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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  * NOTE: This file comes from a partly modified version of files slu_[s,d,c,z]defs.h
12  * -- SuperLU routine (version 4.1) --
13  * Univ. of California Berkeley, Xerox Palo Alto Research Center,
14  * and Lawrence Berkeley National Lab.
15  * November, 2010
16  *
17  * Global data structures used in LU factorization -
18  *
19  *   nsuper: #supernodes = nsuper + 1, numbered [0, nsuper].
20  *   (xsup,supno): supno[i] is the supernode no to which i belongs;
21  *  xsup(s) points to the beginning of the s-th supernode.
22  *  e.g.   supno 0 1 2 2 3 3 3 4 4 4 4 4   (n=12)
23  *          xsup 0 1 2 4 7 12
24  *  Note: dfs will be performed on supernode rep. relative to the new
25  *        row pivoting ordering
26  *
27  *   (xlsub,lsub): lsub[*] contains the compressed subscript of
28  *  rectangular supernodes; xlsub[j] points to the starting
29  *  location of the j-th column in lsub[*]. Note that xlsub
30  *  is indexed by column.
31  *  Storage: original row subscripts
32  *
33  *      During the course of sparse LU factorization, we also use
34  *  (xlsub,lsub) for the purpose of symmetric pruning. For each
35  *  supernode {s,s+1,...,t=s+r} with first column s and last
36  *  column t, the subscript set
37  *    lsub[j], j=xlsub[s], .., xlsub[s+1]-1
38  *  is the structure of column s (i.e. structure of this supernode).
39  *  It is used for the storage of numerical values.
40  *  Furthermore,
41  *    lsub[j], j=xlsub[t], .., xlsub[t+1]-1
42  *  is the structure of the last column t of this supernode.
43  *  It is for the purpose of symmetric pruning. Therefore, the
44  *  structural subscripts can be rearranged without making physical
45  *  interchanges among the numerical values.
46  *
47  *  However, if the supernode has only one column, then we
48  *  only keep one set of subscripts. For any subscript interchange
49  *  performed, similar interchange must be done on the numerical
50  *  values.
51  *
52  *  The last column structures (for pruning) will be removed
53  *  after the numercial LU factorization phase.
54  *
55  *   (xlusup,lusup): lusup[*] contains the numerical values of the
56  *  rectangular supernodes; xlusup[j] points to the starting
57  *  location of the j-th column in storage vector lusup[*]
58  *  Note: xlusup is indexed by column.
59  *  Each rectangular supernode is stored by column-major
60  *  scheme, consistent with Fortran 2-dim array storage.
61  *
62  *   (xusub,ucol,usub): ucol[*] stores the numerical values of
63  *  U-columns outside the rectangular supernodes. The row
64  *  subscript of nonzero ucol[k] is stored in usub[k].
65  *  xusub[i] points to the starting location of column i in ucol.
66  *  Storage: new row subscripts; that is subscripts of PA.
67  */
68 
69 #ifndef EIGEN_LU_STRUCTS
70 #define EIGEN_LU_STRUCTS
71 namespace Eigen {
72 namespace internal {
73 
74 typedef enum {LUSUP, UCOL, LSUB, USUB, LLVL, ULVL} MemType;
75 
76 template <typename IndexVector, typename ScalarVector>
77 struct LU_GlobalLU_t {
78   typedef typename IndexVector::Scalar StorageIndex;
79   IndexVector xsup; //First supernode column ... xsup(s) points to the beginning of the s-th supernode
80   IndexVector supno; // Supernode number corresponding to this column (column to supernode mapping)
81   ScalarVector  lusup; // nonzero values of L ordered by columns
82   IndexVector lsub; // Compressed row indices of L rectangular supernodes.
83   IndexVector xlusup; // pointers to the beginning of each column in lusup
84   IndexVector xlsub; // pointers to the beginning of each column in lsub
85   Index   nzlmax; // Current max size of lsub
86   Index   nzlumax; // Current max size of lusup
87   ScalarVector  ucol; // nonzero values of U ordered by columns
88   IndexVector usub; // row indices of U columns in ucol
89   IndexVector xusub; // Pointers to the beginning of each column of U in ucol
90   Index   nzumax; // Current max size of ucol
91   Index   n; // Number of columns in the matrix
92   Index   num_expansions;
93 };
94 
95 // Values to set for performance
96 struct perfvalues {
97   Index panel_size; // a panel consists of at most <panel_size> consecutive columns
98   Index relax; // To control degree of relaxing supernodes. If the number of nodes (columns)
99                 // in a subtree of the elimination tree is less than relax, this subtree is considered
100                 // as one supernode regardless of the row structures of those columns
101   Index maxsuper; // The maximum size for a supernode in complete LU
102   Index rowblk; // The minimum row dimension for 2-D blocking to be used;
103   Index colblk; // The minimum column dimension for 2-D blocking to be used;
104   Index fillfactor; // The estimated fills factors for L and U, compared with A
105 };
106 
107 } // end namespace internal
108 
109 } // end namespace Eigen
110 #endif // EIGEN_LU_STRUCTS
111