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// This file is part of Eigen, a lightweight C++ template library // for linear algebra. // // Copyright (C) 2012 Désiré Nuentsa-Wakam // // This Source Code Form is subject to the terms of the Mozilla // Public License v. 2.0. If a copy of the MPL was not distributed // with this file, You can obtain one at http://mozilla.org/MPL/2.0/. /* * NOTE: This file is the modified version of xpivotL.c file in SuperLU * -- SuperLU routine (version 3.0) -- * Univ. of California Berkeley, Xerox Palo Alto Research Center, * and Lawrence Berkeley National Lab. * October 15, 2003 * * Copyright (c) 1994 by Xerox Corporation. All rights reserved. * * THIS MATERIAL IS PROVIDED AS IS, WITH ABSOLUTELY NO WARRANTY * EXPRESSED OR IMPLIED. ANY USE IS AT YOUR OWN RISK. * * Permission is hereby granted to use or copy this program for any * purpose, provided the above notices are retained on all copies. * Permission to modify the code and to distribute modified code is * granted, provided the above notices are retained, and a notice that * the code was modified is included with the above copyright notice. */ #ifndef SPARSELU_PIVOTL_H #define SPARSELU_PIVOTL_H // IWYU pragma: private #include "./InternalHeaderCheck.h" namespace Eigen { namespace internal { /** * \brief Performs the numerical pivoting on the current column of L, and the CDIV operation. * * Pivot policy : * (1) Compute thresh = u * max_(i>=j) abs(A_ij); * (2) IF user specifies pivot row k and abs(A_kj) >= thresh THEN * pivot row = k; * ELSE IF abs(A_jj) >= thresh THEN * pivot row = j; * ELSE * pivot row = m; * * Note: If you absolutely want to use a given pivot order, then set u=0.0. * * \param jcol The current column of L * \param diagpivotthresh diagonal pivoting threshold * \param[in,out] perm_r Row permutation (threshold pivoting) * \param[in] iperm_c column permutation - used to finf diagonal of Pc*A*Pc' * \param[out] pivrow The pivot row * \param glu Global LU data * \return 0 if success, i > 0 if U(i,i) is exactly zero * */ template Index SparseLUImpl::pivotL(const Index jcol, const RealScalar& diagpivotthresh, IndexVector& perm_r, IndexVector& iperm_c, Index& pivrow, GlobalLU_t& glu) { Index fsupc = (glu.xsup)((glu.supno)(jcol)); // First column in the supernode containing the column jcol Index nsupc = jcol - fsupc; // Number of columns in the supernode portion, excluding jcol; nsupc >=0 Index lptr = glu.xlsub(fsupc); // pointer to the starting location of the row subscripts for this supernode portion Index nsupr = glu.xlsub(fsupc + 1) - lptr; // Number of rows in the supernode Index lda = glu.xlusup(fsupc + 1) - glu.xlusup(fsupc); // leading dimension Scalar* lu_sup_ptr = &(glu.lusup.data()[glu.xlusup(fsupc)]); // Start of the current supernode Scalar* lu_col_ptr = &(glu.lusup.data()[glu.xlusup(jcol)]); // Start of jcol in the supernode StorageIndex* lsub_ptr = &(glu.lsub.data()[lptr]); // Start of row indices of the supernode // Determine the largest abs numerical value for partial pivoting Index diagind = iperm_c(jcol); // diagonal index RealScalar pivmax(-1.0); Index pivptr = nsupc; Index diag = emptyIdxLU; RealScalar rtemp; Index isub, icol, itemp, k; for (isub = nsupc; isub < nsupr; ++isub) { using std::abs; rtemp = abs(lu_col_ptr[isub]); if (rtemp > pivmax) { pivmax = rtemp; pivptr = isub; } if (lsub_ptr[isub] == diagind) diag = isub; } // Test for singularity if (pivmax <= RealScalar(0.0)) { // if pivmax == -1, the column is structurally empty, otherwise it is only numerically zero pivrow = pivmax < RealScalar(0.0) ? diagind : lsub_ptr[pivptr]; perm_r(pivrow) = StorageIndex(jcol); return (jcol + 1); } RealScalar thresh = diagpivotthresh * pivmax; // Choose appropriate pivotal element { // Test if the diagonal element can be used as a pivot (given the threshold value) if (diag >= 0) { // Diagonal element exists using std::abs; rtemp = abs(lu_col_ptr[diag]); if (rtemp != RealScalar(0.0) && rtemp >= thresh) pivptr = diag; } pivrow = lsub_ptr[pivptr]; } // Record pivot row perm_r(pivrow) = StorageIndex(jcol); // Interchange row subscripts if (pivptr != nsupc) { std::swap(lsub_ptr[pivptr], lsub_ptr[nsupc]); // Interchange numerical values as well, for the two rows in the whole snode // such that L is indexed the same way as A for (icol = 0; icol <= nsupc; icol++) { itemp = pivptr + icol * lda; std::swap(lu_sup_ptr[itemp], lu_sup_ptr[nsupc + icol * lda]); } } // cdiv operations Scalar temp = Scalar(1.0) / lu_col_ptr[nsupc]; for (k = nsupc + 1; k < nsupr; k++) lu_col_ptr[k] *= temp; return 0; } } // end namespace internal } // end namespace Eigen #endif // SPARSELU_PIVOTL_H