SelfadjointRank2Update.h

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
 
#ifndef EIGEN_SELFADJOINTRANK2UPTADE_H
#define EIGEN_SELFADJOINTRANK2UPTADE_H
 
#include "../InternalHeaderCheck.h"
 
namespace Eigen { 
 
namespace internal {
 
/* Optimized selfadjoint matrix += alpha * uv' + conj(alpha)*vu'
 * It corresponds to the Level2 syr2 BLAS routine
 */
 
template<typename Scalar, typename Index, typename UType, typename VType, int UpLo>
struct selfadjoint_rank2_update_selector;
 
template<typename Scalar, typename Index, typename UType, typename VType>
struct selfadjoint_rank2_update_selector<Scalar,Index,UType,VType,Lower>
{
  static EIGEN_DEVICE_FUNC
  void run(Scalar* mat, Index stride, const UType& u, const VType& v, const Scalar& alpha)
  {
    const Index size = u.size();
    for (Index i=0; i<size; ++i)
    {
      Map<Matrix<Scalar,Dynamic,1> >(mat+stride*i+i, size-i) +=
                        (numext::conj(alpha) * numext::conj(u.coeff(i))) * v.tail(size-i)
                      + (alpha * numext::conj(v.coeff(i))) * u.tail(size-i);
    }
  }
};
 
template<typename Scalar, typename Index, typename UType, typename VType>
struct selfadjoint_rank2_update_selector<Scalar,Index,UType,VType,Upper>
{
  static void run(Scalar* mat, Index stride, const UType& u, const VType& v, const Scalar& alpha)
  {
    const Index size = u.size();
    for (Index i=0; i<size; ++i)
      Map<Matrix<Scalar,Dynamic,1> >(mat+stride*i, i+1) +=
                        (numext::conj(alpha)  * numext::conj(u.coeff(i))) * v.head(i+1)
                      + (alpha * numext::conj(v.coeff(i))) * u.head(i+1);
  }
};
 
template<bool Cond, typename T>
using conj_expr_if = std::conditional<!Cond, const T&, CwiseUnaryOp<scalar_conjugate_op<typename traits<T>::Scalar>,T>>;
 
} // end namespace internal
 
template<typename MatrixType, unsigned int UpLo>
template<typename DerivedU, typename DerivedV>
EIGEN_DEVICE_FUNC SelfAdjointView<MatrixType,UpLo>& SelfAdjointView<MatrixType,UpLo>
::rankUpdate(const MatrixBase<DerivedU>& u, const MatrixBase<DerivedV>& v, const Scalar& alpha)
{
  typedef internal::blas_traits<DerivedU> UBlasTraits;
  typedef typename UBlasTraits::DirectLinearAccessType ActualUType;
  typedef internal::remove_all_t<ActualUType> ActualUType_;
  internal::add_const_on_value_type_t<ActualUType> actualU = UBlasTraits::extract(u.derived());
 
  typedef internal::blas_traits<DerivedV> VBlasTraits;
  typedef typename VBlasTraits::DirectLinearAccessType ActualVType;
  typedef internal::remove_all_t<ActualVType> ActualVType_;
  internal::add_const_on_value_type_t<ActualVType> actualV = VBlasTraits::extract(v.derived());
 
  // If MatrixType is row major, then we use the routine for lower triangular in the upper triangular case and
  // vice versa, and take the complex conjugate of all coefficients and vector entries.
 
  enum { IsRowMajor = (internal::traits<MatrixType>::Flags&RowMajorBit) ? 1 : 0 };
  Scalar actualAlpha = alpha * UBlasTraits::extractScalarFactor(u.derived())
                             * numext::conj(VBlasTraits::extractScalarFactor(v.derived()));
  if (IsRowMajor)
    actualAlpha = numext::conj(actualAlpha);
 
  typedef internal::remove_all_t<typename internal::conj_expr_if<int(IsRowMajor) ^ int(UBlasTraits::NeedToConjugate), ActualUType_>::type> UType;
  typedef internal::remove_all_t<typename internal::conj_expr_if<int(IsRowMajor) ^ int(VBlasTraits::NeedToConjugate), ActualVType_>::type> VType;
  internal::selfadjoint_rank2_update_selector<Scalar, Index, UType, VType,
    (IsRowMajor ? int(UpLo==Upper ? Lower : Upper) : UpLo)>
    ::run(_expression().const_cast_derived().data(),_expression().outerStride(),UType(actualU),VType(actualV),actualAlpha);
 
  return *this;
}
 
} // end namespace Eigen
 
#endif // EIGEN_SELFADJOINTRANK2UPTADE_H