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/*
* Copyright (c) 2012, Michael Lehn, Klaus Pototzky * * 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. */ /* Baesed on * SUBROUTINE DGETRI( N, A, LDA, IPIV, WORK, LWORK, INFO ) SUBROUTINE ZGETRI( N, A, LDA, IPIV, WORK, LWORK, INFO ) SUBROUTINE DTRTRI( UPLO, DIAG, N, A, LDA, INFO ) SUBROUTINE ZTRTRI( UPLO, DIAG, N, A, LDA, INFO ) * * -- LAPACK routine (version 3.2) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * November 2006 */ #ifndef FLENS_LAPACK_GE_TRI_TCC #define FLENS_LAPACK_GE_TRI_TCC 1 #include <algorithm> #include <flens/blas/blas.h> #include <flens/lapack/lapack.h> namespace flens { namespace lapack { //== generic lapack implementation ============================================= namespace generic { //-- (ge)tri [real variant] ---------------------------------------------------- template <typename MA, typename VP, typename VWORK> typename GeMatrix<MA>::IndexType tri_impl(GeMatrix<MA> &A, const DenseVector<VP> &piv, DenseVector<VWORK> &work) { using std::max; typedef typename GeMatrix<MA>::ElementType ElementType; typedef typename GeMatrix<MA>::IndexType IndexType; const ElementType Zero(0), One(1); const IndexType n = A.numRows(); const Underscore<IndexType> _; IndexType info = 0; IndexType nb = ilaenv<ElementType>(1, "GETRI", "", n); const IndexType lWorkOpt = n*nb; if (work.length()==0) { work.resize(max(lWorkOpt, IndexType(1))); } work(1) = lWorkOpt; // // Quick return if possible // if (n==0) { return info; } // // Form inv(U). If INFO > 0 from DTRTRI, then U is singular, // and the inverse is not computed. // info = tri(A.upper()); if (info>0) { return info; } IndexType nbMin = 2; const IndexType lWork = work.length();; const IndexType ldWork = n; IndexType iws; if (nb>1 && nb<n) { iws = max(ldWork*nb, IndexType(1)); if (lWork<iws) { nb = lWork / ldWork; nbMin = max(2, ilaenv<ElementType>(2, "GETRI", "", n)); } } else { iws = n; } GeMatrixView<ElementType> Work(n, nb, work); // // Solve the equation inv(A)*L = inv(U) for inv(A). // if (nb<nbMin || nb>=n) { // // Use unblocked code. // for (IndexType j=n; j>=1; --j) { // // Copy current column of L to WORK and replace with zeros. // work(_(j+1,n)) = A(_(j+1,n),j); A(_(j+1,n),j) = Zero;; // // Compute current column of inv(A). // if (j<n) { blas::mv(NoTrans, -One, A(_,_(j+1,n)), work(_(j+1,n)), One, A(_,j)); } } } else { // // Use blocked code. // const IndexType nn = ((n-1)/nb)*nb + 1; for (IndexType j=nn; j>=1; j-=nb) { const IndexType jb = min(nb, n-j+1); // // Copy current block column of L to WORK and replace with // zeros. // for (IndexType jj=j, JJ=1; jj<=j+jb-1; ++jj, ++JJ) { Work(_(jj+1,n),JJ) = A(_(jj+1,n),jj); A(_(jj+1,n),jj) = Zero; } // // Compute current block column of inv(A). // if (j+jb<=n) { blas::mm(NoTrans, NoTrans, -One, A(_,_(j+jb,n)), Work(_(j+jb,n),_(1,jb)), One, A(_,_(j,j+jb-1))); } blas::sm(Right, NoTrans, One, Work(_(j,j+jb-1),_(1,jb)).lowerUnit(), A(_,_(j,j+jb-1))); } } // // Apply column interchanges. // for (IndexType j=n-1; j>=1; --j) { const IndexType jp = piv(j); if (jp!=j) { blas::swap(A(_,j), A(_,jp)); } } work(1) = iws; return info; } } // namespace generic //== interface for native lapack =============================================== #ifdef USE_CXXLAPACK namespace external { //-- (ge)tri [real and complex variant] ---------------------------------------- template <typename MA, typename VP, typename VWORK> typename GeMatrix<MA>::IndexType tri_impl(GeMatrix<MA> &A, const DenseVector<VP> &piv, DenseVector<VWORK> &work) { typedef typename GeMatrix<MA>::ElementType ElementType; typedef typename GeMatrix<MA>::IndexType IndexType; IndexType info; if (work.length()==0) { ElementType WORK; IndexType LWORK = -1; info = cxxlapack::getri<IndexType>(A.numRows(), A.data(), A.leadingDimension(), piv.data(), &WORK, LWORK); work.resize(IndexType(cxxblas::real(WORK))); } info = cxxlapack::getri<IndexType>(A.numRows(), A.data(), A.leadingDimension(), piv.data(), work.data(), work.length()); ASSERT(info>=0); return info; } } // namespace external #endif // USE_CXXLAPACK //== public interface ========================================================== //-- (ge)tri [real variant] ---------------------------------------------------- template <typename MA, typename VPIV, typename VWORK> typename RestrictTo<IsRealGeMatrix<MA>::value && IsIntegerDenseVector<VPIV>::value && IsRealDenseVector<VWORK>::value, typename RemoveRef<MA>::Type::IndexType>::Type tri(MA &&A, const VPIV &piv, VWORK &&work) { using std::max; // // Remove references from rvalue types // typedef typename RemoveRef<MA>::Type MatrixA; typedef typename MatrixA::IndexType IndexType; typedef typename RemoveRef<VPIV>::Type VectorPiv; typedef typename RemoveRef<VWORK>::Type VectorWork; // // Test the input parameters // # ifndef NDEBUG ASSERT(A.firstRow()==1); ASSERT(A.firstCol()==1); ASSERT(A.numRows()==A.numCols()); const IndexType n = A.numRows(); ASSERT(piv.firstIndex()==1); ASSERT(piv.length()==n); const bool lQuery = (work.length()==0); ASSERT(lQuery || work.length()>=max(IndexType(1),n)); # endif // // Make copies of output arguments // # ifdef CHECK_CXXLAPACK typename MatrixA::NoView A_org = A; typename VectorWork::NoView work_org = work; # endif // // Call implementation // const IndexType info = LAPACK_SELECT::tri_impl(A, piv, work); // // Compare results // # ifdef CHECK_CXXLAPACK typename MatrixA::NoView A_generic = A; typename VectorWork::NoView work_generic = work; A = A_org; work = work_org; const IndexType _info = external::tri_impl(A, piv, 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(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) { ASSERT(0); } else { // std::cerr << "passed: (ge)tri.tcc" << std::endl; } # endif return info; } //-- (ge)tri [complex variant] ------------------------------------------------- #ifdef USE_CXXLAPACK template <typename MA, typename VPIV, typename VWORK> typename RestrictTo<IsComplexGeMatrix<MA>::value && IsIntegerDenseVector<VPIV>::value && IsComplexDenseVector<VWORK>::value, typename RemoveRef<MA>::Type::IndexType>::Type tri(MA &&A, const VPIV &piv, VWORK &&work) { using std::max; // // Remove references from rvalue types // typedef typename RemoveRef<MA>::Type MatrixA; typedef typename MatrixA::IndexType IndexType; typedef typename RemoveRef<VPIV>::Type VectorPiv; typedef typename RemoveRef<VWORK>::Type VectorWork; // // Test the input parameters // # ifndef NDEBUG ASSERT(A.firstRow()==1); ASSERT(A.firstCol()==1); ASSERT(A.numRows()==A.numCols()); const IndexType n = A.numRows(); ASSERT(piv.firstIndex()==1); ASSERT(piv.length()==n); const bool lQuery = (work.length()==0); ASSERT(lQuery || work.length()>=max(IndexType(1),n)); # endif // // Call implementation // const IndexType info = external::tri_impl(A, piv, work); return info; } #endif // USE_CXXLAPACK //-- (ge)tri [real/complex variant with temporary workspace] ------------------- template <typename MA, typename VPIV> typename RestrictTo<IsGeMatrix<MA>::value && IsIntegerDenseVector<VPIV>::value, typename RemoveRef<MA>::Type::IndexType>::Type tri(MA &&A, const VPIV &piv) { typedef typename RemoveRef<MA>::Type::Vector WorkVector; WorkVector work; return tri(A, piv, work); } } } // namespace lapack, flens #endif // FLENS_LAPACK_GE_TRI_TCC |