SparseLU_pivotL.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 //
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 
12  * NOTE: This file is the modified version of xpivotL.c file in SuperLU
13 
14  * -- SuperLU routine (version 3.0) --
15  * Univ. of California Berkeley, Xerox Palo Alto Research Center,
16  * and Lawrence Berkeley National Lab.
17  * October 15, 2003
18  *
19  * Copyright (c) 1994 by Xerox Corporation. All rights reserved.
20  *
21  * THIS MATERIAL IS PROVIDED AS IS, WITH ABSOLUTELY NO WARRANTY
22  * EXPRESSED OR IMPLIED. ANY USE IS AT YOUR OWN RISK.
23  *
24  * Permission is hereby granted to use or copy this program for any
25  * purpose, provided the above notices are retained on all copies.
26  * Permission to modify the code and to distribute modified code is
27  * granted, provided the above notices are retained, and a notice that
28  * the code was modified is included with the above copyright notice.
29  */
30 #ifndef SPARSELU_PIVOTL_H
31 #define SPARSELU_PIVOTL_H
32 
33 namespace Eigen {
34 namespace internal {
35 
59 template <typename Scalar, typename StorageIndex>
60 Index SparseLUImpl<Scalar,StorageIndex>::pivotL(const Index jcol, const RealScalar& diagpivotthresh, IndexVector& perm_r, IndexVector& iperm_c, Index& pivrow, GlobalLU_t& glu)
61 {
62 
63  Index fsupc = (glu.xsup)((glu.supno)(jcol)); // First column in the supernode containing the column jcol
64  Index nsupc = jcol - fsupc; // Number of columns in the supernode portion, excluding jcol; nsupc >=0
65  Index lptr = glu.xlsub(fsupc); // pointer to the starting location of the row subscripts for this supernode portion
66  Index nsupr = glu.xlsub(fsupc+1) - lptr; // Number of rows in the supernode
67  Index lda = glu.xlusup(fsupc+1) - glu.xlusup(fsupc); // leading dimension
68  Scalar* lu_sup_ptr = &(glu.lusup.data()[glu.xlusup(fsupc)]); // Start of the current supernode
69  Scalar* lu_col_ptr = &(glu.lusup.data()[glu.xlusup(jcol)]); // Start of jcol in the supernode
70  StorageIndex* lsub_ptr = &(glu.lsub.data()[lptr]); // Start of row indices of the supernode
71 
72  // Determine the largest abs numerical value for partial pivoting
73  Index diagind = iperm_c(jcol); // diagonal index
74  RealScalar pivmax(-1.0);
75  Index pivptr = nsupc;
77  RealScalar rtemp;
78  Index isub, icol, itemp, k;
79  for (isub = nsupc; isub < nsupr; ++isub) {
80  using std::abs;
81  rtemp = abs(lu_col_ptr[isub]);
82  if (rtemp > pivmax) {
83  pivmax = rtemp;
84  pivptr = isub;
85  }
86  if (lsub_ptr[isub] == diagind) diag = isub;
87  }
88 
89  // Test for singularity
90  if ( pivmax <= RealScalar(0.0) ) {
91  // if pivmax == -1, the column is structurally empty, otherwise it is only numerically zero
92  pivrow = pivmax < RealScalar(0.0) ? diagind : lsub_ptr[pivptr];
93  perm_r(pivrow) = StorageIndex(jcol);
94  return (jcol+1);
95  }
96 
97  RealScalar thresh = diagpivotthresh * pivmax;
98 
99  // Choose appropriate pivotal element
100 
101  {
102  // Test if the diagonal element can be used as a pivot (given the threshold value)
103  if (diag >= 0 )
104  {
105  // Diagonal element exists
106  using std::abs;
107  rtemp = abs(lu_col_ptr[diag]);
108  if (rtemp != RealScalar(0.0) && rtemp >= thresh) pivptr = diag;
109  }
110  pivrow = lsub_ptr[pivptr];
111  }
112 
113  // Record pivot row
114  perm_r(pivrow) = StorageIndex(jcol);
115  // Interchange row subscripts
116  if (pivptr != nsupc )
117  {
118  std::swap( lsub_ptr[pivptr], lsub_ptr[nsupc] );
119  // Interchange numerical values as well, for the two rows in the whole snode
120  // such that L is indexed the same way as A
121  for (icol = 0; icol <= nsupc; icol++)
122  {
123  itemp = pivptr + icol * lda;
124  std::swap(lu_sup_ptr[itemp], lu_sup_ptr[nsupc + icol * lda]);
125  }
126  }
127  // cdiv operations
128  Scalar temp = Scalar(1.0) / lu_col_ptr[nsupc];
129  for (k = nsupc+1; k < nsupr; k++)
130  lu_col_ptr[k] *= temp;
131  return 0;
132 }
133 
134 } // end namespace internal
135 } // end namespace Eigen
136 
137 #endif // SPARSELU_PIVOTL_H
SCALAR Scalar
Definition: bench_gemm.cpp:46
Matrix diag(const std::vector< Matrix > &Hs)
Definition: Matrix.cpp:206
Namespace containing all symbols from the Eigen library.
Definition: jet.h:637
EIGEN_DEFAULT_DENSE_INDEX_TYPE Index
The Index type as used for the API.
Definition: Meta.h:74
Index pivotL(const Index jcol, const RealScalar &diagpivotthresh, IndexVector &perm_r, IndexVector &iperm_c, Index &pivrow, GlobalLU_t &glu)
Performs the numerical pivotin on the current column of L, and the CDIV operation.
* lda
Definition: eigenvalues.cpp:59
NumTraits< Scalar >::Real RealScalar
Definition: bench_gemm.cpp:47
void swap(GeographicLib::NearestNeighbor< dist_t, pos_t, distfun_t > &a, GeographicLib::NearestNeighbor< dist_t, pos_t, distfun_t > &b)
The matrix class, also used for vectors and row-vectors.
#define abs(x)
Definition: datatypes.h:17


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autogenerated on Tue Jul 4 2023 02:35:59