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Eigen  3.4.90 (git rev e3e74001f7c4bf95f0dde572e8a08c5b2918a3ab)
SparseColEtree.h
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 
39 template<typename Index, typename IndexVector>
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 
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 
129 template <typename IndexVector>
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 
177 template <typename IndexVector>
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
Namespace containing all symbols from the Eigen library.
Definition: Core:141
EIGEN_DEFAULT_DENSE_INDEX_TYPE Index
The Index type as used for the API.
Definition: Meta.h:74