat_t A, slong c);
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void fmpz_mat_scalar_submul_ui(fmpz_mat_t B, const fmpz_mat_t A, ulong c);
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void fmpz_mat_scalar_addmul_nmod_mat_fmpz(fmpz_mat_t B, const nmod_mat_t A, const fmpz_t c);
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void fmpz_mat_scalar_addmul_nmod_mat_ui(fmpz_mat_t B, const nmod_mat_t A, ulong c);
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void fmpz_mat_scalar_divexact_fmpz(fmpz_mat_t B, const fmpz_mat_t A, const fmpz_t c);
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void fmpz_mat_scalar_divexact_si(fmpz_mat_t B, const fmpz_mat_t A, slong c);
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void fmpz_mat_scalar_divexact_ui(fmpz_mat_t B, const fmpz_mat_t A, ulong c);
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void fmpz_mat_scalar_mod_fmpz(fmpz_mat_t B, const fmpz_mat_t A, const fmpz_t m);
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/* Multiplication */
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void fmpz_mat_mul(fmpz_mat_t C, const fmpz_mat_t A, const fmpz_mat_t B);
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void fmpz_mat_mul_classical(fmpz_mat_t C, const fmpz_mat_t A,
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const fmpz_mat_t B);
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void fmpz_mat_mul_classical_inline(fmpz_mat_t C, const fmpz_mat_t A,
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const fmpz_mat_t B);
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void _fmpz_mat_mul_multi_mod(fmpz_mat_t C, const fmpz_mat_t A,
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const fmpz_mat_t B, mp_bitcnt_t bits);
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void fmpz_mat_mul_multi_mod(fmpz_mat_t C, const fmpz_mat_t A,
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const fmpz_mat_t B);
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void fmpz_mat_sqr(fmpz_mat_t B, const fmpz_mat_t A);
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void fmpz_mat_pow(fmpz_mat_t B, const fmpz_mat_t A, ulong exp);
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/* Permutations */
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static __inline__ void
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fmpz_mat_swap_rows(fmpz_mat_t mat, slong * perm, slong r, slong s)
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{
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if (r != s)
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{
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fmpz * u;
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slong t;
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if (perm)
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{
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t = perm[s];
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perm[s] = perm[r];
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perm[r] = t;
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}
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u = mat->rows[s];
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mat->rows[s] = mat->rows[r];
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mat->rows[r] = u;
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}
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}
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/* Gaussian elimination *****************************************************/
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slong fmpz_mat_find_pivot_any(const fmpz_mat_t mat,
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slong start_row, slong end_row, slong c);
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slong fmpz_mat_fflu(fmpz_mat_t B, fmpz_t den, slong * perm,
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const fmpz_mat_t A, int rank_check);
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slong fmpz_mat_rref(fmpz_mat_t B, fmpz_t den, const fmpz_mat_t A);
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/* Modular gaussian elimination *********************************************/
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slong
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fmpz_mat_rref_mod(slong * perm, fmpz_mat_t A, const fmpz_t p);
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/* Trace ********************************************************************/
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void fmpz_mat_trace(fmpz_t trace, const fmpz_mat_t mat);
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/* Determinant **************************************************************/
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void fmpz_mat_det(fmpz_t det, const fmpz_mat_t A);
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void fmpz_mat_det_cofactor(fmpz_t det, const fmpz_mat_t A);
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void _fmpz_mat_det_cofactor_2x2(fmpz_t det, fmpz ** const x);
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void _fmpz_mat_det_cofactor_3x3(fmpz_t det, fmpz ** const x);
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void _fmpz_mat_det_cofactor_4x4(fmpz_t det, fmpz ** const x);
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void fmpz_mat_det_bareiss(fmpz_t det, const fmpz_mat_t A);
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void fmpz_mat_det_modular(fmpz_t det, const fmpz_mat_t A, int proved);
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void fmpz_mat_det_modular_accelerated(fmpz_t det,
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const fmpz_mat_t A, int proved);
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void fmpz_mat_det_modular_given_divisor(fmpz_t det, const fmpz_mat_t A,
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const fmpz_t d, int proved);
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void fmpz_mat_det_bound(fmpz_t bound, const fmpz_mat_t A);
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void fmpz_mat_det_divisor(fmpz_t d, const fmpz_mat_t A);
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/* Characteristic polynomial ************************************************/
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void _fmpz_mat_charpoly(fmpz *cp, const fmpz_mat_t mat);
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void fmpz_mat_charpoly(fmpz_poly_t cp, const fmpz_mat_t mat);
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/* Rank *********************************************************************/
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slong fmpz_mat_rank(const fmpz_mat_t A);
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/* Nonsingular solving ******************************************************/
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void fmpz_mat_solve_bound(fmpz_t N, fmpz_t D,
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const fmpz_mat_t A, const fmpz_mat_t B);
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int fmpz_mat_solve(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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int 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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int fmpz_mat_solve_fflu(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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void fmpz_mat_solve_fflu_precomp(fmpz_mat_t X, const slong * perm,
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const fmpz_mat_t FFLU, const fmpz_mat_t B);
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int fmpz_mat_solve_dixon(fmpz_mat_t X, fmpz_t mod,
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const fmpz_mat_t A, const fmpz_mat_t B);
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/* Nullspace ****************************************************************/
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slong fmpz_mat_nullspace(fmpz_mat_t res, const fmpz_mat_t mat);
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/* Inverse ******************************************************************/
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int fmpz_mat_inv(fmpz_mat_t B, fmpz_t den, const fmpz_mat_t A);
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/* Modular reduction and reconstruction *************************************/
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void fmpz_mat_set_nmod_mat(fmpz_mat_t A, const nmod_mat_t Amod);
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void fmpz_mat_set_nmod_mat_unsigned(fmpz_mat_t A, const nmod_mat_t Amod);
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void fmpz_mat_get_nmod_mat(nmod_mat_t Amod, const fmpz_mat_t A);
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void fmpz_mat_CRT_ui(fmpz_mat_t res, const fmpz_mat_t mat1,
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const fmpz_t m1, const nmod_mat_t mat2, int sign);
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void
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fmpz_mat_multi_mod_ui_precomp(nmod_mat_t * residues, slong nres,
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const fmpz_mat_t mat, const fmpz_comb_t comb, fmpz_comb_temp_t temp);
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void
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fmpz_mat_multi_mod_ui(nmod_mat_t * residues, slong nres, const fmpz_mat_t mat);
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void
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fmpz_mat_multi_CRT_ui_precomp(fmpz_mat_t mat,
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nmod_mat_t * const residues, slong nres,
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const fmpz_comb_t comb, fmpz_comb_temp_t temp, int sign);
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void fmpz_mat_multi_CRT_ui(fmpz_mat_t mat, nmod_mat_t * const residues,
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slong nres, int sign);
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#ifdef __cplusplus
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}
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#endif
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#endif
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||
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