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nmod_mat.h
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nmod_mat.h
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/*=============================================================================
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) 2010,2011 Fredrik Johansson
******************************************************************************/
#ifndef NMOD_MAT_H
#define NMOD_MAT_H
#undef ulong /* interferes with system includes */
#include <stdlib.h>
#define ulong unsigned long
#include <mpir.h>
#include "flint.h"
#include "longlong.h"
#include "ulong_extras.h"
#include "nmod_vec.h"
#ifdef __cplusplus
extern "C" {
#endif
typedef struct
{
mp_limb_t * entries;
long r;
long c;
mp_limb_t ** rows;
nmod_t mod;
}
nmod_mat_struct;
/* nmod_mat_t allows reference-like semantics for nmod_mat_struct */
typedef nmod_mat_struct nmod_mat_t[1];
#define nmod_mat_entry(mat,i,j) ((mat)->rows[(i)][(j)])
#define nmod_mat_nrows(mat) ((mat)->r)
#define nmod_mat_ncols(mat) ((mat)->c)
static __inline__
void
_nmod_mat_set_mod(nmod_mat_t mat, mp_limb_t n)
{
mat->mod.n = n;
mat->mod.ninv = n_preinvert_limb(n);
count_leading_zeros(mat->mod.norm, n);
}
/* Memory management */
void nmod_mat_init(nmod_mat_t mat, long rows, long cols, mp_limb_t n);
void nmod_mat_init_set(nmod_mat_t mat, const nmod_mat_t src);
void nmod_mat_clear(nmod_mat_t mat);
void nmod_mat_window_init(nmod_mat_t window, const nmod_mat_t mat, long r1, long c1, long r2, long c2);
void nmod_mat_window_clear(nmod_mat_t window);
/* Random matrix generation */
void nmod_mat_randtest(nmod_mat_t mat, flint_rand_t state);
void nmod_mat_randfull(nmod_mat_t mat, flint_rand_t state);
int nmod_mat_randpermdiag(nmod_mat_t mat, flint_rand_t state,
mp_srcptr diag, long n);
void nmod_mat_randrank(nmod_mat_t, flint_rand_t state, long rank);
void nmod_mat_randops(nmod_mat_t mat, long count, flint_rand_t state);
void nmod_mat_randtril(nmod_mat_t mat, flint_rand_t state, int unit);
void nmod_mat_randtriu(nmod_mat_t mat, flint_rand_t state, int unit);
void nmod_mat_print_pretty(const nmod_mat_t mat);
int nmod_mat_equal(const nmod_mat_t mat1, const nmod_mat_t mat2);
void nmod_mat_zero(nmod_mat_t mat);
int nmod_mat_is_zero(const nmod_mat_t mat);
static __inline__ int
nmod_mat_is_empty(const nmod_mat_t mat)
{
return (mat->r == 0) || (mat->c == 0);
}
static __inline__ int
nmod_mat_is_square(const nmod_mat_t mat)
{
return (mat->r == mat->c);
}
void nmod_mat_set(nmod_mat_t B, const nmod_mat_t A);
void nmod_mat_transpose(nmod_mat_t B, const nmod_mat_t A);
/* Addition and subtraction */
void nmod_mat_add(nmod_mat_t C, const nmod_mat_t A, const nmod_mat_t B);
void nmod_mat_sub(nmod_mat_t C, const nmod_mat_t A, const nmod_mat_t B);
void nmod_mat_neg(nmod_mat_t B, const nmod_mat_t A);
/* Matrix-scalar arithmetic */
void nmod_mat_scalar_mul(nmod_mat_t B, const nmod_mat_t A, mp_limb_t c);
/* Matrix multiplication */
void nmod_mat_mul(nmod_mat_t C, const nmod_mat_t A, const nmod_mat_t B);
void nmod_mat_mul_classical(nmod_mat_t C, const nmod_mat_t A, const nmod_mat_t B);
void nmod_mat_mul_strassen(nmod_mat_t C, const nmod_mat_t A, const nmod_mat_t B);
void
_nmod_mat_mul_classical(nmod_mat_t D, const nmod_mat_t C,
const nmod_mat_t A, const nmod_mat_t B, int op);
void nmod_mat_addmul(nmod_mat_t D, const nmod_mat_t C,
const nmod_mat_t A, const nmod_mat_t B);
void nmod_mat_submul(nmod_mat_t D, const nmod_mat_t C,
const nmod_mat_t A, const nmod_mat_t B);
/* Trace */
mp_limb_t nmod_mat_trace(const nmod_mat_t mat);
/* Determinant */
mp_limb_t _nmod_mat_det(nmod_mat_t A);
mp_limb_t nmod_mat_det(const nmod_mat_t A);
/* Rank */
long nmod_mat_rank(const nmod_mat_t A);
/* Inverse */
int nmod_mat_inv(nmod_mat_t B, const nmod_mat_t A);
/* Triangular solving */
void nmod_mat_solve_tril(nmod_mat_t X, const nmod_mat_t L, const nmod_mat_t B, int unit);
void nmod_mat_solve_tril_recursive(nmod_mat_t X, const nmod_mat_t L, const nmod_mat_t B, int unit);
void nmod_mat_solve_tril_classical(nmod_mat_t X, const nmod_mat_t L, const nmod_mat_t B, int unit);
void nmod_mat_solve_triu(nmod_mat_t X, const nmod_mat_t U, const nmod_mat_t B, int unit);
void nmod_mat_solve_triu_recursive(nmod_mat_t X, const nmod_mat_t U, const nmod_mat_t B, int unit);
void nmod_mat_solve_triu_classical(nmod_mat_t X, const nmod_mat_t U, const nmod_mat_t B, int unit);
/* LU decomposition */
long nmod_mat_lu(long * P, nmod_mat_t A, int rank_check);
long nmod_mat_lu_classical(long * P, nmod_mat_t A, int rank_check);
long nmod_mat_lu_recursive(long * P, nmod_mat_t A, int rank_check);
/* Nonsingular solving */
int nmod_mat_solve(nmod_mat_t X, const nmod_mat_t A, const nmod_mat_t B);
int nmod_mat_solve_vec(mp_ptr x, const nmod_mat_t A, mp_srcptr b);
/* Reduced row echelon form */
long nmod_mat_rref(nmod_mat_t A);
/* Nullspace */
long nmod_mat_nullspace(nmod_mat_t X, const nmod_mat_t A);
/* Tuning parameters *********************************************************/
/* Size at which pre-transposing becomes faster in classical multiplication */
#define NMOD_MAT_MUL_TRANSPOSE_CUTOFF 20
/* Strassen multiplication */
#define NMOD_MAT_MUL_STRASSEN_CUTOFF 256
/* Cutoff between classical and recursive triangular solving */
#define NMOD_MAT_SOLVE_TRI_ROWS_CUTOFF 64
#define NMOD_MAT_SOLVE_TRI_COLS_CUTOFF 64
/* Cutoff between classical and recursive LU decomposition */
#define NMOD_MAT_LU_RECURSIVE_CUTOFF 4
/*
Suggested initial modulus size for multimodular algorithms. This should
be chosen so that we get the most number of bits per cycle
in matrix multiplication. On x86-64 it appears to be optimal to use
moduli giving nlimbs = 2. This should hold both in the classical
range and in Strassen blocks.
*/
#define NMOD_MAT_OPTIMAL_MODULUS_BITS (FLINT_BITS-5)
#ifdef __cplusplus
}
#endif
#endif