SparseLU_column_bmod.h
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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 // 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 {
52 template <typename Scalar, typename StorageIndex>
54  BlockIndexVector segrep, BlockIndexVector repfnz, Index fpanelc, GlobalLU_t& glu)
55 {
56  Index jsupno, k, ksub, krep, ksupno;
57  Index lptr, nrow, isub, irow, nextlu, new_next, ufirst;
58  Index fsupc, nsupc, nsupr, luptr, kfnz, no_zeros;
59  /* krep = representative of current k-th supernode
60  * fsupc = first supernodal column
61  * nsupc = number of columns in a supernode
62  * nsupr = number of rows in a supernode
63  * luptr = location of supernodal LU-block in storage
64  * kfnz = first nonz in the k-th supernodal segment
65  * no_zeros = no lf leading zeros in a supernodal U-segment
66  */
67 
68  jsupno = glu.supno(jcol);
69  // For each nonzero supernode segment of U[*,j] in topological order
70  k = nseg - 1;
71  Index d_fsupc; // distance between the first column of the current panel and the
72  // first column of the current snode
73  Index fst_col; // First column within small LU update
74  Index segsize;
75  for (ksub = 0; ksub < nseg; ksub++)
76  {
77  krep = segrep(k); k--;
78  ksupno = glu.supno(krep);
79  if (jsupno != ksupno )
80  {
81  // outside the rectangular supernode
82  fsupc = glu.xsup(ksupno);
83  fst_col = (std::max)(fsupc, fpanelc);
84 
85  // Distance from the current supernode to the current panel;
86  // d_fsupc = 0 if fsupc > fpanelc
87  d_fsupc = fst_col - fsupc;
88 
89  luptr = glu.xlusup(fst_col) + d_fsupc;
90  lptr = glu.xlsub(fsupc) + d_fsupc;
91 
92  kfnz = repfnz(krep);
93  kfnz = (std::max)(kfnz, fpanelc);
94 
95  segsize = krep - kfnz + 1;
96  nsupc = krep - fst_col + 1;
97  nsupr = glu.xlsub(fsupc+1) - glu.xlsub(fsupc);
98  nrow = nsupr - d_fsupc - nsupc;
99  Index lda = glu.xlusup(fst_col+1) - glu.xlusup(fst_col);
100 
101 
102  // Perform a triangular solver and block update,
103  // then scatter the result of sup-col update to dense
104  no_zeros = kfnz - fst_col;
105  if(segsize==1)
106  LU_kernel_bmod<1>::run(segsize, dense, tempv, glu.lusup, luptr, lda, nrow, glu.lsub, lptr, no_zeros);
107  else
108  LU_kernel_bmod<Dynamic>::run(segsize, dense, tempv, glu.lusup, luptr, lda, nrow, glu.lsub, lptr, no_zeros);
109  } // end if jsupno
110  } // end for each segment
111 
112  // Process the supernodal portion of L\U[*,j]
113  nextlu = glu.xlusup(jcol);
114  fsupc = glu.xsup(jsupno);
115 
116  // copy the SPA dense into L\U[*,j]
117  Index mem;
118  new_next = nextlu + glu.xlsub(fsupc + 1) - glu.xlsub(fsupc);
119  Index offset = internal::first_multiple<Index>(new_next, internal::packet_traits<Scalar>::size) - new_next;
120  if(offset)
121  new_next += offset;
122  while (new_next > glu.nzlumax )
123  {
124  mem = memXpand<ScalarVector>(glu.lusup, glu.nzlumax, nextlu, LUSUP, glu.num_expansions);
125  if (mem) return mem;
126  }
127 
128  for (isub = glu.xlsub(fsupc); isub < glu.xlsub(fsupc+1); isub++)
129  {
130  irow = glu.lsub(isub);
131  glu.lusup(nextlu) = dense(irow);
132  dense(irow) = Scalar(0.0);
133  ++nextlu;
134  }
135 
136  if(offset)
137  {
138  glu.lusup.segment(nextlu,offset).setZero();
139  nextlu += offset;
140  }
141  glu.xlusup(jcol + 1) = StorageIndex(nextlu); // close L\U(*,jcol);
142 
143  /* For more updates within the panel (also within the current supernode),
144  * should start from the first column of the panel, or the first column
145  * of the supernode, whichever is bigger. There are two cases:
146  * 1) fsupc < fpanelc, then fst_col <-- fpanelc
147  * 2) fsupc >= fpanelc, then fst_col <-- fsupc
148  */
149  fst_col = (std::max)(fsupc, fpanelc);
150 
151  if (fst_col < jcol)
152  {
153  // Distance between the current supernode and the current panel
154  // d_fsupc = 0 if fsupc >= fpanelc
155  d_fsupc = fst_col - fsupc;
156 
157  lptr = glu.xlsub(fsupc) + d_fsupc;
158  luptr = glu.xlusup(fst_col) + d_fsupc;
159  nsupr = glu.xlsub(fsupc+1) - glu.xlsub(fsupc); // leading dimension
160  nsupc = jcol - fst_col; // excluding jcol
161  nrow = nsupr - d_fsupc - nsupc;
162 
163  // points to the beginning of jcol in snode L\U(jsupno)
164  ufirst = glu.xlusup(jcol) + d_fsupc;
165  Index lda = glu.xlusup(jcol+1) - glu.xlusup(jcol);
166  MappedMatrixBlock A( &(glu.lusup.data()[luptr]), nsupc, nsupc, OuterStride<>(lda) );
167  VectorBlock<ScalarVector> u(glu.lusup, ufirst, nsupc);
168  u = A.template triangularView<UnitLower>().solve(u);
169 
170  new (&A) MappedMatrixBlock ( &(glu.lusup.data()[luptr+nsupc]), nrow, nsupc, OuterStride<>(lda) );
171  VectorBlock<ScalarVector> l(glu.lusup, ufirst+nsupc, nrow);
172  l.noalias() -= A * u;
173 
174  } // End if fst_col
175  return 0;
176 }
177 
178 } // end namespace internal
179 } // end namespace Eigen
180 
181 #endif // SPARSELU_COLUMN_BMOD_H
Eigen::internal::LU_GlobalLU_t::lsub
IndexVector lsub
Definition: SparseLU_Structs.h:82
Eigen
Namespace containing all symbols from the Eigen library.
Definition: jet.h:637
Eigen::internal::packet_traits
Definition: GenericPacketMath.h:106
Eigen::internal::LU_GlobalLU_t::nzlumax
Index nzlumax
Definition: SparseLU_Structs.h:86
Eigen::internal::LU_GlobalLU_t::xsup
IndexVector xsup
Definition: SparseLU_Structs.h:79
Eigen::internal::SparseLUImpl::column_bmod
Index column_bmod(const Index jcol, const Index nseg, BlockScalarVector dense, ScalarVector &tempv, BlockIndexVector segrep, BlockIndexVector repfnz, Index fpanelc, GlobalLU_t &glu)
Performs numeric block updates (sup-col) in topological order.
Definition: SparseLU_column_bmod.h:53
A
Definition: test_numpy_dtypes.cpp:298
Eigen::internal::LUSUP
@ LUSUP
Definition: SparseLU_Structs.h:74
Eigen::internal::LU_kernel_bmod::run
static EIGEN_DONT_INLINE void run(const Index segsize, BlockScalarVector &dense, ScalarVector &tempv, ScalarVector &lusup, Index &luptr, const Index lda, const Index nrow, IndexVector &lsub, const Index lptr, const Index no_zeros)
Definition: SparseLU_kernel_bmod.h:39
l
static const Line3 l(Rot3(), 1, 1)
Eigen::OuterStride
Convenience specialization of Stride to specify only an outer stride See class Map for some examples.
Definition: Stride.h:106
Eigen::internal::LU_GlobalLU_t::num_expansions
Index num_expansions
Definition: SparseLU_Structs.h:92
Eigen::internal::LU_GlobalLU_t::xlusup
IndexVector xlusup
Definition: SparseLU_Structs.h:83
Eigen::Map
A matrix or vector expression mapping an existing array of data.
Definition: Map.h:94
lda
* lda
Definition: eigenvalues.cpp:59
offset
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Definition: gnuplot_common_settings.hh:64
Eigen::Ref
A matrix or vector expression mapping an existing expression.
Definition: Ref.h:281
Eigen::internal::LU_GlobalLU_t::supno
IndexVector supno
Definition: SparseLU_Structs.h:80
Eigen::VectorBlock
Expression of a fixed-size or dynamic-size sub-vector.
Definition: ForwardDeclarations.h:85
Eigen::internal::LU_GlobalLU_t::xlsub
IndexVector xlsub
Definition: SparseLU_Structs.h:84
Eigen::internal::LU_GlobalLU_t::lusup
ScalarVector lusup
Definition: SparseLU_Structs.h:81
Eigen::Matrix< Scalar, Dynamic, 1 >
internal
Definition: BandTriangularSolver.h:13
max
#define max(a, b)
Definition: datatypes.h:20
Eigen::internal::LU_GlobalLU_t
Definition: SparseLU_Structs.h:77
Scalar
SCALAR Scalar
Definition: bench_gemm.cpp:46
Eigen::Index
EIGEN_DEFAULT_DENSE_INDEX_TYPE Index
The Index type as used for the API.
Definition: Meta.h:74


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