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/*
* Copyright (c) 2012, 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 DLAQPS( M, N, OFFSET, NB, KB, A, LDA, JPVT, TAU, VN1, $ VN2, AUXV, F, LDF ) * * -- 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 2011 -- */ #ifndef FLENS_LAPACK_LA_LAQPS_TCC #define FLENS_LAPACK_LA_LAQPS_TCC 1 #include <flens/blas/blas.h> #include <flens/lapack/lapack.h> namespace flens { namespace lapack { //== generic lapack implementation ============================================= namespace generic { template <typename MA, typename JPIV, typename VTAU, typename VN1, typename VN2, typename VAUX, typename MF> void laqps_impl(typename GeMatrix<MA>::IndexType offset, typename GeMatrix<MA>::IndexType nb, typename GeMatrix<MA>::IndexType &kb, GeMatrix<MA> &A, DenseVector<JPIV> &jPiv, DenseVector<VTAU> &tau, DenseVector<VN1> &vn1, DenseVector<VN2> &vn2, DenseVector<VAUX> &aux, GeMatrix<MF> &F) { using std::abs; using std::max; using std::min; using flens::pow; using std::sqrt; using std::swap; typedef typename GeMatrix<MA>::ElementType ElementType; typedef typename GeMatrix<MA>::IndexType IndexType; const Underscore<IndexType> _; const IndexType m = A.numRows(); const IndexType n = A.numCols(); const IndexType lastRk = min(m, n+offset); IndexType lasticc = 0; IndexType k = 0; const ElementType Zero(0), One(1); const ElementType tol3z = sqrt(lamch<ElementType>(Eps)); // // Beginning of while loop. // while (k<nb && lasticc==0) { ++k; const IndexType rk = offset + k; // // Determine ith pivot column and swap if necessary // IndexType pvt = (k-1) + blas::iamax(vn1(_(k,n))); if (pvt!=k) { blas::swap(A(_,pvt), A(_,k)); blas::swap(F(pvt,_(1,k-1)), F(k,_(1,k-1))); swap(jPiv(pvt),jPiv(k)); vn1(pvt) = vn1(k); vn2(pvt) = vn2(k); } // // Apply previous Householder reflectors to column K: // A(RK:M,K) := A(RK:M,K) - A(RK:M,1:K-1)*F(K,1:K-1)**T. // if (k>1) { blas::mv(NoTrans, -One, A(_(rk,m),_(1,k-1)), F(k,_(1,k-1)), One, A(_(rk,m),k)); } // // Generate elementary reflector H(k). // if (rk<m) { larfg(m-rk+1, A(rk,k), A(_(rk+1,m),k), tau(k)); } else { larfg(1, A(m,k), A(_(m+1,m),k), tau(k)); } const ElementType Akk = A(rk,k); A(rk,k) = One; // // Compute Kth column of F: // // Compute F(K+1:N,K) := tau(K)*A(RK:M,K+1:N)**T*A(RK:M,K). // if (k<n) { blas::mv(Trans, tau(k), A(_(rk,m),_(k+1,n)), A(_(rk,m),k), Zero, F(_(k+1,n),k)); } // // Padding F(1:K,K) with zeros. // F(_(1,k),k) = Zero; // // Incremental updating of F: // F(1:N,K) := F(1:N,K) - tau(K)*F(1:N,1:K-1)*A(RK:M,1:K-1)**T // *A(RK:M,K). // if (k>1) { blas::mv(Trans, -tau(k), A(_(rk,m),_(1,k-1)), A(_(rk,m),k), Zero, aux(_(1,k-1))); blas::mv(NoTrans, One, F(_,_(1,k-1)), aux(_(1,k-1)), One, F(_,k)); } // // Update the current row of A: // A(RK,K+1:N) := A(RK,K+1:N) - A(RK,1:K)*F(K+1:N,1:K)**T. // if (k<n) { blas::mv(NoTrans, -One, F(_(k+1,n),_(1,k)), A(rk,_(1,k)), One, A(rk,_(k+1,n))); } // // Update partial column norms. // if (rk<lastRk) { for (IndexType j=k+1; j<=n; ++j) { if (vn1(j)!=Zero) { // // NOTE: The following 4 lines follow from the analysis in // Lapack Working Note 176. // ElementType tmp = abs(A(rk,j)) / vn1(j); tmp = max(Zero, (One+tmp)*(One-tmp)); ElementType tmp2 = tmp*pow(vn1(j)/vn2(j),2); if (tmp2<=tol3z) { vn2(j) = ElementType(lasticc); lasticc = j; } else { vn1(j) *= sqrt(tmp); } } } } A(rk,k) = Akk; // // End of while loop. // } kb = k; const IndexType rk = offset + kb; // // Apply the block reflector to the rest of the matrix: // A(OFFSET+KB+1:M,KB+1:N) := A(OFFSET+KB+1:M,KB+1:N) - // A(OFFSET+KB+1:M,1:KB)*F(KB+1:N,1:KB)**T. // if (kb<min(n,m-offset)) { blas::mm(NoTrans, Trans, -One, A(_(rk+1,m),_(1,kb)), F(_(kb+1,n),_(1,kb)), One, A(_(rk+1,m),_(kb+1,n))); } // // Recomputation of difficult columns. // while (lasticc>0) { IndexType iTmp = nint(vn2(lasticc)); vn1(lasticc) = blas::nrm2(A(_(rk+1,m),lasticc)); // // NOTE: The computation of VN1( LSTICC ) relies on the fact that // SNRM2 does not fail on vectors with norm below the value of // SQRT(DLAMCH('S')) // vn2(lasticc) = vn1(lasticc); lasticc = iTmp; } } } // namespace generic //== interface for native lapack =============================================== #ifdef USE_CXXLAPACK namespace external { template <typename MA, typename JPIV, typename VTAU, typename VN1, typename VN2, typename VAUX, typename MF> void laqps_impl(typename GeMatrix<MA>::IndexType offset, typename GeMatrix<MA>::IndexType nb, typename GeMatrix<MA>::IndexType &kb, GeMatrix<MA> &A, DenseVector<JPIV> &jPiv, DenseVector<VTAU> &tau, DenseVector<VN1> &vn1, DenseVector<VN2> &vn2, DenseVector<VAUX> &aux, GeMatrix<MF> &F) { typedef typename GeMatrix<MA>::IndexType IndexType; cxxlapack::laqps<IndexType>(A.numRows(), A.numCols(), offset, nb, kb, A.data(), A.leadingDimension(), jPiv.data(), tau.data(), vn1.data(), vn2.data(), aux.data(), F.data(), F.leadingDimension()); } } // namespace external #endif // USE_CXXLAPACK //== public interface ========================================================== template <typename MA, typename JPIV, typename VTAU, typename VN1, typename VN2, typename VAUX, typename MF> void laqps(typename GeMatrix<MA>::IndexType offset, typename GeMatrix<MA>::IndexType nb, typename GeMatrix<MA>::IndexType &kb, GeMatrix<MA> &A, DenseVector<JPIV> &jPiv, DenseVector<VTAU> &tau, DenseVector<VN1> &vn1, DenseVector<VN2> &vn2, DenseVector<VAUX> &aux, GeMatrix<MF> &F) { using std::min; typedef typename GeMatrix<MA>::ElementType ElementType; typedef typename GeMatrix<MA>::IndexType IndexType; # ifndef NDEBUG // // Test the input parameters // ASSERT(A.firstRow()==1); ASSERT(A.firstCol()==1); ASSERT(jPiv.firstIndex()==1); ASSERT(tau.firstIndex()==1); ASSERT(vn1.firstIndex()==1); ASSERT(vn2.firstIndex()==1); ASSERT(aux.firstIndex()==1); ASSERT(F.firstRow()==1); ASSERT(F.firstCol()==1); const IndexType n = A.numCols(); ASSERT(jPiv.length()==n); ASSERT(tau.length()>=nb); ASSERT(vn1.length()==n); ASSERT(vn1.length()==n); ASSERT(aux.length()==nb); ASSERT(F.numRows()==n); ASSERT(F.numCols()==nb); # endif # ifdef CHECK_CXXLAPACK // // Make copies of output arguments // typename GeMatrix<MA>::NoView A_org = A; typename DenseVector<JPIV>::NoView jPiv_org = jPiv; typename DenseVector<VTAU>::NoView tau_org = tau; typename DenseVector<VN1>::NoView vn1_org = vn1; typename DenseVector<VN2>::NoView vn2_org = vn2; typename DenseVector<VAUX>::NoView aux_org = aux; typename GeMatrix<MF>::NoView F_org = F; # endif // // Call implementation // LAPACK_SELECT::laqps_impl(offset, nb, kb, A, jPiv, tau, vn1, vn2, aux, F); # ifdef CHECK_CXXLAPACK // // Restore output arguments // typename GeMatrix<MA>::NoView A_generic = A; typename DenseVector<JPIV>::NoView jPiv_generic = jPiv; typename DenseVector<VTAU>::NoView tau_generic = tau; typename DenseVector<VN1>::NoView vn1_generic = vn1; typename DenseVector<VN2>::NoView vn2_generic = vn2; typename DenseVector<VAUX>::NoView aux_generic = aux; typename GeMatrix<MF>::NoView F_generic = F; A = A_org; jPiv = jPiv_org; tau = tau_org; vn1 = vn1_org; vn2 = vn2_org; aux = aux_org; F = F_org; // // Compare results // external::laqps_impl(offset, nb, kb, A, jPiv, tau, vn1, vn2, aux, F); bool failed = false; if (! isIdentical(A_generic, A, "A_generic", "A")) { std::cerr << "CXXLAPACK: A_generic = " << A_generic << std::endl; std::cerr << "F77LAPACK: A = " << A << std::endl; failed = true; } if (! isIdentical(jPiv_generic, jPiv, "jPiv_generic", "jPiv")) { std::cerr << "CXXLAPACK: jPiv_generic = " << jPiv_generic << std::endl; std::cerr << "F77LAPACK: jPiv = " << jPiv << std::endl; failed = true; } if (! isIdentical(tau_generic, tau, "tau_generic", "tau")) { std::cerr << "CXXLAPACK: tau_generic = " << tau_generic << std::endl; std::cerr << "F77LAPACK: tau = " << tau << std::endl; failed = true; } if (! isIdentical(vn1_generic, vn1, "vn1_generic", "vn1")) { std::cerr << "CXXLAPACK: vn1_generic = " << vn1_generic << std::endl; std::cerr << "F77LAPACK: vn1 = " << vn1 << std::endl; failed = true; } if (! isIdentical(vn2_generic, vn2, "vn2_generic", "vn2")) { std::cerr << "CXXLAPACK: vn2_generic = " << vn2_generic << std::endl; std::cerr << "F77LAPACK: vn2 = " << vn2 << std::endl; failed = true; } if (! isIdentical(aux_generic, aux, "aux_generic", "aux")) { std::cerr << "CXXLAPACK: aux_generic = " << aux_generic << std::endl; std::cerr << "F77LAPACK: aux = " << aux << std::endl; failed = true; } if (! isIdentical(F_generic, F, "F_generic", "F")) { std::cerr << "CXXLAPACK: F_generic = " << F_generic << std::endl; std::cerr << "F77LAPACK: F = " << F << std::endl; failed = true; } if (failed) { ASSERT(0); } # endif } //-- forwarding ---------------------------------------------------------------- template <typename MA, typename JPIV, typename VTAU, typename VN1, typename VN2, typename VAUX, typename MF> void laqps(typename MA::IndexType offset, typename MA::IndexType nb, typename MA::IndexType &kb, MA &&A, JPIV &&jPiv, VTAU &&tau, VN1 &&vn1, VN2 &&vn2, VAUX &&aux, MF &&F) { CHECKPOINT_ENTER; laqps(offset, nb, kb, A, jPiv, tau, vn1, vn2, aux, F); CHECKPOINT_LEAVE; } } } // namespace lapack, flens #endif // FLENS_LAPACK_LA_LAQPS_TCC |