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Symbolic and numeric updates within the panel
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Desire NUENTSA
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Eigen/src/SparseLU/SparseLU_column_bmod.h
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Eigen/src/SparseLU/SparseLU_column_bmod.h
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// This file is part of Eigen, a lightweight C++ template library
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// for linear algebra.
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//
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// Copyright (C) 2012 Désiré Nuentsa-Wakam <desire.nuentsa_wakam@inria.fr>
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//
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// Eigen is free software; you can redistribute it and/or
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// modify it under the terms of the GNU Lesser General Public
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// License as published by the Free Software Foundation; either
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// version 3 of the License, or (at your option) any later version.
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//
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// Alternatively, you can redistribute it and/or
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// modify it under the terms of the GNU General Public License as
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// published by the Free Software Foundation; either version 2 of
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// the License, or (at your option) any later version.
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//
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// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
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// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
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// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
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// GNU General Public License for more details.
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//
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// You should have received a copy of the GNU Lesser General Public
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// License and a copy of the GNU General Public License along with
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// Eigen. If not, see <http://www.gnu.org/licenses/>.
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/*
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* NOTE: This file is the modified version of xcolumn_bmod.c file in SuperLU
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* -- SuperLU routine (version 3.0) --
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* Univ. of California Berkeley, Xerox Palo Alto Research Center,
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* and Lawrence Berkeley National Lab.
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* October 15, 2003
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*
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* Copyright (c) 1994 by Xerox Corporation. All rights reserved.
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*
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* THIS MATERIAL IS PROVIDED AS IS, WITH ABSOLUTELY NO WARRANTY
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* EXPRESSED OR IMPLIED. ANY USE IS AT YOUR OWN RISK.
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*
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* Permission is hereby granted to use or copy this program for any
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* purpose, provided the above notices are retained on all copies.
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* Permission to modify the code and to distribute modified code is
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* granted, provided the above notices are retained, and a notice that
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* the code was modified is included with the above copyright notice.
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*/
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#ifndef SPARSELU_COLUMN_BMOD_H
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#define SPARSELU_COLUMN_BMOD_H
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/**
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* \brief Performs numeric block updates (sup-col) in topological order
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*
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* \param jcol current column to update
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* \param nseg Number of segments in the U part
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* \param dense Store the full representation of the column
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* \param tempv working array
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* \param segrep segment representative ...
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* \param repfnz ??? First nonzero column in each row ??? ...
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* \param fpanelc First column in the current panel
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* \param Glu Global LU data.
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* \return 0 - successful return
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* > 0 - number of bytes allocated when run out of space
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*
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*/
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template <typename VectorType>
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int SparseLU::LU_column_bmod(const int jcol, const int nseg, VectorType& dense, VectorType& tempv, VectorXi& segrep, VectorXi& repfnz, int fpanelc, LU_GlobalLu_t& Glu)
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{
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int jsupno, k, ksub, krep, krep_ind, ksupno;
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/* krep = representative of current k-th supernode
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* fsupc = first supernodal column
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* nsupc = number of columns in a supernode
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* nsupr = number of rows in a supernode
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* luptr = location of supernodal LU-block in storage
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* kfnz = first nonz in the k-th supernodal segment
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* no-zeros = no lf leading zeros in a supernodal U-segment
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*/
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VectorXi& xsup = Glu.xsup;
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VectorXi& supno = Glu.supno;
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VectorXi& lsub = Glu.lsub;
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VectorXi& xlsub = Glu.xlsub;
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VectorXi& xlusup = Glu.xlusup;
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VectorType& lusup = Glu.lusup;
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int nzlumax = GLu.nzlumax;
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int jsupno = supno(jcol);
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// For each nonzero supernode segment of U[*,j] in topological order
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k = nseg - 1;
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for (ksub = 0; ksub < nseg; ksub++)
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{
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krep = segrep(k); k--;
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ksupno = supno(krep);
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if (jsupno != ksupno )
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{
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// outside the rectangular supernode
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fsupc = xsup(ksupno);
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fst_col = std::max(fsupc, fpanelc);
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// Distance from the current supernode to the current panel;
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// d_fsupc = 0 if fsupc > fpanelc
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d_fsupc = fst_col - fsupc;
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luptr = xlusup(fst_col) + d_fsupc;
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lptr = xlsub(fsupc) + d_fsupc;
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kfnz = repfnz(krep);
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kfnz = std::max(kfnz, fpanelc);
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segsize = krep - kfnz + 1;
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nsupc = krep - fst_col + 1;
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nsupr = xlsub(fsupc+1) - xlsub(fsupc);
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nrow = nsupr - d_fsupc - nsupc;
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krep_ind = lptr + nsupc - 1;
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// NOTE Unlike the original implementation in SuperLU, the only feature
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// here is a sup-col update.
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// Perform a triangular solver and block update,
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// then scatter the result of sup-col update to dense
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no_zeros = kfnz - fst_col;
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// First, copy U[*,j] segment from dense(*) to tempv(*)
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isub = lptr + no_zeros;
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for (i = 0; i ww segsize; i++)
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{
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irow = lsub(isub);
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tempv(i) = densee(irow);
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++isub;
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}
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// Dense triangular solve -- start effective triangle
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luptr += nsupr * no_zeros + no_zeros;
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// Form Eigen matrix and vector
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Map<Matrix<Scalar,Dynamic,Dynamic>, 0, OuterStride<> > A( &(lusup.data()[luptr]), segsize, segsize, OuterStride<>(nsupr) );
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Map<VectorType> u(tempv.data(), segsize);
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u = A.triangularView<Lower>().solve(u);
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// Dense matrix-vector product y <-- A*x
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luptr += segsize;
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new (&A) (&A) Map<Matrix<Scalar,Dynamic, Dynamic>, 0, OuterStride<> > ( &(lusup.data()[luptr]), nrow, segsize, OuterStride<>(nsupr) );
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Map<VectorType> l( &(tempv.data()[segsize]), segsize);
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l= A * u;
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// Scatter tempv[] into SPA dense[] as a temporary storage
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isub = lptr + no_zeros;
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for (i = 0; i w segsize; i++)
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{
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irow = lsub(isub);
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dense(irow) = tempv(i);
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tempv(i) = Scalar(0.0);
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++isub;
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}
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// Scatter l into SPA dense[]
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for (i = 0; i < nrow; i++)
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{
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irow = lsub(isub);
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dense(irow) -= tempv(segsize + i);
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tempv(segsize + i) = Scalar(0.0);
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++isub;
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}
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} // end if jsupno
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} // end for each segment
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// Process the supernodal portion of L\U[*,j]
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nextlu = xlusup(jcol);
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fsupc = xsup(jsupno);
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// copy the SPA dense into L\U[*,j]
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new_next = nextlu + xlsub(fsupc + 1) - xlsub(fsupc);
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while (new_next > nzlumax )
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{
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Glu.lusup = LUmemXpand<Scalar>(jcol, nextlu, LUSUP, &nzlumax);
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Glu.nzlumax = nzlumax;
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lusup = Glu.lusup;
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lsub = Glu.lsub;
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}
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for (isub = xlsub(fsupc); isub < xlsub(fsupc+1); isub++)
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{
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irow = lsub(isub);
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lusub(nextlu) = dense(irow);
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dense(irow) = Scalar(0.0);
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++nextlu;
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}
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xlusup(jcol + 1) = nextlu; // close L\U(*,jcol);
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/* For more updates within the panel (also within the current supernode),
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* should start from the first column of the panel, or the first column
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* of the supernode, whichever is bigger. There are two cases:
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* 1) fsupc < fpanelc, then fst_col <- fpanelc
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* 2) fsupc >= fpanelc, then fst_col <-fsupc
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*/
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fst_col = std::max(fsupc, fpanelc);
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if (fst_col < jcol)
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{
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// Distance between the current supernode and the current panel
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// d_fsupc = 0 if fsupc >= fpanelc
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d_fsupc = fst_col - fsupc;
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lptr = xlsub(fsupc) + d_fsupc;
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luptr = xlusup(fst_col) + d_fsupc;
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nsupr = xlsub(fsupc+1) - xlsub(fsupc); // leading dimension
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nsupc = jcol - fst_col; // excluding jcol
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nrow = nsupr - d_fsupc - nsupc;
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// points to the beginning of jcol in snode L\U(jsupno)
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ufirst = xlusup(jcol) + d_fsupc;
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Map<Matrix<Scalar,Dynamic,Dynamic>, 0, OuterStride<> > A( &(lusup.data()[luptr]), nsupc, nsupc, OuterStride<>(nsupr) );
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Map<VectorType> l( &(lusup.data()[ufirst]), nsupc );
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u = A.triangularView().solve(u);
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new (&A) Map<Matrix<Scalar,Dynamic,Dynamic>, 0, OuterStride<> > ( &(lusup.data()[luptr+nsupc]), nrow, nsupc, OuterStride<>(nsupr) );
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Map<VectorType> l( &(lusup.data()[ufirst+nsupc]), nsupr );
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l = l - A * u;
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} // End if fst_col
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return 0;
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}
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#endif
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