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
33namespace Eigen {
34namespace internal {
35
36/**
37 * \brief Performs the numerical pivotin on the current column of L, and the CDIV operation.
38 *
39 * Pivot policy :
40 * (1) Compute thresh = u * max_(i>=j) abs(A_ij);
41 * (2) IF user specifies pivot row k and abs(A_kj) >= thresh THEN
42 *           pivot row = k;
43 *       ELSE IF abs(A_jj) >= thresh THEN
44 *           pivot row = j;
45 *       ELSE
46 *           pivot row = m;
47 *
48 *   Note: If you absolutely want to use a given pivot order, then set u=0.0.
49 *
50 * \param jcol The current column of L
51 * \param diagpivotthresh diagonal pivoting threshold
52 * \param[in,out] perm_r Row permutation (threshold pivoting)
53 * \param[in] iperm_c column permutation - used to finf diagonal of Pc*A*Pc'
54 * \param[out] pivrow  The pivot row
55 * \param glu Global LU data
56 * \return 0 if success, i > 0 if U(i,i) is exactly zero
57 *
58 */
59template <typename Scalar, typename Index>
60Index SparseLUImpl<Scalar,Index>::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  Index* 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 = 0.0;
75  Index pivptr = nsupc;
76  Index diag = emptyIdxLU;
77  RealScalar rtemp;
78  Index isub, icol, itemp, k;
79  for (isub = nsupc; isub < nsupr; ++isub) {
80    rtemp = std::abs(lu_col_ptr[isub]);
81    if (rtemp > pivmax) {
82      pivmax = rtemp;
83      pivptr = isub;
84    }
85    if (lsub_ptr[isub] == diagind) diag = isub;
86  }
87
88  // Test for singularity
89  if ( pivmax == 0.0 ) {
90    pivrow = lsub_ptr[pivptr];
91    perm_r(pivrow) = jcol;
92    return (jcol+1);
93  }
94
95  RealScalar thresh = diagpivotthresh * pivmax;
96
97  // Choose appropriate pivotal element
98
99  {
100    // Test if the diagonal element can be used as a pivot (given the threshold value)
101    if (diag >= 0 )
102    {
103      // Diagonal element exists
104      rtemp = std::abs(lu_col_ptr[diag]);
105      if (rtemp != 0.0 && rtemp >= thresh) pivptr = diag;
106    }
107    pivrow = lsub_ptr[pivptr];
108  }
109
110  // Record pivot row
111  perm_r(pivrow) = jcol;
112  // Interchange row subscripts
113  if (pivptr != nsupc )
114  {
115    std::swap( lsub_ptr[pivptr], lsub_ptr[nsupc] );
116    // Interchange numerical values as well, for the two rows in the whole snode
117    // such that L is indexed the same way as A
118    for (icol = 0; icol <= nsupc; icol++)
119    {
120      itemp = pivptr + icol * lda;
121      std::swap(lu_sup_ptr[itemp], lu_sup_ptr[nsupc + icol * lda]);
122    }
123  }
124  // cdiv operations
125  Scalar temp = Scalar(1.0) / lu_col_ptr[nsupc];
126  for (k = nsupc+1; k < nsupr; k++)
127    lu_col_ptr[k] *= temp;
128  return 0;
129}
130
131} // end namespace internal
132} // end namespace Eigen
133
134#endif // SPARSELU_PIVOTL_H
135