[136] | 1 | // This file is part of Eigen, a lightweight C++ template library
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| 2 | // for linear algebra.
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| 3 | //
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| 4 | // Copyright (C) 2012 Désiré Nuentsa-Wakam <desire.nuentsa_wakam@inria.fr>
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| 5 | //
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| 6 | // This Source Code Form is subject to the terms of the Mozilla
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| 7 | // Public License v. 2.0. If a copy of the MPL was not distributed
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| 8 | // with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
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| 9 |
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| 10 | /*
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| 11 |
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| 12 | * NOTE: This file is the modified version of xpivotL.c file in SuperLU
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| 13 |
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| 14 | * -- SuperLU routine (version 3.0) --
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| 15 | * Univ. of California Berkeley, Xerox Palo Alto Research Center,
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| 16 | * and Lawrence Berkeley National Lab.
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| 17 | * October 15, 2003
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| 18 | *
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| 19 | * Copyright (c) 1994 by Xerox Corporation. All rights reserved.
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| 20 | *
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| 21 | * THIS MATERIAL IS PROVIDED AS IS, WITH ABSOLUTELY NO WARRANTY
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| 22 | * EXPRESSED OR IMPLIED. ANY USE IS AT YOUR OWN RISK.
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| 23 | *
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| 24 | * Permission is hereby granted to use or copy this program for any
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| 25 | * purpose, provided the above notices are retained on all copies.
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| 26 | * Permission to modify the code and to distribute modified code is
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| 27 | * granted, provided the above notices are retained, and a notice that
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| 28 | * the code was modified is included with the above copyright notice.
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| 29 | */
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| 30 | #ifndef SPARSELU_PIVOTL_H
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| 31 | #define SPARSELU_PIVOTL_H
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| 32 |
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| 33 | namespace Eigen {
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| 34 | namespace internal {
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| 35 |
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| 36 | /**
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| 37 | * \brief Performs the numerical pivotin on the current column of L, and the CDIV operation.
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| 38 | *
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| 39 | * Pivot policy :
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| 40 | * (1) Compute thresh = u * max_(i>=j) abs(A_ij);
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| 41 | * (2) IF user specifies pivot row k and abs(A_kj) >= thresh THEN
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| 42 | * pivot row = k;
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| 43 | * ELSE IF abs(A_jj) >= thresh THEN
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| 44 | * pivot row = j;
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| 45 | * ELSE
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| 46 | * pivot row = m;
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| 47 | *
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| 48 | * Note: If you absolutely want to use a given pivot order, then set u=0.0.
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| 49 | *
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| 50 | * \param jcol The current column of L
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| 51 | * \param diagpivotthresh diagonal pivoting threshold
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| 52 | * \param[in,out] perm_r Row permutation (threshold pivoting)
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| 53 | * \param[in] iperm_c column permutation - used to finf diagonal of Pc*A*Pc'
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| 54 | * \param[out] pivrow The pivot row
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| 55 | * \param glu Global LU data
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| 56 | * \return 0 if success, i > 0 if U(i,i) is exactly zero
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| 57 | *
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| 58 | */
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| 59 | template <typename Scalar, typename Index>
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| 60 | Index SparseLUImpl<Scalar,Index>::pivotL(const Index jcol, const RealScalar& diagpivotthresh, IndexVector& perm_r, IndexVector& iperm_c, Index& pivrow, GlobalLU_t& glu)
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| 61 | {
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| 62 |
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| 63 | Index fsupc = (glu.xsup)((glu.supno)(jcol)); // First column in the supernode containing the column jcol
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| 64 | Index nsupc = jcol - fsupc; // Number of columns in the supernode portion, excluding jcol; nsupc >=0
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| 65 | Index lptr = glu.xlsub(fsupc); // pointer to the starting location of the row subscripts for this supernode portion
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| 66 | Index nsupr = glu.xlsub(fsupc+1) - lptr; // Number of rows in the supernode
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| 67 | Index lda = glu.xlusup(fsupc+1) - glu.xlusup(fsupc); // leading dimension
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| 68 | Scalar* lu_sup_ptr = &(glu.lusup.data()[glu.xlusup(fsupc)]); // Start of the current supernode
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| 69 | Scalar* lu_col_ptr = &(glu.lusup.data()[glu.xlusup(jcol)]); // Start of jcol in the supernode
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| 70 | Index* lsub_ptr = &(glu.lsub.data()[lptr]); // Start of row indices of the supernode
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| 71 |
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| 72 | // Determine the largest abs numerical value for partial pivoting
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| 73 | Index diagind = iperm_c(jcol); // diagonal index
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| 74 | RealScalar pivmax(-1.0);
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| 75 | Index pivptr = nsupc;
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| 76 | Index diag = emptyIdxLU;
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| 77 | RealScalar rtemp;
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| 78 | Index isub, icol, itemp, k;
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| 79 | for (isub = nsupc; isub < nsupr; ++isub) {
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| 80 | using std::abs;
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| 81 | rtemp = abs(lu_col_ptr[isub]);
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| 82 | if (rtemp > pivmax) {
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| 83 | pivmax = rtemp;
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| 84 | pivptr = isub;
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| 85 | }
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| 86 | if (lsub_ptr[isub] == diagind) diag = isub;
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| 87 | }
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| 88 |
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| 89 | // Test for singularity
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| 90 | if ( pivmax <= RealScalar(0.0) ) {
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| 91 | // if pivmax == -1, the column is structurally empty, otherwise it is only numerically zero
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| 92 | pivrow = pivmax < RealScalar(0.0) ? diagind : lsub_ptr[pivptr];
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| 93 | perm_r(pivrow) = jcol;
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| 94 | return (jcol+1);
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| 95 | }
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| 96 |
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| 97 | RealScalar thresh = diagpivotthresh * pivmax;
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| 98 |
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| 99 | // Choose appropriate pivotal element
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| 100 |
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| 101 | {
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| 102 | // Test if the diagonal element can be used as a pivot (given the threshold value)
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| 103 | if (diag >= 0 )
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| 104 | {
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| 105 | // Diagonal element exists
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| 106 | using std::abs;
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| 107 | rtemp = abs(lu_col_ptr[diag]);
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| 108 | if (rtemp != 0.0 && rtemp >= thresh) pivptr = diag;
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| 109 | }
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| 110 | pivrow = lsub_ptr[pivptr];
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| 111 | }
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| 112 |
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| 113 | // Record pivot row
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| 114 | perm_r(pivrow) = jcol;
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| 115 | // Interchange row subscripts
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| 116 | if (pivptr != nsupc )
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| 117 | {
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| 118 | std::swap( lsub_ptr[pivptr], lsub_ptr[nsupc] );
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| 119 | // Interchange numerical values as well, for the two rows in the whole snode
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| 120 | // such that L is indexed the same way as A
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| 121 | for (icol = 0; icol <= nsupc; icol++)
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| 122 | {
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| 123 | itemp = pivptr + icol * lda;
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| 124 | std::swap(lu_sup_ptr[itemp], lu_sup_ptr[nsupc + icol * lda]);
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| 125 | }
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| 126 | }
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| 127 | // cdiv operations
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| 128 | Scalar temp = Scalar(1.0) / lu_col_ptr[nsupc];
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| 129 | for (k = nsupc+1; k < nsupr; k++)
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| 130 | lu_col_ptr[k] *= temp;
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| 131 | return 0;
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| 132 | }
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| 133 |
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| 134 | } // end namespace internal
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| 135 | } // end namespace Eigen
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| 136 |
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| 137 | #endif // SPARSELU_PIVOTL_H
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