Eigen/src/Core/products/SelfadjointRank2Update.h

// 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

// IWYU pragma: private
#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