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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 DGELSY( M, N, NRHS, A, LDA, B, LDB, JPVT, RCOND, RANK, $ WORK, LWORK, INFO ) * * -- LAPACK driver 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_GE_LSY_TCC #define FLENS_LAPACK_GE_LSY_TCC 1 #include <flens/blas/blas.h> #include <flens/lapack/lapack.h> namespace flens { namespace lapack { //== generic lapack implementation ============================================= namespace generic { //-- (ge)lsy [real variant] ---------------------------------------------------- template <typename MA, typename MB, typename VJPIV, typename RCOND, typename RANK, typename VWORK> void lsy_impl(GeMatrix<MA> &A, GeMatrix<MB> &B, DenseVector<VJPIV> &jPiv, RCOND rCond, RANK &rank, DenseVector<VWORK> &work) { using std::abs; using flens::max; using flens::min; using LASCL::FullMatrix; using LASCL::UpperTriangular; typedef typename GeMatrix<MA>::ElementType ElementType; typedef typename GeMatrix<MA>::IndexType IndexType; const ElementType Zero(0), One(1); const Underscore<IndexType> _; const IndexType m = A.numRows(); const IndexType n = A.numCols(); const IndexType nRhs = B.numCols(); const IndexType mn = min(m, n); // // Figure out optimal block size // IndexType lWork = work.length(); IndexType lWorkMin; IndexType lWorkOpt; if (mn==0 || nRhs==0) { lWorkMin = 1; lWorkOpt = 1; } else { IndexType nb1 = ilaenv<ElementType>(1, "GEQRF", "", m, n); IndexType nb2 = ilaenv<ElementType>(1, "GERQF", "", m, n); IndexType nb3 = ilaenv<ElementType>(1, "ORMQR", "", m, n, nRhs); IndexType nb4 = ilaenv<ElementType>(1, "ORMRQ", "", m, n, nRhs); IndexType nb = max(nb1, nb2, nb3, nb4); lWorkMin = mn + max(2*mn, n+1, mn+nRhs); lWorkOpt = max(lWorkMin, mn+2*n+nb*(n+1), 2*mn+nb*nRhs); } if (lWork==0) { work.resize(lWorkOpt); lWork = work.length(); } work(1) = lWorkOpt; auto sMinWork = work(_(mn+1,2*mn)); auto sMaxWork = work(_(2*mn+1,3*mn)); // // Quick return if possible // if (mn==0 || nRhs==0) { rank = 0; return; } // // Get machine parameters // ElementType smallNum = lamch<ElementType>(SafeMin) / lamch<ElementType>(Precision); ElementType bigNum = One / smallNum; labad(smallNum, bigNum); // // Scale A, B if max entries outside range [SMLNUM,BIGNUM] // ElementType normA = lan(MaximumNorm, A); IndexType scaleA = 0; if (normA>Zero && normA<smallNum) { // // Scale matrix norm up to SMLNUM // lascl(FullMatrix, 0, 0, normA, smallNum, A); scaleA = 1; } else if (normA>bigNum) { // // Scale matrix norm down to BIGNUM // lascl(FullMatrix, 0, 0, normA, bigNum, A); scaleA = 2; } else if (normA==Zero) { // // Matrix all zero. Return zero solution. // B = Zero; rank = 0; work(1) = lWorkOpt; return; } auto B_ = B(_(1,m),_); ElementType normB = lan(MaximumNorm, B_); IndexType scaleB = 0; if (normB>Zero && normB<smallNum) { // // Scale matrix norm up to SMLNUM // lascl(FullMatrix, 0, 0, normB, smallNum, B_); scaleB = 1; } else if (normB>bigNum) { // // Scale matrix norm down to BIGNUM // lascl(FullMatrix, 0, 0, normB, bigNum, B_); scaleB = 2; } // // Compute QR factorization with column pivoting of A: // A * P = Q * R // auto tau1 = work(_(1,mn)); auto qp3Work = work(_(mn+1,lWork)); qp3(A, jPiv, tau1, qp3Work); // // workspace: MN+2*N+NB*(N+1). // Details of Householder rotations stored in WORK(1:MN). // // Determine RANK using incremental condition estimation // sMinWork(1) = One; sMaxWork(1) = One; ElementType sMax = abs(A(1,1)); ElementType sMin = sMax; if (abs(A(1,1))==Zero) { rank = 0; B = Zero; work(1) = lWorkOpt; return; } else { rank = 1; } while (rank<mn) { IndexType i = rank+1; const auto sMinWork_ = sMinWork(_(1,rank)); const auto sMaxWork_ = sMaxWork(_(1,rank)); const auto A_i = A(_(1,rank),i); ElementType sMinPr, sMaxPr, s1, s2, c1, c2; laic1(LAIC1::Min, sMinWork_, sMin, A_i, A(i,i), sMinPr, s1, c1); laic1(LAIC1::Max, sMaxWork_, sMax, A_i, A(i,i), sMaxPr, s2, c2); if (sMaxPr*rCond<=sMinPr) { for (IndexType i=1; i<=rank; ++i) { sMinWork(i) *= s1; sMaxWork(i) *= s2; } sMinWork(rank+1) = c1; sMaxWork(rank+1) = c2; sMin = sMinPr; sMax = sMaxPr; ++rank; } else { break; } } // // workspace: 3*MN. // // Logically partition R = [ R11 R12 ] // [ 0 R22 ] // where R11 = R(1:RANK,1:RANK) // // [R11,R12] = [ T11, 0 ] * Y // auto tau2 = work(_(mn+1,mn+rank)); auto work_ = work(_(2*mn+1,lWork)); if (rank<n) { auto A_ = A(_(1,rank),_); tzrzf(A_, tau2, work_); } auto T11 = A(_(1,rank),_(1,rank)).upper(); // // workspace: 2*MN. // Details of Householder rotations stored in WORK(MN+1:2*MN) // // B(1:M,1:NRHS) := Q**T * B(1:M,1:NRHS) // ormqr(Left, Trans, A(_,_(1,mn)), tau1, B_, work_); // // workspace: 2*MN+NB*NRHS. // // B(1:RANK,1:NRHS) := inv(T11) * B(1:RANK,1:NRHS) // blas::sm(Left, NoTrans, One, T11, B(_(1,rank),_)); B(_(rank+1,n),_) = Zero; // // B(1:N,1:NRHS) := Y**T * B(1:N,1:NRHS) // if (rank<n) { ormrz(Left, Trans, n-rank, A(_(1,rank),_), tau2, B(_(1,n),_), work_); } // // workspace: 2*MN+NRHS. // // B(1:N,1:NRHS) := P * B(1:N,1:NRHS) // for (IndexType j=1; j<=nRhs; ++j) { for (IndexType i=1; i<=n; ++i) { work(jPiv(i)) = B(i,j); } B(_(1,n),j) = work(_(1,n)); } // // workspace: N // // Undo scaling // if (scaleA==1) { lascl(FullMatrix, 0, 0, normA, smallNum, B(_(1,n),_)); lascl(UpperTriangular, 0, 0, smallNum, normA, A(_(1,rank),_(1,rank))); } else if (scaleA==2) { lascl(FullMatrix, 0, 0, normA, bigNum, B(_(1,n),_)); lascl(UpperTriangular, 0, 0, bigNum, normA, A(_(1,rank),_(1,rank))); } if (scaleB==1) { lascl(FullMatrix, 0, 0, smallNum, normB, B(_(1,n),_)); } else if (scaleB==2) { lascl(FullMatrix, 0, 0, bigNum, normB, B(_(1,n),_)); } work(1) = lWorkOpt; } } // namespace generic //== interface for native lapack =============================================== #ifdef USE_CXXLAPACK namespace external { //-- (ge)lsy [real variant] ---------------------------------------------------- template <typename MA, typename MB, typename VJPIV, typename RCOND, typename RANK, typename VWORK> void lsy_impl(GeMatrix<MA> &A, GeMatrix<MB> &B, DenseVector<VJPIV> &jPiv, RCOND rCond, RANK &rank, DenseVector<VWORK> &work) { typedef typename GeMatrix<MA>::ElementType ElementType; typedef typename GeMatrix<MA>::IndexType IndexType; if (work.length()==0) { ElementType WORK; IndexType LWORK = -1; cxxlapack::gelsy<IndexType>(A.numRows(), A.numCols(), B.numCols(), A.data(), A.leadingDimension(), B.data(), B.leadingDimension(), jPiv.data(), rCond, rank, &WORK, LWORK); work.resize(IndexType(WORK)); } cxxlapack::gelsy<IndexType>(A.numRows(), A.numCols(), B.numCols(), A.data(), A.leadingDimension(), B.data(), B.leadingDimension(), jPiv.data(), rCond, rank, work.data(), work.length()); } //-- (ge)lsy [complex variant] ------------------------------------------------- template <typename MA, typename MB, typename VJPIV, typename RCOND, typename RANK, typename VWORK, typename VRWORK> void lsy_impl(GeMatrix<MA> &A, GeMatrix<MB> &B, DenseVector<VJPIV> &jPiv, RCOND rCond, RANK &rank, DenseVector<VWORK> &work, DenseVector<VRWORK> &rwork) { typedef typename GeMatrix<MA>::ElementType ElementType; typedef typename GeMatrix<MA>::IndexType IndexType; if (work.length()==0) { ElementType WORK; IndexType LWORK = -1; cxxlapack::gelsy<IndexType>(A.numRows(), A.numCols(), B.numCols(), A.data(), A.leadingDimension(), B.data(), B.leadingDimension(), jPiv.data(), rCond, rank, &WORK, LWORK, rwork.data()); work.resize(IndexType(cxxblas::real(WORK))); } cxxlapack::gelsy<IndexType>(A.numRows(), A.numCols(), B.numCols(), A.data(), A.leadingDimension(), B.data(), B.leadingDimension(), jPiv.data(), rCond, rank, work.data(), work.length(), rwork.data()); } } // namespace external #endif // USE_CXXLAPACK //== public interface ========================================================== //-- (ge)lsy [real variant] ---------------------------------------------------- template <typename MA, typename MB, typename VJPIV, typename RCOND, typename VWORK> typename RestrictTo<IsRealGeMatrix<MA>::value && IsRealGeMatrix<MB>::value && IsIntegerDenseVector<VJPIV>::value && IsReal<RCOND>::value && IsRealDenseVector<VWORK>::value, typename RemoveRef<MA>::Type::IndexType>::Type lsy(MA &&A, MB &&B, VJPIV &&jPiv, RCOND rCond, VWORK &&work) { using flens::max; using std::min; LAPACK_DEBUG_OUT("(ge)lsy [real]"); // // Remove references from rvalue types // typedef typename RemoveRef<MA>::Type MatrixA; typedef typename RemoveRef<MB>::Type MatrixB; typedef typename RemoveRef<VJPIV>::Type VectorJPiv; typedef typename RemoveRef<VWORK>::Type VectorWork; typedef typename MatrixA::IndexType IndexType; // // Test the input parameters // const IndexType m = A.numRows(); const IndexType n = A.numCols(); const IndexType nRhs = B.numCols(); # ifndef NDEBUG ASSERT(A.firstRow()==1); ASSERT(A.firstCol()==1); ASSERT(B.firstRow()==1); ASSERT(B.firstCol()==1); ASSERT(jPiv.firstIndex()==1); ASSERT(work.firstIndex()==1); ASSERT(B.numRows()==max(m,n)); ASSERT(jPiv.length()==0 || jPiv.length()==n); if (work.length()>0) { const IndexType mn = min(m, n); const IndexType lWorkMin = mn + max(2*mn, n + 1, mn + nRhs); ASSERT(work.length()>=lWorkMin); } # endif if (jPiv.length()==0) { jPiv.resize(n, jPiv.firstIndex(), IndexType(0)); } // // Make copies of output arguments // # ifdef CHECK_CXXLAPACK typename MatrixA::NoView A_org = A; typename MatrixB::NoView B_org = B; typename VectorJPiv::NoView jPiv_org = jPiv; typename VectorWork::NoView work_org = work; # endif // // Call implementation // IndexType rank; LAPACK_SELECT::lsy_impl(A, B, jPiv, rCond, rank, work); # ifdef CHECK_CXXLAPACK // // Make copies of results computed by the generic implementation // typename MatrixA::NoView A_generic = A; typename MatrixB::NoView B_generic = B; typename VectorJPiv::NoView jPiv_generic = jPiv; IndexType rank_generic = rank; typename VectorWork::NoView work_generic = work; // // restore output arguments // A = A_org; B = B_org; jPiv = jPiv_org; rank = 0; work = work_org; // // Compare generic results with results from the native implementation // external::lsy_impl(A, B, jPiv, rCond, rank, work); 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(B_generic, B, "B_generic", "B")) { std::cerr << "CXXLAPACK: B_generic = " << B_generic << std::endl; std::cerr << "F77LAPACK: B = " << B << 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(rank_generic, rank, "rank_generic", "rank")) { std::cerr << "CXXLAPACK: rank_generic = " << rank_generic << std::endl; std::cerr << "F77LAPACK: rank = " << rank << 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 (failed) { std::cerr << "A.numRows() = " << A.numRows() << std::endl; std::cerr << "A.numCols() = " << A.numCols() << std::endl; std::cerr << "A = " << A << std::endl; std::cerr << "rank_generic = " << rank_generic << std::endl; std::cerr << "rank = " << rank << std::endl; std::cerr << "error in: lsy.tcc" << std::endl; ASSERT(0); } else { // std::cerr << "passed: lsy.tcc" << std::endl; } # endif return rank; } //-- (ge)lsy [complex variant] ------------------------------------------------- #ifdef USE_CXXLAPACK template <typename MA, typename MB, typename VJPIV, typename RCOND, typename VWORK, typename VRWORK> typename RestrictTo<IsComplexGeMatrix<MA>::value && IsComplexGeMatrix<MB>::value && IsIntegerDenseVector<VJPIV>::value && IsReal<RCOND>::value && IsComplexDenseVector<VWORK>::value && IsRealDenseVector<VRWORK>::value, typename RemoveRef<MA>::Type::IndexType>::Type lsy(MA &&A, MB &&B, VJPIV &&jPiv, RCOND rCond, VWORK &&work, VRWORK &&rwork) { using flens::max; using flens::min; LAPACK_DEBUG_OUT("(ge)lsy [complex]"); // // Remove references from rvalue types // typedef typename RemoveRef<MA>::Type MatrixA; typedef typename RemoveRef<MB>::Type MatrixB; typedef typename RemoveRef<VJPIV>::Type VectorJPiv; typedef typename RemoveRef<VWORK>::Type VectorWork; typedef typename MatrixA::IndexType IndexType; // // Test the input parameters // const IndexType m = A.numRows(); const IndexType n = A.numCols(); const IndexType nRhs = B.numCols(); # ifndef NDEBUG ASSERT(A.firstRow()==1); ASSERT(A.firstCol()==1); ASSERT(B.firstRow()==1); ASSERT(B.firstCol()==1); ASSERT(jPiv.firstIndex()==1); ASSERT(work.firstIndex()==1); ASSERT(B.numRows()==max(m,n)); ASSERT(jPiv.length()==0 || jPiv.length()==n); if (work.length()>0) { const IndexType mn = min(m, n); const IndexType lWorkMin = mn + max(2*mn, n + 1, mn + nRhs); ASSERT(work.length()>=lWorkMin); } ASSERT(rwork.length()==0 || rwork.length()==2*n); # endif if (jPiv.length()==0) { jPiv.resize(n, jPiv.firstIndex(), IndexType(0)); } if (rwork.length()==0) { rwork.resize(2*n); } // // Call implementation // IndexType rank; external::lsy_impl(A, B, jPiv, rCond, rank, work, rwork); return rank; } #endif // USE_CXXLAPACK //-- (ge)lsy [real variant with temporary workspace] --------------------------- template <typename MA, typename MB, typename VJPIV, typename RCOND> typename RestrictTo<IsRealGeMatrix<MA>::value && IsRealGeMatrix<MB>::value && IsIntegerDenseVector<VJPIV>::value && IsReal<RCOND>::value, typename RemoveRef<MA>::Type::IndexType>::Type lsy(MA &&A, MB &&B, VJPIV &&jPiv, RCOND rCond) { typedef typename RemoveRef<MA>::Type::Vector WorkVector; WorkVector work; return lsy(A, B, jPiv, rCond); } //-- (ge)lsy [complex variant with temporary workspace] ------------------------ #ifdef USE_CXXLAPACK template <typename MA, typename MB, typename VJPIV, typename RCOND> typename RestrictTo<IsComplexGeMatrix<MA>::value && IsComplexGeMatrix<MB>::value && IsIntegerDenseVector<VJPIV>::value && IsReal<RCOND>::value, typename RemoveRef<MA>::Type::IndexType>::Type lsy(MA &&A, MB &&B, VJPIV &&jPiv, RCOND rCond) { typedef typename RemoveRef<MA>::Type::Vector WorkVector; typedef typename RemoveRef<MA>::Type::ElementType T; typedef typename ComplexTrait<T>::PrimitiveType PT; typedef DenseVector<Array<PT> > RealWorkVector; WorkVector work; RealWorkVector rwork; return lsy(A, B, jPiv, rCond, work, rwork); } #endif // USE_CXXLAPACK //== (ge)lsy variant if B is vector ============================================ //-- (ge)lsy [real variant] ---------------------------------------------------- template <typename MA, typename VB, typename VJPIV, typename RCOND, typename VWORK> typename RestrictTo<IsRealGeMatrix<MA>::value && IsRealDenseVector<VB>::value && IsIntegerDenseVector<VJPIV>::value && IsReal<RCOND>::value && IsRealDenseVector<VWORK>::value, typename RemoveRef<MA>::Type::IndexType>::Type lsy(MA &&A, VB &&b, VJPIV &&jPiv, RCOND rCond, VWORK &&work) { // // Remove references from rvalue types // typedef typename RemoveRef<MA>::Type MatrixA; typedef typename RemoveRef<VB>::Type VectorB; typedef typename VectorB::ElementType ElementType; typedef typename VectorB::IndexType IndexType; const IndexType n = b.length(); const StorageOrder order = MatrixA::Engine::order; GeMatrix<FullStorageView<ElementType, order> > B(n, 1, b, n); return lsy(A, B, jPiv, rCond, work); } //-- (ge)lsy [complex variant] ------------------------------------------------- #ifdef USE_CXXLAPACK template <typename MA, typename VB, typename VJPIV, typename RCOND, typename VWORK, typename VRWORK> typename RestrictTo<IsComplexGeMatrix<MA>::value && IsComplexDenseVector<VB>::value && IsIntegerDenseVector<VJPIV>::value && IsReal<RCOND>::value && IsComplexDenseVector<VWORK>::value && IsRealDenseVector<VRWORK>::value, typename RemoveRef<MA>::Type::IndexType>::Type lsy(MA &&A, VB &&b, VJPIV &&jPiv, RCOND rCond, VWORK &&work, VRWORK &&rwork) { // // Remove references from rvalue types // typedef typename RemoveRef<MA>::Type MatrixA; typedef typename RemoveRef<VB>::Type VectorB; typedef typename VectorB::ElementType ElementType; typedef typename VectorB::IndexType IndexType; const IndexType n = b.length(); const StorageOrder order = MatrixA::Engine::order; GeMatrix<FullStorageView<ElementType, order> > B(n, 1, b, n); return lsy(A, B, jPiv, rCond, work, rwork); } #endif // USE_CXXLAPACK //-- (ge)lsy [real variant with temporary workspace] --------------------------- template <typename MA, typename VB, typename VJPIV, typename RCOND> typename RestrictTo<IsRealGeMatrix<MA>::value && IsRealDenseVector<VB>::value && IsIntegerDenseVector<VJPIV>::value && IsReal<RCOND>::value, typename RemoveRef<MA>::Type::IndexType>::Type lsy(MA &&A, VB &&b, VJPIV &&jPiv, RCOND rCond) { typedef typename RemoveRef<MA>::Type::Vector WorkVector; WorkVector work; return lsy(A, b, jPiv, rCond, work); } //-- (ge)lsy [complex variant with temporary workspace] ------------------------ #ifdef USE_CXXLAPACK template <typename MA, typename VB, typename VJPIV, typename RCOND> typename RestrictTo<IsComplexGeMatrix<MA>::value && IsComplexDenseVector<VB>::value && IsIntegerDenseVector<VJPIV>::value && IsReal<RCOND>::value, typename RemoveRef<MA>::Type::IndexType>::Type lsy(MA &&A, VB &&b, VJPIV &&jPiv, RCOND rCond) { typedef typename RemoveRef<MA>::Type::Vector WorkVector; typedef typename RemoveRef<MA>::Type::ElementType T; typedef typename ComplexTrait<T>::PrimitiveType PT; typedef DenseVector<Array<PT> > RealWorkVector; WorkVector work; RealWorkVector rwork; return lsy(A, b, jPiv, rCond, work, rwork); } #endif // USE_CXXLAPACK } } // namespace lapack, flens #endif // FLENS_LAPACK_GE_LSY_TCC |