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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 DTRSEN( JOB, COMPQ, SELECT, N, T, LDT, Q, LDQ, WR, WI, $ M, S, SEP, WORK, LWORK, IWORK, LIWORK, 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 2011 -- * */ #ifndef FLENS_LAPACK_IMPL_TRSEN_TCC #define FLENS_LAPACK_IMPL_TRSEN_TCC 1 #include <cmath> #include <flens/blas/blas.h> #include <flens/lapack/lapack.h> namespace flens { namespace lapack { //== generic lapack implementation ============================================= namespace generic { template <typename SELECT, typename MT, typename IndexType> Pair<IndexType> trsen_wsq_impl(TRSEN::Job job, const DenseVector<SELECT> &select, GeMatrix<MT> &T, IndexType &m) { using std::max; typedef typename GeMatrix<MT>::ElementType ElementType; const ElementType Zero(0); const IndexType n = T.numRows(); // // Decode and test the input parameters // const bool wantBH = (job==TRSEN::Both); const bool wantSP = (job==TRSEN::InvariantSubspaceOnly) || wantBH; // // Set M to the dimension of the specified invariant subspace, // and test LWORK and LIWORK. // m = 0; bool pair = false; for (IndexType k=1; k<=n; ++k) { if (pair) { pair = false; } else { if (k<n) { if (T(k+1,k)==Zero) { if (select(k)) { ++m; } } else { pair = true; if (select(k) || select(k+1)) { m += 2; } } } else { if (select(n)) { ++m; } } } } IndexType n1 = m; IndexType n2 = n - m; IndexType nn = n1*n2; IndexType workMin = 0, iWorkMin = 0; if (wantSP) { workMin = max(IndexType(1), 2*nn); iWorkMin = max(IndexType(1), nn); } else if (job==TRSEN::None) { workMin = max(IndexType(1), n); iWorkMin = 1; } else if (job==TRSEN::EigenvaluesOnly) { workMin = max(IndexType(1), nn); iWorkMin = 1; } return Pair<IndexType>(workMin, iWorkMin); } template <typename SELECT, typename MT, typename MQ, typename WR, typename WI, typename IndexType, typename S, typename SEP, typename WORK, typename IWORK> IndexType trsen_impl(TRSEN::Job job, bool computeQ, const DenseVector<SELECT> &select, GeMatrix<MT> &T, GeMatrix<MQ> &Q, DenseVector<WR> &wr, DenseVector<WI> &wi, IndexType &m, S &s, SEP &sep, DenseVector<WORK> &work, DenseVector<IWORK> &iwork) { using std::abs; typedef typename GeMatrix<MT>::ElementType ElementType; const ElementType Zero(0), One(1); const IndexType n = T.numRows(); const Underscore<IndexType> _; IndexType info = 0; // // .. Local Arrays .. // this array is used to save variables between calls to lacn2 // IndexType _isaveData[3] = {0, 0, 0}; DenseVectorView<IndexType> isave = typename DenseVectorView<IndexType>::Engine(3, _isaveData); // // Decode and test the input parameters // const bool wantBH = (job==TRSEN::Both); const bool wantS = (job==TRSEN::EigenvaluesOnly) || wantBH; const bool wantSP = (job==TRSEN::InvariantSubspaceOnly) || wantBH; // // Set M to the dimension of the specified invariant subspace, // and compute minimal size of WORK and IWORK // auto wsq = trsen_wsq_impl(job, select, T, m); const IndexType workMin = wsq.first; const IndexType iWorkMin = wsq.second; IndexType lWork = work.length(); IndexType liWork = iwork.length(); if (lWork<workMin && lWork>0) { ASSERT(0); return -1; } else if (liWork<iWorkMin && liWork>0) { ASSERT(0); return -2; } if (lWork==0) { work.resize(workMin); } if (liWork==0) { iwork.resize(iWorkMin); } work(1) = workMin; iwork(1) = iWorkMin; IndexType n1 = m; IndexType n2 = n - m; IndexType nn = n1*n2; bool pair; IndexType ks; ElementType scale; // // Quick return if possible. // if (m==n || m==0) { if (wantS) { s = One; } if (wantSP) { sep = lan(OneNorm, T); } goto DONE; } // // Collect the selected blocks at the top-left corner of T. // ks = 0; pair = false; for (IndexType k=1; k<=n; ++k) { if (pair) { pair = false; } else { bool swap = select(k); if (k<n) { if (T(k+1,k)!=Zero) { pair = true; swap = swap || select(k+1); } } if (swap) { ++ks; // // Swap the K-th block to position KS. // IndexType iErr = 0; IndexType kk = k; if (k!=ks) { trexc(computeQ, T, Q, kk, ks, work(_(1,n))); } if (iErr==1 || iErr==2) { // // Blocks too close to swap: exit. // info = 1; if (wantS) { s = Zero; } if (wantSP) { sep = Zero; } goto DONE; } if (pair) { ++ks; } } } } if (wantS) { GeMatrixView<ElementType> Work(n1, n2, work, n1); // // Solve Sylvester equation for R: // // T11*R - R*T22 = scale*T12 // Work = T(_(1,n1),_(n1+1,n1+n2)); auto T11 = T(_(1,n1),_(1,n1)); auto T22 = T(_(n1+1,n1+n2),_(n1+1,n1+n2)); trsyl(NoTrans, NoTrans, -1, T11, T22, Work, scale); // // Estimate the reciprocal of the condition number of the cluster // of eigenvalues. // ElementType rNorm = lan(FrobeniusNorm, Work); if (rNorm==Zero) { s = One; } else { s = scale / (sqrt(scale*scale/rNorm + rNorm)*sqrt(rNorm)); } } if (wantSP) { // // Estimate sep(T11,T22). // ElementType est = Zero; IndexType kase = 0; do { auto _v = work(_(nn+1,nn+nn)); auto _x = work(_(1,nn)); auto _isgn = iwork(_(1,nn)); lacn2(_v, _x, _isgn, est, kase, isave); if (kase==0) { break; } GeMatrixView<ElementType> Work(n1, n2, work, n1); auto T11 = T(_(1,n1),_(1,n1)); auto T22 = T(_(n1+1,n1+n2),_(n1+1,n1+n2)); if (kase==1) { // // Solve T11*R - R*T22 = scale*X. // trsyl(NoTrans, NoTrans, -1, T11, T22, Work, scale); } else { // // Solve T11**T*R - R*T22**T = scale*X. // trsyl(Trans, Trans, -1, T11, T22, Work, scale); } } while (true); sep = scale / est; } DONE: // // Store the output eigenvalues in WR and WI. // for (IndexType k=1; k<=n; ++k) { wr(k) = T(k,k); wi(k) = Zero; } for (IndexType k=1; k<=n-1; ++k) { if (T(k+1,k)!=Zero) { wi(k) = sqrt(abs(T(k,k+1)))*sqrt(abs(T(k+1,k))); wi(k+1) = -wi(k); } } work(1) = workMin; iwork(1) = iWorkMin; return info; } } // namespace generic //== interface for native lapack =============================================== #ifdef USE_CXXLAPACK namespace external { template <typename SELECT, typename MT, typename MQ, typename WR, typename WI, typename IndexType, typename S, typename SEP, typename WORK, typename IWORK> IndexType trsen_impl(TRSEN::Job job, bool computeQ, const DenseVector<SELECT> &select, GeMatrix<MT> &T, GeMatrix<MQ> &Q, DenseVector<WR> &wr, DenseVector<WI> &wi, IndexType &m, S &s, SEP &sep, DenseVector<WORK> &work, DenseVector<IWORK> &iwork) { IndexType info; info = cxxlapack::trsen<IndexType>(getF77Char(job), computeQ ? 'V' : 'N', select.data(), T.numRows(), T.data(), T.leadingDimension(), Q.data(), Q.leadingDimension(), wr.data(), wi.data(), m, s, sep, work.data(), work.length(), iwork.data(), iwork.length()); ASSERT(info>=0); return info; } } // namespace external #endif // USE_CXXLAPACK //== public interface ========================================================== template <typename SELECT, typename MT, typename MQ, typename WR, typename WI, typename IndexType, typename S, typename SEP, typename WORK, typename IWORK> IndexType trsen(TRSEN::Job job, bool computeQ, const DenseVector<SELECT> &select, GeMatrix<MT> &T, GeMatrix<MQ> &Q, DenseVector<WR> &wr, DenseVector<WI> &wi, IndexType &m, S &s, SEP &sep, DenseVector<WORK> &work, DenseVector<IWORK> &iwork) { LAPACK_DEBUG_OUT("trsen"); // // Test the input parameters // # ifndef NDEBUG ASSERT(T.firstRow()==1); ASSERT(T.firstCol()==1); ASSERT(T.numRows()==T.numCols()); const IndexType n = T.numRows(); if (computeQ) { ASSERT(Q.firstRow()==1); ASSERT(Q.firstCol()==1); ASSERT(Q.numRows()==n); ASSERT(Q.numCols()==n); } ASSERT(wr.firstIndex()==1); ASSERT(wr.length()==n); ASSERT(wi.firstIndex()==1); ASSERT(wi.length()==n); # endif # ifdef CHECK_CXXLAPACK // // Make copies of output arguments // const typename GeMatrix<MT>::NoView T_org = T; const typename GeMatrix<MQ>::NoView Q_org = Q; const typename DenseVector<WR>::NoView wr_org = wr; const typename DenseVector<WI>::NoView wi_org = wi; const IndexType m_org = m; const S s_org = s; const SEP sep_org = sep; const typename DenseVector<WORK>::NoView work_org = work; const typename DenseVector<IWORK>::NoView iwork_org = iwork; # endif // // Call implementation // IndexType info = LAPACK_SELECT::trsen_impl(job, computeQ, select, T, Q, wr, wi, m, s, sep, work, iwork); # ifdef CHECK_CXXLAPACK // // Make copies of results computed by generic implementation // const typename GeMatrix<MT>::NoView T_generic = T; const typename GeMatrix<MQ>::NoView Q_generic = Q; const typename DenseVector<WR>::NoView wr_generic = wr; const typename DenseVector<WI>::NoView wi_generic = wi; const IndexType m_generic = m; const S s_generic = s; const SEP sep_generic = sep; const typename DenseVector<WORK>::NoView work_generic = work; const typename DenseVector<IWORK>::NoView iwork_generic = iwork; // // restore output arguments // T = T_org; Q = Q_org; wr = wr_org; wi = wi_org; m = m_org; s = s_org; sep = sep_org; work = work_org; iwork = iwork_org; // // Compare generic results with results from the native implementation // IndexType _info = external::trsen_impl(job, computeQ, select, T, Q, wr, wi, m, s, sep, work, iwork); bool failed = false; if (! isIdentical(T_generic, T, "T_generic", "T")) { std::cerr << "CXXLAPACK: T_generic = " << T_generic << std::endl; std::cerr << "F77LAPACK: T = " << T << std::endl; failed = true; } if (! isIdentical(Q_generic, Q, "Q_generic", "Q")) { std::cerr << "CXXLAPACK: Q_generic = " << Q_generic << std::endl; std::cerr << "F77LAPACK: Q = " << Q << std::endl; failed = true; } if (! isIdentical(wr_generic, wr, "wr_generic", "wr")) { std::cerr << "CXXLAPACK: wr_generic = " << wr_generic << std::endl; std::cerr << "F77LAPACK: wr = " << wr << std::endl; failed = true; } if (! isIdentical(wi_generic, wi, "wi_generic", "wi")) { std::cerr << "CXXLAPACK: wi_generic = " << wi_generic << std::endl; std::cerr << "F77LAPACK: wi = " << wi << std::endl; failed = true; } if (! isIdentical(m_generic, m, "m_generic", "m")) { std::cerr << "CXXLAPACK: m_generic = " << m_generic << std::endl; std::cerr << "F77LAPACK: m = " << m << std::endl; failed = true; } if (! isIdentical(s_generic, s, "s_generic", "s")) { std::cerr << "CXXLAPACK: s_generic = " << s_generic << std::endl; std::cerr << "F77LAPACK: s = " << s << std::endl; failed = true; } if (! isIdentical(sep_generic, sep, "sep_generic", "sep")) { std::cerr << "CXXLAPACK: sep_generic = " << sep_generic << std::endl; std::cerr << "F77LAPACK: sep = " << sep << std::endl; failed = true; } if (! isIdentical(work_generic, work, "work_generic", "work")) { std::cerr << "CXXLAPACK: work_generic = " << work_generic << std::endl; std::cerr << "F77LAPACK: work = " << work << std::endl; failed = true; } if (! isIdentical(iwork_generic, iwork, "iwork_generic", "iwork")) { std::cerr << "CXXLAPACK: iwork_generic = " << iwork_generic << std::endl; std::cerr << "F77LAPACK: iwork = " << iwork << std::endl; failed = true; } if (! isIdentical(info, _info, "info", "_info")) { std::cerr << "CXXLAPACK: info = " << info << std::endl; std::cerr << "F77LAPACK: _info = " << _info << std::endl; failed = true; } if (failed) { std::cerr << "error in: trsen.tcc" << std::endl; ASSERT(0); } else { // std::cerr << "passed: trsen.tcc" << std::endl; } # endif return info; } //-- forwarding ---------------------------------------------------------------- template <typename SELECT, typename MT, typename MQ, typename WR, typename WI, typename IndexType, typename S, typename SEP, typename WORK, typename IWORK> IndexType trsen(TRSEN::Job job, bool computeQ, const DenseVector<SELECT> &select, MT &&T, MQ &&Q, WR &&wr, WI &&wi, IndexType &&m, S &&s, SEP &&sep, WORK &&work, IWORK &&iwork) { trsen(job, computeQ, select, T, Q, wr, wi, m, s, sep, work, iwork); } } } // namespace lapack, flens #endif // FLENS_LAPACK_IMPL_TRSEN_TCC |