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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
// Copyright (C) 2012 Désiré Nuentsa-Wakam <>
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at
* NOTE: This file comes from a partly modified version of files slu_[s,d,c,z]defs.h
* -- SuperLU routine (version 4.1) --
* Univ. of California Berkeley, Xerox Palo Alto Research Center,
* and Lawrence Berkeley National Lab.
* November, 2010
* Global data structures used in LU factorization -
* nsuper: #supernodes = nsuper + 1, numbered [0, nsuper].
* (xsup,supno): supno[i] is the supernode no to which i belongs;
* xsup(s) points to the beginning of the s-th supernode.
* e.g. supno 0 1 2 2 3 3 3 4 4 4 4 4 (n=12)
* xsup 0 1 2 4 7 12
* Note: dfs will be performed on supernode rep. relative to the new
* row pivoting ordering
* (xlsub,lsub): lsub[*] contains the compressed subscript of
* rectangular supernodes; xlsub[j] points to the starting
* location of the j-th column in lsub[*]. Note that xlsub
* is indexed by column.
* Storage: original row subscripts
* During the course of sparse LU factorization, we also use
* (xlsub,lsub) for the purpose of symmetric pruning. For each
* supernode {s,s+1,...,t=s+r} with first column s and last
* column t, the subscript set
* lsub[j], j=xlsub[s], .., xlsub[s+1]-1
* is the structure of column s (i.e. structure of this supernode).
* It is used for the storage of numerical values.
* Furthermore,
* lsub[j], j=xlsub[t], .., xlsub[t+1]-1
* is the structure of the last column t of this supernode.
* It is for the purpose of symmetric pruning. Therefore, the
* structural subscripts can be rearranged without making physical
* interchanges among the numerical values.
* However, if the supernode has only one column, then we
* only keep one set of subscripts. For any subscript interchange
* performed, similar interchange must be done on the numerical
* values.
* The last column structures (for pruning) will be removed
* after the numercial LU factorization phase.
* (xlusup,lusup): lusup[*] contains the numerical values of the
* rectangular supernodes; xlusup[j] points to the starting
* location of the j-th column in storage vector lusup[*]
* Note: xlusup is indexed by column.
* Each rectangular supernode is stored by column-major
* scheme, consistent with Fortran 2-dim array storage.
* (xusub,ucol,usub): ucol[*] stores the numerical values of
* U-columns outside the rectangular supernodes. The row
* subscript of nonzero ucol[k] is stored in usub[k].
* xusub[i] points to the starting location of column i in ucol.
* Storage: new row subscripts; that is subscripts of PA.
namespace Eigen {
namespace internal {
typedef enum {LUSUP, UCOL, LSUB, USUB, LLVL, ULVL} MemType;
template <typename IndexVector, typename ScalarVector>
struct LU_GlobalLU_t {
typedef typename IndexVector::Scalar StorageIndex;
IndexVector xsup; //First supernode column ... xsup(s) points to the beginning of the s-th supernode
IndexVector supno; // Supernode number corresponding to this column (column to supernode mapping)
ScalarVector lusup; // nonzero values of L ordered by columns
IndexVector lsub; // Compressed row indices of L rectangular supernodes.
IndexVector xlusup; // pointers to the beginning of each column in lusup
IndexVector xlsub; // pointers to the beginning of each column in lsub
Index nzlmax; // Current max size of lsub
Index nzlumax; // Current max size of lusup
ScalarVector ucol; // nonzero values of U ordered by columns
IndexVector usub; // row indices of U columns in ucol
IndexVector xusub; // Pointers to the beginning of each column of U in ucol
Index nzumax; // Current max size of ucol
Index n; // Number of columns in the matrix
Index num_expansions;
// Values to set for performance
struct perfvalues {
Index panel_size; // a panel consists of at most <panel_size> consecutive columns
Index relax; // To control degree of relaxing supernodes. If the number of nodes (columns)
// in a subtree of the elimination tree is less than relax, this subtree is considered
// as one supernode regardless of the row structures of those columns
Index maxsuper; // The maximum size for a supernode in complete LU
Index rowblk; // The minimum row dimension for 2-D blocking to be used;
Index colblk; // The minimum column dimension for 2-D blocking to be used;
Index fillfactor; // The estimated fills factors for L and U, compared with A
} // end namespace internal
} // end namespace Eigen