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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 DTRTI2( 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_TI2_TCC #define FLENS_LAPACK_TR_TI2_TCC 1 #include <algorithm> #include <flens/blas/blas.h> #include <flens/lapack/lapack.h> namespace flens { namespace lapack { //== generic lapack implementation ============================================= namespace generic { template <typename MA> typename TrMatrix<MA>::IndexType ti2_impl(TrMatrix<MA> &A) { typedef typename TrMatrix<MA>::ElementType ElementType; typedef typename TrMatrix<MA>::IndexType IndexType; const Underscore<IndexType> _; const bool upper = (A.upLo()==Upper); const bool noUnit = (A.diag()==NonUnit); const IndexType n = A.dim(); const ElementType One(1); IndexType info = 0; if (upper) { // // Compute inverse of upper triangular matrix. // for (IndexType j=1; j<=n; ++j) { ElementType Ajj; if (noUnit) { A(j,j) = One / A(j,j); Ajj = -A(j,j); } else { Ajj = -One; } // // Compute elements 1:j-1 of j-th column. // const auto range = _(1,j-1); const auto U11 = (noUnit) ? A(range,range).upper() : A(range,range).upperUnit(); auto u12 = A(range,j); blas::mv(NoTrans, U11, u12); u12 *= Ajj; } } else { // // Compute inverse of lower triangular matrix. // for (IndexType j=n; j>=1; --j) { ElementType Ajj; if (noUnit) { A(j,j) = One / A(j,j); Ajj = -A(j,j); } else { Ajj = -One; } if (j<n) { // // Compute elements j+1:n of j-th column. // const auto range = _(j+1,n); const auto L22 = (noUnit) ? A(range,range).lower() : A(range,range).lowerUnit(); auto l21 = A(range,j); blas::mv(NoTrans, L22, l21); l21 *= Ajj; } } } return info; } } // namespace generic //== interface for native lapack =============================================== #ifdef USE_CXXLAPACK namespace external { template <typename MA> typename TrMatrix<MA>::IndexType ti2_impl(TrMatrix<MA> &A) { typedef typename GeMatrix<MA>::IndexType IndexType; IndexType info = cxxlapack::trti2<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 ========================================================== template <typename MA> typename TrMatrix<MA>::IndexType ti2(TrMatrix<MA> &A) { typedef typename GeMatrix<MA>::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 TrMatrix<MA>::NoView A_org = A; # endif // // Call implementation // const IndexType info = LAPACK_SELECT::ti2_impl(A); // // Compare results // # ifdef CHECK_CXXLAPACK typename TrMatrix<MA>::NoView A_generic = A; A = A_org; const IndexType _info = external::ti2_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); } # endif return info; } //-- forwarding ---------------------------------------------------------------- template <typename MA> typename MA::IndexType ti2(MA &&A) { typedef typename MA::IndexType IndexType; CHECKPOINT_ENTER; IndexType info = ti2(A); CHECKPOINT_LEAVE; return info; } } } // namespace lapack, flens #endif // FLENS_LAPACK_TR_TI2_TCC |