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
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 */
59 template <typename Scalar, typename StorageIndex>
pivotL(const Index jcol,const RealScalar & diagpivotthresh,IndexVector & perm_r,IndexVector & iperm_c,Index & pivrow,GlobalLU_t & glu)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;
76 Index diag = emptyIdxLU;
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
138