flint-sys 0.9.0

/*
    Copyright (C) 2010 William Hart
    Copyright (C) 2010,2011 Fredrik Johansson
    Copyright (C) 2014 Ashish Kedia

    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/>.
*/

#ifndef NMOD_MAT_H
#define NMOD_MAT_H

#ifdef NMOD_MAT_INLINES_C
#define NMOD_MAT_INLINE
#else
#define NMOD_MAT_INLINE static inline
#endif

#include "nmod_types.h"

#ifdef __cplusplus
extern "C" {
#endif

#define nmod_mat_entry(mat,i,j) ((mat)->entries[(i) * (mat)->stride + (j)])

NMOD_MAT_INLINE
ulong nmod_mat_get_entry(const nmod_mat_t mat, slong i, slong j)
{
   return nmod_mat_entry(mat, i, j);
}

NMOD_MAT_INLINE
ulong * nmod_mat_entry_ptr(const nmod_mat_t mat, slong i, slong j)
{
   return &nmod_mat_entry(mat, i, j);
}

NMOD_MAT_INLINE
ulong * nmod_mat_row_ptr(const nmod_mat_t mat, slong i)
{
   return &nmod_mat_entry(mat, i, 0);
}
/* See inlines.c */

NMOD_MAT_INLINE
slong nmod_mat_nrows(const nmod_mat_t mat)
{
   return mat->r;
}

NMOD_MAT_INLINE
slong nmod_mat_ncols(const nmod_mat_t mat)
{
   return mat->c;
}

void nmod_mat_set_mod(nmod_mat_t mat, ulong n);

NMOD_MAT_INLINE
nmod_t nmod_mat_mod(const nmod_mat_t mat)
{
   return mat->mod;
}

/* Memory management */
void nmod_mat_init(nmod_mat_t mat, slong rows, slong cols, ulong 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_one(nmod_mat_t mat);

void nmod_mat_swap(nmod_mat_t mat1, nmod_mat_t mat2);

NMOD_MAT_INLINE void
nmod_mat_swap_entrywise(nmod_mat_t mat1, nmod_mat_t mat2)
{
    slong i, j;
    for (i = 0; i < nmod_mat_nrows(mat1); i++)
    {
       ulong * row1 = nmod_mat_entry_ptr(mat1, i, 0);
       ulong * row2 = nmod_mat_entry_ptr(mat2, i, 0);
       for (j = 0; j < nmod_mat_ncols(mat1); j++)
          FLINT_SWAP(ulong, row1[j], row2[j]);
    }
}

/* Windows and concatenation */

NMOD_MAT_INLINE void
nmod_mat_window_init(nmod_mat_t window, const nmod_mat_t mat,
    slong r1, slong c1, slong r2, slong c2)
{
    FLINT_ASSERT(r1 >= 0 && r1 <= r2 && r2 <= mat->r);
    FLINT_ASSERT(c2 >= 0 && c1 <= c2 && c2 <= mat->c);

    window->entries = nmod_mat_entry_ptr(mat, r1, c1);
    window->r = r2 - r1;
    window->c = c2 - c1;
    window->stride = mat->stride;
    window->mod = mat->mod;
}

NMOD_MAT_INLINE void
nmod_mat_window_clear(nmod_mat_t FLINT_UNUSED(window))
{
}

void nmod_mat_concat_horizontal(nmod_mat_t res,
                           const nmod_mat_t mat1,  const nmod_mat_t mat2);
void nmod_mat_concat_vertical(nmod_mat_t res,
                           const nmod_mat_t mat1,  const nmod_mat_t mat2);

/* 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);
void nmod_mat_rand(nmod_mat_t mat, flint_rand_t state);
int nmod_mat_randpermdiag(nmod_mat_t mat, flint_rand_t state,
                 nn_srcptr diag, slong n);
void nmod_mat_randrank(nmod_mat_t mat, flint_rand_t state, slong rank);
void nmod_mat_randops(nmod_mat_t mat, flint_rand_t state, slong count);
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);

#ifdef FLINT_HAVE_FILE
int nmod_mat_fprint_pretty(FILE* file, const nmod_mat_t mat);
int nmod_mat_fprint(FILE* f, const nmod_mat_t mat);
#endif

void nmod_mat_print_pretty(const nmod_mat_t mat);
int nmod_mat_print(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);
int nmod_mat_is_one(const nmod_mat_t mat);
int nmod_mat_is_zero_row(const nmod_mat_t mat, slong i);

NMOD_MAT_INLINE
int nmod_mat_is_empty(const nmod_mat_t mat)
{
    return (mat->r == 0) || (mat->c == 0);
}

NMOD_MAT_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_generic(nmod_mat_t B, const nmod_mat_t A, ulong c);
void _nmod_mat_scalar_mul_precomp(nmod_mat_t B, const nmod_mat_t A, ulong c, ulong c_pr);
void nmod_mat_scalar_mul(nmod_mat_t B, const nmod_mat_t A, ulong c);
void nmod_mat_scalar_mul_fmpz(nmod_mat_t B, const nmod_mat_t A, const fmpz_t c);
void _nmod_mat_scalar_addmul_ui_generic(nmod_mat_t C, const nmod_mat_t A, const nmod_mat_t B, const ulong c);
void _nmod_mat_scalar_addmul_ui_precomp(nmod_mat_t C, const nmod_mat_t A, const nmod_mat_t B, const ulong c, const ulong c_pr);
void nmod_mat_scalar_addmul_ui(nmod_mat_t C, const nmod_mat_t A, const nmod_mat_t B, const ulong c);

/* Matrix multiplication */

void nmod_mat_mul(nmod_mat_t C, const nmod_mat_t A, const nmod_mat_t B);

int nmod_mat_mul_blas(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_classical_threaded_pool_op(nmod_mat_t D, const nmod_mat_t C,
		            const nmod_mat_t A, const nmod_mat_t B, int op,
			      thread_pool_handle * threads, slong num_threads);

void nmod_mat_mul_classical_threaded(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_op(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);

void nmod_mat_mul_nmod_vec(ulong * c, const nmod_mat_t A,
                                              const ulong * b, slong blen);

void nmod_mat_mul_nmod_vec_ptr(ulong * const * c,
                  const nmod_mat_t A, const ulong * const * b, slong blen);

void nmod_mat_nmod_vec_mul(ulong * c, const ulong * a,
                                               slong alen, const nmod_mat_t B);

void nmod_mat_nmod_vec_mul_ptr(ulong * const * c,
                  const ulong * const * a, slong alen, const nmod_mat_t B);

/* Exponent */

void _nmod_mat_pow(nmod_mat_t dest, const nmod_mat_t mat, ulong pow);
void nmod_mat_pow(nmod_mat_t dest, const nmod_mat_t mat, ulong pow);

/* Trace */

ulong nmod_mat_trace(const nmod_mat_t mat);

/* Determinant */

ulong _nmod_mat_det(nmod_mat_t A);
ulong nmod_mat_det(const nmod_mat_t A);

ulong _nmod_mat_det_howell(nmod_mat_t A);
ulong nmod_mat_det_howell(const nmod_mat_t A);

/* Rank */

slong nmod_mat_rank(const nmod_mat_t A);

/* Inverse */

int nmod_mat_inv(nmod_mat_t B, const nmod_mat_t A);

/* Permutations */

NMOD_MAT_INLINE
void nmod_mat_swap_rows(nmod_mat_t mat, slong * perm, slong r, slong s)
{
    if (r != s && !nmod_mat_is_empty(mat))
    {
        slong i;
        nn_ptr u, v;

        if (perm)
            FLINT_SWAP(slong, perm[r], perm[s]);

        u = nmod_mat_entry_ptr(mat, r, 0);
        v = nmod_mat_entry_ptr(mat, s, 0);

        for (i = 0; i < mat->c; i++)
            FLINT_SWAP(ulong, u[i], v[i]);
    }
}

NMOD_MAT_INLINE
void nmod_mat_invert_rows(nmod_mat_t mat, slong * perm)
{
    slong i;

    for (i = 0; i < mat->r/2; i++)
        nmod_mat_swap_rows(mat, perm, i, mat->r - i - 1);
}

NMOD_MAT_INLINE
void nmod_mat_swap_cols(nmod_mat_t mat, slong * perm, slong r, slong s)
{
    if (r != s && !nmod_mat_is_empty(mat))
    {
        slong i;

        if (perm != NULL)
            FLINT_SWAP(slong, perm[r], perm[s]);

        for (i = 0; i < mat->r; i++)
            FLINT_SWAP(ulong, nmod_mat_entry(mat, i, r), nmod_mat_entry(mat, i, s));
    }
}

NMOD_MAT_INLINE
void nmod_mat_invert_cols(nmod_mat_t mat, slong * perm)
{
    if (!nmod_mat_is_empty(mat))
    {
        slong t, i;
        slong c = mat->c;
        slong k = mat->c/2;

        if (perm != NULL)
            for (i = 0; i < k; i++)
                FLINT_SWAP(slong, perm[i], perm[c - i - 1]);

        for (t = 0; t < mat->r; t++)
            for (i = 0; i < k; i++)
                FLINT_SWAP(ulong, nmod_mat_entry(mat, t, i), nmod_mat_entry(mat, t, c - i - 1));
    }
}

void nmod_mat_permute_rows(nmod_mat_t mat, const slong * perm_act, slong * perm_store);

/* 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 */

slong nmod_mat_lu(slong * P, nmod_mat_t A, int rank_check);
slong nmod_mat_lu_classical(slong * P, nmod_mat_t A, int rank_check);
slong nmod_mat_lu_classical_delayed(slong * P, nmod_mat_t A, int rank_check);
slong nmod_mat_lu_recursive(slong * 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(nn_ptr x, const nmod_mat_t A, nn_srcptr b);

/* Solving */

int nmod_mat_can_solve_inner(slong * rank, slong * prm, slong * piv,
                          nmod_mat_t X, const nmod_mat_t A, const nmod_mat_t B);

int nmod_mat_can_solve(nmod_mat_t X, const nmod_mat_t A,
                                                            const nmod_mat_t B);

/* Reduced row echelon form */

slong nmod_mat_rref(nmod_mat_t A);
slong _nmod_mat_rref(nmod_mat_t A, slong * pivots_nonpivots, slong * P);
slong nmod_mat_rref_classical(nmod_mat_t A);
slong _nmod_mat_rref_classical(nmod_mat_t A, slong * pivots_nonpivots);
slong nmod_mat_rref_storjohann(nmod_mat_t A);
slong _nmod_mat_rref_storjohann(nmod_mat_t A, slong * pivots_nonpivots);

slong nmod_mat_reduce_row(nmod_mat_t M, slong * P, slong * L, slong m);

/* Nullspace */

slong nmod_mat_nullspace(nmod_mat_t X, const nmod_mat_t A);
slong nmod_mat_left_nullspace(nmod_mat_t X, const nmod_mat_t A);

/* Howell form */

void nmod_mat_strong_echelon_form(nmod_mat_t A);

slong nmod_mat_howell_form(nmod_mat_t A);

/* Transforms */

void nmod_mat_similarity(nmod_mat_t M, slong r, ulong d);

/* Characteristic polynomial and minimal polynomial */

/* The following prototype actually lives in nmod_poly.h
 *
 * void nmod_mat_charpoly_danilevsky(nmod_poly_t p, const nmod_mat_t M);
 *
 * void nmod_mat_minpoly(nmod_poly_t p, const nmod_mat_t M);
*/

/* Tuning parameters *********************************************************/

/* Size at which pre-transposing becomes faster in classical multiplication */
#define NMOD_MAT_MUL_TRANSPOSE_CUTOFF 20

/* Cutoff between classical and recursive triangular solving */
#define NMOD_MAT_SOLVE_TRI_ROWS_CUTOFF 64
#define NMOD_MAT_SOLVE_TRI_COLS_CUTOFF 64

/*
   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)

/* Inlines *******************************************************************/

void nmod_mat_set_entry(nmod_mat_t mat, slong i, slong j, ulong x);

#ifdef __cplusplus
}
#endif

#endif