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1 // This file is part of Eigen, a lightweight C++ template library
2 // for linear algebra.
3 //
4 // Copyright (C) 2012 Désiré Nuentsa-Wakam <desire.nuentsa_wakam@inria.fr>
5 //
6 // This Source Code Form is subject to the terms of the Mozilla
7 // Public License v. 2.0. If a copy of the MPL was not distributed
8 // with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
9 
10 
11 /*
12 
13  * NOTE: This file is the modified version of sp_coletree.c file in SuperLU
14 
15  * -- SuperLU routine (version 3.1) --
16  * Univ. of California Berkeley, Xerox Palo Alto Research Center,
17  * and Lawrence Berkeley National Lab.
18  * August 1, 2008
19  *
20  * Copyright (c) 1994 by Xerox Corporation.  All rights reserved.
21  *
22  * THIS MATERIAL IS PROVIDED AS IS, WITH ABSOLUTELY NO WARRANTY
23  * EXPRESSED OR IMPLIED.  ANY USE IS AT YOUR OWN RISK.
24  *
25  * Permission is hereby granted to use or copy this program for any
26  * purpose, provided the above notices are retained on all copies.
27  * Permission to modify the code and to distribute modified code is
28  * granted, provided the above notices are retained, and a notice that
29  * the code was modified is included with the above copyright notice.
30  */
31 #ifndef SPARSE_COLETREE_H
32 #define SPARSE_COLETREE_H
33 
34 namespace Eigen {
35 
36 namespace internal {
37 
38 /** Find the root of the tree/set containing the vertex i : Use Path halving */
39 template<typename Index, typename IndexVector>
etree_find(Index i,IndexVector & pp)40 Index etree_find (Index i, IndexVector& pp)
41 {
42   Index p = pp(i); // Parent
43   Index gp = pp(p); // Grand parent
44   while (gp != p)
45   {
46     pp(i) = gp; // Parent pointer on find path is changed to former grand parent
47     i = gp;
48     p = pp(i);
49     gp = pp(p);
50   }
51   return p;
52 }
53 
54 /** Compute the column elimination tree of a sparse matrix
55   * \param mat The matrix in column-major format.
56   * \param parent The elimination tree
57   * \param firstRowElt The column index of the first element in each row
58   * \param perm The permutation to apply to the column of \b mat
59   */
60 template <typename MatrixType, typename IndexVector>
61 int coletree(const MatrixType& mat, IndexVector& parent, IndexVector& firstRowElt, typename MatrixType::StorageIndex *perm=0)
62 {
63   typedef typename MatrixType::StorageIndex StorageIndex;
64   StorageIndex nc = convert_index<StorageIndex>(mat.cols()); // Number of columns
65   StorageIndex m = convert_index<StorageIndex>(mat.rows());
66   StorageIndex diagSize = (std::min)(nc,m);
67   IndexVector root(nc); // root of subtree of etree
68   root.setZero();
69   IndexVector pp(nc); // disjoint sets
70   pp.setZero(); // Initialize disjoint sets
71   parent.resize(mat.cols());
72   //Compute first nonzero column in each row
73   firstRowElt.resize(m);
74   firstRowElt.setConstant(nc);
75   firstRowElt.segment(0, diagSize).setLinSpaced(diagSize, 0, diagSize-1);
76   bool found_diag;
77   for (StorageIndex col = 0; col < nc; col++)
78   {
79     StorageIndex pcol = col;
80     if(perm) pcol  = perm[col];
81     for (typename MatrixType::InnerIterator it(mat, pcol); it; ++it)
82     {
83       Index row = it.row();
84       firstRowElt(row) = (std::min)(firstRowElt(row), col);
85     }
86   }
87   /* Compute etree by Liu's algorithm for symmetric matrices,
88           except use (firstRowElt[r],c) in place of an edge (r,c) of A.
89     Thus each row clique in A'*A is replaced by a star
90     centered at its first vertex, which has the same fill. */
91   StorageIndex rset, cset, rroot;
92   for (StorageIndex col = 0; col < nc; col++)
93   {
94     found_diag = col>=m;
95     pp(col) = col;
96     cset = col;
97     root(cset) = col;
98     parent(col) = nc;
99     /* The diagonal element is treated here even if it does not exist in the matrix
100      * hence the loop is executed once more */
101     StorageIndex pcol = col;
102     if(perm) pcol  = perm[col];
103     for (typename MatrixType::InnerIterator it(mat, pcol); it||!found_diag; ++it)
104     { //  A sequence of interleaved find and union is performed
105       Index i = col;
106       if(it) i = it.index();
107       if (i == col) found_diag = true;
108 
109       StorageIndex row = firstRowElt(i);
110       if (row >= col) continue;
111       rset = internal::etree_find(row, pp); // Find the name of the set containing row
112       rroot = root(rset);
113       if (rroot != col)
114       {
115         parent(rroot) = col;
116         pp(cset) = rset;
117         cset = rset;
118         root(cset) = col;
119       }
120     }
121   }
122   return 0;
123 }
124 
125 /**
126   * Depth-first search from vertex n.  No recursion.
127   * This routine was contributed by Cédric Doucet, CEDRAT Group, Meylan, France.
128 */
129 template <typename IndexVector>
nr_etdfs(typename IndexVector::Scalar n,IndexVector & parent,IndexVector & first_kid,IndexVector & next_kid,IndexVector & post,typename IndexVector::Scalar postnum)130 void nr_etdfs (typename IndexVector::Scalar n, IndexVector& parent, IndexVector& first_kid, IndexVector& next_kid, IndexVector& post, typename IndexVector::Scalar postnum)
131 {
132   typedef typename IndexVector::Scalar StorageIndex;
133   StorageIndex current = n, first, next;
134   while (postnum != n)
135   {
136     // No kid for the current node
137     first = first_kid(current);
138 
139     // no kid for the current node
140     if (first == -1)
141     {
142       // Numbering this node because it has no kid
143       post(current) = postnum++;
144 
145       // looking for the next kid
146       next = next_kid(current);
147       while (next == -1)
148       {
149         // No more kids : back to the parent node
150         current = parent(current);
151         // numbering the parent node
152         post(current) = postnum++;
153 
154         // Get the next kid
155         next = next_kid(current);
156       }
157       // stopping criterion
158       if (postnum == n+1) return;
159 
160       // Updating current node
161       current = next;
162     }
163     else
164     {
165       current = first;
166     }
167   }
168 }
169 
170 
171 /**
172   * \brief Post order a tree
173   * \param n the number of nodes
174   * \param parent Input tree
175   * \param post postordered tree
176   */
177 template <typename IndexVector>
treePostorder(typename IndexVector::Scalar n,IndexVector & parent,IndexVector & post)178 void treePostorder(typename IndexVector::Scalar n, IndexVector& parent, IndexVector& post)
179 {
180   typedef typename IndexVector::Scalar StorageIndex;
181   IndexVector first_kid, next_kid; // Linked list of children
182   StorageIndex postnum;
183   // Allocate storage for working arrays and results
184   first_kid.resize(n+1);
185   next_kid.setZero(n+1);
186   post.setZero(n+1);
187 
188   // Set up structure describing children
189   first_kid.setConstant(-1);
190   for (StorageIndex v = n-1; v >= 0; v--)
191   {
192     StorageIndex dad = parent(v);
193     next_kid(v) = first_kid(dad);
194     first_kid(dad) = v;
195   }
196 
197   // Depth-first search from dummy root vertex #n
198   postnum = 0;
199   internal::nr_etdfs(n, parent, first_kid, next_kid, post, postnum);
200 }
201 
202 } // end namespace internal
203 
204 } // end namespace Eigen
205 
206 #endif // SPARSE_COLETREE_H
207