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 [s,d,c,z]panel_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_PANEL_BMOD_H
32#define SPARSELU_PANEL_BMOD_H
33
34namespace Eigen {
35namespace internal {
36
37/**
38 * \brief Performs numeric block updates (sup-panel) in topological order.
39 *
40 * Before entering this routine, the original nonzeros in the panel
41 * were already copied i nto the spa[m,w]
42 *
43 * \param m number of rows in the matrix
44 * \param w Panel size
45 * \param jcol Starting  column of the panel
46 * \param nseg Number of segments in the U part
47 * \param dense Store the full representation of the panel
48 * \param tempv working array
49 * \param segrep segment representative... first row in the segment
50 * \param repfnz First nonzero rows
51 * \param glu Global LU data.
52 *
53 *
54 */
55template <typename Scalar, typename StorageIndex>
56void SparseLUImpl<Scalar,StorageIndex>::panel_bmod(const Index m, const Index w, const Index jcol,
57                                            const Index nseg, ScalarVector& dense, ScalarVector& tempv,
58                                            IndexVector& segrep, IndexVector& repfnz, GlobalLU_t& glu)
59{
60
61  Index ksub,jj,nextl_col;
62  Index fsupc, nsupc, nsupr, nrow;
63  Index krep, kfnz;
64  Index lptr; // points to the row subscripts of a supernode
65  Index luptr; // ...
66  Index segsize,no_zeros ;
67  // For each nonz supernode segment of U[*,j] in topological order
68  Index k = nseg - 1;
69  const Index PacketSize = internal::packet_traits<Scalar>::size;
70
71  for (ksub = 0; ksub < nseg; ksub++)
72  { // For each updating supernode
73    /* krep = representative of current k-th supernode
74     * fsupc =  first supernodal column
75     * nsupc = number of columns in a supernode
76     * nsupr = number of rows in a supernode
77     */
78    krep = segrep(k); k--;
79    fsupc = glu.xsup(glu.supno(krep));
80    nsupc = krep - fsupc + 1;
81    nsupr = glu.xlsub(fsupc+1) - glu.xlsub(fsupc);
82    nrow = nsupr - nsupc;
83    lptr = glu.xlsub(fsupc);
84
85    // loop over the panel columns to detect the actual number of columns and rows
86    Index u_rows = 0;
87    Index u_cols = 0;
88    for (jj = jcol; jj < jcol + w; jj++)
89    {
90      nextl_col = (jj-jcol) * m;
91      VectorBlock<IndexVector> repfnz_col(repfnz, nextl_col, m); // First nonzero column index for each row
92
93      kfnz = repfnz_col(krep);
94      if ( kfnz == emptyIdxLU )
95        continue; // skip any zero segment
96
97      segsize = krep - kfnz + 1;
98      u_cols++;
99      u_rows = (std::max)(segsize,u_rows);
100    }
101
102    if(nsupc >= 2)
103    {
104      Index ldu = internal::first_multiple<Index>(u_rows, PacketSize);
105      Map<ScalarMatrix, Aligned,  OuterStride<> > U(tempv.data(), u_rows, u_cols, OuterStride<>(ldu));
106
107      // gather U
108      Index u_col = 0;
109      for (jj = jcol; jj < jcol + w; jj++)
110      {
111        nextl_col = (jj-jcol) * m;
112        VectorBlock<IndexVector> repfnz_col(repfnz, nextl_col, m); // First nonzero column index for each row
113        VectorBlock<ScalarVector> dense_col(dense, nextl_col, m); // Scatter/gather entire matrix column from/to here
114
115        kfnz = repfnz_col(krep);
116        if ( kfnz == emptyIdxLU )
117          continue; // skip any zero segment
118
119        segsize = krep - kfnz + 1;
120        luptr = glu.xlusup(fsupc);
121        no_zeros = kfnz - fsupc;
122
123        Index isub = lptr + no_zeros;
124        Index off = u_rows-segsize;
125        for (Index i = 0; i < off; i++) U(i,u_col) = 0;
126        for (Index i = 0; i < segsize; i++)
127        {
128          Index irow = glu.lsub(isub);
129          U(i+off,u_col) = dense_col(irow);
130          ++isub;
131        }
132        u_col++;
133      }
134      // solve U = A^-1 U
135      luptr = glu.xlusup(fsupc);
136      Index lda = glu.xlusup(fsupc+1) - glu.xlusup(fsupc);
137      no_zeros = (krep - u_rows + 1) - fsupc;
138      luptr += lda * no_zeros + no_zeros;
139      MappedMatrixBlock A(glu.lusup.data()+luptr, u_rows, u_rows, OuterStride<>(lda) );
140      U = A.template triangularView<UnitLower>().solve(U);
141
142      // update
143      luptr += u_rows;
144      MappedMatrixBlock B(glu.lusup.data()+luptr, nrow, u_rows, OuterStride<>(lda) );
145      eigen_assert(tempv.size()>w*ldu + nrow*w + 1);
146
147      Index ldl = internal::first_multiple<Index>(nrow, PacketSize);
148      Index offset = (PacketSize-internal::first_default_aligned(B.data(), PacketSize)) % PacketSize;
149      MappedMatrixBlock L(tempv.data()+w*ldu+offset, nrow, u_cols, OuterStride<>(ldl));
150
151      L.setZero();
152      internal::sparselu_gemm<Scalar>(L.rows(), L.cols(), B.cols(), B.data(), B.outerStride(), U.data(), U.outerStride(), L.data(), L.outerStride());
153
154      // scatter U and L
155      u_col = 0;
156      for (jj = jcol; jj < jcol + w; jj++)
157      {
158        nextl_col = (jj-jcol) * m;
159        VectorBlock<IndexVector> repfnz_col(repfnz, nextl_col, m); // First nonzero column index for each row
160        VectorBlock<ScalarVector> dense_col(dense, nextl_col, m); // Scatter/gather entire matrix column from/to here
161
162        kfnz = repfnz_col(krep);
163        if ( kfnz == emptyIdxLU )
164          continue; // skip any zero segment
165
166        segsize = krep - kfnz + 1;
167        no_zeros = kfnz - fsupc;
168        Index isub = lptr + no_zeros;
169
170        Index off = u_rows-segsize;
171        for (Index i = 0; i < segsize; i++)
172        {
173          Index irow = glu.lsub(isub++);
174          dense_col(irow) = U.coeff(i+off,u_col);
175          U.coeffRef(i+off,u_col) = 0;
176        }
177
178        // Scatter l into SPA dense[]
179        for (Index i = 0; i < nrow; i++)
180        {
181          Index irow = glu.lsub(isub++);
182          dense_col(irow) -= L.coeff(i,u_col);
183          L.coeffRef(i,u_col) = 0;
184        }
185        u_col++;
186      }
187    }
188    else // level 2 only
189    {
190      // Sequence through each column in the panel
191      for (jj = jcol; jj < jcol + w; jj++)
192      {
193        nextl_col = (jj-jcol) * m;
194        VectorBlock<IndexVector> repfnz_col(repfnz, nextl_col, m); // First nonzero column index for each row
195        VectorBlock<ScalarVector> dense_col(dense, nextl_col, m); // Scatter/gather entire matrix column from/to here
196
197        kfnz = repfnz_col(krep);
198        if ( kfnz == emptyIdxLU )
199          continue; // skip any zero segment
200
201        segsize = krep - kfnz + 1;
202        luptr = glu.xlusup(fsupc);
203
204        Index lda = glu.xlusup(fsupc+1)-glu.xlusup(fsupc);// nsupr
205
206        // Perform a trianglar solve and block update,
207        // then scatter the result of sup-col update to dense[]
208        no_zeros = kfnz - fsupc;
209              if(segsize==1)  LU_kernel_bmod<1>::run(segsize, dense_col, tempv, glu.lusup, luptr, lda, nrow, glu.lsub, lptr, no_zeros);
210        else  if(segsize==2)  LU_kernel_bmod<2>::run(segsize, dense_col, tempv, glu.lusup, luptr, lda, nrow, glu.lsub, lptr, no_zeros);
211        else  if(segsize==3)  LU_kernel_bmod<3>::run(segsize, dense_col, tempv, glu.lusup, luptr, lda, nrow, glu.lsub, lptr, no_zeros);
212        else                  LU_kernel_bmod<Dynamic>::run(segsize, dense_col, tempv, glu.lusup, luptr, lda, nrow, glu.lsub, lptr, no_zeros);
213      } // End for each column in the panel
214    }
215
216  } // End for each updating supernode
217} // end panel bmod
218
219} // end namespace internal
220
221} // end namespace Eigen
222
223#endif // SPARSELU_PANEL_BMOD_H
224