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/*
* Copyright (c) 2011, Michael Lehn * * All rights reserved. * * Redistribution and use in source and binary forms, with or without * modification, are permitted provided that the following conditions * are met: * * 1) Redistributions of source code must retain the above copyright * notice, this list of conditions and the following disclaimer. * 2) Redistributions in binary form must reproduce the above copyright * notice, this list of conditions and the following disclaimer in * the documentation and/or other materials provided with the * distribution. * 3) Neither the name of the FLENS development group nor the names of * its contributors may be used to endorse or promote products derived * from this software without specific prior written permission. * * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR * A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT * OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT * LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE * OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. */ /* Based on * SUBROUTINE DGEHRD( N, ILO, IHI, A, LDA, TAU, WORK, LWORK, INFO ) * * -- LAPACK routine (version 3.3.1) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * -- April 2009 -- */ #ifndef FLENS_LAPACK_GE_HRD_TCC #define FLENS_LAPACK_GE_HRD_TCC 1 #include <flens/blas/blas.h> #include <flens/lapack/lapack.h> namespace flens { namespace lapack { //== generic lapack implementation ============================================= namespace generic { template <typename IndexType, typename MA> IndexType hrd_wsq_impl(IndexType iLo, IndexType iHi, const GeMatrix<MA> &A) { using std::min; typedef typename GeMatrix<MA>::ElementType T; // // Perform and apply workspace query // const IndexType nbMax = 64; const IndexType n = A.numCols(); return n*min(nbMax, IndexType(ilaenv<T>(1,"GEHRD", "", n, iLo, iHi))); } template <typename IndexType, typename MA, typename VTAU, typename VWORK> void hrd_impl(IndexType iLo, IndexType iHi, GeMatrix<MA> &A, DenseVector<VTAU> &tau, DenseVector<VWORK> &work) { using std::max; using std::min; typedef typename GeMatrix<MA>::ElementType T; typedef typename GeMatrix<MA>::View GeView; typedef typename GeView::Engine GeViewEngine; const Underscore<IndexType> _; // // Paramters, e.g. maximum block size and buffer on stack for TrMatrix Tr. // const T One(1); const IndexType nbMax = 64; const IndexType ldt = nbMax + 1; T trBuffer[nbMax*ldt]; GeView _Tr = GeViewEngine(ldt, nbMax, trBuffer, ldt); // // Perform and apply workspace query // const IndexType n = A.numCols(); IndexType nb = min(nbMax, IndexType(ilaenv<T>(1,"GEHRD", "", n, iLo, iHi))); const IndexType lWorkOpt = n*nb; if (work.length()==0) { work.resize(lWorkOpt); work(1) = lWorkOpt; } // // Set elements 1:iLo-1 and iHi:n-1 of tau to zero // tau(_(1,iLo-1)) = 0; tau(_(max(IndexType(1),iHi),n-1)) = 0; // // Quick return if possible // const IndexType nh = iHi - iLo + 1; if (nh<=1) { work(1) = 1; return; } // // Determine the block size // IndexType nbMin = 2; IndexType iws = 1; IndexType nx = 0; if (nb>1 && nb<nh) { // // Determine when to cross over from blocked to unblocked code // (last block is always handled by unblocked code) // nx = max(nb, IndexType(ilaenv<T>(3, "GEHRD", "", n, iLo, iHi))); if (nx<nh) { // // Determine if workspace is large enough for blocked code // iws = n*nb; if (work.length()<iws) { // // Not enough workspace to use optimal NB: determine the // minimum value of NB, and reduce NB or force use of // unblocked code // nbMin = max(2, ilaenv<T>(2, "GEHRD", "", n, iLo, iHi)); if (work.length()>=n*nbMin) { nb = work.length() / n; } else { nb = 1; } } } } IndexType ldWork = n; IndexType i = iLo; if (nb<nbMin || nb>=nh) { // // Use unblocked code below // } else { // // Use blocked code // for (i=iLo; i<=iHi-1-nx; i+=nb) { const IndexType ib = min(nb, iHi-i); auto Tr = _Tr(_(1,ib),_(1,ib)).upper(); GeView Y(iHi, ib, work, ldWork); // // Reduce columns i:i+ib-1 to Hessenberg form, returning the // matrices V and T of the block reflector H = I - V*T*V**T // which performs the reduction, and also the matrix Y = A*V*T // lahr2(i, ib, A(_(1,iHi),_(i,iHi)), tau(_(i,i+ib-1)), Tr, Y); // // Partition V and the parts of matrix A that get modified // auto V1 = A(_(i+1, i+ib-1),_(i,i+ib-2)); auto V2 = A(_(i+ib, iHi),_(i,i+ib-1)); // // Apply the block reflector H to A(1:ihi,i+ib:ihi) from the // right, computing A := A - Y * V**T. V(i+ib,ib-1) must be set // to 1 // T ei = A(i+ib,i+ib-1); A(i+ib,i+ib-1) = One; blas::mm(NoTrans, Trans, -One, Y, V2, One, A(_(1,iHi),_(i+ib,iHi))); A(i+ib,i+ib-1) = ei; // // Apply the block reflector H to A(1:i,i+1:i+ib-1) from the // right // blas::mm(Right, Trans, One, V1.lowerUnit(), Y(_(1,i),_(1,ib-1))); A(_(1,i),_(i+1,i+ib-1)) -= Y(_(1,i),_(1,ib-1)); // // Apply the block reflector H to A(i+1:ihi,i+ib:n) from the // left // GeView Work(n-i-ib+1, ib, work, ldWork); larfb(Left, Trans, Forward, ColumnWise, A(_(i+1,iHi),_(i,i+ib-1)), Tr, A(_(i+1,iHi),_(i+ib,n)), Work); } } // // Use unblocked code to reduce the rest of the matrix // hd2(i, iHi, A, tau, work); work(1) = iws; } } // namespace generic //== interface for native lapack =============================================== #ifdef USE_CXXLAPACK namespace external { template <typename IndexType, typename MA> IndexType hrd_wsq_impl(IndexType iLo, IndexType iHi, const GeMatrix<MA> &A) { typedef typename GeMatrix<MA>::ElementType T; T WORK, DUMMY; const IndexType LWORK = -1; cxxlapack::gehrd<IndexType>(A.numRows(), iLo, iHi, &DUMMY, A.leadingDimension(), &DUMMY, &WORK, LWORK); return WORK; } template <typename IndexType, typename MA, typename VTAU, typename VWORK> void hrd_impl(IndexType iLo, IndexType iHi, GeMatrix<MA> &A, DenseVector<VTAU> &tau, DenseVector<VWORK> &work) { cxxlapack::gehrd<IndexType>(A.numRows(), iLo, iHi, A.data(), A.leadingDimension(), tau.data(), work.data(), work.length()); } } // namespace external #endif // USE_CXXLAPACK //== public interface ========================================================== template <typename IndexType, typename MA> IndexType hrd_wsq(IndexType iLo, IndexType iHi, const GeMatrix<MA> &A) { LAPACK_DEBUG_OUT("hrd_wsq"); // // Test the input parameters // # ifndef NDEBUG ASSERT(A.firstRow()==1); ASSERT(A.firstCol()==1); ASSERT(A.numRows()==A.numCols()); # endif // // Call implementation // IndexType info = LAPACK_SELECT::hrd_wsq_impl(iLo, iHi, A); # ifdef CHECK_CXXLAPACK // // Compare results // IndexType _info = external::hrd_wsq_impl(iLo, iHi, A); if (! isIdentical(info, _info, " info", "_info")) { ASSERT(0); } # endif return info; } template <typename IndexType, typename MA, typename VTAU, typename VWORK> void hrd(IndexType iLo, IndexType iHi, GeMatrix<MA> &A, DenseVector<VTAU> &tau, DenseVector<VWORK> &work) { LAPACK_DEBUG_OUT("hrd"); using std::max; // // Test the input parameters // # ifndef NDEBUG ASSERT(A.firstRow()==1); ASSERT(A.firstCol()==1); ASSERT(A.numRows()==A.numCols()); ASSERT(tau.firstIndex()==1); const IndexType n = A.numCols(); if (n==0) { ASSERT(iLo==1); ASSERT(iHi==0); } else { ASSERT(1<=iLo); ASSERT(iLo<=iHi); ASSERT(iHi<=n); } ASSERT(tau.length()==(n-1)); const bool lQuery = (work.length()==0); ASSERT(lQuery || (work.length()>=max(IndexType(1),n))); # endif // // Make copies of output arguments // # ifdef CHECK_CXXLAPACK typename GeMatrix<MA>::NoView _A = A; typename DenseVector<VTAU>::NoView _tau = tau; typename DenseVector<VWORK>::NoView _work = work; # endif // // Call implementation // LAPACK_SELECT::hrd_impl(iLo, iHi, A, tau, work); # ifdef CHECK_CXXLAPACK // // Compare results // if (_work.length()==0) { _work.resize(work.length()); } external::hrd_impl(iLo, iHi, _A, _tau, _work); bool failed = false; if (! isIdentical(A, _A, " A", "_A")) { std::cerr << "CXXLAPACK: A = " << A << std::endl; std::cerr << "F77LAPACK: _A = " << _A << std::endl; failed = true; } if (! isIdentical(tau, _tau, " tau", "_tau")) { std::cerr << "CXXLAPACK: tau = " << tau << std::endl; std::cerr << "F77LAPACK: _tau = " << _tau << std::endl; failed = true; } if (! isIdentical(work, _work, " work", "_work")) { std::cerr << "CXXLAPACK: work = " << work << std::endl; std::cerr << "F77LAPACK: _work = " << _work << std::endl; failed = true; } if (failed) { std::cerr << "error in: hrd.tcc" << std::endl; ASSERT(0); } else { // std::cerr << "passed: hrd.tcc" << std::endl; } # endif } //-- forwarding ---------------------------------------------------------------- template <typename IndexType, typename MA> IndexType hrd_wsq(IndexType iLo, IndexType iHi, const MA &&A) { CHECKPOINT_ENTER; const IndexType info = hrd_wsq(iLo, iHi, A); CHECKPOINT_LEAVE; return info; } template <typename IndexType, typename MA, typename VTAU, typename VWORK> void hrd(IndexType iLo, IndexType iHi, MA &&A, VTAU &&tau, VWORK &&work) { CHECKPOINT_ENTER; hrd(iLo, iHi, A, tau, work); CHECKPOINT_LEAVE; } } } // namespace lapack, flens #endif // FLENS_LAPACK_GE_HRD_TCC |