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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 DGEESX( JOBVS, SORT, SELECT, SENSE, N, A, LDA, SDIM, $ WR, WI, VS, LDVS, RCONDE, RCONDV, WORK, LWORK, $ IWORK, LIWORK, BWORK, INFO ) SUBROUTINE ZGEESX( JOBVS, SORT, SELECT, SENSE, N, A, LDA, SDIM, W, $ VS, LDVS, RCONDE, RCONDV, WORK, LWORK, RWORK, $ BWORK, INFO ) * * -- LAPACK driver routine (version 3.2.2) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * June 2010 */ #ifndef FLENS_LAPACK_GE_ESX_TCC #define FLENS_LAPACK_GE_ESX_TCC 1 #include <cmath> #include <flens/blas/blas.h> #include <flens/lapack/lapack.h> namespace flens { namespace lapack { //== generic lapack implementation ============================================= namespace generic { //-- (ge)esx_wsq [real variant] ------------------------------------------------ template <typename MA> Quadruple<typename GeMatrix<MA>::IndexType> esx_wsq_impl(bool computeSchurVectors, SENSE::Sense sense, const GeMatrix<MA> &A) { using std::max; typedef typename GeMatrix<MA>::ElementType T; typedef typename GeMatrix<MA>::IndexType IndexType; const IndexType n = A.numRows(); const bool wantSN = (sense==SENSE::None); const bool wantSV = (sense==SENSE::InvariantSubspaceOnly); const bool wantSB = (sense==SENSE::Both); IndexType minWork, maxWork, liWork, lWork; liWork = 1; if (n==0) { minWork = 1; maxWork = 1; lWork = 1; } else { maxWork = 2*n + n*ilaenv<T>(1, "GEHRD", "", n, 1, n, 0); minWork = 3*n; HSEQR::ComputeZ computeZ = (computeSchurVectors) ? HSEQR::NoInit : HSEQR::No; IndexType hsWork = hseqr_wsq(HSEQR::Schur, computeZ, IndexType(1), n, A); if (!computeSchurVectors) { maxWork = max(maxWork, n + hsWork); } else { maxWork = max(maxWork, 2*n + (n-1)*ilaenv<T>(1, "ORGHR", "", n, 1, n)); maxWork = max(maxWork, n +hsWork); } lWork = maxWork; if (!wantSN) { lWork = max(lWork, n + (n*n)/2); } if (wantSV || wantSB) { liWork = (n*n)/4; } } return Quadruple<IndexType>(minWork, maxWork, lWork, liWork); } //-- (ge)esx [real variant] ---------------------------------------------------- template <typename SelectFunction, typename MA, typename IndexType, typename VWR, typename VWI, typename MVS, typename RCONDE, typename RCONDV, typename VWORK, typename VIWORK, typename BWORK> IndexType esx_impl(bool computeSchurVectors, bool sortEigenvalues, SelectFunction selectFunction, SENSE::Sense sense, GeMatrix<MA> &A, IndexType &sDim, DenseVector<VWR> &wr, DenseVector<VWI> &wi, GeMatrix<MVS> &VS, RCONDE &rCondE, RCONDV &rCondV, DenseVector<VWORK> &work, DenseVector<VIWORK> &iWork, DenseVector<BWORK> &bWork) { using std::sqrt; typedef typename GeMatrix<MA>::ElementType T; const Underscore<IndexType> _; const IndexType n = A.numRows(); const T Zero(0), One(1); // // .. Local Arrays .. // this array is used to save variables between calls to lacn2 // T _dum[1]; DenseVectorView<T> dum = typename DenseVectorView<T>::Engine(1, _dum); // // Test the input arguments // IndexType info = 0; const bool wantSN = (sense==SENSE::None); const bool wantSV = (sense==SENSE::InvariantSubspaceOnly); const bool wantSB = (sense==SENSE::Both); // // Compute workspace // (Note: Comments in the code beginning "RWorkspace:" describe the // minimal amount of real workspace needed at that point in the // code, as well as the preferred amount for good performance. // IWorkspace refers to integer workspace. // NB refers to the optimal block size for the immediately // following subroutine, as returned by ILAENV. // HSWORK refers to the workspace preferred by DHSEQR, as // calculated below. HSWORK is computed assuming ILO=1 and IHI=N, // the worst case. // If SENSE = 'E', 'V' or 'B', then the amount of workspace needed // depends on SDIM, which is computed by the routine DTRSEN later // in the code.) // Quadruple<IndexType> wsQuery = esx_wsq(computeSchurVectors, sense, A); IndexType minWork = wsQuery.first; IndexType maxWork = wsQuery.second; IndexType lWork = wsQuery.third; IndexType liWork = wsQuery.forth; if (work.length()!=0 && work.length()<minWork) { ASSERT(0); } else if (work.length()==0) { work.resize(lWork); } work(1) = lWork; if (iWork.length()!=0 && iWork.length()<liWork) { ASSERT(0); } else if (iWork.length()==0) { iWork.resize(liWork); } iWork(1) = liWork; // // Quick return if possible // if (n==0) { sDim = 0; return info; } // // Get machine constants // const T eps = lamch<T>(Precision); T smallNum = lamch<T>(SafeMin); T bigNum = One / smallNum; labad(smallNum, bigNum); smallNum = sqrt(smallNum) / eps; bigNum = One / smallNum; // // Scale A if max element outside range [SMLNUM,BIGNUM] // const T normA = lan(MaximumNorm, A); bool scaleA = false; T cScale; if (normA>Zero && normA<smallNum) { scaleA = true; cScale = smallNum; } else if (normA>bigNum) { scaleA = true; cScale = bigNum; } if (scaleA) { lascl(LASCL::FullMatrix, IndexType(0), IndexType(0), normA, cScale, A); } // // Permute the matrix to make it more nearly triangular // (RWorkspace: need N) // IndexType iBal = 1; auto balWork = work(_(iBal,iBal+n-1)); IndexType iLo, iHi; bal(BALANCE::PermuteOnly, A, iLo, iHi, balWork); // // Reduce to upper Hessenberg form // (RWorkspace: need 3*N, prefer 2*N+N*NB) // IndexType iTau = iBal + n; IndexType iWrk = iTau + n; lWork = work.length(); auto tau = work(_(iTau, iTau+n-2)); auto hrdWork = work(_(iWrk, lWork)); hrd(iLo, iHi, A, tau, hrdWork); if (computeSchurVectors) { // // Copy Householder vectors to VS // VS.lower() = A.lower(); // // Generate orthogonal matrix in VS // (RWorkspace: need 3*N-1, prefer 2*N+(N-1)*NB) // orghr(iLo, iHi, VS, tau, hrdWork); } sDim = 0; // // Perform QR iteration, accumulating Schur vectors in VS if desired // (RWorkspace: need N+1, prefer N+HSWORK (see comments) ) // iWrk = iTau; auto hseqrWork = work(_(iWrk, lWork)); HSEQR::ComputeZ computeZ = (computeSchurVectors) ? HSEQR::NoInit : HSEQR::No; IndexType iEval = hseqr(HSEQR::Schur, computeZ, iLo, iHi, A, wr, wi, VS, hseqrWork); if (iEval>0) { info = iEval; } // // Sort eigenvalues if desired // if (sortEigenvalues && info==0) { if (scaleA) { lascl(LASCL::FullMatrix, IndexType(0), IndexType(0), cScale, normA, wr); lascl(LASCL::FullMatrix, IndexType(0), IndexType(0), cScale, normA, wi); } for (IndexType i=1; i<=n; ++i) { bWork(i) = selectFunction(wr(i), wi(i)); } // // Reorder eigenvalues, transform Schur vectors, and compute // reciprocal condition numbers // (RWorkspace: if SENSE is not 'N', need N+2*SDIM*(N-SDIM) // otherwise, need N ) // (IWorkspace: if SENSE is 'V' or 'B', need SDIM*(N-SDIM) // otherwise, need 0 ) // IndexType iCond = trsen(TRSEN::Job(sense), computeSchurVectors, bWork, A, VS, wr, wi, sDim, rCondE, rCondV, hseqrWork, iWork); if (!wantSN) { maxWork = max(maxWork, n+2*sDim*(n-sDim)); } if (iCond>0) { // // DTRSEN failed to reorder or to restore standard Schur form // info = iCond + n; } } if (computeSchurVectors) { // // Undo balancing // (Workspace: need N) // bak(BALANCE::PermuteOnly, Right, iLo, iHi, balWork, VS); } if (scaleA) { // // Undo scaling for the Schur form of A // lascl(LASCL::UpperHessenberg, IndexType(0), IndexType(0), cScale, normA, A); wr = A.diag(0); if ((wantSV || wantSB) && info==0) { dum(1) = rCondV; lascl(LASCL::FullMatrix, IndexType(0), IndexType(0), cScale, normA, dum); rCondV = dum(1); } if (cScale==smallNum) { // // If scaling back towards underflow, adjust WI if an // offdiagonal element of a 2-by-2 block in the Schur form // underflows. // IndexType i1, i2; if (iEval>0) { i1 = iEval + 1; i2 = iHi - 1; lascl(LASCL::FullMatrix, IndexType(0), IndexType(0), cScale, normA, wi(_(1,iLo-1))); } else if (sortEigenvalues) { i1 = 1; i2 = n - 1; } else { i1 = iLo; i2 = iHi - 1; } IndexType iNext = i1-1; for (IndexType i=i1; i<=i2; ++i) { if (i<iNext) { continue; } if (wi(i)==Zero) { iNext = i + 1; } else { if (A(i+1,i)==Zero) { wi(i) = Zero; wi(i+1) = Zero; } else if (A(i+1,i)!=Zero && A(i,i+1)==Zero) { wi(i) = Zero; wi(i+1) = Zero; if (i>1) { blas::swap(A(_(1,i-1),i), A(_(1,i-1),i+1)); } if (n>i+1) { blas::swap(A(i,_(i+2,n)), A(i+1,_(i+2,n))); } blas::swap(VS(_,i), VS(_,i+1)); A(i,i+1) = A(i+1,i); A(i+1,i) = Zero; } iNext = i + 2; } } } lascl(LASCL::FullMatrix, IndexType(0), IndexType(0), cScale, normA, wi(_(iEval+1,n))); } if (sortEigenvalues && info==0) { // // Check if reordering successful // bool lastSelect = true; bool last2Select = true; sDim = 0; IndexType ip = 0; for (IndexType i=1; i<=n; ++i) { bool currentSelect = selectFunction(wr(i), wi(i)); if (wi(i)==Zero) { if (currentSelect) { ++sDim; } ip = 0; if (currentSelect && !lastSelect) { info = n + 2; } } else { if (ip==1) { // // Last eigenvalue of conjugate pair // currentSelect = currentSelect || lastSelect; lastSelect = currentSelect; if (currentSelect) { sDim += 2; } ip = -1; if (currentSelect && !last2Select) { info = n + 2; } } else { // // First eigenvalue of conjugate pair // ip = 1; } } last2Select = lastSelect; lastSelect = currentSelect; } } work(1) = maxWork; if (wantSV || wantSB) { iWork(1) = max(IndexType(1), sDim*(n-sDim)); } else { iWork(1) = 1; } return info; } } // namespace generic //== interface for native lapack =============================================== #ifdef USE_CXXLAPACK namespace external { //-- (ge)esx_wsq [worksize query real variant] --------------------------------- template <typename MA> typename RestrictTo<IsNotComplex<typename MA::ElementType>::value, Quadruple<typename MA::IndexType> >::Type esx_wsq_impl(bool computeSchurVectors, SENSE::Sense sense, const GeMatrix<MA> &A) { using std::max; typedef typename GeMatrix<MA>::ElementType T; typedef typename GeMatrix<MA>::IndexType IndexType; const IndexType n = A.numRows(); //const bool wantSN = (sense==SENSE::None); const bool wantSV = (sense==SENSE::InvariantSubspaceOnly); const bool wantSB = (sense==SENSE::Both); IndexType minWork, maxWork, liWork, lWork; liWork = 1; if (n==0) { minWork = 1; } else { minWork = 3*n; if (wantSV || wantSB) { liWork = (n*n)/4; } } // // Compute optimal size for work // const IndexType LDVS = max(IndexType(1), A.numRows()); IndexType IDUMMY, IWORK; T DUMMY; const IndexType LWORK = -1; T WORK; cxxlapack::geesx<IndexType>(computeSchurVectors ? 'V' : 'N', 'S', 0, getF77Char(sense), n, 0, A.leadingDimension(), IDUMMY, &DUMMY, &DUMMY, &DUMMY, LDVS, DUMMY, DUMMY, &WORK, LWORK, &IWORK, IDUMMY, &IDUMMY); return Quadruple<IndexType>(minWork, WORK, WORK, liWork); } //-- (ge)esx_wsq [worksize query complex variant] ------------------------------ template <typename MA> typename RestrictTo<IsComplex<typename MA::ElementType>::value, Triple<typename MA::IndexType> >::Type esx_wsq_impl(bool computeSchurVectors, SENSE::Sense sense, const GeMatrix<MA> &A) { using std::max; typedef typename GeMatrix<MA>::ElementType T; typedef typename ComplexTrait<T>::PrimitiveType RT; typedef typename GeMatrix<MA>::IndexType IndexType; const IndexType n = A.numRows(); //const bool wantSN = (sense==SENSE::None); //const bool wantSV = (sense==SENSE::InvariantSubspaceOnly); //const bool wantSB = (sense==SENSE::Both); IndexType minWork, maxWork, lWork; if (n==0) { minWork = 1; } else { minWork = 2*n; } // // Compute optimal size for work // const IndexType LDVS = max(IndexType(1), A.numRows()); IndexType IDUMMY, IWORK; T DUMMY; RT RDUMMY; const IndexType LWORK = -1; T WORK; cxxlapack::geesx<IndexType>(computeSchurVectors ? 'V' : 'N', 'S', 0, getF77Char(sense), n, 0, A.leadingDimension(), IDUMMY, &DUMMY, &DUMMY, LDVS, RDUMMY, RDUMMY, &DUMMY, LWORK, &RDUMMY, &IDUMMY); return Triple<IndexType>(minWork, WORK.real(), WORK.real()); } //-- (ge)esx [real variant] ---------------------------------------------------- template <typename SelectFunction, typename MA, typename IndexType, typename VWR, typename VWI, typename MVS, typename RCONDE, typename RCONDV, typename VWORK, typename VIWORK, typename BWORK> IndexType esx_impl(bool computeSchurVectors, bool sortEigenvalues, SelectFunction selectFunction, SENSE::Sense sense, GeMatrix<MA> &A, IndexType &sDim, DenseVector<VWR> &wr, DenseVector<VWI> &wi, GeMatrix<MVS> &VS, RCONDE &rCondE, RCONDV &rCondV, DenseVector<VWORK> &work, DenseVector<VIWORK> &iWork, DenseVector<BWORK> &bWork) { if (work.length()==0 || iWork.length()==0) { const auto ws = esx_wsq_impl(computeSchurVectors, sense, A); if (work.length()==0) { work.resize(ws.third, 1); } if (iWork.length()==0) { iWork.resize(ws.forth, 1); } } IndexType info; info = cxxlapack::geesx<IndexType>(computeSchurVectors ? 'V' : 'N', sortEigenvalues ? 'S' : 'N', selectFunction.select, getF77Char(sense), A.numRows(), A.data(), A.leadingDimension(), sDim, wr.data(), wi.data(), VS.data(), VS.leadingDimension(), rCondE, rCondV, work.data(), work.length(), iWork.data(), iWork.length(), bWork.data()); ASSERT(info>=0); return info; } //-- (ge)esx [complex variant] ------------------------------------------------- template <typename SelectFunction, typename MA, typename IndexType, typename VW, typename MVS, typename RCONDE, typename RCONDV, typename VWORK, typename VRWORK, typename BWORK> IndexType esx_impl(bool computeSchurVectors, bool sortEigenvalues, SelectFunction selectFunction, SENSE::Sense sense, GeMatrix<MA> &A, IndexType &sDim, DenseVector<VW> &w, GeMatrix<MVS> &VS, RCONDE &rCondE, RCONDV &rCondV, DenseVector<VWORK> &work, DenseVector<VRWORK> &rWork, DenseVector<BWORK> &bWork) { if (work.length()==0) { const auto ws = esx_wsq_impl(computeSchurVectors, sense, A); work.resize(IndexType(ws.third), 1); } IndexType info; info = cxxlapack::geesx<IndexType>(computeSchurVectors ? 'V' : 'N', sortEigenvalues ? 'S' : 'N', selectFunction.select, getF77Char(sense), A.numRows(), A.data(), A.leadingDimension(), sDim, w.data(), VS.data(), VS.leadingDimension(), rCondE, rCondV, work.data(), work.length(), rWork.data(), bWork.data()); ASSERT(info>=0); return info; } } // namespace external #endif // USE_CXXLAPACK //== public interface ========================================================== //-- (ge)esx [real variant] ---------------------------------------------------- template <typename SelectFunction, typename MA, typename IndexType, typename VWR, typename VWI, typename MVS, typename RCONDE, typename RCONDV, typename VWORK, typename VIWORK, typename VBWORK> typename RestrictTo<IsRealGeMatrix<MA>::value && IsInteger<IndexType>::value && IsRealDenseVector<VWR>::value && IsRealDenseVector<VWI>::value && IsRealGeMatrix<MVS>::value && IsNotComplex<RCONDE>::value && IsNotComplex<RCONDV>::value && IsRealDenseVector<VWORK>::value && IsRealDenseVector<VIWORK>::value && IsRealDenseVector<VBWORK>::value, IndexType>::Type esx(bool computeSchurVectors, bool sortEigenvalues, SelectFunction selectFunction, SENSE::Sense sense, MA &&A, IndexType &sDim, VWR &&wr, VWI &&wi, MVS &&VS, RCONDE &rCondE, RCONDV &rCondV, VWORK &&work, VIWORK &&iWork, VBWORK &&bWork) { LAPACK_DEBUG_OUT("(ge)esx [real]"); // // Remove references from rvalue types // typedef typename RemoveRef<MA>::Type MatrixA; typedef typename RemoveRef<VWR>::Type VectorWR; typedef typename RemoveRef<VWI>::Type VectorWI; typedef typename RemoveRef<MVS>::Type MatrixVS; typedef typename RemoveRef<VWORK>::Type VectorWork; typedef typename RemoveRef<VIWORK>::Type VectorIWork; typedef typename RemoveRef<VBWORK>::Type VectorBWork; // // Test the input parameters // IndexType n = A.numRows(); # ifndef NDEBUG ASSERT(A.numRows()==A.numCols()); ASSERT(A.firstRow()==1); ASSERT(A.firstCol()==1); ASSERT(work.firstIndex()==1); ASSERT(iWork.firstIndex()==1); ASSERT(bWork.firstIndex()==1); ASSERT(wr.firstIndex()==1); ASSERT(wr.length()==0 || wr.length()==n); ASSERT(wi.firstIndex()==1); ASSERT(wi.length()==0 || wi.length()==n); if (computeSchurVectors) { ASSERT(VS.numRows()==VS.numCols()); ASSERT(VS.numRows()==0 || VS.numRows()==n); ASSERT(VS.firstRow()==1); ASSERT(VS.firstCol()==1); } if (sortEigenvalues) { ASSERT(bWork.firstIndex()==1); ASSERT(bWork.length()==0 || bWork.length()==n); } # endif // // Resize output arguments if they are empty and needed // if (wr.length()==0) { wr.resize(n, 1); } if (wi.length()==0) { wi.resize(n, 1); } if (computeSchurVectors && VS.numRows()==0) { VS.resize(n, n, 1, 1); } if (sortEigenvalues && bWork.length()==0) { bWork.resize(n, 1); } // // Make copies of output arguments // # ifdef CHECK_CXXLAPACK typename MatrixA::NoView A_org = A; IndexType sDim_org = sDim; typename VectorWR::NoView wr_org = wr; typename VectorWI::NoView wi_org = wi; typename MatrixVS::NoView VS_org = VS; RCONDE rCondE_org = rCondE; RCONDV rCondV_org = rCondV; typename VectorWork::NoView work_org = work; typename VectorIWork::NoView iWork_org = iWork; typename VectorBWork::NoView bWork_org = bWork; # endif // // Call implementation // IndexType result = LAPACK_SELECT::esx_impl(computeSchurVectors, sortEigenvalues, selectFunction, sense, A, sDim, wr, wi, VS, rCondE, rCondV, work, iWork, bWork); # ifdef CHECK_CXXLAPACK // // Make copies of results computed by the generic implementation // typename MatrixA::NoView A_generic = A; IndexType sDim_generic = sDim; typename VectorWR::NoView wr_generic = wr; typename VectorWI::NoView wi_generic = wi; typename MatrixVS::NoView VS_generic = VS; RCONDE rCondE_generic = rCondE; RCONDV rCondV_generic = rCondV; typename VectorWork::NoView work_generic = work; typename VectorIWork::NoView iWork_generic = iWork; typename VectorBWork::NoView bWork_generic = bWork; // // restore output arguments // A = A_org; sDim = sDim_org; wr = wr_org; wi = wi_org; VS = VS_org; rCondE = rCondE_org; rCondV = rCondV_org; work = work_org; iWork = iWork_org; bWork = bWork_org; // // Compare generic results with results from the native implementation // IndexType _result = external::esx_impl(computeSchurVectors, sortEigenvalues, selectFunction, sense, A, sDim, wr, wi, VS, rCondE, rCondV, work, iWork, bWork); 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(sDim_generic, sDim, "sDim_generic", "sDim")) { std::cerr << "CXXLAPACK: sDim_generic = " << sDim_generic << std::endl; std::cerr << "F77LAPACK: sDim = " << sDim << 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(VS_generic, VS, "VS_generic", "VS")) { std::cerr << "CXXLAPACK: VS_generic = " << VS_generic << std::endl; std::cerr << "F77LAPACK: VS = " << VS << std::endl; failed = true; } if (! isIdentical(rCondE_generic, rCondE, "rCondE_generic", "rCondE")) { std::cerr << "CXXLAPACK: rCondE_generic = " << rCondE_generic << std::endl; std::cerr << "F77LAPACK: rCondE = " << rCondE << std::endl; failed = true; } if (! isIdentical(rCondV_generic, rCondV, "rCondV_generic", "rCondV")) { std::cerr << "CXXLAPACK: rCondV_generic = " << rCondV_generic << std::endl; std::cerr << "F77LAPACK: rCondV = " << rCondV << 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(bWork_generic, bWork, "bWork_generic", "bWork")) { std::cerr << "CXXLAPACK: bWork_generic = " << bWork_generic << std::endl; std::cerr << "F77LAPACK: bWork = " << bWork << std::endl; failed = true; } if (! isIdentical(result, _result, " result", "_result")) { std::cerr << "CXXLAPACK: result = " << result << std::endl; std::cerr << "F77LAPACK: _result = " << _result << std::endl; failed = true; } if (failed) { ASSERT(0); } else { // std::cerr << "passed: esx.tcc" << std::endl; } # endif return result; } #ifdef USE_CXXLAPACK //-- (ge)esx [complex variant] ------------------------------------------------- template <typename SelectFunction, typename MA, typename IndexType, typename VW, typename MVS, typename RCONDE, typename RCONDV, typename VWORK, typename VRWORK, typename VBWORK> typename RestrictTo<IsComplexGeMatrix<MA>::value && IsInteger<IndexType>::value && IsComplexDenseVector<VW>::value && IsComplexGeMatrix<MVS>::value && IsNotComplex<RCONDE>::value && IsNotComplex<RCONDV>::value && IsComplexDenseVector<VWORK>::value && IsRealDenseVector<VRWORK>::value && IsRealDenseVector<VBWORK>::value, IndexType>::Type esx(bool computeSchurVectors, bool sortEigenvalues, SelectFunction selectFunction, SENSE::Sense sense, MA &&A, IndexType &sDim, VW &&w, MVS &&VS, RCONDE &rCondE, RCONDV &rCondV, VWORK &&work, VRWORK &&rWork, VBWORK &&bWork) { LAPACK_DEBUG_OUT("(ge)esx [complex]"); // // Remove references from rvalue types // typedef typename RemoveRef<MA>::Type MatrixA; typedef typename RemoveRef<VW>::Type VectorW; typedef typename RemoveRef<MVS>::Type MatrixVS; typedef typename RemoveRef<VWORK>::Type VectorWork; typedef typename RemoveRef<VRWORK>::Type VectorRWork; typedef typename RemoveRef<VBWORK>::Type VectorBWork; IndexType n = A.numRows(); // // Test the input parameters // # ifndef NDEBUG ASSERT(A.numRows()==A.numCols()); ASSERT(A.firstRow()==1); ASSERT(A.firstCol()==1); ASSERT(work.firstIndex()==1); ASSERT(rWork.firstIndex()==1); ASSERT(bWork.firstIndex()==1); ASSERT(w.firstIndex()==1); ASSERT(w.length()==0 || w.length()==n); if (computeSchurVectors) { ASSERT(VS.numRows()==VS.numCols()); ASSERT(VS.numRows()==0 || VS.numRows()==n); ASSERT(VS.firstRow()==1); ASSERT(VS.firstCol()==1); } if (sortEigenvalues) { ASSERT(bWork.firstIndex()==1); ASSERT(bWork.length()==0 || bWork.length()==n); } # endif // // Resize output arguments if they are empty and needed // if (w.length()==0) { w.resize(n, 1); } if (computeSchurVectors && VS.numRows()==0) { VS.resize(n, n, 1, 1); } if (sortEigenvalues && bWork.length()==0) { bWork.resize(n, 1); } // // Call external implementation // IndexType result = external::esx_impl(computeSchurVectors, sortEigenvalues, selectFunction, sense, A, sDim, w, VS, rCondE, rCondV, work, rWork, bWork); return result; } #endif // USE_CXXLAPACK //-- (ge)esx [worksize query, real variant] ------------------------------------ template <typename MA> typename RestrictTo<IsNotComplex<typename MA::ElementType>::value, Quadruple<typename MA::IndexType> >::Type esx_wsq(bool computeSchurVectors, SENSE::Sense sense, const GeMatrix<MA> &A) { LAPACK_DEBUG_OUT("ev_wsq [real]"); // // Test the input parameters // # ifndef NDEBUG ASSERT(A.numRows()==A.numCols()); ASSERT(A.firstRow()==1); ASSERT(A.firstCol()==1); # endif // // Call implementation // const auto ws = LAPACK_SELECT::esx_wsq_impl(computeSchurVectors, sense, A); # ifdef CHECK_CXXLAPACK // // Compare results // const auto _ws = external::esx_wsq_impl(computeSchurVectors, sense, A); if (! isIdentical(ws.first, _ws.first, "ws.first", "_ws.first")) { ASSERT(0); } if (! isIdentical(ws.third, _ws.third, "ws.third", "_ws.third")) { ASSERT(0); } if (! isIdentical(ws.forth, _ws.forth, "ws.forth", "_ws.forth")) { ASSERT(0); } # endif return ws; } #ifdef USE_CXXLAPACK //-- (ge)esx [worksize query, complex variant] --------------------------------- template <typename MA> typename RestrictTo<IsComplex<typename MA::ElementType>::value, Triple<typename MA::IndexType> >::Type esx_wsq(bool computeSchurVectors, SENSE::Sense sense, const GeMatrix<MA> &A) { LAPACK_DEBUG_OUT("ev_wsq [complex]"); // // Test the input parameters // # ifndef NDEBUG ASSERT(A.numRows()==A.numCols()); ASSERT(A.firstRow()==1); ASSERT(A.firstCol()==1); # endif // // Call external implementation // const auto ws = external::esx_wsq_impl(computeSchurVectors, sense, A); return ws; } #endif // USE_CXXLAPACK } } // namespace lapack, flens #endif // FLENS_LAPACK_GE_ESX_TCC |