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-// 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] = numext::ceil((in.dimension(idxRows) - patchRowsEff + 1.f) / static_cast<float>(strideRows));
- post_reduce_dims[idxCols] = numext::ceil((in.dimension(idxCols) - patchColsEff + 1.f) / static_cast<float>(strideCols));
- } else {
- post_reduce_dims[idxRows] = numext::ceil(in.dimension(idxRows) / static_cast<float>(strideRows));
- post_reduce_dims[idxCols] = numext::ceil(in.dimension(idxCols) / static_cast<float>(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] = numext::ceil((in.dimension(idxPlanes) - patchPlanes + 1.f) / static_cast<float>(stridePlanes));
- post_reduce_dims[idxRows] = numext::ceil((in.dimension(idxRows) - patchRows + 1.f) / static_cast<float>(strideRows));
- post_reduce_dims[idxCols] = numext::ceil((in.dimension(idxCols) - patchCols + 1.f) / static_cast<float>(strideCols));
- } else {
- post_reduce_dims[idxPlanes] = numext::ceil(in.dimension(idxPlanes) / static_cast<float>(stridePlanes));
- post_reduce_dims[idxRows] = numext::ceil(in.dimension(idxRows) / static_cast<float>(strideRows));
- post_reduce_dims[idxCols] = numext::ceil(in.dimension(idxCols) / static_cast<float>(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_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] = numext::ceil((in.dimension(idxRows) - patchRowsEff + 1.f) / static_cast<float>(strideRows));
- post_reduce_dims[idxCols] = numext::ceil((in.dimension(idxCols) - patchColsEff + 1.f) / static_cast<float>(strideCols));
- } else {
- post_reduce_dims[idxRows] = numext::ceil(in.dimension(idxRows) / static_cast<float>(strideRows));
- post_reduce_dims[idxCols] = numext::ceil(in.dimension(idxCols) / static_cast<float>(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] = numext::ceil((in.dimension(idxPlanes) - patchPlanes + 1.f) / static_cast<float>(stridePlanes));
- post_reduce_dims[idxRows] = numext::ceil((in.dimension(idxRows) - patchRows + 1.f) / static_cast<float>(strideRows));
- post_reduce_dims[idxCols] = numext::ceil((in.dimension(idxCols) - patchCols + 1.f) / static_cast<float>(strideCols));
- } else {
- post_reduce_dims[idxPlanes] = numext::ceil(in.dimension(idxPlanes) / static_cast<float>(stridePlanes));
- post_reduce_dims[idxRows] = numext::ceil(in.dimension(idxRows) / static_cast<float>(strideRows));
- post_reduce_dims[idxCols] = numext::ceil(in.dimension(idxCols) / static_cast<float>(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