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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 DGELS( TRANS, M, N, NRHS, A, LDA, B, LDB, WORK, LWORK, INFO ) SUBROUTINE ZGELS( TRANS, M, N, NRHS, A, LDA, B, LDB, 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_LS_TCC #define FLENS_LAPACK_GE_LS_TCC 1 #include <flens/blas/blas.h> #include <flens/lapack/lapack.h> namespace flens { namespace lapack { //== generic lapack implementation ============================================= namespace generic { //-- (ge)ls [real variant] ----------------------------------------------------- template <typename MA, typename MB, typename VWORK> typename GeMatrix<MA>::IndexType ls_impl(Transpose trans, GeMatrix<MA> &A, GeMatrix<MB> &B, DenseVector<VWORK> &work) { using flens::max; using flens::min; typedef typename GeMatrix<MB>::ElementType ElementType; typedef typename GeMatrix<MB>::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); IndexType info = 0; // // Figure out optimal block size // IndexType nb; bool tpsd = (trans==NoTrans) ? false : true; if (m>=n) { nb = ilaenv<ElementType>(1, "GEQRF", "", m, n); if (tpsd) { nb = max(nb, ilaenv<ElementType>(1, "ORMQR", "LN", m, nRhs, n)); } else { nb = max(nb, ilaenv<ElementType>(1, "ORMQR", "LT", m, nRhs, n)); } } else { nb = ilaenv<ElementType>(1, "GELQF", "", m, n); if (tpsd) { nb = max(nb, ilaenv<ElementType>(1, "ORMLQ", "LT", n, nRhs, m)); } else { nb = max(nb, ilaenv<ElementType>(1, "ORMLQ", "LN", n, nRhs, m)); } } IndexType wSize = max(IndexType(1), mn+max(mn,nRhs)*nb); if (work.length()==0) { work.resize(wSize); } work(1) = ElementType(wSize); const IndexType lWork = work.length(); // // Quick return if possible // if (min(m, n, nRhs)==IndexType(0)) { B = Zero; return info; } // // Get machine parameters // ElementType smallNum = lamch<ElementType>(SafeMin) / lamch<ElementType>(Precision); ElementType bigNum = One / smallNum; labad(smallNum, bigNum); // // Scale A, B if max element outside range [SMLNUM,BIGNUM] // const ElementType normA = lan(MaximumNorm, A); IndexType iScaleA = 0; if (normA>Zero && normA<smallNum) { // // Scale matrix norm up to SMLNUM // lascl(LASCL::FullMatrix, 0, 0, normA, smallNum, A); iScaleA = 1; } else if (normA>bigNum) { // // Scale matrix norm down to BIGNUM // lascl(LASCL::FullMatrix, 0, 0, normA, bigNum, A); iScaleA = 2; } else if (normA==Zero) { // // Matrix all zero. Return zero solution. // lascl(LASCL::FullMatrix, max(m,n), nRhs, Zero, Zero, A); work(1) = wSize; } auto _B = (tpsd) ? B(_(1,n),_) : B(_(1,m),_); const ElementType normB = lan(MaximumNorm, _B); IndexType iScaleB = 0; IndexType scaleLen = 0; if (normB>Zero && normB<smallNum) { // // Scale matrix norm up to SMLNUM // lascl(LASCL::FullMatrix, 0, 0, normB, smallNum, B); iScaleB = 1; } else if (normB>bigNum) { // // Scale matrix norm down to BIGNUM // lascl(LASCL::FullMatrix, 0, 0, normB, bigNum, B); iScaleB = 2; } auto tau = work(_(1,mn)); auto _work = work(_(mn+1,lWork)); if (m>=n) { // // compute QR factorization of A // qrf(A, tau, _work); const auto R = A(_(1,n),_(1,n)).upper(); // // workspace at least N, optimally N*NB // if (!tpsd) { // // Least-Squares Problem min || A * X - B || // // B(1:M,1:NRHS) := Q**T * B(1:M,1:NRHS) // ormqr(Left, Trans, A, tau, B, _work); // // workspace at least NRHS, optimally NRHS*NB // // B(1:N,1:NRHS) := inv(R) * B(1:N,1:NRHS) // info = trs(NoTrans, R, B(_(1,n),_)); if (info>0) { return info; } scaleLen = n; } else { // // Overdetermined system of equations A**T * X = B // // B(1:N,1:NRHS) := inv(R**T) * B(1:N,1:NRHS) // info = trs(Trans, R, B(_(1,n),_)); if (info>0) { return info; } // // B(N+1:M,1:NRHS) = ZERO // B(_(n+1,m),_) = Zero; // // B(1:M,1:NRHS) := Q(1:N,:) * B(1:N,1:NRHS) // ormqr(Left, NoTrans, A, tau, B, _work); // // workspace at least NRHS, optimally NRHS*NB // scaleLen = m; } } else { // // Compute LQ factorization of A // lqf(A, tau, _work); const auto L = A(_(1,m),_(1,m)).lower(); // // workspace at least M, optimally M*NB. // if (!tpsd) { // // underdetermined system of equations A * X = B // // B(1:M,1:NRHS) := inv(L) * B(1:M,1:NRHS) // info = trs(NoTrans, L, B(_(1,m),_)); if (info>0) { return info; } // // B(M+1:N,1:NRHS) = 0 // B(_(m+1,n),_) = Zero; // // B(1:N,1:NRHS) := Q(1:N,:)**T * B(1:M,1:NRHS) // ormlq(Left, Trans, A, tau, B, _work); // // workspace at least NRHS, optimally NRHS*NB // scaleLen = n; // } else { // // overdetermined system min || A**T * X - B || // // B(1:N,1:NRHS) := Q * B(1:N,1:NRHS) // ormlq(Left, NoTrans, A, tau, B, _work); // // workspace at least NRHS, optimally NRHS*NB // // B(1:M,1:NRHS) := inv(L**T) * B(1:M,1:NRHS) // info = trs(Trans, L, B(_(1,m),_)); if (info>0) { return info; } scaleLen = m; } } // // Undo scaling // auto __B = B(_(1,scaleLen),_); if (iScaleA==1) { lascl(LASCL::FullMatrix, 0, 0, normA, smallNum, __B); } else if (iScaleA==2) { lascl(LASCL::FullMatrix, 0, 0, normA, bigNum, __B); } if (iScaleB==1) { lascl(LASCL::FullMatrix, 0, 0, smallNum, normB, __B); } else if (iScaleB==2) { lascl(LASCL::FullMatrix, 0, 0, bigNum, normB, __B); } work(1) = ElementType(wSize); return info; } } // namespace generic //== interface for native lapack =============================================== #ifdef USE_CXXLAPACK namespace external { //-- (ge)ls [real and complex variant] ----------------------------------------- template <typename MA, typename MB, typename VWORK> typename GeMatrix<MA>::IndexType ls_impl(Transpose trans, GeMatrix<MA> &A, GeMatrix<MB> &B, 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::gels<IndexType>(getF77Char(trans), A.numRows(), A.numCols(), B.numCols(), A.data(), A.leadingDimension(), B.data(), B.leadingDimension(), &WORK, LWORK); work.resize(IndexType(cxxblas::real(WORK))); } IndexType info = cxxlapack::gels<IndexType>(getF77Char(trans), A.numRows(), A.numCols(), B.numCols(), A.data(), A.leadingDimension(), B.data(), B.leadingDimension(), work.data(), work.length()); ASSERT(info>=0); return info; } } // namespace external #endif // USE_CXXLAPACK //== public interface ========================================================== //-- (ge)ls [real variant] ----------------------------------------------------- template <typename MA, typename MB, typename VWORK> typename RestrictTo<IsRealGeMatrix<MA>::value && IsRealGeMatrix<MB>::value && IsRealDenseVector<VWORK>::value, typename RemoveRef<MA>::Type::IndexType>::Type ls(Transpose trans, MA &&A, MB &&B, VWORK &&work) { using std::max; using std::min; LAPACK_DEBUG_OUT("(ge)ls [real]"); // // Remove references from rvalue types // typedef typename RemoveRef<MA>::Type MatrixA; typedef typename MatrixA::IndexType IndexType; typedef typename RemoveRef<MB>::Type MatrixB; typedef typename RemoveRef<VWORK>::Type VectorWork; // // Test the input parameters // # ifndef NDEBUG const IndexType m = A.numRows(); const IndexType n = A.numCols(); const IndexType nRhs = B.numCols(); ASSERT(B.numRows()==max(m,n)); if (work.length()>0) { const IndexType mn = min(m, n); ASSERT(work.length()>=max(IndexType(1),mn+max(mn,nRhs))); } # endif // // Make copies of output arguments // # ifdef CHECK_CXXLAPACK typename MatrixA::NoView A_org = A; typename MatrixB::NoView B_org = B; typename VectorWork::NoView work_org = work; # endif // // Call implementation // IndexType info = LAPACK_SELECT::ls_impl(trans, A, B, 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 VectorWork::NoView work_generic = work; // // restore output arguments // A = A_org; B = B_org; work = work_org; // // Compare generic results with results from the native implementation // IndexType _info = external::ls_impl(trans, A, B, 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(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(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: ls.tcc" << std::endl; ASSERT(0); } else { // std::cerr << "passed: ls.tcc" << std::endl; } # endif return info; } //-- (ge)ls [complex variant] -------------------------------------------------- #ifdef USE_CXXLAPACK template <typename MA, typename MB, typename VWORK> typename RestrictTo<IsComplexGeMatrix<MA>::value && IsComplexGeMatrix<MB>::value && IsComplexDenseVector<VWORK>::value, typename RemoveRef<MA>::Type::IndexType>::Type ls(Transpose trans, MA &&A, MB &&B, VWORK &&work) { using std::max; using std::min; LAPACK_DEBUG_OUT("(ge)ls [complex]"); // // Remove references from rvalue types // typedef typename RemoveRef<MA>::Type MatrixA; typedef typename MatrixA::IndexType IndexType; typedef typename RemoveRef<MB>::Type MatrixB; typedef typename RemoveRef<VWORK>::Type VectorWork; // // Test the input parameters // # ifndef NDEBUG const IndexType m = A.numRows(); const IndexType n = A.numCols(); const IndexType nRhs = B.numCols(); ASSERT(B.numRows()==max(m,n)); if (work.length()>0) { const IndexType mn = min(m, n); ASSERT(work.length()>=max(IndexType(1),mn+max(mn,nRhs))); } # endif // // Make copies of output arguments // # ifdef CHECK_CXXLAPACK typename MatrixA::NoView A_org = A; typename MatrixB::NoView B_org = B; typename VectorWork::NoView work_org = work; # endif // // Call implementation // IndexType info = external::ls_impl(trans, A, B, work); return info; } #endif // USE_CXXLAPACK //-- (ge)ls [real/complex variant with temporary workspace] -------------------- template <typename MA, typename MB> typename RestrictTo<IsGeMatrix<MA>::value && IsGeMatrix<MB>::value, typename RemoveRef<MA>::Type::IndexType>::Type ls(Transpose trans, MA &&A, MB &&B) { typedef typename RemoveRef<MA>::Type::Vector WorkVector; WorkVector work; return ls(trans, A, B, work); } //-- (ge)ls [variant if rhs is vector] ----------------------------------------- template <typename MA, typename VB, typename VWORK> typename RestrictTo<IsGeMatrix<MA>::value && IsDenseVector<VB>::value && IsDenseVector<VWORK>::value, typename RemoveRef<MA>::Type::IndexType>::Type ls(Transpose trans, MA &&A, VB &&b, 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 ls(trans, A, B, work); } //-- (ge)ls [real/complex variant with temporary workspace] -------------------- template <typename MA, typename VB> typename RestrictTo<IsGeMatrix<MA>::value && IsDenseVector<VB>::value, typename RemoveRef<MA>::Type::IndexType>::Type ls(Transpose trans, MA &&A, VB &&b) { typedef typename RemoveRef<MA>::Type::Vector WorkVector; WorkVector work; return ls(trans, A, b, work); } } } // namespace lapack, flens #endif // FLENS_LAPACK_GE_LS_TCC |