X-Git-Url: http://review.tizen.org/git/?a=blobdiff_plain;f=isl_mat.c;h=129cdc749eb81f10d549d6e46f01aaff2c67d42b;hb=63fb8a7f484648c3caa25351c8c94ac2395ec563;hp=c96017edb5ea474e740addfa820cd2f10ce4cb92;hpb=15b829fd4f5a937541acac277ef097a6e3738775;p=platform%2Fupstream%2Fisl.git

diff --git a/isl_mat.c b/isl_mat.c
index c96017e..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)
@@ -44,6 +61,7 @@ struct isl_mat *isl_mat_extend(struct isl_mat *mat,
 {
 	int i;
 	isl_int *old;
+	isl_int **row;
 
 	if (!mat)
 		return NULL;
@@ -72,14 +90,14 @@ struct isl_mat *isl_mat_extend(struct isl_mat *mat,
 	if (!mat)
 		goto error;
 
-	assert(mat->ref == 1);
 	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;
-	mat->row = isl_realloc_array(mat->ctx, mat->row, isl_int *, n_row);
-	if (!mat->row)
+	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);
@@ -95,7 +113,7 @@ error:
 	return NULL;
 }
 
-struct isl_mat *isl_mat_sub_alloc(struct isl_ctx *ctx, isl_int **row,
+__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;
@@ -122,6 +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)
 {
@@ -178,22 +205,123 @@ struct isl_mat *isl_mat_cow(struct isl_mat *mat)
 	return mat2;
 }
 
-void isl_mat_free(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(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]);
 }
 
-struct isl_mat *isl_mat_identity(struct isl_ctx *ctx, unsigned n_row)
+__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;
@@ -203,13 +331,20 @@ 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;
 }
 
+__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;
@@ -218,7 +353,7 @@ struct isl_vec *isl_mat_vec_product(struct isl_mat *mat, struct isl_vec *vec)
 	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(mat->ctx, mat->n_row);
 	if (!prod)
@@ -236,6 +371,63 @@ error:
 	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)
 {
@@ -245,14 +437,14 @@ struct isl_mat *isl_mat_aff_direct_sum(struct isl_mat *left,
 	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);
 
@@ -416,6 +608,7 @@ error:
 		isl_mat_free(*U);
 		*U = NULL;
 	}
+	isl_mat_free(M);
 	return NULL;
 }
 
@@ -457,7 +650,7 @@ struct isl_mat *isl_mat_lin_to_aff(struct isl_mat *mat)
 		return NULL;
 	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) {
@@ -466,6 +659,45 @@ struct isl_mat *isl_mat_lin_to_aff(struct isl_mat *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)
@@ -550,7 +782,7 @@ struct isl_mat *isl_mat_inverse_product(struct isl_mat *left,
 		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)
@@ -575,11 +807,11 @@ struct isl_mat *isl_mat_inverse_product(struct isl_mat *left,
 			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);
 		}
@@ -591,7 +823,7 @@ struct isl_mat *isl_mat_inverse_product(struct isl_mat *left,
 		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]);
@@ -656,7 +888,7 @@ struct isl_mat *isl_mat_right_inverse(struct isl_mat *mat)
 		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)
@@ -708,6 +940,7 @@ struct isl_mat *isl_mat_right_inverse(struct isl_mat *mat)
 	return inv;
 error:
 	isl_mat_free(mat);
+	isl_mat_free(inv);
 	return NULL;
 }
 
@@ -716,6 +949,9 @@ struct isl_mat *isl_mat_transpose(struct isl_mat *mat)
 	struct isl_mat *transpose = NULL;
 	int i, j;
 
+	if (!mat)
+		return NULL;
+
 	if (mat->n_col == mat->n_row) {
 		mat = isl_mat_cow(mat);
 		if (!mat)
@@ -745,8 +981,8 @@ struct isl_mat *isl_mat_swap_cols(struct isl_mat *mat, unsigned i, unsigned j)
 	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]);
@@ -771,20 +1007,23 @@ struct isl_mat *isl_mat_swap_rows(struct isl_mat *mat, unsigned i, unsigned j)
 	return mat;
 }
 
-struct isl_mat *isl_mat_product(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);
+	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) {
@@ -830,7 +1069,7 @@ static int preimage(struct isl_ctx *ctx, isl_int **q, unsigned n,
 	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_alloc(mat->ctx, q, 0, n, has_div, mat->n_row);
+	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;
@@ -869,12 +1108,14 @@ struct isl_basic_set *isl_basic_set_preimage(struct isl_basic_set *bset,
 
 	isl_assert(ctx, bset->dim->nparam == 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;
@@ -925,7 +1166,7 @@ struct isl_set *isl_set_preimage(struct isl_set *set, struct isl_mat *mat)
 			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;
@@ -940,7 +1181,74 @@ error:
 	return NULL;
 }
 
-void isl_mat_dump(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;
 
@@ -969,10 +1277,18 @@ void isl_mat_dump(struct isl_mat *mat, FILE *out, int indent)
 	}
 }
 
+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;
 
+	if (n == 0)
+		return mat;
+
 	mat = isl_mat_cow(mat);
 	if (!mat)
 		return NULL;
@@ -1001,6 +1317,112 @@ struct isl_mat *isl_mat_drop_rows(struct isl_mat *mat, unsigned row, unsigned n)
 	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)
 {
@@ -1010,6 +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;
@@ -1023,14 +1457,17 @@ struct isl_mat *isl_mat_unimodular_complete(struct isl_mat *M, int row)
 	int r;
 	struct isl_mat *H = NULL, *Q = NULL;
 
-	isl_assert(ctx, M->n_row == M->n_col, goto error);
+	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(ctx, isl_int_is_one(H->row[r][r]), goto error);
+		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);
@@ -1042,3 +1479,216 @@ error:
 	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;
+}