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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 DLAHR2( N, K, NB, A, LDA, TAU, T, LDT, Y, LDY ) * * -- LAPACK auxiliary 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_LA_LAHR2_TCC #define FLENS_LAPACK_LA_LAHR2_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, typename VTAU, typename MTR, typename MY> void lahr2_impl(IndexType k, IndexType nb, GeMatrix<MA> &A, DenseVector<VTAU> &tau, TrMatrix<MTR> &Tr, GeMatrix<MY> &Y) { using lapack::larfg; using std::min; typedef typename GeMatrix<MA>::ElementType T; const Underscore<IndexType> _; const IndexType n = A.numRows(); const T Zero(0), One(1); // TODO: as long as view creation is not supported by the TrMatrix interface // we get them through a GeMatrix::View auto _Tr = Tr.general(); // // Quick return if possible // if (n<=1) { return; } T ei = T(0); for (IndexType i=1; i<=nb; ++i) { if (i>1) { // // Update A(K+1:N,I) // // Update I-th column of A - Y * V**T // blas::mv(NoTrans, -One, Y(_(k+1,n),_(1,i-1)), A(k+i-1,_(1,i-1)), One, A(_(k+1,n),i)); // // Apply I - V * T**T * V**T to this column (call it b) from the // left, using the last column of T as workspace // // Let V = ( V1 ) and b = ( b1 ) (first I-1 rows) // ( V2 ) ( b2 ) // // where V1 is unit lower triangular // // w := V1**T * b1 // _Tr(_(1,i-1),nb) = A(_(k+1,k+i-1),i); blas::mv(Trans, A(_(k+1,k+i-1),_(1,i-1)).lowerUnit(), _Tr(_(1,i-1),nb)); // // w := w + V2**T * b2 // blas::mv(Trans, One, A(_(k+i,n),_(1,i-1)), A(_(k+i,n),i), One, _Tr(_(1,i-1),nb)); // // w := T**T * w // blas::mv(Trans, _Tr(_(1,i-1),_(1,i-1)).upper(), _Tr(_(1,i-1),nb)); // // b2 := b2 - V2*w // blas::mv(NoTrans, -One, A(_(k+i,n),_(1,i-1)), _Tr(_(1,i-1),nb), One, A(_(k+i,n),i)); // // b1 := b1 - V1*w // blas::mv(NoTrans, A(_(k+1,k+i-1),_(1,i-1)).lowerUnit(), _Tr(_(1,i-1),nb)); A(_(k+1,k+i-1),i) -= _Tr(_(1,i-1),nb); A(k+i-1,i-1) = ei; } // // Generate the elementary reflector H(I) to annihilate // A(K+I+1:N,I) // larfg(n-k-i+1, A(k+i,i), A(_(min(k+i+1,n),n), i), tau(i)); ei = A(k+i, i); A(k+i, i) = One; // // Compute Y(K+1:N,I) // blas::mv(NoTrans, One, A(_(k+1,n),_(i+1,n-k+1)), A(_(k+i,n),i), Zero, Y(_(k+1,n),i)); blas::mv(Trans, One, A(_(k+i,n),_(1,i-1)), A(_(k+i,n),i), Zero, _Tr(_(1,i-1),i)); blas::mv(NoTrans, -One, Y(_(k+1,n),_(1,i-1)), _Tr(_(1,i-1),i), One, Y(_(k+1,n),i)); blas::scal(tau(i),Y(_(k+1,n),i)); // // Compute T(1:I,I) // blas::scal(-tau(i), _Tr(_(1,i-1),i)); blas::mv(NoTrans, _Tr(_(1,i-1),_(1,i-1)).upper(), _Tr(_(1,i-1),i)); Tr(i,i) = tau(i); } A(k+nb, nb) = ei; // // Compute Y(1:K,1:NB) // Y(_(1,k),_(1,nb)) = A(_(1,k),_(2,2+nb-1)); blas::mm(Right, NoTrans, One, A(_(k+1,k+nb),_(1,nb)).lowerUnit(), Y(_(1,k),_(1,nb))); if (n>k+nb) { blas::mm(NoTrans, NoTrans, One, A(_(1,k),_(2+nb,n-k+1)), A(_(k+1+nb,n),_(1,nb)), One, Y(_(1,k),_(1,nb))); } blas::mm(Right, NoTrans, One, Tr, Y(_(1,k),_(1,nb))); } } // namespace generic //== interface for native lapack =============================================== #ifdef USE_CXXLAPACK namespace external { template <typename IndexType, typename MA, typename VTAU, typename MTR, typename MY> void lahr2_impl(IndexType k, IndexType nb, GeMatrix<MA> &A, DenseVector<VTAU> &tau, TrMatrix<MTR> &Tr, GeMatrix<MY> &Y) { cxxlapack::lahr2<IndexType>(A.numRows(), k, nb, A.data(), A.leadingDimension(), tau.data(), Tr.data(), Tr.leadingDimension(), Y.data(), Y.leadingDimension()); } } // namespace external #endif // USE_CXXLAPACK //== public interface ========================================================== template <typename IndexType, typename MA, typename VTAU, typename MTR, typename MY> void lahr2(IndexType k, IndexType nb, GeMatrix<MA> &A, DenseVector<VTAU> &tau, TrMatrix<MTR> &Tr, GeMatrix<MY> &Y) { LAPACK_DEBUG_OUT("lahr2"); // // Test the input parameters // ASSERT(k<A.numRows()); ASSERT(A.firstRow()==1); ASSERT(A.firstCol()==1); ASSERT(A.numCols()==A.numRows()-k+1); ASSERT(tau.length()==nb); ASSERT(Tr.dim()==nb); ASSERT(Y.numRows()==A.numRows()); ASSERT(Y.numCols()==nb); // // Make copies of output arguments // # ifdef CHECK_CXXLAPACK typename GeMatrix<MA>::NoView _A = A; typename DenseVector<VTAU>::NoView _tau = tau; typename GeMatrix<MTR>::NoView __Tr = Tr.general(); typename GeMatrix<MY>::NoView _Y = Y; auto _Tr = (Tr.upLo()==Upper) ? __Tr.upper() : __Tr.lower(); # endif // // Call implementation // LAPACK_SELECT::lahr2_impl(k, nb, A, tau, Tr, Y); // // Compare results // # ifdef CHECK_CXXLAPACK external::lahr2_impl(k, nb, _A, _tau, _Tr, _Y); 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(Tr.general(), _Tr.general(), " Tr", "_Tr")) { std::cerr << "CXXLAPACK: Tr = " << Tr.general() << std::endl; std::cerr << "F77LAPACK: _Tr = " << _Tr.general() << std::endl; failed = true; } if (! isIdentical(Y, _Y, " Y", "_Y")) { std::cerr << "CXXLAPACK: Y = " << Y << std::endl; std::cerr << "F77LAPACK: _Y = " << _Y << std::endl; failed = true; } if (failed) { std::cerr << "error in: lahr2.tcc" << std::endl; std::cerr << "k = " << k << ", nb = " << nb << std::endl; ASSERT(0); } else { // std::cerr << "passed: lahr2.tcc" << std::endl; } # endif } //-- forwarding ---------------------------------------------------------------- template <typename IndexType, typename MA, typename VTAU, typename MTR, typename MY> void lahr2(IndexType k, IndexType nb, MA &&A, VTAU &&tau, MTR &&Tr, MY &&Y) { CHECKPOINT_ENTER; lahr2(k, nb, A, tau, Tr, Y); CHECKPOINT_LEAVE; } } } // namespace lapack, flens #endif // FLENS_LAPACK_LA_LAHR2_TCC |