X-Git-Url: http://review.tizen.org/git/?a=blobdiff_plain;f=isl_mat.c;h=cff812334e9fc5d625bcf64b96fc0ad4d3d36e2c;hb=de51a9bc4da5dd3f1f9f57c2362da6f9752c44e0;hp=660ed234e235d632c66ce0a07386191d3e603660;hpb=d059396b4e4cda927161af041ea3b07913400b28;p=platform%2Fupstream%2Fisl.git

diff --git a/isl_mat.c b/isl_mat.c
index 660ed23..cff8123 100644
--- a/isl_mat.c
+++ b/isl_mat.c
@@ -1,7 +1,23 @@
-#include "isl_dim.h"
-#include "isl_seq.h"
-#include "isl_mat.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/space.h>
+#include <isl/seq.h>
+#include <isl_mat_private.h>
 #include "isl_map_private.h"
+#include <isl_space_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 +60,7 @@ struct isl_mat *isl_mat_extend(struct isl_mat *mat,
 {
 	int i;
 	isl_int *old;
+	isl_int **row;
 
 	if (!mat)
 		return NULL;
@@ -72,14 +89,14 @@ 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 +112,7 @@ 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 +139,15 @@ 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)
 {
@@ -193,7 +219,69 @@ void isl_mat_free(struct isl_mat *mat)
 	free(mat);
 }
 
-struct isl_mat *isl_mat_identity(struct isl_ctx *ctx, unsigned n_row)
+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;
+}
+
+__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;
+}
+
+__isl_give isl_mat *isl_mat_diag(isl_ctx *ctx, unsigned n_row, isl_int d)
 {
 	int i;
 	struct isl_mat *mat;
@@ -203,13 +291,20 @@ 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;
@@ -473,6 +568,7 @@ error:
 		isl_mat_free(*U);
 		*U = NULL;
 	}
+	isl_mat_free(M);
 	return NULL;
 }
 
@@ -514,7 +610,7 @@ 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) {
@@ -523,6 +619,45 @@ 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)
@@ -713,7 +848,7 @@ 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)
@@ -765,6 +900,7 @@ struct isl_mat *isl_mat_right_inverse(struct isl_mat *mat)
 	return inv;
 error:
 	isl_mat_free(mat);
+	isl_mat_free(inv);
 	return NULL;
 }
 
@@ -773,6 +909,9 @@ 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)
@@ -842,6 +981,8 @@ struct isl_mat *isl_mat_product(struct isl_mat *left, struct isl_mat *right)
 	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) {
@@ -887,7 +1028,7 @@ 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;
@@ -926,12 +1067,14 @@ 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;
@@ -982,7 +1125,7 @@ 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;
@@ -997,7 +1140,74 @@ 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;
 
@@ -1026,6 +1236,11 @@ 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;
@@ -1058,6 +1273,112 @@ 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)
 {
@@ -1067,6 +1388,18 @@ 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;
@@ -1156,3 +1489,162 @@ int isl_mat_is_equal(__isl_keep isl_mat *mat1, __isl_keep isl_mat *mat2)
 
 	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;
+}