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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_TR_TRI_TCC #define FLENS_LAPACK_TR_TRI_TCC 1 #include <algorithm> #include <flens/blas/blas.h> #include <flens/lapack/lapack.h> namespace flens { namespace lapack { //== generic lapack implementation ============================================= namespace generic { //-- (tr)tri [real variant] ---------------------------------------------------- template <typename MA> typename GeMatrix<MA>::IndexType tri_impl(TrMatrix<MA> &A) { using std::min; using cxxblas::getF77BlasChar; typedef typename TrMatrix<MA>::ElementType ElementType; typedef typename TrMatrix<MA>::IndexType IndexType; const Underscore<IndexType> _; const IndexType n = A.dim(); const bool upper = (A.upLo()==Upper); const bool noUnit = (A.diag()==NonUnit); const ElementType Zero(0), One(1); IndexType info = 0; // // Quick return if possible // if (n==0) { return info; } // // Check for singularity if non-unit. // if (noUnit) { for (info=1; info<=n; ++info) { if (A(info,info)==Zero) { return info; } } info = 0; } // // Determine the block size for this environment. // const char upLoDiag[2] = { getF77BlasChar(A.upLo()), getF77BlasChar(A.diag()) }; const IndexType nb = ilaenv<ElementType>(1, "TRTRI", upLoDiag, n); if (nb<=1 || nb>=n) { // // Use unblocked code // info = ti2(A); } else { // // Use blocked code // if (upper) { // // Compute inverse of upper triangular matrix // for (IndexType j=1; j<=n; j+=nb) { const IndexType jb = min(nb, n-j+1); // // Compute rows 1:j-1 of current block column // const auto range1 = _(1,j-1); const auto range2 = _(j,j+jb-1); const auto U11 = (noUnit) ? A(range1, range1).upper() : A(range1, range1).upperUnit(); auto U22 = (noUnit) ? A(range2, range2).upper() : A(range2, range2).upperUnit(); auto U12 = A(range1, range2); blas::mm(Left, NoTrans, One, U11, U12); blas::sm(Right, NoTrans, -One, U22, U12); // // Compute inverse of current diagonal block // info = ti2(U22); } } else { // // Compute inverse of lower triangular matrix // const IndexType nn = ((n-1)/nb)*nb + 1; for (IndexType j=nn; j>=1; j-=nb) { const IndexType jb = min(nb, n-j+1); const auto range1 = _(j,j+jb-1); auto L11 = (noUnit) ? A(range1,range1).lower() : A(range1,range1).lowerUnit(); if (j+jb<=n) { // // Compute rows j+jb:n of current block column // const auto range2 = _(j+jb,n); const auto L22 = (noUnit) ? A(range2,range2).lower() : A(range2,range2).lowerUnit(); auto L21 = A(range2, range1); blas::mm(Left, NoTrans, One, L22, L21); blas::sm(Right, NoTrans, -One, L11, L21); } // // Compute inverse of current diagonal block // info = ti2(L11); } } } return info; } } // namespace generic //== interface for native lapack =============================================== #ifdef USE_CXXLAPACK namespace external { //-- (tr)tri [real and complex variant] ---------------------------------------- template <typename MA> typename GeMatrix<MA>::IndexType tri_impl(TrMatrix<MA> &A) { typedef typename TrMatrix<MA>::IndexType IndexType; IndexType info = cxxlapack::trtri<IndexType>(getF77Char(A.upLo()), getF77Char(A.diag()), A.dim(), A.data(), A.leadingDimension()); ASSERT(info>=0); return info; } } // namespace external #endif // USE_CXXLAPACK //== public interface ========================================================== //-- (tr)tri [real variant] ---------------------------------------------------- template <typename MA> typename RestrictTo<IsRealTrMatrix<MA>::value, typename RemoveRef<MA>::Type::IndexType>::Type tri(MA &&A) { // // Remove references from rvalue types // typedef typename RemoveRef<MA>::Type MatrixA; typedef typename MatrixA::IndexType IndexType; // // Test the input parameters // # ifndef NDEBUG ASSERT(A.firstRow()==1); ASSERT(A.firstCol()==1); # endif // // Make copies of output arguments // # ifdef CHECK_CXXLAPACK typename MatrixA::NoView A_org = A; # endif // // Call implementation // const IndexType info = LAPACK_SELECT::tri_impl(A); // // Compare results // # ifdef CHECK_CXXLAPACK typename MatrixA::NoView A_generic = A; A = A_org; const IndexType _info = external::tri_impl(A); 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(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: (tr)tri.tcc" << std::endl; } # endif return info; } //-- (tr)tri [complex variant] ------------------------------------------------- #ifdef USE_CXXLAPACK template <typename MA> typename RestrictTo<IsComplexTrMatrix<MA>::value, typename RemoveRef<MA>::Type::IndexType>::Type tri(MA &&A) { // // Remove references from rvalue types // typedef typename RemoveRef<MA>::Type MatrixA; typedef typename MatrixA::IndexType IndexType; // // Test the input parameters // # ifndef NDEBUG ASSERT(A.firstRow()==1); ASSERT(A.firstCol()==1); # endif // // Make copies of output arguments // # ifdef CHECK_CXXLAPACK typename MatrixA::NoView A_org = A; # endif // // Call implementation // const IndexType info = external::tri_impl(A); return info; } #endif // USE_CXXLAPACK } } // namespace lapack, flens #endif // FLENS_LAPACK_TR_TRI_TCC |