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 // Copyright (C) 2012 Gael Guennebaud <gael.guennebaud@inria.fr>
6 //
7 // This Source Code Form is subject to the terms of the Mozilla
8 // Public License v. 2.0. If a copy of the MPL was not distributed
9 // with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
10 
11 /*
12 
13  * NOTE: This file is the modified version of xcolumn_bmod.c file in SuperLU
14 
15  * -- SuperLU routine (version 3.0) --
16  * Univ. of California Berkeley, Xerox Palo Alto Research Center,
17  * and Lawrence Berkeley National Lab.
18  * October 15, 2003
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 SPARSELU_COLUMN_BMOD_H
32 #define SPARSELU_COLUMN_BMOD_H
33 
34 namespace Eigen {
35 
36 namespace internal {
37 /**
38  * \brief Performs numeric block updates (sup-col) in topological order
39  *
40  * \param jcol current column to update
41  * \param nseg Number of segments in the U part
42  * \param dense Store the full representation of the column
43  * \param tempv working array
44  * \param segrep segment representative ...
45  * \param repfnz ??? First nonzero column in each row ???  ...
46  * \param fpanelc First column in the current panel
47  * \param glu Global LU data.
48  * \return 0 - successful return
49  *         > 0 - number of bytes allocated when run out of space
50  *
51  */
52 template <typename Scalar, typename Index>
column_bmod(const Index jcol,const Index nseg,BlockScalarVector dense,ScalarVector & tempv,BlockIndexVector segrep,BlockIndexVector repfnz,Index fpanelc,GlobalLU_t & glu)53 Index SparseLUImpl<Scalar,Index>::column_bmod(const Index jcol, const Index nseg, BlockScalarVector dense, ScalarVector& tempv, BlockIndexVector segrep, BlockIndexVector repfnz, Index fpanelc, GlobalLU_t& glu)
54 {
55   Index  jsupno, k, ksub, krep, ksupno;
56   Index lptr, nrow, isub, irow, nextlu, new_next, ufirst;
57   Index fsupc, nsupc, nsupr, luptr, kfnz, no_zeros;
58   /* krep = representative of current k-th supernode
59     * fsupc =  first supernodal column
60     * nsupc = number of columns in a supernode
61     * nsupr = number of rows in a supernode
62     * luptr = location of supernodal LU-block in storage
63     * kfnz = first nonz in the k-th supernodal segment
64     * no_zeros = no lf leading zeros in a supernodal U-segment
65     */
66 
67   jsupno = glu.supno(jcol);
68   // For each nonzero supernode segment of U[*,j] in topological order
69   k = nseg - 1;
70   Index d_fsupc; // distance between the first column of the current panel and the
71                // first column of the current snode
72   Index fst_col; // First column within small LU update
73   Index segsize;
74   for (ksub = 0; ksub < nseg; ksub++)
75   {
76     krep = segrep(k); k--;
77     ksupno = glu.supno(krep);
78     if (jsupno != ksupno )
79     {
80       // outside the rectangular supernode
81       fsupc = glu.xsup(ksupno);
82       fst_col = (std::max)(fsupc, fpanelc);
83 
84       // Distance from the current supernode to the current panel;
85       // d_fsupc = 0 if fsupc > fpanelc
86       d_fsupc = fst_col - fsupc;
87 
88       luptr = glu.xlusup(fst_col) + d_fsupc;
89       lptr = glu.xlsub(fsupc) + d_fsupc;
90 
91       kfnz = repfnz(krep);
92       kfnz = (std::max)(kfnz, fpanelc);
93 
94       segsize = krep - kfnz + 1;
95       nsupc = krep - fst_col + 1;
96       nsupr = glu.xlsub(fsupc+1) - glu.xlsub(fsupc);
97       nrow = nsupr - d_fsupc - nsupc;
98       Index lda = glu.xlusup(fst_col+1) - glu.xlusup(fst_col);
99 
100 
101       // Perform a triangular solver and block update,
102       // then scatter the result of sup-col update to dense
103       no_zeros = kfnz - fst_col;
104       if(segsize==1)
105         LU_kernel_bmod<1>::run(segsize, dense, tempv, glu.lusup, luptr, lda, nrow, glu.lsub, lptr, no_zeros);
106       else
107         LU_kernel_bmod<Dynamic>::run(segsize, dense, tempv, glu.lusup, luptr, lda, nrow, glu.lsub, lptr, no_zeros);
108     } // end if jsupno
109   } // end for each segment
110 
111   // Process the supernodal portion of  L\U[*,j]
112   nextlu = glu.xlusup(jcol);
113   fsupc = glu.xsup(jsupno);
114 
115   // copy the SPA dense into L\U[*,j]
116   Index mem;
117   new_next = nextlu + glu.xlsub(fsupc + 1) - glu.xlsub(fsupc);
118   Index offset = internal::first_multiple<Index>(new_next, internal::packet_traits<Scalar>::size) - new_next;
119   if(offset)
120     new_next += offset;
121   while (new_next > glu.nzlumax )
122   {
123     mem = memXpand<ScalarVector>(glu.lusup, glu.nzlumax, nextlu, LUSUP, glu.num_expansions);
124     if (mem) return mem;
125   }
126 
127   for (isub = glu.xlsub(fsupc); isub < glu.xlsub(fsupc+1); isub++)
128   {
129     irow = glu.lsub(isub);
130     glu.lusup(nextlu) = dense(irow);
131     dense(irow) = Scalar(0.0);
132     ++nextlu;
133   }
134 
135   if(offset)
136   {
137     glu.lusup.segment(nextlu,offset).setZero();
138     nextlu += offset;
139   }
140   glu.xlusup(jcol + 1) = nextlu;  // close L\U(*,jcol);
141 
142   /* For more updates within the panel (also within the current supernode),
143    * should start from the first column of the panel, or the first column
144    * of the supernode, whichever is bigger. There are two cases:
145    *  1) fsupc < fpanelc, then fst_col <-- fpanelc
146    *  2) fsupc >= fpanelc, then fst_col <-- fsupc
147    */
148   fst_col = (std::max)(fsupc, fpanelc);
149 
150   if (fst_col  < jcol)
151   {
152     // Distance between the current supernode and the current panel
153     // d_fsupc = 0 if fsupc >= fpanelc
154     d_fsupc = fst_col - fsupc;
155 
156     lptr = glu.xlsub(fsupc) + d_fsupc;
157     luptr = glu.xlusup(fst_col) + d_fsupc;
158     nsupr = glu.xlsub(fsupc+1) - glu.xlsub(fsupc); // leading dimension
159     nsupc = jcol - fst_col; // excluding jcol
160     nrow = nsupr - d_fsupc - nsupc;
161 
162     // points to the beginning of jcol in snode L\U(jsupno)
163     ufirst = glu.xlusup(jcol) + d_fsupc;
164     Index lda = glu.xlusup(jcol+1) - glu.xlusup(jcol);
165     Map<Matrix<Scalar,Dynamic,Dynamic>, 0,  OuterStride<> > A( &(glu.lusup.data()[luptr]), nsupc, nsupc, OuterStride<>(lda) );
166     VectorBlock<ScalarVector> u(glu.lusup, ufirst, nsupc);
167     u = A.template triangularView<UnitLower>().solve(u);
168 
169     new (&A) Map<Matrix<Scalar,Dynamic,Dynamic>, 0, OuterStride<> > ( &(glu.lusup.data()[luptr+nsupc]), nrow, nsupc, OuterStride<>(lda) );
170     VectorBlock<ScalarVector> l(glu.lusup, ufirst+nsupc, nrow);
171     l.noalias() -= A * u;
172 
173   } // End if fst_col
174   return 0;
175 }
176 
177 } // end namespace internal
178 } // end namespace Eigen
179 
180 #endif // SPARSELU_COLUMN_BMOD_H
181