/*

 * Copyright 2008-2009 Katholieke Universiteit Leuven

 * Copyright 2014      Ecole Normale Superieure

 *

 * Use of this software is governed by the MIT license

 *

 * Written by Sven Verdoolaege, K.U.Leuven, Departement

 * Computerwetenschappen, Celestijnenlaan 200A, B-3001 Leuven, Belgium

 * and Ecole Normale Superieure, 45 rue d'Ulm, 75230 Paris, France

 */

#include <isl_ctx_private.h>

#include <isl_map_private.h>

#include <isl/space.h>

#include <isl_seq.h>

#include <isl_mat_private.h>

#include <isl_vec_private.h>

#include <isl_space_private.h>

#include <isl_val_private.h>

#include <isl/deprecated/mat_int.h>

isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat)

{

	return mat ? mat->ctx : NULL;

}

struct isl_mat *isl_mat_alloc(struct isl_ctx *ctx,

	unsigned n_row, unsigned n_col)

{

	int i;

	struct isl_mat *mat;

	mat = isl_alloc_type(ctx, struct isl_mat);

	if (!mat)

		return NULL;

	mat->row = NULL;

	mat->block = isl_blk_alloc(ctx, n_row * n_col);

	if (isl_blk_is_error(mat->block))

		goto error;

	mat->row = isl_alloc_array(ctx, isl_int *, n_row);

	if (n_row && !mat->row)

		goto error;

	for (i = 0; i < n_row; ++i)

		mat->row[i] = mat->block.data + i * n_col;

	mat->ctx = ctx;

	isl_ctx_ref(ctx);

	mat->ref = 1;

	mat->n_row = n_row;

	mat->n_col = n_col;

	mat->max_col = n_col;

	mat->flags = 0;

	return mat;

error:

	isl_blk_free(ctx, mat->block);

	free(mat);

	return NULL;

}

struct isl_mat *isl_mat_extend(struct isl_mat *mat,

	unsigned n_row, unsigned n_col)

{

	int i;

	isl_int *old;

	isl_int **row;

	if (!mat)

		return NULL;

	if (mat->max_col >= n_col && mat->n_row >= n_row) {

		if (mat->n_col < n_col)

			mat->n_col = n_col;

		return mat;

	}

	if (mat->max_col < n_col) {

		struct isl_mat *new_mat;

		if (n_row < mat->n_row)

			n_row = mat->n_row;

		new_mat = isl_mat_alloc(mat->ctx, n_row, n_col);

		if (!new_mat)

			goto error;

		for (i = 0; i < mat->n_row; ++i)

			isl_seq_cpy(new_mat->row[i], mat->row[i], mat->n_col);

		isl_mat_free(mat);

		return new_mat;

	}

	mat = isl_mat_cow(mat);

	if (!mat)

		goto error;

	old = mat->block.data;

	mat->block = isl_blk_extend(mat->ctx, mat->block, n_row * mat->max_col);

	if (isl_blk_is_error(mat->block))

		goto error;

	row = isl_realloc_array(mat->ctx, mat->row, isl_int *, n_row);

	if (n_row && !row)

		goto error;

	mat->row = row;

	for (i = 0; i < mat->n_row; ++i)

		mat->row[i] = mat->block.data + (mat->row[i] - old);

	for (i = mat->n_row; i < n_row; ++i)

		mat->row[i] = mat->block.data + i * mat->max_col;

	mat->n_row = n_row;

	if (mat->n_col < n_col)

		mat->n_col = n_col;

	return mat;

error:

	isl_mat_free(mat);

	return NULL;

}

__isl_give isl_mat *isl_mat_sub_alloc6(isl_ctx *ctx, isl_int **row,

	unsigned first_row, unsigned n_row, unsigned first_col, unsigned n_col)

{

	int i;

	struct isl_mat *mat;

	mat = isl_alloc_type(ctx, struct isl_mat);

	if (!mat)

		return NULL;

	mat->row = isl_alloc_array(ctx, isl_int *, n_row);

	if (n_row && !mat->row)

		goto error;

	for (i = 0; i < n_row; ++i)

		mat->row[i] = row[first_row+i] + first_col;

	mat->ctx = ctx;

	isl_ctx_ref(ctx);

	mat->ref = 1;

	mat->n_row = n_row;

	mat->n_col = n_col;

	mat->block = isl_blk_empty();

	mat->flags = ISL_MAT_BORROWED;

	return mat;

error:

	free(mat);

	return NULL;

}

__isl_give isl_mat *isl_mat_sub_alloc(__isl_keep isl_mat *mat,

	unsigned first_row, unsigned n_row, unsigned first_col, unsigned n_col)

{

	if (!mat)

		return NULL;

	return isl_mat_sub_alloc6(mat->ctx, mat->row, first_row, n_row,

				  first_col, n_col);

}

void isl_mat_sub_copy(struct isl_ctx *ctx, isl_int **dst, isl_int **src,

	unsigned n_row, unsigned dst_col, unsigned src_col, unsigned n_col)

{

	int i;

	for (i = 0; i < n_row; ++i)

		isl_seq_cpy(dst[i]+dst_col, src[i]+src_col, n_col);

}

void isl_mat_sub_neg(struct isl_ctx *ctx, isl_int **dst, isl_int **src,

	unsigned n_row, unsigned dst_col, unsigned src_col, unsigned n_col)

{

	int i;

	for (i = 0; i < n_row; ++i)

		isl_seq_neg(dst[i]+dst_col, src[i]+src_col, n_col);

}

struct isl_mat *isl_mat_copy(struct isl_mat *mat)

{

	if (!mat)

		return NULL;

	mat->ref++;

	return mat;

}

struct isl_mat *isl_mat_dup(struct isl_mat *mat)

{

	int i;

	struct isl_mat *mat2;

	if (!mat)

		return NULL;

	mat2 = isl_mat_alloc(mat->ctx, mat->n_row, mat->n_col);

	if (!mat2)

		return NULL;

	for (i = 0; i < mat->n_row; ++i)

		isl_seq_cpy(mat2->row[i], mat->row[i], mat->n_col);

	return mat2;

}

struct isl_mat *isl_mat_cow(struct isl_mat *mat)

{

	struct isl_mat *mat2;

	if (!mat)

		return NULL;

	if (mat->ref == 1 && !ISL_F_ISSET(mat, ISL_MAT_BORROWED))

		return mat;

	mat2 = isl_mat_dup(mat);

	isl_mat_free(mat);

	return mat2;

}

__isl_null isl_mat *isl_mat_free(__isl_take isl_mat *mat)

{

	if (!mat)

		return NULL;

	if (--mat->ref > 0)

		return NULL;

	if (!ISL_F_ISSET(mat, ISL_MAT_BORROWED))

		isl_blk_free(mat->ctx, mat->block);

	isl_ctx_deref(mat->ctx);

	free(mat->row);

	free(mat);

	return NULL;

}

int isl_mat_rows(__isl_keep isl_mat *mat)

{

	return mat ? mat->n_row : -1;

}

int isl_mat_cols(__isl_keep isl_mat *mat)

{

	return mat ? mat->n_col : -1;

}

int isl_mat_get_element(__isl_keep isl_mat *mat, int row, int col, isl_int *v)

{

	if (!mat)

		return -1;

	if (row < 0 || row >= mat->n_row)

		isl_die(mat->ctx, isl_error_invalid, "row out of range",

			return -1);

	if (col < 0 || col >= mat->n_col)

		isl_die(mat->ctx, isl_error_invalid, "column out of range",

			return -1);

	isl_int_set(*v, mat->row[row][col]);

	return 0;

}

/* Extract the element at row "row", oolumn "col" of "mat".

 */

__isl_give isl_val *isl_mat_get_element_val(__isl_keep isl_mat *mat,

	int row, int col)

{

	isl_ctx *ctx;

	if (!mat)

		return NULL;

	ctx = isl_mat_get_ctx(mat);

	if (row < 0 || row >= mat->n_row)

		isl_die(ctx, isl_error_invalid, "row out of range",

			return NULL);

	if (col < 0 || col >= mat->n_col)

		isl_die(ctx, isl_error_invalid, "column out of range",

			return NULL);

	return isl_val_int_from_isl_int(ctx, mat->row[row][col]);

}

__isl_give isl_mat *isl_mat_set_element(__isl_take isl_mat *mat,

	int row, int col, isl_int v)

{

	mat = isl_mat_cow(mat);

	if (!mat)

		return NULL;

	if (row < 0 || row >= mat->n_row)

		isl_die(mat->ctx, isl_error_invalid, "row out of range",

			goto error);

	if (col < 0 || col >= mat->n_col)

		isl_die(mat->ctx, isl_error_invalid, "column out of range",

			goto error);

	isl_int_set(mat->row[row][col], v);

	return mat;

error:

	isl_mat_free(mat);

	return NULL;

}

__isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,

	int row, int col, int v)

{

	mat = isl_mat_cow(mat);

	if (!mat)

		return NULL;

	if (row < 0 || row >= mat->n_row)

		isl_die(mat->ctx, isl_error_invalid, "row out of range",

			goto error);

	if (col < 0 || col >= mat->n_col)

		isl_die(mat->ctx, isl_error_invalid, "column out of range",

			goto error);

	isl_int_set_si(mat->row[row][col], v);

	return mat;

error:

	isl_mat_free(mat);

	return NULL;

}

/* Replace the element at row "row", column "col" of "mat" by "v".

 */

__isl_give isl_mat *isl_mat_set_element_val(__isl_take isl_mat *mat,

	int row, int col, __isl_take isl_val *v)

{

	if (!v)

		return isl_mat_free(mat);

	if (!isl_val_is_int(v))

		isl_die(isl_val_get_ctx(v), isl_error_invalid,

			"expecting integer value", goto error);

	mat = isl_mat_set_element(mat, row, col, v->n);

	isl_val_free(v);

	return mat;

error:

	isl_val_free(v);

	return isl_mat_free(mat);

}

__isl_give isl_mat *isl_mat_diag(isl_ctx *ctx, unsigned n_row, isl_int d)

{

	int i;

	struct isl_mat *mat;

	mat = isl_mat_alloc(ctx, n_row, n_row);

	if (!mat)

		return NULL;

	for (i = 0; i < n_row; ++i) {

		isl_seq_clr(mat->row[i], i);

		isl_int_set(mat->row[i][i], d);

		isl_seq_clr(mat->row[i]+i+1, n_row-(i+1));

	}

	return mat;

}

__isl_give isl_mat *isl_mat_identity(isl_ctx *ctx, unsigned n_row)

{

	if (!ctx)

		return NULL;

	return isl_mat_diag(ctx, n_row, ctx->one);

}

/* Is "mat" a (possibly scaled) identity matrix?

 */

int isl_mat_is_scaled_identity(__isl_keep isl_mat *mat)

{

	int i;

	if (!mat)

		return -1;

	if (mat->n_row != mat->n_col)

		return 0;

	for (i = 0; i < mat->n_row; ++i) {

		if (isl_seq_first_non_zero(mat->row[i], i) != -1)

			return 0;

		if (isl_int_ne(mat->row[0][0], mat->row[i][i]))

			return 0;

		if (isl_seq_first_non_zero(mat->row[i] + i + 1,

					    mat->n_col - (i + 1)) != -1)

			return 0;

	}

	return 1;

}

struct isl_vec *isl_mat_vec_product(struct isl_mat *mat, struct isl_vec *vec)

{

	int i;

	struct isl_vec *prod;

	if (!mat || !vec)

		goto error;

	isl_assert(mat->ctx, mat->n_col == vec->size, goto error);

	prod = isl_vec_alloc(mat->ctx, mat->n_row);

	if (!prod)

		goto error;

	for (i = 0; i < prod->size; ++i)

		isl_seq_inner_product(mat->row[i], vec->el, vec->size,

					&prod->block.data[i]);

	isl_mat_free(mat);

	isl_vec_free(vec);

	return prod;

error:

	isl_mat_free(mat);

	isl_vec_free(vec);

	return NULL;

}

__isl_give isl_vec *isl_mat_vec_inverse_product(__isl_take isl_mat *mat,

	__isl_take isl_vec *vec)

{

	struct isl_mat *vec_mat;

	int i;

	if (!mat || !vec)

		goto error;

	vec_mat = isl_mat_alloc(vec->ctx, vec->size, 1);

	if (!vec_mat)

		goto error;

	for (i = 0; i < vec->size; ++i)

		isl_int_set(vec_mat->row[i][0], vec->el[i]);

	vec_mat = isl_mat_inverse_product(mat, vec_mat);

	isl_vec_free(vec);

	if (!vec_mat)

		return NULL;

	vec = isl_vec_alloc(vec_mat->ctx, vec_mat->n_row);

	if (vec)

		for (i = 0; i < vec->size; ++i)

			isl_int_set(vec->el[i], vec_mat->row[i][0]);

	isl_mat_free(vec_mat);

	return vec;

error:

	isl_mat_free(mat);

	isl_vec_free(vec);

	return NULL;

}

struct isl_vec *isl_vec_mat_product(struct isl_vec *vec, struct isl_mat *mat)

{

	int i, j;

	struct isl_vec *prod;

	if (!mat || !vec)

		goto error;

	isl_assert(mat->ctx, mat->n_row == vec->size, goto error);

	prod = isl_vec_alloc(mat->ctx, mat->n_col);

	if (!prod)

		goto error;

	for (i = 0; i < prod->size; ++i) {

		isl_int_set_si(prod->el[i], 0);

		for (j = 0; j < vec->size; ++j)

			isl_int_addmul(prod->el[i], vec->el[j], mat->row[j][i]);

	}

	isl_mat_free(mat);

	isl_vec_free(vec);

	return prod;

error:

	isl_mat_free(mat);

	isl_vec_free(vec);

	return NULL;

}

struct isl_mat *isl_mat_aff_direct_sum(struct isl_mat *left,

	struct isl_mat *right)

{

	int i;

	struct isl_mat *sum;

	if (!left || !right)

		goto error;

	isl_assert(left->ctx, left->n_row == right->n_row, goto error);

	isl_assert(left->ctx, left->n_row >= 1, goto error);

	isl_assert(left->ctx, left->n_col >= 1, goto error);

	isl_assert(left->ctx, right->n_col >= 1, goto error);

	isl_assert(left->ctx,

	    isl_seq_first_non_zero(left->row[0]+1, left->n_col-1) == -1,

	    goto error);

	isl_assert(left->ctx,

	    isl_seq_first_non_zero(right->row[0]+1, right->n_col-1) == -1,

	    goto error);

	sum = isl_mat_alloc(left->ctx, left->n_row, left->n_col + right->n_col - 1);

	if (!sum)

		goto error;

	isl_int_lcm(sum->row[0][0], left->row[0][0], right->row[0][0]);

	isl_int_divexact(left->row[0][0], sum->row[0][0], left->row[0][0]);

	isl_int_divexact(right->row[0][0], sum->row[0][0], right->row[0][0]);

	isl_seq_clr(sum->row[0]+1, sum->n_col-1);

	for (i = 1; i < sum->n_row; ++i) {

		isl_int_mul(sum->row[i][0], left->row[0][0], left->row[i][0]);

		isl_int_addmul(sum->row[i][0],

				right->row[0][0], right->row[i][0]);

		isl_seq_scale(sum->row[i]+1, left->row[i]+1, left->row[0][0],

				left->n_col-1);

		isl_seq_scale(sum->row[i]+left->n_col,

				right->row[i]+1, right->row[0][0],

				right->n_col-1);

	}

	isl_int_divexact(left->row[0][0], sum->row[0][0], left->row[0][0]);

	isl_int_divexact(right->row[0][0], sum->row[0][0], right->row[0][0]);

	isl_mat_free(left);

	isl_mat_free(right);

	return sum;

error:

	isl_mat_free(left);

	isl_mat_free(right);

	return NULL;

}

static void exchange(struct isl_mat *M, struct isl_mat **U,

	struct isl_mat **Q, unsigned row, unsigned i, unsigned j)

{

	int r;

	for (r = row; r < M->n_row; ++r)

		isl_int_swap(M->row[r][i], M->row[r][j]);

	if (U) {

		for (r = 0; r < (*U)->n_row; ++r)

			isl_int_swap((*U)->row[r][i], (*U)->row[r][j]);

	}

	if (Q)

		isl_mat_swap_rows(*Q, i, j);

}

static void subtract(struct isl_mat *M, struct isl_mat **U,

	struct isl_mat **Q, unsigned row, unsigned i, unsigned j, isl_int m)

{

	int r;

	for (r = row; r < M->n_row; ++r)

		isl_int_submul(M->row[r][j], m, M->row[r][i]);

	if (U) {

		for (r = 0; r < (*U)->n_row; ++r)

			isl_int_submul((*U)->row[r][j], m, (*U)->row[r][i]);

	}

	if (Q) {

		for (r = 0; r < (*Q)->n_col; ++r)

			isl_int_addmul((*Q)->row[i][r], m, (*Q)->row[j][r]);

	}

}

static void oppose(struct isl_mat *M, struct isl_mat **U,

	struct isl_mat **Q, unsigned row, unsigned col)

{

	int r;

	for (r = row; r < M->n_row; ++r)

		isl_int_neg(M->row[r][col], M->row[r][col]);

	if (U) {

		for (r = 0; r < (*U)->n_row; ++r)

			isl_int_neg((*U)->row[r][col], (*U)->row[r][col]);

	}

	if (Q)

		isl_seq_neg((*Q)->row[col], (*Q)->row[col], (*Q)->n_col);

}

/* Given matrix M, compute

 *

 *		M U = H

 *		M   = H Q

 *

 * with U and Q unimodular matrices and H a matrix in column echelon form

 * such that on each echelon row the entries in the non-echelon column

 * are non-negative (if neg == 0) or non-positive (if neg == 1)

 * and strictly smaller (in absolute value) than the entries in the echelon

 * column.

 * If U or Q are NULL, then these matrices are not computed.

 */

struct isl_mat *isl_mat_left_hermite(struct isl_mat *M, int neg,

	struct isl_mat **U, struct isl_mat **Q)

{

	isl_int c;

	int row, col;

	if (U)

		*U = NULL;

	if (Q)

		*Q = NULL;

	if (!M)

		goto error;

	M = isl_mat_cow(M);

	if (!M)

		goto error;

	if (U) {

		*U = isl_mat_identity(M->ctx, M->n_col);

		if (!*U)

			goto error;

	}

	if (Q) {

		*Q = isl_mat_identity(M->ctx, M->n_col);

		if (!*Q)

			goto error;

	}

	col = 0;

	isl_int_init(c);

	for (row = 0; row < M->n_row; ++row) {

		int first, i, off;

		first = isl_seq_abs_min_non_zero(M->row[row]+col, M->n_col-col);

		if (first == -1)

			continue;

		first += col;

		if (first != col)

			exchange(M, U, Q, row, first, col);

		if (isl_int_is_neg(M->row[row][col]))

			oppose(M, U, Q, row, col);

		first = col+1;

		while ((off = isl_seq_first_non_zero(M->row[row]+first,

						       M->n_col-first)) != -1) {

			first += off;

			isl_int_fdiv_q(c, M->row[row][first], M->row[row][col]);

			subtract(M, U, Q, row, col, first, c);

			if (!isl_int_is_zero(M->row[row][first]))

				exchange(M, U, Q, row, first, col);

			else

				++first;

		}

		for (i = 0; i < col; ++i) {

			if (isl_int_is_zero(M->row[row][i]))

				continue;

			if (neg)

				isl_int_cdiv_q(c, M->row[row][i], M->row[row][col]);

			else

				isl_int_fdiv_q(c, M->row[row][i], M->row[row][col]);

			if (isl_int_is_zero(c))

				continue;

			subtract(M, U, Q, row, col, i, c);

		}

		++col;

	}

	isl_int_clear(c);

	return M;

error:

	if (Q) {

		isl_mat_free(*Q);

		*Q = NULL;

	}

	if (U) {

		isl_mat_free(*U);

		*U = NULL;

	}

	isl_mat_free(M);

	return NULL;

}

struct isl_mat *isl_mat_right_kernel(struct isl_mat *mat)

{

	int i, rank;

	struct isl_mat *U = NULL;

	struct isl_mat *K;

	mat = isl_mat_left_hermite(mat, 0, &U, NULL);

	if (!mat || !U)

		goto error;

	for (i = 0, rank = 0; rank < mat->n_col; ++rank) {

		while (i < mat->n_row && isl_int_is_zero(mat->row[i][rank]))

			++i;

		if (i >= mat->n_row)

			break;

	}

	K = isl_mat_alloc(U->ctx, U->n_row, U->n_col - rank);

	if (!K)

		goto error;

	isl_mat_sub_copy(K->ctx, K->row, U->row, U->n_row, 0, rank, U->n_col-rank);

	isl_mat_free(mat);

	isl_mat_free(U);

	return K;

error:

	isl_mat_free(mat);

	isl_mat_free(U);

	return NULL;

}

struct isl_mat *isl_mat_lin_to_aff(struct isl_mat *mat)

{

	int i;

	struct isl_mat *mat2;

	if (!mat)

		return NULL;

	mat2 = isl_mat_alloc(mat->ctx, 1+mat->n_row, 1+mat->n_col);

	if (!mat2)

		goto error;

	isl_int_set_si(mat2->row[0][0], 1);

	isl_seq_clr(mat2->row[0]+1, mat->n_col);

	for (i = 0; i < mat->n_row; ++i) {

		isl_int_set_si(mat2->row[1+i][0], 0);

		isl_seq_cpy(mat2->row[1+i]+1, mat->row[i], mat->n_col);

	}

	isl_mat_free(mat);

	return mat2;

error:

	isl_mat_free(mat);

	return NULL;

}

/* Given two matrices M1 and M2, return the block matrix

 *

 *	[ M1  0  ]

 *	[ 0   M2 ]

 */

__isl_give isl_mat *isl_mat_diagonal(__isl_take isl_mat *mat1,

	__isl_take isl_mat *mat2)

{

	int i;

	isl_mat *mat;

	if (!mat1 || !mat2)

		goto error;

	mat = isl_mat_alloc(mat1->ctx, mat1->n_row + mat2->n_row,

				       mat1->n_col + mat2->n_col);

	if (!mat)

		goto error;

	for (i = 0; i < mat1->n_row; ++i) {

		isl_seq_cpy(mat->row[i], mat1->row[i], mat1->n_col);

		isl_seq_clr(mat->row[i] + mat1->n_col, mat2->n_col);

	}

	for (i = 0; i < mat2->n_row; ++i) {

		isl_seq_clr(mat->row[mat1->n_row + i], mat1->n_col);

		isl_seq_cpy(mat->row[mat1->n_row + i] + mat1->n_col,

						    mat2->row[i], mat2->n_col);

	}

	isl_mat_free(mat1);

	isl_mat_free(mat2);

	return mat;

error:

	isl_mat_free(mat1);

	isl_mat_free(mat2);

	return NULL;

}

static int row_first_non_zero(isl_int **row, unsigned n_row, unsigned col)

{

	int i;

	for (i = 0; i < n_row; ++i)

		if (!isl_int_is_zero(row[i][col]))

			return i;

	return -1;

}

static int row_abs_min_non_zero(isl_int **row, unsigned n_row, unsigned col)

{

	int i, min = row_first_non_zero(row, n_row, col);

	if (min < 0)

		return -1;

	for (i = min + 1; i < n_row; ++i) {

		if (isl_int_is_zero(row[i][col]))

			continue;

		if (isl_int_abs_lt(row[i][col], row[min][col]))

			min = i;

	}

	return min;

}

static void inv_exchange(struct isl_mat *left, struct isl_mat *right,

	unsigned i, unsigned j)

{

	left = isl_mat_swap_rows(left, i, j);

	right = isl_mat_swap_rows(right, i, j);

}

static void inv_oppose(

	struct isl_mat *left, struct isl_mat *right, unsigned row)

{

	isl_seq_neg(left->row[row]+row, left->row[row]+row, left->n_col-row);

	isl_seq_neg(right->row[row], right->row[row], right->n_col);

}

static void inv_subtract(struct isl_mat *left, struct isl_mat *right,

	unsigned row, unsigned i, isl_int m)

{

	isl_int_neg(m, m);

	isl_seq_combine(left->row[i]+row,

			left->ctx->one, left->row[i]+row,

			m, left->row[row]+row,

			left->n_col-row);

	isl_seq_combine(right->row[i], right->ctx->one, right->row[i],

			m, right->row[row], right->n_col);

}

/* Compute inv(left)*right

 */

struct isl_mat *isl_mat_inverse_product(struct isl_mat *left,

	struct isl_mat *right)

{

	int row;

	isl_int a, b;

	if (!left || !right)

		goto error;

	isl_assert(left->ctx, left->n_row == left->n_col, goto error);

	isl_assert(left->ctx, left->n_row == right->n_row, goto error);

	if (left->n_row == 0) {

		isl_mat_free(left);

		return right;

	}

	left = isl_mat_cow(left);

	right = isl_mat_cow(right);

	if (!left || !right)

		goto error;

	isl_int_init(a);

	isl_int_init(b);

	for (row = 0; row < left->n_row; ++row) {

		int pivot, first, i, off;

		pivot = row_abs_min_non_zero(left->row+row, left->n_row-row, row);

		if (pivot < 0) {

			isl_int_clear(a);

			isl_int_clear(b);

			isl_assert(left->ctx, pivot >= 0, goto error);

		}

		pivot += row;

		if (pivot != row)

			inv_exchange(left, right, pivot, row);

		if (isl_int_is_neg(left->row[row][row]))

			inv_oppose(left, right, row);

		first = row+1;

		while ((off = row_first_non_zero(left->row+first,

					left->n_row-first, row)) != -1) {

			first += off;

			isl_int_fdiv_q(a, left->row[first][row],

					left->row[row][row]);

			inv_subtract(left, right, row, first, a);

			if (!isl_int_is_zero(left->row[first][row]))

				inv_exchange(left, right, row, first);

			else

				++first;

		}

		for (i = 0; i < row; ++i) {

			if (isl_int_is_zero(left->row[i][row]))

				continue;

			isl_int_gcd(a, left->row[row][row], left->row[i][row]);

			isl_int_divexact(b, left->row[i][row], a);

			isl_int_divexact(a, left->row[row][row], a);

			isl_int_neg(b, b);

			isl_seq_combine(left->row[i] + i,

					a, left->row[i] + i,

					b, left->row[row] + i,

					left->n_col - i);

			isl_seq_combine(right->row[i], a, right->row[i],

					b, right->row[row], right->n_col);

		}

	}

	isl_int_clear(b);

	isl_int_set(a, left->row[0][0]);

	for (row = 1; row < left->n_row; ++row)

		isl_int_lcm(a, a, left->row[row][row]);

	if (isl_int_is_zero(a)){

		isl_int_clear(a);

		isl_assert(left->ctx, 0, goto error);

	}

	for (row = 0; row < left->n_row; ++row) {

		isl_int_divexact(left->row[row][row], a, left->row[row][row]);

		if (isl_int_is_one(left->row[row][row]))

			continue;

		isl_seq_scale(right->row[row], right->row[row],

				left->row[row][row], right->n_col);

	}

	isl_int_clear(a);

	isl_mat_free(left);

	return right;

error:

	isl_mat_free(left);

	isl_mat_free(right);

	return NULL;

}

void isl_mat_col_scale(struct isl_mat *mat, unsigned col, isl_int m)

{

	int i;

	for (i = 0; i < mat->n_row; ++i)

		isl_int_mul(mat->row[i][col], mat->row[i][col], m);

}