X-Git-Url: http://review.tizen.org/git/?a=blobdiff_plain;f=isl_mat.c;h=129cdc749eb81f10d549d6e46f01aaff2c67d42b;hb=63fb8a7f484648c3caa25351c8c94ac2395ec563;hp=e89b5b363233fc4474d85fafb6e6a85d501687d0;hpb=df2859f75a416641f48e993eaa4feb9945d955cb;p=platform%2Fupstream%2Fisl.git

diff --git a/isl_mat.c b/isl_mat.c
index e89b5b3..129cdc7 100644
--- a/isl_mat.c
+++ b/isl_mat.c
@@ -1,7 +1,24 @@
-#include "isl_dim.h"
-#include "isl_seq.h"
-#include "isl_mat.h"
-#include "isl_map_private.h"
+/*
+ * Copyright 2008-2009 Katholieke Universiteit Leuven
+ *
+ * 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
+ */
+
+#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_space_private.h>
+#include <isl_val_private.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)
@@ -24,9 +41,12 @@ struct isl_mat *isl_mat_alloc(struct isl_ctx *ctx,
 	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;
@@ -36,7 +56,64 @@ error:
 	return NULL;
 }
 
-struct isl_mat *isl_mat_sub_alloc(struct isl_ctx *ctx, isl_int **row,
+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 (!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;
@@ -50,6 +127,8 @@ struct isl_mat *isl_mat_sub_alloc(struct isl_ctx *ctx, isl_int **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;
@@ -61,6 +140,15 @@ error:
 	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)
 {
@@ -79,7 +167,7 @@ void isl_mat_sub_neg(struct isl_ctx *ctx, isl_int **dst, isl_int **src,
 		isl_seq_neg(dst[i]+dst_col, src[i]+src_col, n_col);
 }
 
-struct isl_mat *isl_mat_copy(struct isl_ctx *ctx, struct isl_mat *mat)
+struct isl_mat *isl_mat_copy(struct isl_mat *mat)
 {
 	if (!mat)
 		return NULL;
@@ -88,14 +176,14 @@ struct isl_mat *isl_mat_copy(struct isl_ctx *ctx, struct isl_mat *mat)
 	return mat;
 }
 
-struct isl_mat *isl_mat_dup(struct isl_ctx *ctx, struct isl_mat *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(ctx, mat->n_row, mat->n_col);
+	mat2 = isl_mat_alloc(mat->ctx, mat->n_row, mat->n_col);
 	if (!mat2)
 		return NULL;
 	for (i = 0; i < mat->n_row; ++i)
@@ -103,7 +191,7 @@ struct isl_mat *isl_mat_dup(struct isl_ctx *ctx, struct isl_mat *mat)
 	return mat2;
 }
 
-struct isl_mat *isl_mat_cow(struct isl_ctx *ctx, struct isl_mat *mat)
+struct isl_mat *isl_mat_cow(struct isl_mat *mat)
 {
 	struct isl_mat *mat2;
 	if (!mat)
@@ -112,26 +200,128 @@ struct isl_mat *isl_mat_cow(struct isl_ctx *ctx, struct isl_mat *mat)
 	if (mat->ref == 1 && !ISL_F_ISSET(mat, ISL_MAT_BORROWED))
 		return mat;
 
-	mat2 = isl_mat_dup(ctx, mat);
-	isl_mat_free(ctx, mat);
+	mat2 = isl_mat_dup(mat);
+	isl_mat_free(mat);
 	return mat2;
 }
 
-void isl_mat_free(struct isl_ctx *ctx, struct isl_mat *mat)
+void *isl_mat_free(struct isl_mat *mat)
 {
 	if (!mat)
-		return;
+		return NULL;
 
 	if (--mat->ref > 0)
-		return;
+		return NULL;
 
 	if (!ISL_F_ISSET(mat, ISL_MAT_BORROWED))
-		isl_blk_free(ctx, mat->block);
+		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;
 }
 
-struct isl_mat *isl_mat_identity(struct isl_ctx *ctx, unsigned n_row)
+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;
@@ -141,15 +331,21 @@ struct isl_mat *isl_mat_identity(struct isl_ctx *ctx, unsigned n_row)
 		return NULL;
 	for (i = 0; i < n_row; ++i) {
 		isl_seq_clr(mat->row[i], i);
-		isl_int_set_si(mat->row[i][i], 1);
+		isl_int_set(mat->row[i][i], d);
 		isl_seq_clr(mat->row[i]+i+1, n_row-(i+1));
 	}
 
 	return mat;
 }
 
-struct isl_vec *isl_mat_vec_product(struct isl_ctx *ctx,
-	struct isl_mat *mat, struct isl_vec *vec)
+__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);
+}
+
+struct isl_vec *isl_mat_vec_product(struct isl_mat *mat, struct isl_vec *vec)
 {
 	int i;
 	struct isl_vec *prod;
@@ -157,26 +353,83 @@ struct isl_vec *isl_mat_vec_product(struct isl_ctx *ctx,
 	if (!mat || !vec)
 		goto error;
 
-	isl_assert(ctx, mat->n_col == vec->size, goto error);
+	isl_assert(mat->ctx, mat->n_col == vec->size, goto error);
 
-	prod = isl_vec_alloc(ctx, mat->n_row);
+	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->block.data, vec->size,
+		isl_seq_inner_product(mat->row[i], vec->el, vec->size,
 					&prod->block.data[i]);
-	isl_mat_free(ctx, mat);
-	isl_vec_free(ctx, vec);
+	isl_mat_free(mat);
+	isl_vec_free(vec);
 	return prod;
 error:
-	isl_mat_free(ctx, mat);
-	isl_vec_free(ctx, vec);
+	isl_mat_free(mat);
+	isl_vec_free(vec);
 	return NULL;
 }
 
-struct isl_mat *isl_mat_aff_direct_sum(struct isl_ctx *ctx,
-	struct isl_mat *left, struct isl_mat *right)
+__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;
@@ -184,18 +437,18 @@ struct isl_mat *isl_mat_aff_direct_sum(struct isl_ctx *ctx,
 	if (!left || !right)
 		goto error;
 
-	isl_assert(ctx, left->n_row == right->n_row, goto error);
-	isl_assert(ctx, left->n_row >= 1, goto error);
-	isl_assert(ctx, left->n_col >= 1, goto error);
-	isl_assert(ctx, right->n_col >= 1, goto error);
-	isl_assert(ctx,
+	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(ctx,
+	isl_assert(left->ctx,
 	    isl_seq_first_non_zero(right->row[0]+1, right->n_col-1) == -1,
 	    goto error);
 
-	sum = isl_mat_alloc(ctx, left->n_row, left->n_col + right->n_col - 1);
+	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]);
@@ -216,16 +469,16 @@ struct isl_mat *isl_mat_aff_direct_sum(struct isl_ctx *ctx,
 
 	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(ctx, left);
-	isl_mat_free(ctx, right);
+	isl_mat_free(left);
+	isl_mat_free(right);
 	return sum;
 error:
-	isl_mat_free(ctx, left);
-	isl_mat_free(ctx, right);
+	isl_mat_free(left);
+	isl_mat_free(right);
 	return NULL;
 }
 
-static void exchange(struct isl_ctx *ctx, struct isl_mat *M, struct isl_mat **U,
+static void exchange(struct isl_mat *M, struct isl_mat **U,
 	struct isl_mat **Q, unsigned row, unsigned i, unsigned j)
 {
 	int r;
@@ -236,7 +489,7 @@ static void exchange(struct isl_ctx *ctx, struct isl_mat *M, struct isl_mat **U,
 			isl_int_swap((*U)->row[r][i], (*U)->row[r][j]);
 	}
 	if (Q)
-		isl_mat_swap_rows(ctx, *Q, i, j);
+		isl_mat_swap_rows(*Q, i, j);
 }
 
 static void subtract(struct isl_mat *M, struct isl_mat **U,
@@ -255,7 +508,7 @@ static void subtract(struct isl_mat *M, struct isl_mat **U,
 	}
 }
 
-static void oppose(struct isl_ctx *ctx, struct isl_mat *M, struct isl_mat **U,
+static void oppose(struct isl_mat *M, struct isl_mat **U,
 	struct isl_mat **Q, unsigned row, unsigned col)
 {
 	int r;
@@ -281,8 +534,8 @@ static void oppose(struct isl_ctx *ctx, struct isl_mat *M, struct isl_mat **U,
  * column.
  * If U or Q are NULL, then these matrices are not computed.
  */
-struct isl_mat *isl_mat_left_hermite(struct isl_ctx *ctx,
-	struct isl_mat *M, int neg, struct isl_mat **U, struct isl_mat **Q)
+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;
@@ -293,16 +546,16 @@ struct isl_mat *isl_mat_left_hermite(struct isl_ctx *ctx,
 		*Q = NULL;
 	if (!M)
 		goto error;
-	M = isl_mat_cow(ctx, M);
+	M = isl_mat_cow(M);
 	if (!M)
 		goto error;
 	if (U) {
-		*U = isl_mat_identity(ctx, M->n_col);
+		*U = isl_mat_identity(M->ctx, M->n_col);
 		if (!*U)
 			goto error;
 	}
 	if (Q) {
-		*Q = isl_mat_identity(ctx, M->n_col);
+		*Q = isl_mat_identity(M->ctx, M->n_col);
 		if (!*Q)
 			goto error;
 	}
@@ -316,9 +569,9 @@ struct isl_mat *isl_mat_left_hermite(struct isl_ctx *ctx,
 			continue;
 		first += col;
 		if (first != col)
-			exchange(ctx, M, U, Q, row, first, col);
+			exchange(M, U, Q, row, first, col);
 		if (isl_int_is_neg(M->row[row][col]))
-			oppose(ctx, M, U, Q, 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) {
@@ -326,7 +579,7 @@ struct isl_mat *isl_mat_left_hermite(struct isl_ctx *ctx,
 			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(ctx, M, U, Q, row, first, col);
+				exchange(M, U, Q, row, first, col);
 			else
 				++first;
 		}
@@ -348,23 +601,24 @@ struct isl_mat *isl_mat_left_hermite(struct isl_ctx *ctx,
 	return M;
 error:
 	if (Q) {
-		isl_mat_free(ctx, *Q);
+		isl_mat_free(*Q);
 		*Q = NULL;
 	}
 	if (U) {
-		isl_mat_free(ctx, *U);
+		isl_mat_free(*U);
 		*U = NULL;
 	}
+	isl_mat_free(M);
 	return NULL;
 }
 
-struct isl_mat *isl_mat_right_kernel(struct isl_ctx *ctx, struct isl_mat *mat)
+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(ctx, mat, 0, &U, NULL);
+	mat = isl_mat_left_hermite(mat, 0, &U, NULL);
 	if (!mat || !U)
 		goto error;
 
@@ -374,37 +628,76 @@ struct isl_mat *isl_mat_right_kernel(struct isl_ctx *ctx, struct isl_mat *mat)
 		if (i >= mat->n_row)
 			break;
 	}
-	K = isl_mat_alloc(ctx, U->n_row, U->n_col - rank);
+	K = isl_mat_alloc(U->ctx, U->n_row, U->n_col - rank);
 	if (!K)
 		goto error;
-	isl_mat_sub_copy(ctx, K->row, U->row, U->n_row, 0, rank, U->n_col-rank);
-	isl_mat_free(ctx, mat);
-	isl_mat_free(ctx, U);
+	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(ctx, mat);
-	isl_mat_free(ctx, U);
+	isl_mat_free(mat);
+	isl_mat_free(U);
 	return NULL;
 }
 
-struct isl_mat *isl_mat_lin_to_aff(struct isl_ctx *ctx, struct isl_mat *mat)
+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(ctx, 1+mat->n_row, 1+mat->n_col);
+	mat2 = isl_mat_alloc(mat->ctx, 1+mat->n_row, 1+mat->n_col);
 	if (!mat2)
-		return NULL;
+		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(ctx, mat);
+	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)
@@ -431,38 +724,36 @@ static int row_abs_min_non_zero(isl_int **row, unsigned n_row, unsigned col)
 	return min;
 }
 
-static void inv_exchange(struct isl_ctx *ctx,
-	struct isl_mat *left, struct isl_mat *right,
+static void inv_exchange(struct isl_mat *left, struct isl_mat *right,
 	unsigned i, unsigned j)
 {
-	left = isl_mat_swap_rows(ctx, left, i, j);
-	right = isl_mat_swap_rows(ctx, right, i, j);
+	left = isl_mat_swap_rows(left, i, j);
+	right = isl_mat_swap_rows(right, i, j);
 }
 
-static void inv_oppose(struct isl_ctx *ctx,
+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_ctx *ctx,
-	struct isl_mat *left, struct isl_mat *right,
+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,
-			ctx->one, 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], ctx->one, right->row[i],
+	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_ctx *ctx,
-	struct isl_mat *left, struct isl_mat *right)
+struct isl_mat *isl_mat_inverse_product(struct isl_mat *left,
+	struct isl_mat *right)
 {
 	int row;
 	isl_int a, b;
@@ -470,16 +761,16 @@ struct isl_mat *isl_mat_inverse_product(struct isl_ctx *ctx,
 	if (!left || !right)
 		goto error;
 
-	isl_assert(ctx, left->n_row == left->n_col, goto error);
-	isl_assert(ctx, left->n_row == right->n_row, 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(ctx, left);
+		isl_mat_free(left);
 		return right;
 	}
 
-	left = isl_mat_cow(ctx, left);
-	right = isl_mat_cow(ctx, right);
+	left = isl_mat_cow(left);
+	right = isl_mat_cow(right);
 	if (!left || !right)
 		goto error;
 
@@ -491,22 +782,22 @@ struct isl_mat *isl_mat_inverse_product(struct isl_ctx *ctx,
 		if (pivot < 0) {
 			isl_int_clear(a);
 			isl_int_clear(b);
-			isl_assert(ctx, pivot >= 0, goto error);
+			isl_assert(left->ctx, pivot >= 0, goto error);
 		}
 		pivot += row;
 		if (pivot != row)
-			inv_exchange(ctx, left, right, pivot, row);
+			inv_exchange(left, right, pivot, row);
 		if (isl_int_is_neg(left->row[row][row]))
-			inv_oppose(ctx, left, right, 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(ctx, left, right, row, first, a);
+			inv_subtract(left, right, row, first, a);
 			if (!isl_int_is_zero(left->row[first][row]))
-				inv_exchange(ctx, left, right, row, first);
+				inv_exchange(left, right, row, first);
 			else
 				++first;
 		}
@@ -516,11 +807,11 @@ struct isl_mat *isl_mat_inverse_product(struct isl_ctx *ctx,
 			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(a, a);
-			isl_seq_combine(left->row[i]+row,
-					a, left->row[i]+row,
-					b, left->row[row]+row,
-					left->n_col-row);
+			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);
 		}
@@ -532,7 +823,7 @@ struct isl_mat *isl_mat_inverse_product(struct isl_ctx *ctx,
 		isl_int_lcm(a, a, left->row[row][row]);
 	if (isl_int_is_zero(a)){
 		isl_int_clear(a);
-		isl_assert(ctx, 0, goto error);
+		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]);
@@ -543,11 +834,11 @@ struct isl_mat *isl_mat_inverse_product(struct isl_ctx *ctx,
 	}
 	isl_int_clear(a);
 
-	isl_mat_free(ctx, left);
+	isl_mat_free(left);
 	return right;
 error:
-	isl_mat_free(ctx, left);
-	isl_mat_free(ctx, right);
+	isl_mat_free(left);
+	isl_mat_free(right);
 	return NULL;
 }
 
@@ -574,19 +865,18 @@ void isl_mat_col_combine(struct isl_mat *mat, unsigned dst,
 	isl_int_clear(tmp);
 }
 
-struct isl_mat *isl_mat_right_inverse(struct isl_ctx *ctx,
-	struct isl_mat *mat)
+struct isl_mat *isl_mat_right_inverse(struct isl_mat *mat)
 {
 	struct isl_mat *inv;
 	int row;
 	isl_int a, b;
 
-	mat = isl_mat_cow(ctx, mat);
+	mat = isl_mat_cow(mat);
 	if (!mat)
 		return NULL;
 
-	inv = isl_mat_identity(ctx, mat->n_col);
-	inv = isl_mat_cow(ctx, inv);
+	inv = isl_mat_identity(mat->ctx, mat->n_col);
+	inv = isl_mat_cow(inv);
 	if (!inv)
 		goto error;
 
@@ -598,13 +888,13 @@ struct isl_mat *isl_mat_right_inverse(struct isl_ctx *ctx,
 		if (pivot < 0) {
 			isl_int_clear(a);
 			isl_int_clear(b);
-			goto error;
+			isl_assert(mat->ctx, pivot >= 0, goto error);
 		}
 		pivot += row;
 		if (pivot != row)
-			exchange(ctx, mat, &inv, NULL, row, pivot, row);
+			exchange(mat, &inv, NULL, row, pivot, row);
 		if (isl_int_is_neg(mat->row[row][row]))
-			oppose(ctx, mat, &inv, NULL, row, row);
+			oppose(mat, &inv, NULL, row, row);
 		first = row+1;
 		while ((off = isl_seq_first_non_zero(mat->row[row]+first,
 						    mat->n_col-first)) != -1) {
@@ -613,7 +903,7 @@ struct isl_mat *isl_mat_right_inverse(struct isl_ctx *ctx,
 						    mat->row[row][row]);
 			subtract(mat, &inv, NULL, row, row, first, a);
 			if (!isl_int_is_zero(mat->row[row][first]))
-				exchange(ctx, mat, &inv, NULL, row, row, first);
+				exchange(mat, &inv, NULL, row, row, first);
 			else
 				++first;
 		}
@@ -645,58 +935,70 @@ struct isl_mat *isl_mat_right_inverse(struct isl_ctx *ctx,
 	}
 	isl_int_clear(a);
 
-	isl_mat_free(ctx, mat);
+	isl_mat_free(mat);
 
 	return inv;
 error:
-	isl_mat_free(ctx, mat);
+	isl_mat_free(mat);
+	isl_mat_free(inv);
 	return NULL;
 }
 
-struct isl_mat *isl_mat_transpose(struct isl_ctx *ctx, struct isl_mat *mat)
+struct isl_mat *isl_mat_transpose(struct isl_mat *mat)
 {
+	struct isl_mat *transpose = NULL;
 	int i, j;
 
-	mat = isl_mat_cow(ctx, mat);
 	if (!mat)
 		return NULL;
-	isl_assert(ctx, mat->n_col == mat->n_row, goto error);
+
+	if (mat->n_col == mat->n_row) {
+		mat = isl_mat_cow(mat);
+		if (!mat)
+			return NULL;
+		for (i = 0; i < mat->n_row; ++i)
+			for (j = i + 1; j < mat->n_col; ++j)
+				isl_int_swap(mat->row[i][j], mat->row[j][i]);
+		return mat;
+	}
+	transpose = isl_mat_alloc(mat->ctx, mat->n_col, mat->n_row);
+	if (!transpose)
+		goto error;
 	for (i = 0; i < mat->n_row; ++i)
-		for (j = i + 1; j < mat->n_col; ++j)
-			isl_int_swap(mat->row[i][j], mat->row[j][i]);
-	return mat;
+		for (j = 0; j < mat->n_col; ++j)
+			isl_int_set(transpose->row[j][i], mat->row[i][j]);
+	isl_mat_free(mat);
+	return transpose;
 error:
-	isl_mat_free(ctx, mat);
+	isl_mat_free(mat);
 	return NULL;
 }
 
-struct isl_mat *isl_mat_swap_cols(struct isl_ctx *ctx,
-	struct isl_mat *mat, unsigned i, unsigned j)
+struct isl_mat *isl_mat_swap_cols(struct isl_mat *mat, unsigned i, unsigned j)
 {
 	int r;
 
-	mat = isl_mat_cow(ctx, mat);
+	mat = isl_mat_cow(mat);
 	if (!mat)
 		return NULL;
-	isl_assert(ctx, i < mat->n_col, goto error);
-	isl_assert(ctx, j < mat->n_col, goto error);
+	isl_assert(mat->ctx, i < mat->n_col, goto error);
+	isl_assert(mat->ctx, j < mat->n_col, goto error);
 
 	for (r = 0; r < mat->n_row; ++r)
 		isl_int_swap(mat->row[r][i], mat->row[r][j]);
 	return mat;
 error:
-	isl_mat_free(ctx, mat);
+	isl_mat_free(mat);
 	return NULL;
 }
 
-struct isl_mat *isl_mat_swap_rows(struct isl_ctx *ctx,
-	struct isl_mat *mat, unsigned i, unsigned j)
+struct isl_mat *isl_mat_swap_rows(struct isl_mat *mat, unsigned i, unsigned j)
 {
 	isl_int *t;
 
 	if (!mat)
 		return NULL;
-	mat = isl_mat_cow(ctx, mat);
+	mat = isl_mat_cow(mat);
 	if (!mat)
 		return NULL;
 	t = mat->row[i];
@@ -705,21 +1007,23 @@ struct isl_mat *isl_mat_swap_rows(struct isl_ctx *ctx,
 	return mat;
 }
 
-struct isl_mat *isl_mat_product(struct isl_ctx *ctx,
-	struct isl_mat *left, struct isl_mat *right)
+__isl_give isl_mat *isl_mat_product(__isl_take isl_mat *left,
+	__isl_take isl_mat *right)
 {
 	int i, j, k;
 	struct isl_mat *prod;
 
 	if (!left || !right)
 		goto error;
-	isl_assert(ctx, left->n_col == right->n_row, goto error);
-	prod = isl_mat_alloc(ctx, left->n_row, right->n_col);
+	isl_assert(left->ctx, left->n_col == right->n_row, goto error);
+	prod = isl_mat_alloc(left->ctx, left->n_row, right->n_col);
 	if (!prod)
 		goto error;
 	if (left->n_col == 0) {
 		for (i = 0; i < prod->n_row; ++i)
 			isl_seq_clr(prod->row[i], prod->n_col);
+		isl_mat_free(left);
+		isl_mat_free(right);
 		return prod;
 	}
 	for (i = 0; i < prod->n_row; ++i) {
@@ -731,15 +1035,54 @@ struct isl_mat *isl_mat_product(struct isl_ctx *ctx,
 					    left->row[i][k], right->row[k][j]);
 		}
 	}
-	isl_mat_free(ctx, left);
-	isl_mat_free(ctx, right);
+	isl_mat_free(left);
+	isl_mat_free(right);
 	return prod;
 error:
-	isl_mat_free(ctx, left);
-	isl_mat_free(ctx, right);
+	isl_mat_free(left);
+	isl_mat_free(right);
 	return NULL;
 }
 
+/* Replace the variables x in the rows q by x' given by x = M x',
+ * with M the matrix mat.
+ *
+ * If the number of new variables is greater than the original
+ * number of variables, then the rows q have already been
+ * preextended.  If the new number is smaller, then the coefficients
+ * of the divs, which are not changed, need to be shifted down.
+ * The row q may be the equalities, the inequalities or the
+ * div expressions.  In the latter case, has_div is true and
+ * we need to take into account the extra denominator column.
+ */
+static int preimage(struct isl_ctx *ctx, isl_int **q, unsigned n,
+	unsigned n_div, int has_div, struct isl_mat *mat)
+{
+	int i;
+	struct isl_mat *t;
+	int e;
+
+	if (mat->n_col >= mat->n_row)
+		e = 0;
+	else
+		e = mat->n_row - mat->n_col;
+	if (has_div)
+		for (i = 0; i < n; ++i)
+			isl_int_mul(q[i][0], q[i][0], mat->row[0][0]);
+	t = isl_mat_sub_alloc6(mat->ctx, q, 0, n, has_div, mat->n_row);
+	t = isl_mat_product(t, mat);
+	if (!t)
+		return -1;
+	for (i = 0; i < n; ++i) {
+		isl_seq_swp_or_cpy(q[i] + has_div, t->row[i], t->n_col);
+		isl_seq_cpy(q[i] + has_div + t->n_col,
+			    q[i] + has_div + t->n_col + e, n_div);
+		isl_seq_clr(q[i] + has_div + t->n_col + n_div, e);
+	}
+	isl_mat_free(t);
+	return 0;
+}
+
 /* Replace the variables x in bset by x' given by x = M x', with
  * M the matrix mat.
  *
@@ -750,67 +1093,65 @@ error:
  * the div array too as the number of rows in this array is assumed
  * to be equal to extra.
  */
-struct isl_basic_set *isl_basic_set_preimage(struct isl_ctx *ctx,
-	struct isl_basic_set *bset, struct isl_mat *mat)
+struct isl_basic_set *isl_basic_set_preimage(struct isl_basic_set *bset,
+	struct isl_mat *mat)
 {
-	struct isl_mat *t;
-	int i;
+	struct isl_ctx *ctx;
 
 	if (!bset || !mat)
 		goto error;
 
+	ctx = bset->ctx;
 	bset = isl_basic_set_cow(bset);
 	if (!bset)
 		goto error;
 
 	isl_assert(ctx, bset->dim->nparam == 0, goto error);
-	isl_assert(ctx, bset->n_div == 0, goto error);
 	isl_assert(ctx, 1+bset->dim->n_out == mat->n_row, goto error);
+	isl_assert(ctx, mat->n_col > 0, goto error);
 
-	if (mat->n_col > mat->n_row)
-		bset = isl_basic_set_extend(bset, 0, mat->n_col-1, 0,
-						0, 0);
-	else if (mat->n_col < mat->n_row) {
-		bset->dim = isl_dim_cow(bset->dim);
+	if (mat->n_col > mat->n_row) {
+		bset = isl_basic_set_extend(bset, 0, mat->n_col-1, 0, 0, 0);
+		if (!bset)
+			goto error;
+	} else if (mat->n_col < mat->n_row) {
+		bset->dim = isl_space_cow(bset->dim);
 		if (!bset->dim)
 			goto error;
 		bset->dim->n_out -= mat->n_row - mat->n_col;
 	}
 
-	t = isl_mat_sub_alloc(ctx, bset->eq, 0, bset->n_eq, 0, mat->n_row);
-	t = isl_mat_product(ctx, t, isl_mat_copy(ctx, mat));
-	if (!t)
+	if (preimage(ctx, bset->eq, bset->n_eq, bset->n_div, 0,
+			isl_mat_copy(mat)) < 0)
 		goto error;
-	for (i = 0; i < bset->n_eq; ++i) {
-		isl_seq_swp_or_cpy(bset->eq[i], t->row[i], t->n_col);
-		isl_seq_clr(bset->eq[i]+t->n_col, bset->extra);
-	}
-	isl_mat_free(ctx, t);
 
-	t = isl_mat_sub_alloc(ctx, bset->ineq, 0, bset->n_ineq, 0, mat->n_row);
-	t = isl_mat_product(ctx, t, mat);
-	if (!t)
+	if (preimage(ctx, bset->ineq, bset->n_ineq, bset->n_div, 0,
+			isl_mat_copy(mat)) < 0)
+		goto error;
+
+	if (preimage(ctx, bset->div, bset->n_div, bset->n_div, 1, mat) < 0)
 		goto error2;
-	for (i = 0; i < bset->n_ineq; ++i) {
-		isl_seq_swp_or_cpy(bset->ineq[i], t->row[i], t->n_col);
-		isl_seq_clr(bset->ineq[i]+t->n_col, bset->extra);
-	}
-	isl_mat_free(ctx, t);
+
+	ISL_F_CLR(bset, ISL_BASIC_SET_NO_IMPLICIT);
+	ISL_F_CLR(bset, ISL_BASIC_SET_NO_REDUNDANT);
+	ISL_F_CLR(bset, ISL_BASIC_SET_NORMALIZED);
+	ISL_F_CLR(bset, ISL_BASIC_SET_NORMALIZED_DIVS);
+	ISL_F_CLR(bset, ISL_BASIC_SET_ALL_EQUALITIES);
 
 	bset = isl_basic_set_simplify(bset);
 	bset = isl_basic_set_finalize(bset);
 
 	return bset;
 error:
-	isl_mat_free(ctx, mat);
+	isl_mat_free(mat);
 error2:
 	isl_basic_set_free(bset);
 	return NULL;
 }
 
-struct isl_set *isl_set_preimage(struct isl_ctx *ctx,
-	struct isl_set *set, struct isl_mat *mat)
+struct isl_set *isl_set_preimage(struct isl_set *set, struct isl_mat *mat)
 {
+	struct isl_ctx *ctx;
 	int i;
 
 	set = isl_set_cow(set);
@@ -819,29 +1160,95 @@ struct isl_set *isl_set_preimage(struct isl_ctx *ctx,
 
 	ctx = set->ctx;
 	for (i = 0; i < set->n; ++i) {
-		set->p[i] = isl_basic_set_preimage(ctx, set->p[i],
-						    isl_mat_copy(ctx, mat));
+		set->p[i] = isl_basic_set_preimage(set->p[i],
+						    isl_mat_copy(mat));
 		if (!set->p[i])
 			goto error;
 	}
 	if (mat->n_col != mat->n_row) {
-		set->dim = isl_dim_cow(set->dim);
+		set->dim = isl_space_cow(set->dim);
 		if (!set->dim)
 			goto error;
 		set->dim->n_out += mat->n_col;
 		set->dim->n_out -= mat->n_row;
 	}
-	isl_mat_free(ctx, mat);
+	isl_mat_free(mat);
 	ISL_F_CLR(set, ISL_SET_NORMALIZED);
 	return set;
 error:
 	isl_set_free(set);
-	isl_mat_free(ctx, mat);
+	isl_mat_free(mat);
 	return NULL;
 }
 
-void isl_mat_dump(struct isl_ctx *ctx, struct isl_mat *mat,
-				FILE *out, int indent)
+/* Replace the variables x starting at pos in the rows q
+ * by x' with x = M x' with M the matrix mat.
+ * That is, replace the corresponding coefficients c by c M.
+ */
+static int transform(isl_ctx *ctx, isl_int **q, unsigned n,
+	unsigned pos, __isl_take isl_mat *mat)
+{
+	int i;
+	isl_mat *t;
+
+	t = isl_mat_sub_alloc6(ctx, q, 0, n, pos, mat->n_row);
+	t = isl_mat_product(t, mat);
+	if (!t)
+		return -1;
+	for (i = 0; i < n; ++i)
+		isl_seq_swp_or_cpy(q[i] + pos, t->row[i], t->n_col);
+	isl_mat_free(t);
+	return 0;
+}
+
+/* Replace the variables x of type "type" starting at "first" in "bset"
+ * by x' with x = M x' with M the matrix trans.
+ * That is, replace the corresponding coefficients c by c M.
+ *
+ * The transformation matrix should be a square matrix.
+ */
+__isl_give isl_basic_set *isl_basic_set_transform_dims(
+	__isl_take isl_basic_set *bset, enum isl_dim_type type, unsigned first,
+	__isl_take isl_mat *trans)
+{
+	isl_ctx *ctx;
+	unsigned pos;
+
+	bset = isl_basic_set_cow(bset);
+	if (!bset || !trans)
+		goto error;
+
+	ctx = isl_basic_set_get_ctx(bset);
+	if (trans->n_row != trans->n_col)
+		isl_die(trans->ctx, isl_error_invalid,
+			"expecting square transformation matrix", goto error);
+	if (first + trans->n_row > isl_basic_set_dim(bset, type))
+		isl_die(trans->ctx, isl_error_invalid,
+			"oversized transformation matrix", goto error);
+
+	pos = isl_basic_set_offset(bset, type) + first;
+
+	if (transform(ctx, bset->eq, bset->n_eq, pos, isl_mat_copy(trans)) < 0)
+		goto error;
+	if (transform(ctx, bset->ineq, bset->n_ineq, pos,
+		      isl_mat_copy(trans)) < 0)
+		goto error;
+	if (transform(ctx, bset->div, bset->n_div, 1 + pos,
+		      isl_mat_copy(trans)) < 0)
+		goto error;
+
+	ISL_F_CLR(bset, ISL_BASIC_SET_NORMALIZED);
+	ISL_F_CLR(bset, ISL_BASIC_SET_NORMALIZED_DIVS);
+
+	isl_mat_free(trans);
+	return bset;
+error:
+	isl_mat_free(trans);
+	isl_basic_set_free(bset);
+	return NULL;
+}
+
+void isl_mat_print_internal(__isl_keep isl_mat *mat, FILE *out, int indent)
 {
 	int i, j;
 
@@ -870,12 +1277,19 @@ void isl_mat_dump(struct isl_ctx *ctx, struct isl_mat *mat,
 	}
 }
 
-struct isl_mat *isl_mat_drop_cols(struct isl_ctx *ctx, struct isl_mat *mat,
-				unsigned col, unsigned n)
+void isl_mat_dump(__isl_keep isl_mat *mat)
+{
+	isl_mat_print_internal(mat, stderr, 0);
+}
+
+struct isl_mat *isl_mat_drop_cols(struct isl_mat *mat, unsigned col, unsigned n)
 {
 	int r;
 
-	mat = isl_mat_cow(ctx, mat);
+	if (n == 0)
+		return mat;
+
+	mat = isl_mat_cow(mat);
 	if (!mat)
 		return NULL;
 
@@ -888,12 +1302,11 @@ struct isl_mat *isl_mat_drop_cols(struct isl_ctx *ctx, struct isl_mat *mat,
 	return mat;
 }
 
-struct isl_mat *isl_mat_drop_rows(struct isl_ctx *ctx, struct isl_mat *mat,
-				unsigned row, unsigned n)
+struct isl_mat *isl_mat_drop_rows(struct isl_mat *mat, unsigned row, unsigned n)
 {
 	int r;
 
-	mat = isl_mat_cow(ctx, mat);
+	mat = isl_mat_cow(mat);
 	if (!mat)
 		return NULL;
 
@@ -904,6 +1317,112 @@ struct isl_mat *isl_mat_drop_rows(struct isl_ctx *ctx, struct isl_mat *mat,
 	return mat;
 }
 
+__isl_give isl_mat *isl_mat_insert_cols(__isl_take isl_mat *mat,
+				unsigned col, unsigned n)
+{
+	isl_mat *ext;
+
+	if (!mat)
+		return NULL;
+	if (n == 0)
+		return mat;
+
+	ext = isl_mat_alloc(mat->ctx, mat->n_row, mat->n_col + n);
+	if (!ext)
+		goto error;
+
+	isl_mat_sub_copy(mat->ctx, ext->row, mat->row, mat->n_row, 0, 0, col);
+	isl_mat_sub_copy(mat->ctx, ext->row, mat->row, mat->n_row,
+				col + n, col, mat->n_col - col);
+
+	isl_mat_free(mat);
+	return ext;
+error:
+	isl_mat_free(mat);
+	return NULL;
+}
+
+__isl_give isl_mat *isl_mat_insert_zero_cols(__isl_take isl_mat *mat,
+	unsigned first, unsigned n)
+{
+	int i;
+
+	if (!mat)
+		return NULL;
+	mat = isl_mat_insert_cols(mat, first, n);
+	if (!mat)
+		return NULL;
+
+	for (i = 0; i < mat->n_row; ++i)
+		isl_seq_clr(mat->row[i] + first, n);
+
+	return mat;
+}
+
+__isl_give isl_mat *isl_mat_add_zero_cols(__isl_take isl_mat *mat, unsigned n)
+{
+	if (!mat)
+		return NULL;
+
+	return isl_mat_insert_zero_cols(mat, mat->n_col, n);
+}
+
+__isl_give isl_mat *isl_mat_insert_rows(__isl_take isl_mat *mat,
+				unsigned row, unsigned n)
+{
+	isl_mat *ext;
+
+	if (!mat)
+		return NULL;
+	if (n == 0)
+		return mat;
+
+	ext = isl_mat_alloc(mat->ctx, mat->n_row + n, mat->n_col);
+	if (!ext)
+		goto error;
+
+	isl_mat_sub_copy(mat->ctx, ext->row, mat->row, row, 0, 0, mat->n_col);
+	isl_mat_sub_copy(mat->ctx, ext->row + row + n, mat->row + row,
+				mat->n_row - row, 0, 0, mat->n_col);
+
+	isl_mat_free(mat);
+	return ext;
+error:
+	isl_mat_free(mat);
+	return NULL;
+}
+
+__isl_give isl_mat *isl_mat_add_rows(__isl_take isl_mat *mat, unsigned n)
+{
+	if (!mat)
+		return NULL;
+
+	return isl_mat_insert_rows(mat, mat->n_row, n);
+}
+
+__isl_give isl_mat *isl_mat_insert_zero_rows(__isl_take isl_mat *mat,
+	unsigned row, unsigned n)
+{
+	int i;
+
+	mat = isl_mat_insert_rows(mat, row, n);
+	if (!mat)
+		return NULL;
+	
+	for (i = 0; i < n; ++i)
+		isl_seq_clr(mat->row[row + i], mat->n_col);
+
+	return mat;
+}
+
+__isl_give isl_mat *isl_mat_add_zero_rows(__isl_take isl_mat *mat, unsigned n)
+{
+	if (!mat)
+		return NULL;
+
+	return isl_mat_insert_zero_rows(mat, mat->n_row, n);
+}
+
 void isl_mat_col_submul(struct isl_mat *mat,
 			int dst_col, isl_int f, int src_col)
 {
@@ -913,6 +1432,18 @@ void isl_mat_col_submul(struct isl_mat *mat,
 		isl_int_submul(mat->row[i][dst_col], f, mat->row[i][src_col]);
 }
 
+void isl_mat_col_add(__isl_keep isl_mat *mat, int dst_col, int src_col)
+{
+	int i;
+
+	if (!mat)
+		return;
+
+	for (i = 0; i < mat->n_row; ++i)
+		isl_int_add(mat->row[i][dst_col],
+			    mat->row[i][dst_col], mat->row[i][src_col]);
+}
+
 void isl_mat_col_mul(struct isl_mat *mat, int dst_col, isl_int f, int src_col)
 {
 	int i;
@@ -920,3 +1451,244 @@ void isl_mat_col_mul(struct isl_mat *mat, int dst_col, isl_int f, int src_col)
 	for (i = 0; i < mat->n_row; ++i)
 		isl_int_mul(mat->row[i][dst_col], f, mat->row[i][src_col]);
 }
+
+struct isl_mat *isl_mat_unimodular_complete(struct isl_mat *M, int row)
+{
+	int r;
+	struct isl_mat *H = NULL, *Q = NULL;
+
+	if (!M)
+		return NULL;
+
+	isl_assert(M->ctx, M->n_row == M->n_col, goto error);
+	M->n_row = row;
+	H = isl_mat_left_hermite(isl_mat_copy(M), 0, NULL, &Q);
+	M->n_row = M->n_col;
+	if (!H)
+		goto error;
+	for (r = 0; r < row; ++r)
+		isl_assert(M->ctx, isl_int_is_one(H->row[r][r]), goto error);
+	for (r = row; r < M->n_row; ++r)
+		isl_seq_cpy(M->row[r], Q->row[r], M->n_col);
+	isl_mat_free(H);
+	isl_mat_free(Q);
+	return M;
+error:
+	isl_mat_free(H);
+	isl_mat_free(Q);
+	isl_mat_free(M);
+	return NULL;
+}
+
+__isl_give isl_mat *isl_mat_concat(__isl_take isl_mat *top,
+	__isl_take isl_mat *bot)
+{
+	struct isl_mat *mat;
+
+	if (!top || !bot)
+		goto error;
+
+	isl_assert(top->ctx, top->n_col == bot->n_col, goto error);
+	if (top->n_row == 0) {
+		isl_mat_free(top);
+		return bot;
+	}
+	if (bot->n_row == 0) {
+		isl_mat_free(bot);
+		return top;
+	}
+
+	mat = isl_mat_alloc(top->ctx, top->n_row + bot->n_row, top->n_col);
+	if (!mat)
+		goto error;
+	isl_mat_sub_copy(mat->ctx, mat->row, top->row, top->n_row,
+			 0, 0, mat->n_col);
+	isl_mat_sub_copy(mat->ctx, mat->row + top->n_row, bot->row, bot->n_row,
+			 0, 0, mat->n_col);
+	isl_mat_free(top);
+	isl_mat_free(bot);
+	return mat;
+error:
+	isl_mat_free(top);
+	isl_mat_free(bot);
+	return NULL;
+}
+
+int isl_mat_is_equal(__isl_keep isl_mat *mat1, __isl_keep isl_mat *mat2)
+{
+	int i;
+
+	if (!mat1 || !mat2)
+		return -1;
+
+	if (mat1->n_row != mat2->n_row)
+		return 0;
+
+	if (mat1->n_col != mat2->n_col)
+		return 0;
+
+	for (i = 0; i < mat1->n_row; ++i)
+		if (!isl_seq_eq(mat1->row[i], mat2->row[i], mat1->n_col))
+			return 0;
+
+	return 1;
+}
+
+__isl_give isl_mat *isl_mat_from_row_vec(__isl_take isl_vec *vec)
+{
+	struct isl_mat *mat;
+
+	if (!vec)
+		return NULL;
+	mat = isl_mat_alloc(vec->ctx, 1, vec->size);
+	if (!mat)
+		goto error;
+
+	isl_seq_cpy(mat->row[0], vec->el, vec->size);
+
+	isl_vec_free(vec);
+	return mat;
+error:
+	isl_vec_free(vec);
+	return NULL;
+}
+
+__isl_give isl_mat *isl_mat_vec_concat(__isl_take isl_mat *top,
+	__isl_take isl_vec *bot)
+{
+	return isl_mat_concat(top, isl_mat_from_row_vec(bot));
+}
+
+__isl_give isl_mat *isl_mat_move_cols(__isl_take isl_mat *mat,
+	unsigned dst_col, unsigned src_col, unsigned n)
+{
+	isl_mat *res;
+
+	if (!mat)
+		return NULL;
+	if (n == 0 || dst_col == src_col)
+		return mat;
+
+	res = isl_mat_alloc(mat->ctx, mat->n_row, mat->n_col);
+	if (!res)
+		goto error;
+
+	if (dst_col < src_col) {
+		isl_mat_sub_copy(res->ctx, res->row, mat->row, mat->n_row,
+				 0, 0, dst_col);
+		isl_mat_sub_copy(res->ctx, res->row, mat->row, mat->n_row,
+				 dst_col, src_col, n);
+		isl_mat_sub_copy(res->ctx, res->row, mat->row, mat->n_row,
+				 dst_col + n, dst_col, src_col - dst_col);
+		isl_mat_sub_copy(res->ctx, res->row, mat->row, mat->n_row,
+				 src_col + n, src_col + n,
+				 res->n_col - src_col - n);
+	} else {
+		isl_mat_sub_copy(res->ctx, res->row, mat->row, mat->n_row,
+				 0, 0, src_col);
+		isl_mat_sub_copy(res->ctx, res->row, mat->row, mat->n_row,
+				 src_col, src_col + n, dst_col - src_col);
+		isl_mat_sub_copy(res->ctx, res->row, mat->row, mat->n_row,
+				 dst_col, src_col, n);
+		isl_mat_sub_copy(res->ctx, res->row, mat->row, mat->n_row,
+				 dst_col + n, dst_col + n,
+				 res->n_col - dst_col - n);
+	}
+	isl_mat_free(mat);
+
+	return res;
+error:
+	isl_mat_free(mat);
+	return NULL;
+}
+
+void isl_mat_gcd(__isl_keep isl_mat *mat, isl_int *gcd)
+{
+	int i;
+	isl_int g;
+
+	isl_int_set_si(*gcd, 0);
+	if (!mat)
+		return;
+
+	isl_int_init(g);
+	for (i = 0; i < mat->n_row; ++i) {
+		isl_seq_gcd(mat->row[i], mat->n_col, &g);
+		isl_int_gcd(*gcd, *gcd, g);
+	}
+	isl_int_clear(g);
+}
+
+__isl_give isl_mat *isl_mat_scale_down(__isl_take isl_mat *mat, isl_int m)
+{
+	int i;
+
+	if (isl_int_is_one(m))
+		return mat;
+
+	mat = isl_mat_cow(mat);
+	if (!mat)
+		return NULL;
+
+	for (i = 0; i < mat->n_row; ++i)
+		isl_seq_scale_down(mat->row[i], mat->row[i], m, mat->n_col);
+
+	return mat;
+}
+
+__isl_give isl_mat *isl_mat_scale_down_row(__isl_take isl_mat *mat, int row,
+	isl_int m)
+{
+	if (isl_int_is_one(m))
+		return mat;
+
+	mat = isl_mat_cow(mat);
+	if (!mat)
+		return NULL;
+
+	isl_seq_scale_down(mat->row[row], mat->row[row], m, mat->n_col);
+
+	return mat;
+}
+
+__isl_give isl_mat *isl_mat_normalize(__isl_take isl_mat *mat)
+{
+	isl_int gcd;
+
+	if (!mat)
+		return NULL;
+
+	isl_int_init(gcd);
+	isl_mat_gcd(mat, &gcd);
+	mat = isl_mat_scale_down(mat, gcd);
+	isl_int_clear(gcd);
+
+	return mat;
+}
+
+__isl_give isl_mat *isl_mat_normalize_row(__isl_take isl_mat *mat, int row)
+{
+	mat = isl_mat_cow(mat);
+	if (!mat)
+		return NULL;
+
+	isl_seq_normalize(mat->ctx, mat->row[row], mat->n_col);
+
+	return mat;
+}
+
+/* Number of initial non-zero columns.
+ */
+int isl_mat_initial_non_zero_cols(__isl_keep isl_mat *mat)
+{
+	int i;
+
+	if (!mat)
+		return -1;
+
+	for (i = 0; i < mat->n_col; ++i)
+		if (row_first_non_zero(mat->row, mat->n_row, i) < 0)
+			break;
+
+	return i;
+}