flint-sys 0.9.0

/*
    Copyright (C) 2011 Fredrik Johansson

    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 FMPQ_MAT_H
#define FMPQ_MAT_H

#ifdef FMPQ_MAT_INLINES_C
#define FMPQ_MAT_INLINE
#else
#define FMPQ_MAT_INLINE static inline
#endif

#include "fmpq_types.h"

#ifdef __cplusplus
extern "C" {
#endif

FMPQ_MAT_INLINE
fmpq * fmpq_mat_entry(const fmpq_mat_t mat, slong i, slong j)
{
   return mat->entries + (i * mat->stride + j);
}

FMPQ_MAT_INLINE
fmpz * fmpq_mat_entry_num(const fmpq_mat_t mat, slong i, slong j)
{
   return (fmpz *)(&((*fmpq_mat_entry(mat, i, j)).num));
}

FMPQ_MAT_INLINE
fmpz * fmpq_mat_entry_den(const fmpq_mat_t mat, slong i, slong j)
{
   return (fmpz *)(&((*fmpq_mat_entry(mat, i, j)).den));
}

FMPQ_MAT_INLINE
slong fmpq_mat_nrows(const fmpq_mat_t mat)
{
   return mat->r;
}

FMPQ_MAT_INLINE
slong fmpq_mat_ncols(const fmpq_mat_t mat)
{
   return mat->c;
}

void fmpq_mat_init(fmpq_mat_t mat, slong rows, slong cols);
void fmpq_mat_init_set(fmpq_mat_t mat1, const fmpq_mat_t mat2);
void fmpq_mat_clear(fmpq_mat_t mat);

FMPQ_MAT_INLINE
void fmpq_mat_swap(fmpq_mat_t mat1, fmpq_mat_t mat2)
{
    FLINT_SWAP(fmpq_mat_struct, *mat1, *mat2);
}

void fmpq_mat_swap_entrywise(fmpq_mat_t mat1, fmpq_mat_t mat2);

/* Windows and concatenation */

FMPQ_MAT_INLINE void
fmpq_mat_window_init(fmpq_mat_t window, const fmpq_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 = fmpq_mat_entry(mat, r1, c1);
    window->r = r2 - r1;
    window->c = c2 - c1;
    window->stride = mat->stride;
}

FMPQ_MAT_INLINE void
fmpq_mat_window_clear(fmpq_mat_t FLINT_UNUSED(window))
{
}

void fmpq_mat_concat_horizontal(fmpq_mat_t res, const fmpq_mat_t mat1,  const fmpq_mat_t mat2);
void fmpq_mat_concat_vertical(fmpq_mat_t res, const fmpq_mat_t mat1,  const fmpq_mat_t mat2);

/* Input and output  */

void fmpq_mat_print(const fmpq_mat_t mat);

/* Random matrix generation **************************************************/

void fmpq_mat_randbits(fmpq_mat_t mat, flint_rand_t state, flint_bitcnt_t bits);
void fmpq_mat_randtest(fmpq_mat_t mat, flint_rand_t state, flint_bitcnt_t bits);

/* Special matrices **********************************************************/

void fmpq_mat_hilbert_matrix(fmpq_mat_t mat);

/* Basic assignment **********************************************************/

void fmpq_mat_set(fmpq_mat_t dest, const fmpq_mat_t src);

void fmpq_mat_zero(fmpq_mat_t mat);
void fmpq_mat_one(fmpq_mat_t mat);

void fmpq_mat_transpose(fmpq_mat_t rop, const fmpq_mat_t op);

/* Addition, scalar multiplication  ******************************************/

void fmpq_mat_add(fmpq_mat_t mat, const fmpq_mat_t mat1, const fmpq_mat_t mat2);
void fmpq_mat_sub(fmpq_mat_t mat, const fmpq_mat_t mat1, const fmpq_mat_t mat2);
void fmpq_mat_neg(fmpq_mat_t rop, const fmpq_mat_t op);

void fmpq_mat_scalar_mul_fmpz(fmpq_mat_t rop, const fmpq_mat_t op, const fmpz_t x);
void fmpq_mat_scalar_mul_fmpq(fmpq_mat_t rop, const fmpq_mat_t op, const fmpq_t x);

void fmpq_mat_scalar_div_fmpz(fmpq_mat_t rop, const fmpq_mat_t op, const fmpz_t x);

/* Basic comparison and properties *******************************************/

int fmpq_mat_equal(const fmpq_mat_t mat1, const fmpq_mat_t mat2);

int fmpq_mat_is_zero(const fmpq_mat_t mat);
int fmpq_mat_is_one(const fmpq_mat_t mat);
int fmpq_mat_is_integral(const fmpq_mat_t mat);

FMPQ_MAT_INLINE
int fmpq_mat_is_empty(const fmpq_mat_t mat)
{
    return (mat->r == 0) || (mat->c == 0);
}

FMPQ_MAT_INLINE
int fmpq_mat_is_square(const fmpq_mat_t mat)
{
    return (mat->r == mat->c);
}

/* Integer matrix conversion *************************************************/

int fmpq_mat_get_fmpz_mat(fmpz_mat_t dest, const fmpq_mat_t mat);
void fmpq_mat_set_fmpz_mat(fmpq_mat_t dest, const fmpz_mat_t mat);

void fmpq_mat_get_fmpz_mat_entrywise(fmpz_mat_t num, fmpz_mat_t den, const fmpq_mat_t mat);
void fmpq_mat_get_fmpz_mat_matwise(fmpz_mat_t num, fmpz_t den, const fmpq_mat_t mat);
void fmpq_mat_get_fmpz_mat_rowwise(fmpz_mat_t num, fmpz * den, const fmpq_mat_t mat);
void fmpq_mat_get_fmpz_mat_colwise(fmpz_mat_t num, fmpz * den, const fmpq_mat_t mat);

void fmpq_mat_get_fmpz_mat_rowwise_2(fmpz_mat_t num, fmpz_mat_t num2,
        fmpz * den, const fmpq_mat_t mat, const fmpq_mat_t mat2);

void fmpq_mat_get_fmpz_mat_mod_fmpz(fmpz_mat_t dest, const fmpq_mat_t mat, const fmpz_t mod);
int fmpq_mat_set_fmpz_mat_mod_fmpz(fmpq_mat_t X, const fmpz_mat_t Xmod, const fmpz_t mod);

void fmpq_mat_set_fmpz_mat_div_fmpz(fmpq_mat_t X, const fmpz_mat_t Xmod, const fmpz_t div);

/* Matrix multiplication *****************************************************/

void fmpq_mat_mul_direct(fmpq_mat_t C, const fmpq_mat_t A, const fmpq_mat_t B);

void fmpq_mat_mul_cleared(fmpq_mat_t C, const fmpq_mat_t A, const fmpq_mat_t B);

void fmpq_mat_mul_fmpz_mat(fmpq_mat_t C, const fmpq_mat_t A, const fmpz_mat_t B);
void fmpq_mat_mul(fmpq_mat_t C, const fmpq_mat_t A, const fmpq_mat_t B);

void fmpq_mat_mul_r_fmpz_mat(fmpq_mat_t C, const fmpz_mat_t A, const fmpq_mat_t B);

void fmpq_mat_mul_fmpz_vec(fmpq* c, const fmpq_mat_t A, const fmpz * b, slong blen);
void fmpq_mat_mul_fmpq_vec(fmpq * c, const fmpq_mat_t A, const fmpq * b, slong blen);

void fmpq_mat_mul_fmpz_vec_ptr(fmpq * const * c, const fmpq_mat_t A, const fmpz * const * b, slong blen);
void fmpq_mat_mul_fmpq_vec_ptr(fmpq * const * c, const fmpq_mat_t A, const fmpq * const * b, slong blen);

void fmpq_mat_fmpz_vec_mul(fmpq * c, const fmpz * a, slong alen, const fmpq_mat_t B);
void fmpq_mat_fmpq_vec_mul(fmpq* c, const fmpq* a, slong alen, const fmpq_mat_t B);

void fmpq_mat_fmpz_vec_mul_ptr(fmpq * const * c, const fmpz * const * a, slong alen, const fmpq_mat_t B);
void fmpq_mat_fmpq_vec_mul_ptr(fmpq * const * c, const fmpq * const * a, slong alen, const fmpq_mat_t B);

/* Kronecker product *********************************************************/

void fmpq_mat_kronecker_product(fmpq_mat_t C, const fmpq_mat_t A, const fmpq_mat_t B);

/* Permutations **************************************************************/

void fmpq_mat_swap_rows(fmpq_mat_t mat, slong * perm, slong r, slong s);
void fmpq_mat_swap_cols(fmpq_mat_t mat, slong * perm, slong r, slong s);

void fmpq_mat_invert_rows(fmpq_mat_t mat, slong * perm);
void fmpq_mat_invert_cols(fmpq_mat_t mat, slong * perm);

/* Trace *********************************************************************/

void fmpq_mat_trace(fmpq_t trace, const fmpq_mat_t mat);

/* Determinant ***************************************************************/

void fmpq_mat_det(fmpq_t det, const fmpq_mat_t mat);

int fmpq_mat_permanent(fmpq_t res, const fmpq_mat_t A);

/* Nonsingular solving *******************************************************/

int fmpq_mat_solve_fmpz_mat_fraction_free(fmpq_mat_t X, const fmpz_mat_t A, const fmpz_mat_t B);
int fmpq_mat_solve_fraction_free(fmpq_mat_t X, const fmpq_mat_t A, const fmpq_mat_t B);

int fmpq_mat_solve_fmpz_mat_dixon(fmpq_mat_t X, const fmpz_mat_t A, const fmpz_mat_t B);
int fmpq_mat_solve_dixon(fmpq_mat_t X, const fmpq_mat_t A, const fmpq_mat_t B);

int fmpq_mat_solve_fmpz_mat_multi_mod(fmpq_mat_t X, const fmpz_mat_t A, const fmpz_mat_t B);
int fmpq_mat_solve_multi_mod(fmpq_mat_t X, const fmpq_mat_t A, const fmpq_mat_t B);

int fmpq_mat_can_solve_fmpz_mat_multi_mod(fmpq_mat_t X, const fmpz_mat_t A, const fmpz_mat_t B);
int fmpq_mat_can_solve_multi_mod(fmpq_mat_t X, const fmpq_mat_t A, const fmpq_mat_t B);

int fmpq_mat_can_solve_fraction_free(fmpq_mat_t X, const fmpq_mat_t A, const fmpq_mat_t B);

int fmpq_mat_can_solve_fmpz_mat_dixon(fmpq_mat_t X, const fmpz_mat_t A, const fmpz_mat_t B);
int fmpq_mat_can_solve_dixon(fmpq_mat_t X, const fmpq_mat_t A, const fmpq_mat_t B);

int fmpq_mat_can_solve(fmpq_mat_t X, const fmpq_mat_t A, const fmpq_mat_t B);

int fmpq_mat_solve_fmpz_mat(fmpq_mat_t X, const fmpz_mat_t A, const fmpz_mat_t B);
int fmpq_mat_solve(fmpq_mat_t X, const fmpq_mat_t A, const fmpq_mat_t B);

/* Inverse *******************************************************************/

int fmpq_mat_inv(fmpq_mat_t B, const fmpq_mat_t A);

/* Echelon form **************************************************************/

int fmpq_mat_pivot(slong * perm, fmpq_mat_t mat, slong r, slong c);

slong fmpq_mat_rref_classical(fmpq_mat_t B, const fmpq_mat_t A);
slong fmpq_mat_rref_fraction_free(fmpq_mat_t B, const fmpq_mat_t A);
slong fmpq_mat_rref(fmpq_mat_t B, const fmpq_mat_t A);

/* Gram-Schmidt Orthogonalisation  *******************************************/

void fmpq_mat_gso(fmpq_mat_t B, const fmpq_mat_t A);

/* Characteristic polynomial *************************************************/

void fmpq_mat_similarity(fmpq_mat_t A, slong r, fmpq_t d);

/* Characteristic polynomial *************************************************/

void _fmpq_mat_charpoly(fmpz * coeffs, fmpz_t den, const fmpq_mat_t mat);
void fmpq_mat_charpoly(fmpq_poly_t pol, const fmpq_mat_t mat);

/* Minimal polynomial ********************************************************/

slong _fmpq_mat_minpoly(fmpz * coeffs, fmpz_t den, const fmpq_mat_t mat);
void fmpq_mat_minpoly(fmpq_poly_t pol, const fmpq_mat_t mat);

#ifdef __cplusplus
}
#endif

#endif