/*
* Copyright 2008-2009 Katholieke Universiteit Leuven
+ * Copyright 2010 INRIA Saclay
*
* 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 INRIA Saclay - Ile-de-France, Parc Club Orsay Universite,
+ * ZAC des vignes, 4 rue Jacques Monod, 91893 Orsay, France
*/
#include <isl_mat_private.h>
/* Given a set of equalities
*
+ * B(y) + A x = 0 (*)
+ *
+ * compute and return an affine transformation T,
+ *
+ * y = T y'
+ *
+ * that bijectively maps the integer vectors y' to integer
+ * vectors y that satisfy the modulo constraints for some value of x.
+ *
+ * Let [H 0] be the Hermite Normal Form of A, i.e.,
+ *
+ * A = [H 0] Q
+ *
+ * Then y is a solution of (*) iff
+ *
+ * H^-1 B(y) (= - [I 0] Q x)
+ *
+ * is an integer vector. Let d be the common denominator of H^-1.
+ * We impose
+ *
+ * d H^-1 B(y) = 0 mod d
+ *
+ * and compute the solution using isl_mat_parameter_compression.
+ */
+__isl_give isl_mat *isl_mat_parameter_compression_ext(__isl_take isl_mat *B,
+ __isl_take isl_mat *A)
+{
+ isl_ctx *ctx;
+ isl_vec *d;
+ int n_row, n_col;
+
+ if (!A)
+ return isl_mat_free(B);
+
+ ctx = isl_mat_get_ctx(A);
+ n_row = A->n_row;
+ n_col = A->n_col;
+ A = isl_mat_left_hermite(A, 0, NULL, NULL);
+ A = isl_mat_drop_cols(A, n_row, n_col - n_row);
+ A = isl_mat_lin_to_aff(A);
+ A = isl_mat_right_inverse(A);
+ d = isl_vec_alloc(ctx, n_row);
+ if (A)
+ d = isl_vec_set(d, A->row[0][0]);
+ A = isl_mat_drop_rows(A, 0, 1);
+ A = isl_mat_drop_cols(A, 0, 1);
+ B = isl_mat_product(A, B);
+
+ return isl_mat_parameter_compression(B, d);
+}
+
+/* Given a set of equalities
+ *
* M x - c = 0
*
* this function computes a unimodular transformation from a lower-dimensional