unsupported/Eigen/CXX11/src/NeuralNetworks/Pooling.h

// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>
//
// 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_CXX11_NEURAL_NETWORKS_POOLING_H
#define EIGEN_CXX11_NEURAL_NETWORKS_POOLING_H

#include "Patch3d.h"

namespace Eigen {

/** SpatialMaxPooling
  * \ingroup CXX11_NeuralNetworks_Module
  *
  * \brief Applies a max-pooling over a multichannel input image.
  *
  * The input parameter is expected to be a with a rank of 4 (channels, height, width, others in col-major, and the reverse of that in row-major).
  *
  * The result can be assigned to a tensor of rank equal to the rank of the input. The dimensions of the result will be channels, height, width, and others (in col-major, and the reverse of that if the input was row-major).
  *
  * The order of the width and height dimensions can be swapped if needed.
  *
*/
#if !defined(EIGEN_HAS_INDEX_LIST)
template <typename Input>
EIGEN_ALWAYS_INLINE
static const TensorReshapingOp<const Eigen::DSizes<typename internal::traits<Input>::Index, internal::traits<Input>::NumDimensions>, const TensorReductionOp<internal::MaxReducer<typename internal::remove_const<typename internal::traits<Input>::Scalar>::type>, const Eigen::array<int, 2>, const TensorImagePatchOp<Dynamic, Dynamic, const Input> > >
#else
template <typename Input>
EIGEN_ALWAYS_INLINE
static const TensorReshapingOp<const Eigen::DSizes<typename internal::traits<Input>::Index, internal::traits<Input>::NumDimensions>, const TensorReductionOp<internal::MaxReducer<typename internal::remove_const<typename internal::traits<Input>::Scalar>::type>, typename internal::conditional<internal::traits<Input>::Layout == ColMajor, const Eigen::IndexList<Eigen::type2index<1>, Eigen::type2index<2> >, const Eigen::IndexList<Eigen::type2index<2>, Eigen::type2index<3> > >::type, const TensorImagePatchOp<Dynamic, Dynamic, const Input> > >
#endif
SpatialMaxPooling(const Input& input, DenseIndex patchRows, DenseIndex patchCols,
                  DenseIndex strideRows, DenseIndex strideCols, const PaddingType padding_type,
                  DenseIndex in_strideRows = 1, DenseIndex in_strideCols = 1)
{
  EIGEN_STATIC_ASSERT(internal::traits<Input>::NumDimensions == 4, YOU_MADE_A_PROGRAMMING_MISTAKE);

  typedef typename internal::traits<Input>::Index TensorIndex;
  TensorRef<Tensor<typename internal::traits<Input>::Scalar, internal::traits<Input>::NumDimensions, internal::traits<Input>::Layout, TensorIndex> > in(input);

  const DenseIndex patchRowsEff = patchRows + (patchRows - 1) * (in_strideRows - 1);
  const DenseIndex patchColsEff = patchCols + (patchCols - 1) * (in_strideCols - 1);

  static const bool isColMajor = (internal::traits<Input>::Layout == ColMajor);
  static const int idxRows = isColMajor ? 1 : 2;
  static const int idxCols = isColMajor ? 2 : 1;

  // Molds the output of the reduction into the shape expected by the user.
  // (assuming col-major):
  // - 1st dim: channels
  // - 2nd dim: output height
  // - 3rd dim: output width
  // - 4th dim and beyond: everything else including batch size
  Eigen::DSizes<TensorIndex, internal::traits<Input>::NumDimensions> post_reduce_dims;
  post_reduce_dims[0] = in.dimension(0);
  if (padding_type == PADDING_VALID) {
    post_reduce_dims[idxRows] = Eigen::divup(static_cast<DenseIndex>(in.dimension(idxRows)) - patchRowsEff + 1, strideRows);
    post_reduce_dims[idxCols] = Eigen::divup(static_cast<DenseIndex>(in.dimension(idxCols)) - patchColsEff + 1, strideCols);
  } else {
    post_reduce_dims[idxRows] = Eigen::divup(static_cast<DenseIndex>(in.dimension(idxRows)), strideRows);
    post_reduce_dims[idxCols] = Eigen::divup(static_cast<DenseIndex>(in.dimension(idxCols)), strideCols);
  }
  post_reduce_dims[3] = in.dimension(3);

#if !defined(EIGEN_HAS_INDEX_LIST)
  // nvcc doesn't support cxx11
  Eigen::array<int, 2> reduction_dims;
  if (isColMajor) {
    reduction_dims[0] = 1;
    reduction_dims[1] = 2;
  } else {
    reduction_dims[0] = 2;
    reduction_dims[1] = 3;
  }
#else
  // Take advantage of cxx11 to give the compiler information it can use to
  // optimize the code.
  typename internal::conditional<internal::traits<Input>::Layout == ColMajor, const Eigen::IndexList<Eigen::type2index<1>, Eigen::type2index<2> >, const Eigen::IndexList<Eigen::type2index<2>, Eigen::type2index<3> > >::type reduction_dims;
#endif

  return input.extract_image_patches(patchRows, patchCols, strideRows, strideCols, in_strideRows, in_strideCols, padding_type, -Eigen::NumTraits<typename internal::remove_const<typename internal::traits<Input>::Scalar>::type>::highest()).maximum(reduction_dims).reshape(post_reduce_dims);
}

/** CuboidMaxPooling
  * \ingroup CXX11_NeuralNetworks_Module
  *
  * \brief Applies a max-pooling over a multichannel input volume.
  *
  * The input parameter is expected to be a tensor with a rank of 5 (channels, depth, height, width, others in col-major, and the reverse of that in row-major).
  *
  * The result can be assigned to a tensor of rank equal to the rank of the input. The dimensions of the result will be channels, depth, height, width, and others (in col-major, and the reverse of that if the input was row-major).
  *
  * The order of the depth, width and height dimensions can be swapped if needed.
  *
*/
#if !defined(EIGEN_HAS_INDEX_LIST)
template <typename Input>
EIGEN_ALWAYS_INLINE static const TensorReshapingOp<
    const Eigen::DSizes<DenseIndex, internal::traits<Input>::NumDimensions>,
    const TensorReductionOp<
        internal::MaxReducer<float>, const Eigen::array<int, 1>,
        const TensorReshapingOp<
            const Eigen::DSizes<DenseIndex, 3>,
            const TensorVolumePatchOp<Dynamic, Dynamic, Dynamic, const Input> > > >
#else
template <typename Input>
EIGEN_ALWAYS_INLINE static const TensorReshapingOp<
    const Eigen::DSizes<DenseIndex, internal::traits<Input>::NumDimensions>,
    const TensorReductionOp<
        internal::MaxReducer<float>,
        const Eigen::IndexList<Eigen::type2index<1> >,
        const TensorReshapingOp<
            const Eigen::DSizes<DenseIndex, 3>,
            const TensorVolumePatchOp<Dynamic, Dynamic, Dynamic, const Input> > > >
#endif
CuboidMaxPooling(const Input& input, DenseIndex patchPlanes,
                 DenseIndex patchRows, DenseIndex patchCols,
                 DenseIndex stridePlanes, DenseIndex strideRows,
                 DenseIndex strideCols, const PaddingType padding_type) {
  EIGEN_STATIC_ASSERT(internal::traits<Input>::NumDimensions == 5, YOU_MADE_A_PROGRAMMING_MISTAKE);
  static const bool isColMajor = (internal::traits<Input>::Layout == ColMajor);

  typedef typename internal::traits<Input>::Index TensorIndex;
  TensorRef<Tensor<typename internal::traits<Input>::Scalar, internal::traits<Input>::NumDimensions, internal::traits<Input>::Layout, TensorIndex> > in(input);

  static const int idxPlanes = isColMajor ? 1 : 3;
  static const int idxRows = 2;
  static const int idxCols = isColMajor ? 3 : 1;

  // Molds the output of the reduction into the shape expected by the used
  // (assuming col-major):
  // - 1st dim: channels
  // - 2nd dim: output depth
  // - 3rd dim: output height
  // - 4th dim: output width
  // - 5th dim and beyond: everything else including batch size
  Eigen::DSizes<DenseIndex, internal::traits<Input>::NumDimensions> post_reduce_dims;
  post_reduce_dims[0] = in.dimension(0);
  if (padding_type == PADDING_VALID) {
    post_reduce_dims[idxPlanes] = Eigen::divup(static_cast<DenseIndex>(in.dimension(idxPlanes)) - patchPlanes + 1, stridePlanes);
    post_reduce_dims[idxRows] = Eigen::divup(static_cast<DenseIndex>(in.dimension(idxRows)) - patchRows + 1, strideRows);
    post_reduce_dims[idxCols] = Eigen::divup(static_cast<DenseIndex>(in.dimension(idxCols)) - patchCols + 1, strideCols);
  } else {
    post_reduce_dims[idxPlanes] = Eigen::divup(static_cast<DenseIndex>(in.dimension(idxPlanes)), stridePlanes);
    post_reduce_dims[idxRows] = Eigen::divup(static_cast<DenseIndex>(in.dimension(idxRows)), strideRows);
    post_reduce_dims[idxCols] = Eigen::divup(static_cast<DenseIndex>(in.dimension(idxCols)), strideCols);
  }
  post_reduce_dims[4] = in.dimension(4);

  Eigen::DSizes<DenseIndex, 3> pre_reduce_dims;
  pre_reduce_dims[1] = patchRows * patchCols * patchPlanes;
  if (isColMajor) {
    pre_reduce_dims[0] = post_reduce_dims[0];
    pre_reduce_dims[2] = post_reduce_dims[1] * post_reduce_dims[2] * post_reduce_dims[3] * post_reduce_dims[4];
  } else {
    pre_reduce_dims[0] = post_reduce_dims[0] * post_reduce_dims[1] * post_reduce_dims[2] * post_reduce_dims[3];
    pre_reduce_dims[2] = post_reduce_dims[4];
  }

#if !defined(EIGEN_HAS_INDEX_LIST)
  // nvcc doesn't support cxx11
  Eigen::array<int, 1> reduction_dims;
  reduction_dims[0] = 1;
#else
  // Take advantage of cxx11 to give the compiler information it can use to
  // optimize the code.
  Eigen::IndexList<Eigen::type2index<1> > reduction_dims;
#endif
  return input.extract_volume_patches(patchPlanes, patchRows, patchCols,
                                      stridePlanes, strideRows, strideCols,
                                      padding_type, -Eigen::NumTraits<float>::highest())
      .reshape(pre_reduce_dims)
      .maximum(reduction_dims)
      .reshape(post_reduce_dims);
}


/** SpatialAvgPooling
  * \ingroup CXX11_NeuralNetworks_Module
  *
  * \brief Applies an average pooling over a multichannel input image.
  *
  * The input parameter is expected to be a tensor with a rank of 4 (channels, height, width, others in col-major, and the reverse of that in row-major).
  *
  * The result can be assigned to a tensor of rank equal to the rank of the input. The dimensions of the result will be channels, height, width, and others (in col-major, and the reverse of that if the input was row-major).
  *
  * The order of the width and height dimensions can be swapped if needed.
  *
*/
namespace internal {

template <typename T> struct AvgPoolMeanReducer
{
#if (EIGEN_ARCH_i386 || EIGEN_ARCH_x86_64) && !defined(__CUDACC__)
  // We only support packet access for floats.
  static const bool PacketAccess = internal::is_same<T, float>::value;
#else
  static const bool PacketAccess = false;
#endif
  static const bool IsStateful = true;

  EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE AvgPoolMeanReducer() : scalarCount_(0) {
    typedef typename packet_traits<T>::type Packet;
    packetCount_ = pset1<Packet>(0.0);
  }

  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void reduce(const T t, T* accum) {
    if (t != -Eigen::NumTraits<T>::highest()) {
      (*accum) = (*accum) + t;
      scalarCount_++;
    }
  }

  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE T initialize() const {
    return static_cast<T>(0);
  }

  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE T finalize(const T accum) const {
    eigen_assert(scalarCount_ > 0);
    return accum / scalarCount_;
  }

#if (EIGEN_ARCH_i386 || EIGEN_ARCH_x86_64) && !defined(__CUDACC__)
#ifdef EIGEN_VECTORIZE_AVX512
#define pequal(a, b) \
    _mm512_maskz_set1_epi32(_mm512_cmp_ps_mask(a, b, _CMP_EQ_UQ), -1)
#define psel(a, b, false_mask) _mm512_ternarylogic_epi64(false_mask, a, b, 0xca)
#elif defined EIGEN_VECTORIZE_AVX
#define pequal(a,b) _mm256_cmp_ps(a,b,_CMP_EQ_UQ)
#define psel(a,b,false_mask) _mm256_blendv_ps(a,b,false_mask)
#else
#define pequal(a,b) _mm_cmpeq_ps(a,b)
#define psel(a,b,false_mask) _mm_or_ps(_mm_andnot_ps(false_mask, a), _mm_and_ps(false_mask, b))
#endif

  template <typename Packet>
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void reducePacket(const Packet& p, Packet* accum) {
    reducePacketWithType(static_cast<T>(0), p, accum);
  }

  template <typename Packet>
  void reducePacketWithType(T, const Packet& p, Packet* accum) {
    Packet skip_mask = pequal(p, pset1<Packet>(-Eigen::NumTraits<T>::highest()));
    (*accum) = padd<Packet>(*accum, psel(p, pset1<Packet>(0), skip_mask));
    packetCount_ = padd<Packet>(packetCount_, psel(pset1<Packet>(1), pset1<Packet>(0), skip_mask));
  }

  template <typename Packet>
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet initializePacket() const {
    return pset1<Packet>(0);
  }

  template <typename Packet>
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet finalizePacket(const Packet& vaccum) const {
    return pdiv(vaccum, packetCount_);
  }
  template <typename Packet>
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE T finalizeBoth(const T saccum, const Packet& vaccum) const {
    return (saccum + predux(vaccum)) / (scalarCount_ + predux(packetCount_));
  }
#endif

 protected:
    typedef typename packet_traits<T>::type Packet;
    int scalarCount_;
    Packet packetCount_;
};

}  // namespace internal

#if !defined(EIGEN_HAS_INDEX_LIST)
template <typename Input>
EIGEN_ALWAYS_INLINE
static const TensorReshapingOp<const Eigen::DSizes<typename internal::traits<Input>::Index, internal::traits<Input>::NumDimensions>, const TensorReductionOp<internal::AvgPoolMeanReducer<typename internal::remove_const<typename internal::traits<Input>::Scalar>::type>, const Eigen::array<int, 2>, const TensorImagePatchOp<Dynamic, Dynamic, const Input> > >
#else
template <typename Input>
EIGEN_ALWAYS_INLINE
static const TensorReshapingOp<const Eigen::DSizes<typename internal::traits<Input>::Index, internal::traits<Input>::NumDimensions>, const TensorReductionOp<internal::AvgPoolMeanReducer<typename internal::remove_const<typename internal::traits<Input>::Scalar>::type>, typename internal::conditional<internal::traits<Input>::Layout == ColMajor, const Eigen::IndexList<Eigen::type2index<1>, Eigen::type2index<2> >, const Eigen::IndexList<Eigen::type2index<2>, Eigen::type2index<3> > >::type, const TensorImagePatchOp<Dynamic, Dynamic, const Input> > >
#endif
SpatialAvgPooling(const Input& input, DenseIndex patchRows, DenseIndex patchCols,
                  DenseIndex strideRows, DenseIndex strideCols, const PaddingType padding_type,
                  DenseIndex in_strideRows = 1, DenseIndex in_strideCols = 1)
{
  EIGEN_STATIC_ASSERT(internal::traits<Input>::NumDimensions == 4, YOU_MADE_A_PROGRAMMING_MISTAKE);

  typedef typename internal::traits<Input>::Index TensorIndex;
  TensorRef<Tensor<typename internal::traits<Input>::Scalar, internal::traits<Input>::NumDimensions, internal::traits<Input>::Layout, TensorIndex> > in(input);

  const DenseIndex patchRowsEff = patchRows + (patchRows - 1) * (in_strideRows - 1);
  const DenseIndex patchColsEff = patchCols + (patchCols - 1) * (in_strideCols - 1);

  static const bool isColMajor = (internal::traits<Input>::Layout == ColMajor);
  static const int idxRows = isColMajor ? 1 : 2;
  static const int idxCols = isColMajor ? 2 : 1;

  // Molds the output of the reduction into the shape expected by the user.
  // (assuming col-major):
  // - 1st dim: channels
  // - 2nd dim: output height
  // - 3rd dim: output width
  // - 4th dim and beyond: everything else including batch size
  Eigen::DSizes<TensorIndex, internal::traits<Input>::NumDimensions> post_reduce_dims;
  post_reduce_dims[0] = in.dimension(0);
  if (padding_type == PADDING_VALID) {
    post_reduce_dims[idxRows] = Eigen::divup(static_cast<DenseIndex>(in.dimension(idxRows)) - patchRowsEff + 1, strideRows);
    post_reduce_dims[idxCols] = Eigen::divup(static_cast<DenseIndex>(in.dimension(idxCols)) - patchColsEff + 1, strideCols);
  } else {
    post_reduce_dims[idxRows] = Eigen::divup(static_cast<DenseIndex>(in.dimension(idxRows)), strideRows);
    post_reduce_dims[idxCols] = Eigen::divup(static_cast<DenseIndex>(in.dimension(idxCols)), strideCols);
  }
  post_reduce_dims[3] = in.dimension(3);

  typedef typename internal::remove_const<typename internal::traits<Input>::Scalar>::type CoeffReturnType;
  internal::AvgPoolMeanReducer<CoeffReturnType> mean_with_nan;

#if !defined(EIGEN_HAS_INDEX_LIST)
  // nvcc doesn't support cxx11
  Eigen::array<int, 2> reduction_dims;
  if (isColMajor) {
    reduction_dims[0] = 1;
    reduction_dims[1] = 2;
  } else {
    reduction_dims[0] = 2;
    reduction_dims[1] = 3;
  }
#else
  // Take advantage of cxx11 to give the compiler information it can use to
  // optimize the code.
  typename internal::conditional<internal::traits<Input>::Layout == ColMajor, const Eigen::IndexList<Eigen::type2index<1>, Eigen::type2index<2> >, const Eigen::IndexList<Eigen::type2index<2>, Eigen::type2index<3> > >::type reduction_dims;
#endif
  return input.extract_image_patches(patchRows, patchCols, strideRows, strideCols, in_strideRows, in_strideCols, padding_type, -Eigen::NumTraits<typename internal::remove_const<typename internal::traits<Input>::Scalar>::type>::highest()).reduce(reduction_dims, mean_with_nan).reshape(post_reduce_dims);
}


/** CuboidAvgPooling
  * \ingroup CXX11_NeuralNetworks_Module
  *
  * \brief Applies an average pooling over a multichannel input volume.
  *
  * The input parameter is expected to be a tensor with a rank of 5 (channels, depth, height, width, others, and the reverse of that in row-major).
  *
  * The result can be assigned to a tensor of rank equal to the rank of the input. The dimensions of the result will be channels, depth, width, and others (in col-major, and the reverse of that if the input was row-major).
  *
  * The order of the depth, width and height dimensions can be swapped if needed.
  *
*/
#if !defined(EIGEN_HAS_INDEX_LIST)
template <typename Input>
EIGEN_ALWAYS_INLINE static const TensorReshapingOp<
    const Eigen::DSizes<DenseIndex, internal::traits<Input>::NumDimensions>,
    const TensorReductionOp<
        internal::AvgPoolMeanReducer<float>, const Eigen::array<int, 1>,
        const TensorReshapingOp<
            const Eigen::DSizes<DenseIndex, 3>,
            const TensorVolumePatchOp<Dynamic, Dynamic, Dynamic, const Input> > > >
#else
template <typename Input>
EIGEN_ALWAYS_INLINE static const TensorReshapingOp<
      const Eigen::DSizes<DenseIndex, internal::traits<Input>::NumDimensions>,
      const TensorReductionOp<
          internal::AvgPoolMeanReducer<float>,
          const Eigen::IndexList<Eigen::type2index<1> >,
          const TensorReshapingOp<
              const Eigen::DSizes<DenseIndex, 3>,
              const TensorVolumePatchOp<Dynamic, Dynamic, Dynamic, const Input> > > >
#endif
CuboidAvgPooling(const Input& input, DenseIndex patchPlanes,
                 DenseIndex patchRows, DenseIndex patchCols,
                 DenseIndex stridePlanes, DenseIndex strideRows,
                 DenseIndex strideCols, const PaddingType padding_type) {
  EIGEN_STATIC_ASSERT(internal::traits<Input>::NumDimensions == 5, YOU_MADE_A_PROGRAMMING_MISTAKE);
  static const bool isColMajor = (internal::traits<Input>::Layout == ColMajor);

  typedef typename internal::traits<Input>::Index TensorIndex;
  TensorRef<Tensor<typename internal::traits<Input>::Scalar, internal::traits<Input>::NumDimensions, internal::traits<Input>::Layout, TensorIndex> > in(input);

  static const int idxPlanes = isColMajor ? 1 : 3;
  static const int idxRows = 2;
  static const int idxCols = isColMajor ? 3 : 1;
  // Molds the output of the reduction into the shape expected by the used
  // (assuming col-major):
  // - 1st dim: channels
  // - 2nd dim: outupt depth
  // - 3rd dim: output height
  // - 4th dim: output width
  // - 5th dim and beyond: everything else including batch size
  Eigen::DSizes<DenseIndex, internal::traits<Input>::NumDimensions> post_reduce_dims;
  post_reduce_dims[0] = in.dimension(0);
  if (padding_type == PADDING_VALID) {
    post_reduce_dims[idxPlanes] = Eigen::divup(static_cast<DenseIndex>(in.dimension(idxPlanes)) - patchPlanes + 1, stridePlanes);
    post_reduce_dims[idxRows] = Eigen::divup(static_cast<DenseIndex>(in.dimension(idxRows)) - patchRows + 1, strideRows);
    post_reduce_dims[idxCols] = Eigen::divup(static_cast<DenseIndex>(in.dimension(idxCols)) - patchCols + 1, strideCols);
  } else {
    post_reduce_dims[idxPlanes] = Eigen::divup(static_cast<DenseIndex>(in.dimension(idxPlanes)), stridePlanes);
    post_reduce_dims[idxRows] = Eigen::divup(static_cast<DenseIndex>(in.dimension(idxRows)), strideRows);
    post_reduce_dims[idxCols] = Eigen::divup(static_cast<DenseIndex>(in.dimension(idxCols)), strideCols);
  }
  post_reduce_dims[4] = in.dimension(4);

  Eigen::DSizes<DenseIndex, 3> pre_reduce_dims;
  pre_reduce_dims[1] = patchRows * patchCols * patchPlanes;
  if (isColMajor) {
    pre_reduce_dims[0] = post_reduce_dims[0];
    pre_reduce_dims[2] = post_reduce_dims[1] * post_reduce_dims[2] * post_reduce_dims[3] * post_reduce_dims[4];
  } else {
    pre_reduce_dims[0] = post_reduce_dims[0] * post_reduce_dims[1] * post_reduce_dims[2] * post_reduce_dims[3];
    pre_reduce_dims[2] = post_reduce_dims[4];
  }

  typedef typename internal::remove_const<typename internal::traits<Input>::Scalar>::type CoeffReturnType;
  internal::AvgPoolMeanReducer<CoeffReturnType> mean_with_nan;

#if !defined(EIGEN_HAS_INDEX_LIST)
  // nvcc doesn't support cxx11
  Eigen::array<int, 1> reduction_dims;
  reduction_dims[0] = 1;
#else
  // Take advantage of cxx11 to give the compiler information it can use to
  // optimize the code.
  Eigen::IndexList<Eigen::type2index<1> > reduction_dims;
#endif
  return input.extract_volume_patches(patchPlanes, patchRows, patchCols,
                                      stridePlanes, strideRows, strideCols,
                                      padding_type, -Eigen::NumTraits<float>::highest())
      .reshape(pre_reduce_dims)
      .reduce(reduction_dims, mean_with_nan)
      .reshape(post_reduce_dims);
}

} // end namespace Eigen

#endif // EIGEN_CXX11_NEURAL_NETWORKS_POOLING_H