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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 DPOTRF( UPLO, N, A, LDA, INFO ) SUBROUTINE ZPOTRF( UPLO, N, A, LDA, 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_PO_POTRF_TCC #define FLENS_LAPACK_PO_POTRF_TCC 1 #include <algorithm> #include <flens/blas/blas.h> #include <flens/lapack/lapack.h> namespace flens { namespace lapack { //== generic lapack implementation ============================================= namespace generic { //-- potrf [real variant] ------------------------------------------------------ template <typename MA> typename SyMatrix<MA>::IndexType potrf_impl(SyMatrix<MA> &A) { typedef typename SyMatrix<MA>::ElementType T; typedef typename SyMatrix<MA>::IndexType IndexType; const Underscore<IndexType> _; const IndexType n = A.dim(); const bool upper = (A.upLo()==Upper); const T One(1); IndexType info = 0; // // Quick return if possible // if (n==0) { return info; } // // Determine the block size for this environment. // const char *upLo = (upper) ? "U" : "L"; IndexType nb = ilaenv<T>(1, "POGTRF", upLo, n); if ((nb<=1) || (nb>=n)) { // // Use unblocked code. // info = potf2(A); } else { // // Use blocked code. // if (upper) { // // Compute the Cholesky factorization A = U**T*U. // for (IndexType j=1; j<=n; j+=nb) { // // Partition matrix // IndexType jb = min(nb, n-j+1); const auto range1 = _(1,j-1); const auto range2 = _(j,j+jb-1); const auto range3 = _(j+jb,n); const auto A12 = A(range1,range2); const auto A13 = A(range1,range3); const auto U22 = A(range2,range2).upper(); auto A22 = A(range2,range2).upper().symmetric(); auto A23 = A(range2,range3); // // Update and factorize the current diagonal block and test // for non-positive-definiteness. // blas::rk(Trans, -One, A12, One, A22); info = potf2(A22); if (info!=0) { info += j-1; break; } if (j+jb<=n) { // // Compute the current block row. // blas::mm(Trans, NoTrans, -One, A12, A13, One, A23); blas::sm(Left, Trans, One, U22, A23); } } } else { // // Compute the Cholesky factorization A = L*L**T. // for (IndexType j=1; j<=n; j+=nb) { // // Partition matrix // IndexType jb = min(nb, n-j+1); const auto range1 = _(1,j-1); const auto range2 = _(j,j+jb-1); const auto range3 = _(j+jb,n); const auto A21 = A(range2,range1); const auto A31 = A(range3,range1); const auto L22 = A(range2,range2).lower(); auto A22 = A(range2,range2).lower().symmetric(); auto A32 = A(range3,range2); // // Update and factorize the current diagonal block and test // for non-positive-definiteness. // blas::rk(NoTrans, -One, A21, One, A22); info = potf2(A22); if (info!=0) { info += j-1; break; } if (j+jb<=n) { // // Compute the current block column. // blas::mm(NoTrans, Trans, -One, A31, A21, One, A32); blas::sm(Right, Trans, One, L22, A32); } } } } return info; } } // namespace generic //== interface for native lapack =============================================== #ifdef USE_CXXLAPACK namespace external { //-- potrf [real variant] ------------------------------------------------------ template <typename MA> typename SyMatrix<MA>::IndexType potrf_impl(SyMatrix<MA> &A) { typedef typename SyMatrix<MA>::IndexType IndexType; IndexType info = cxxlapack::potrf<IndexType>(getF77Char(A.upLo()), A.dim(), A.data(), A.leadingDimension()); ASSERT(info>=0); return info; } //-- potrf [complex variant] --------------------------------------------------- template <typename MA> typename HeMatrix<MA>::IndexType potrf_impl(HeMatrix<MA> &A) { typedef typename HeMatrix<MA>::IndexType IndexType; IndexType info = cxxlapack::potrf<IndexType>(getF77Char(A.upLo()), A.dim(), A.data(), A.leadingDimension()); ASSERT(info>=0); return info; } } // namespace external #endif // USE_CXXLAPACK //== public interface ========================================================== //-- potrf [real variant] ------------------------------------------------------ template <typename MA> typename RestrictTo<IsRealSyMatrix<MA>::value, typename RemoveRef<MA>::Type::IndexType>::Type potrf(MA &&A) { // // Remove references from rvalue types // typedef typename RemoveRef<MA>::Type MatrixA; typedef typename MatrixA::IndexType IndexType; // // Test the input parameters // ASSERT(A.firstRow()==1); ASSERT(A.firstCol()==1); # ifdef CHECK_CXXLAPACK // // Make copies of output arguments // typename MatrixA::NoView _A = A; # endif // // Call implementation // const IndexType info = LAPACK_SELECT::potrf_impl(A); # ifdef CHECK_CXXLAPACK // // Compare results // const IndexType _info = external::potrf_impl(_A); bool failed = false; if (! isIdentical(A, _A, " A", "_A")) { std::cerr << "CXXLAPACK: A = " << A << std::endl; std::cerr << "F77LAPACK: _A = " << _A << 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) { ASSERT(0); } # endif return info; } #ifdef USE_CXXLAPACK //-- potrf [complex variant] --------------------------------------------------- template <typename MA> typename RestrictTo<IsHeMatrix<MA>::value, typename RemoveRef<MA>::Type::IndexType>::Type potrf(MA &&A) { // // Remove references from rvalue types // typedef typename RemoveRef<MA>::Type MatrixA; typedef typename MatrixA::IndexType IndexType; // // Test the input parameters // ASSERT(A.firstRow()==1); ASSERT(A.firstCol()==1); // // Call implementation // const IndexType info = external::potrf_impl(A); return info; } #endif // USE_CXXLAPACK } } // namespace lapack, flens #endif // FLENS_LAPACK_PO_POTRF_TCC |