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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 DPOTF2( 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_POTF2_TCC #define FLENS_LAPACK_PO_POTF2_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 SyMatrix<MA>::IndexType potf2_impl(SyMatrix<MA> &A) { using std::isnan; using std::sqrt; 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 Zero(0), One(1); IndexType info = 0; // // Quick return if possible // if (n==0) { return info; } if (upper) { // // Compute the Cholesky factorization A = U**T *U. // for (IndexType j=1; j<=n; ++j) { // // Partition matrix // const auto range1 = _(1,j-1); const auto range3 = _(j+1,n); const auto a12 = A(range1,j); const auto A13 = A(range1,range3); auto a23 = A(j,range3); // // Compute U(J,J) and test for non-positive-definiteness. // T a22 = A(j,j) - a12*a12; if (a22<=Zero || isnan(a22)) { A(j,j) = a22; info = j; break; } a22 = sqrt(a22); A(j,j) = a22; // // Compute elements J+1:N of row J. // if (j<n) { blas::mv(Trans, -One, A13, a12, One, a23); a23 *= One / a22; } } } else { // // Compute the Cholesky factorization A = L*L**T. // for (IndexType j=1; j<=n; ++j) { // // Partition matrix // const auto range1 = _(1,j-1); const auto range3 = _(j+1,n); const auto a21 = A(j,range1); const auto A31 = A(range3,range1); auto a32 = A(range3,j); // // Compute L(J,J) and test for non-positive-definiteness. // T a22 = A(j,j) - a21*a21; if (a22<=Zero || isnan(a22)) { A(j,j) = a22; info = j; break; } a22 = sqrt(a22); A(j,j) = a22; // // Compute elements J+1:N of column J. // if (j<n) { blas::mv(NoTrans, -One, A31, a21, One, a32); a32 *= One / a22; } } } return info; } } // namespace generic //== interface for native lapack =============================================== #ifdef USE_CXXLAPACK namespace external { template <typename MA> typename SyMatrix<MA>::IndexType potf2_impl(SyMatrix<MA> &A) { typedef typename SyMatrix<MA>::IndexType IndexType; IndexType info = cxxlapack::potf2<IndexType>(getF77Char(A.upLo()), A.dim(), A.data(), A.leadingDimension()); ASSERT(info>=0); return info; } } // namespace external #endif // USE_CXXLAPACK //== public interface ========================================================== template <typename MA> typename SyMatrix<MA>::IndexType potf2(SyMatrix<MA> &A) { typedef typename SyMatrix<MA>::IndexType IndexType; // // Test the input parameters // ASSERT(A.firstRow()==1); ASSERT(A.firstCol()==1); # ifdef CHECK_CXXLAPACK // // Make copies of output arguments // typename SyMatrix<MA>::NoView A_org = A; # endif // // Call implementation // IndexType info = LAPACK_SELECT::potf2_impl(A); # ifdef CHECK_CXXLAPACK // // Make copies of generic results // typename SyMatrix<MA>::NoView A_generic = A; // // Restore output arguments // A = A_org; // // Compare results // IndexType _info = external::potf2_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 potf2(MA &&A) { typedef typename MA::IndexType IndexType; CHECKPOINT_ENTER; IndexType info = potf2(A); CHECKPOINT_LEAVE; return info; } } } // namespace lapack, flens #endif // FLENS_LAPACK_PO_POTF2_TCC |