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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 Dsir Nuentsa-Wakam <desire.nuentsa_wakam (at) 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 Index;
     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 template <typename Index>
     97 struct perfvalues {
     98   Index panel_size; // a panel consists of at most <panel_size> consecutive columns
     99   Index relax; // To control degree of relaxing supernodes. If the number of nodes (columns)
    100                 // in a subtree of the elimination tree is less than relax, this subtree is considered
    101                 // as one supernode regardless of the row structures of those columns
    102   Index maxsuper; // The maximum size for a supernode in complete LU
    103   Index rowblk; // The minimum row dimension for 2-D blocking to be used;
    104   Index colblk; // The minimum column dimension for 2-D blocking to be used;
    105   Index fillfactor; // The estimated fills factors for L and U, compared with A
    106 };
    107 
    108 } // end namespace internal
    109 
    110 } // end namespace Eigen
    111 #endif // EIGEN_LU_STRUCTS
    112