/*============================================================================= This file is part of FLINT. FLINT is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. FLINT is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with FLINT; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2010 William Hart Copyright (C) 2010 Fredrik Johansson ******************************************************************************/ #ifndef FMPZ_MAT_H #define FMPZ_MAT_H #undef ulong #define ulong ulongxx /* interferes with system includes */ #include #undef ulong #include #define ulong mp_limb_t #include "flint.h" #include "fmpz.h" #include "nmod_mat.h" #include "fmpz_poly.h" #ifdef __cplusplus extern "C" { #endif typedef struct { fmpz * entries; slong r; slong c; fmpz ** rows; } fmpz_mat_struct; typedef fmpz_mat_struct fmpz_mat_t[1]; /* Memory management ********************************************************/ #define fmpz_mat_entry(mat,i,j) ((mat)->rows[i] + (j)) #define fmpz_mat_nrows(mat) ((mat)->r) #define fmpz_mat_ncols(mat) ((mat)->c) void fmpz_mat_init(fmpz_mat_t mat, slong rows, slong cols); void fmpz_mat_init_set(fmpz_mat_t mat, const fmpz_mat_t src); void fmpz_mat_swap(fmpz_mat_t mat1, fmpz_mat_t mat2); void fmpz_mat_set(fmpz_mat_t mat1, const fmpz_mat_t mat2); void fmpz_mat_clear(fmpz_mat_t mat); int fmpz_mat_equal(const fmpz_mat_t mat1, const fmpz_mat_t mat2); int fmpz_mat_is_zero(const fmpz_mat_t mat); static __inline__ int fmpz_mat_is_empty(const fmpz_mat_t mat) { return (mat->r == 0) || (mat->c == 0); } static __inline__ int fmpz_mat_is_square(const fmpz_mat_t mat) { return (mat->r == mat->c); } void fmpz_mat_zero(fmpz_mat_t mat); void fmpz_mat_one(fmpz_mat_t mat); /* Input and output *********************************************************/ int fmpz_mat_fprint(FILE * file, const fmpz_mat_t mat); int fmpz_mat_fprint_pretty(FILE * file, const fmpz_mat_t mat); static __inline__ int fmpz_mat_print(const fmpz_mat_t mat) { return fmpz_mat_fprint(stdout, mat); } static __inline__ int fmpz_mat_print_pretty(const fmpz_mat_t mat) { return fmpz_mat_fprint_pretty(stdout, mat); } int fmpz_mat_fread(FILE* file, fmpz_mat_t mat); static __inline__ int fmpz_mat_read(fmpz_mat_t mat) { return fmpz_mat_fread(stdin, mat); } /* Random matrix generation *************************************************/ void fmpz_mat_randbits(fmpz_mat_t mat, flint_rand_t state, mp_bitcnt_t bits); void fmpz_mat_randtest(fmpz_mat_t mat, flint_rand_t state, mp_bitcnt_t bits); void fmpz_mat_randtest_unsigned(fmpz_mat_t mat, flint_rand_t state, mp_bitcnt_t bits); void fmpz_mat_randintrel(fmpz_mat_t mat, flint_rand_t state, mp_bitcnt_t bits); void fmpz_mat_randsimdioph(fmpz_mat_t mat, flint_rand_t state, mp_bitcnt_t bits, mp_bitcnt_t bits2); void fmpz_mat_randntrulike(fmpz_mat_t mat, flint_rand_t state, mp_bitcnt_t bits, ulong q); void fmpz_mat_randntrulike2(fmpz_mat_t mat, flint_rand_t state, mp_bitcnt_t bits, ulong q); void fmpz_mat_randajtai(fmpz_mat_t mat, flint_rand_t state, double alpha); void fmpz_mat_randrank(fmpz_mat_t mat, flint_rand_t state, slong rank, mp_bitcnt_t bits); void fmpz_mat_randdet(fmpz_mat_t mat, flint_rand_t state, const fmpz_t det); void fmpz_mat_randops(fmpz_mat_t mat, flint_rand_t state, slong count); int fmpz_mat_randpermdiag(fmpz_mat_t mat, flint_rand_t state, const fmpz * diag, slong n); /* Norms */ slong fmpz_mat_max_bits(const fmpz_mat_t mat); /* Transpose */ void fmpz_mat_transpose(fmpz_mat_t B, const fmpz_mat_t A); /* Addition and subtraction */ void fmpz_mat_add(fmpz_mat_t C, const fmpz_mat_t A, const fmpz_mat_t B); void fmpz_mat_sub(fmpz_mat_t C, const fmpz_mat_t A, const fmpz_mat_t B); void fmpz_mat_neg(fmpz_mat_t B, const fmpz_mat_t A); /* Scalar operations */ void fmpz_mat_scalar_mul_fmpz(fmpz_mat_t B, const fmpz_mat_t A, const fmpz_t c); void fmpz_mat_scalar_mul_si(fmpz_mat_t B, const fmpz_mat_t A, slong c); void fmpz_mat_scalar_mul_ui(fmpz_mat_t B, const fmpz_mat_t A, ulong c); void fmpz_mat_scalar_addmul_fmpz(fmpz_mat_t B, const fmpz_mat_t A, const fmpz_t c); void fmpz_mat_scalar_addmul_si(fmpz_mat_t B, const fmpz_mat_t A, slong c); void fmpz_mat_scalar_addmul_ui(fmpz_mat_t B, const fmpz_mat_t A, ulong c); void fmpz_mat_scalar_submul_fmpz(fmpz_mat_t B, const fmpz_mat_t A, const fmpz_t c); void fmpz_mat_scalar_submul_si(fmpz_mat_t B, const fmpz_mat_t A, slong c); void fmpz_mat_scalar_submul_ui(fmpz_mat_t B, const fmpz_mat_t A, ulong c); void fmpz_mat_scalar_addmul_nmod_mat_fmpz(fmpz_mat_t B, const nmod_mat_t A, const fmpz_t c); void fmpz_mat_scalar_addmul_nmod_mat_ui(fmpz_mat_t B, const nmod_mat_t A, ulong c); void fmpz_mat_scalar_divexact_fmpz(fmpz_mat_t B, const fmpz_mat_t A, const fmpz_t c); void fmpz_mat_scalar_divexact_si(fmpz_mat_t B, const fmpz_mat_t A, slong c); void fmpz_mat_scalar_divexact_ui(fmpz_mat_t B, const fmpz_mat_t A, ulong c); void fmpz_mat_scalar_mod_fmpz(fmpz_mat_t B, const fmpz_mat_t A, const fmpz_t m); /* Multiplication */ void fmpz_mat_mul(fmpz_mat_t C, const fmpz_mat_t A, const fmpz_mat_t B); void fmpz_mat_mul_classical(fmpz_mat_t C, const fmpz_mat_t A, const fmpz_mat_t B); void fmpz_mat_mul_classical_inline(fmpz_mat_t C, const fmpz_mat_t A, const fmpz_mat_t B); void _fmpz_mat_mul_multi_mod(fmpz_mat_t C, const fmpz_mat_t A, const fmpz_mat_t B, mp_bitcnt_t bits); void fmpz_mat_mul_multi_mod(fmpz_mat_t C, const fmpz_mat_t A, const fmpz_mat_t B); void fmpz_mat_sqr(fmpz_mat_t B, const fmpz_mat_t A); void fmpz_mat_pow(fmpz_mat_t B, const fmpz_mat_t A, ulong exp); /* Permutations */ static __inline__ void fmpz_mat_swap_rows(fmpz_mat_t mat, slong * perm, slong r, slong s) { if (r != s) { fmpz * u; slong t; if (perm) { t = perm[s]; perm[s] = perm[r]; perm[r] = t; } u = mat->rows[s]; mat->rows[s] = mat->rows[r]; mat->rows[r] = u; } } /* Gaussian elimination *****************************************************/ slong fmpz_mat_find_pivot_any(const fmpz_mat_t mat, slong start_row, slong end_row, slong c); slong fmpz_mat_fflu(fmpz_mat_t B, fmpz_t den, slong * perm, const fmpz_mat_t A, int rank_check); slong fmpz_mat_rref(fmpz_mat_t B, fmpz_t den, const fmpz_mat_t A); /* Modular gaussian elimination *********************************************/ slong fmpz_mat_rref_mod(slong * perm, fmpz_mat_t A, const fmpz_t p); /* Trace ********************************************************************/ void fmpz_mat_trace(fmpz_t trace, const fmpz_mat_t mat); /* Determinant **************************************************************/ void fmpz_mat_det(fmpz_t det, const fmpz_mat_t A); void fmpz_mat_det_cofactor(fmpz_t det, const fmpz_mat_t A); void _fmpz_mat_det_cofactor_2x2(fmpz_t det, fmpz ** const x); void _fmpz_mat_det_cofactor_3x3(fmpz_t det, fmpz ** const x); void _fmpz_mat_det_cofactor_4x4(fmpz_t det, fmpz ** const x); void fmpz_mat_det_bareiss(fmpz_t det, const fmpz_mat_t A); void fmpz_mat_det_modular(fmpz_t det, const fmpz_mat_t A, int proved); void fmpz_mat_det_modular_accelerated(fmpz_t det, const fmpz_mat_t A, int proved); void fmpz_mat_det_modular_given_divisor(fmpz_t det, const fmpz_mat_t A, const fmpz_t d, int proved); void fmpz_mat_det_bound(fmpz_t bound, const fmpz_mat_t A); void fmpz_mat_det_divisor(fmpz_t d, const fmpz_mat_t A); /* Characteristic polynomial ************************************************/ void _fmpz_mat_charpoly(fmpz *cp, const fmpz_mat_t mat); void fmpz_mat_charpoly(fmpz_poly_t cp, const fmpz_mat_t mat); /* Rank *********************************************************************/ slong fmpz_mat_rank(const fmpz_mat_t A); /* Nonsingular solving ******************************************************/ void fmpz_mat_solve_bound(fmpz_t N, fmpz_t D, const fmpz_mat_t A, const fmpz_mat_t B); int fmpz_mat_solve(fmpz_mat_t X, fmpz_t den, const fmpz_mat_t A, const fmpz_mat_t B); int fmpz_mat_solve_cramer(fmpz_mat_t X, fmpz_t den, const fmpz_mat_t A, const fmpz_mat_t B); int fmpz_mat_solve_fflu(fmpz_mat_t X, fmpz_t den, const fmpz_mat_t A, const fmpz_mat_t B); void fmpz_mat_solve_fflu_precomp(fmpz_mat_t X, const slong * perm, const fmpz_mat_t FFLU, const fmpz_mat_t B); int fmpz_mat_solve_dixon(fmpz_mat_t X, fmpz_t mod, const fmpz_mat_t A, const fmpz_mat_t B); /* Nullspace ****************************************************************/ slong fmpz_mat_nullspace(fmpz_mat_t res, const fmpz_mat_t mat); /* Inverse ******************************************************************/ int fmpz_mat_inv(fmpz_mat_t B, fmpz_t den, const fmpz_mat_t A); /* Modular reduction and reconstruction *************************************/ void fmpz_mat_set_nmod_mat(fmpz_mat_t A, const nmod_mat_t Amod); void fmpz_mat_set_nmod_mat_unsigned(fmpz_mat_t A, const nmod_mat_t Amod); void fmpz_mat_get_nmod_mat(nmod_mat_t Amod, const fmpz_mat_t A); void fmpz_mat_CRT_ui(fmpz_mat_t res, const fmpz_mat_t mat1, const fmpz_t m1, const nmod_mat_t mat2, int sign); void fmpz_mat_multi_mod_ui_precomp(nmod_mat_t * residues, slong nres, const fmpz_mat_t mat, const fmpz_comb_t comb, fmpz_comb_temp_t temp); void fmpz_mat_multi_mod_ui(nmod_mat_t * residues, slong nres, const fmpz_mat_t mat); void fmpz_mat_multi_CRT_ui_precomp(fmpz_mat_t mat, nmod_mat_t * const residues, slong nres, const fmpz_comb_t comb, fmpz_comb_temp_t temp, int sign); void fmpz_mat_multi_CRT_ui(fmpz_mat_t mat, nmod_mat_t * const residues, slong nres, int sign); #ifdef __cplusplus } #endif #endif