TensorVolumePatch.h

// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
 
#ifndef EIGEN_CXX11_TENSOR_TENSOR_VOLUME_PATCH_H
#define EIGEN_CXX11_TENSOR_TENSOR_VOLUME_PATCH_H
 
// IWYU pragma: private
#include "./InternalHeaderCheck.h"
 
namespace Eigen {
 
namespace internal {
 
template <DenseIndex Planes, DenseIndex Rows, DenseIndex Cols, typename XprType>
struct traits<TensorVolumePatchOp<Planes, Rows, Cols, XprType> > : public traits<XprType> {
  typedef std::remove_const_t<typename XprType::Scalar> Scalar;
  typedef traits<XprType> XprTraits;
  typedef typename XprTraits::StorageKind StorageKind;
  typedef typename XprTraits::Index Index;
  typedef typename XprType::Nested Nested;
  typedef std::remove_reference_t<Nested> Nested_;
  static constexpr int NumDimensions = XprTraits::NumDimensions + 1;
  static constexpr int Layout = XprTraits::Layout;
  typedef typename XprTraits::PointerType PointerType;
};
 
template <DenseIndex Planes, DenseIndex Rows, DenseIndex Cols, typename XprType>
struct eval<TensorVolumePatchOp<Planes, Rows, Cols, XprType>, Eigen::Dense> {
  typedef const TensorVolumePatchOp<Planes, Rows, Cols, XprType>& type;
};
 
template <DenseIndex Planes, DenseIndex Rows, DenseIndex Cols, typename XprType>
struct nested<TensorVolumePatchOp<Planes, Rows, Cols, XprType>, 1,
              typename eval<TensorVolumePatchOp<Planes, Rows, Cols, XprType> >::type> {
  typedef TensorVolumePatchOp<Planes, Rows, Cols, XprType> type;
};
 
}  // end namespace internal

template <DenseIndex Planes, DenseIndex Rows, DenseIndex Cols, typename XprType>
class TensorVolumePatchOp : public TensorBase<TensorVolumePatchOp<Planes, Rows, Cols, XprType>, ReadOnlyAccessors> {
 public:
  typedef typename Eigen::internal::traits<TensorVolumePatchOp>::Scalar Scalar;
  typedef typename Eigen::NumTraits<Scalar>::Real RealScalar;
  typedef typename XprType::CoeffReturnType CoeffReturnType;
  typedef typename Eigen::internal::nested<TensorVolumePatchOp>::type Nested;
  typedef typename Eigen::internal::traits<TensorVolumePatchOp>::StorageKind StorageKind;
  typedef typename Eigen::internal::traits<TensorVolumePatchOp>::Index Index;
 
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorVolumePatchOp(
      const XprType& expr, DenseIndex patch_planes, DenseIndex patch_rows, DenseIndex patch_cols,
      DenseIndex plane_strides, DenseIndex row_strides, DenseIndex col_strides, DenseIndex in_plane_strides,
      DenseIndex in_row_strides, DenseIndex in_col_strides, DenseIndex plane_inflate_strides,
      DenseIndex row_inflate_strides, DenseIndex col_inflate_strides, PaddingType padding_type, Scalar padding_value)
      : m_xpr(expr),
        m_patch_planes(patch_planes),
        m_patch_rows(patch_rows),
        m_patch_cols(patch_cols),
        m_plane_strides(plane_strides),
        m_row_strides(row_strides),
        m_col_strides(col_strides),
        m_in_plane_strides(in_plane_strides),
        m_in_row_strides(in_row_strides),
        m_in_col_strides(in_col_strides),
        m_plane_inflate_strides(plane_inflate_strides),
        m_row_inflate_strides(row_inflate_strides),
        m_col_inflate_strides(col_inflate_strides),
        m_padding_explicit(false),
        m_padding_top_z(0),
        m_padding_bottom_z(0),
        m_padding_top(0),
        m_padding_bottom(0),
        m_padding_left(0),
        m_padding_right(0),
        m_padding_type(padding_type),
        m_padding_value(padding_value) {}
 
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorVolumePatchOp(
      const XprType& expr, DenseIndex patch_planes, DenseIndex patch_rows, DenseIndex patch_cols,
      DenseIndex plane_strides, DenseIndex row_strides, DenseIndex col_strides, DenseIndex in_plane_strides,
      DenseIndex in_row_strides, DenseIndex in_col_strides, DenseIndex plane_inflate_strides,
      DenseIndex row_inflate_strides, DenseIndex col_inflate_strides, DenseIndex padding_top_z,
      DenseIndex padding_bottom_z, DenseIndex padding_top, DenseIndex padding_bottom, DenseIndex padding_left,
      DenseIndex padding_right, Scalar padding_value)
      : m_xpr(expr),
        m_patch_planes(patch_planes),
        m_patch_rows(patch_rows),
        m_patch_cols(patch_cols),
        m_plane_strides(plane_strides),
        m_row_strides(row_strides),
        m_col_strides(col_strides),
        m_in_plane_strides(in_plane_strides),
        m_in_row_strides(in_row_strides),
        m_in_col_strides(in_col_strides),
        m_plane_inflate_strides(plane_inflate_strides),
        m_row_inflate_strides(row_inflate_strides),
        m_col_inflate_strides(col_inflate_strides),
        m_padding_explicit(true),
        m_padding_top_z(padding_top_z),
        m_padding_bottom_z(padding_bottom_z),
        m_padding_top(padding_top),
        m_padding_bottom(padding_bottom),
        m_padding_left(padding_left),
        m_padding_right(padding_right),
        m_padding_type(PADDING_VALID),
        m_padding_value(padding_value) {}
 
  EIGEN_DEVICE_FUNC DenseIndex patch_planes() const { return m_patch_planes; }
  EIGEN_DEVICE_FUNC DenseIndex patch_rows() const { return m_patch_rows; }
  EIGEN_DEVICE_FUNC DenseIndex patch_cols() const { return m_patch_cols; }
  EIGEN_DEVICE_FUNC DenseIndex plane_strides() const { return m_plane_strides; }
  EIGEN_DEVICE_FUNC DenseIndex row_strides() const { return m_row_strides; }
  EIGEN_DEVICE_FUNC DenseIndex col_strides() const { return m_col_strides; }
  EIGEN_DEVICE_FUNC DenseIndex in_plane_strides() const { return m_in_plane_strides; }
  EIGEN_DEVICE_FUNC DenseIndex in_row_strides() const { return m_in_row_strides; }
  EIGEN_DEVICE_FUNC DenseIndex in_col_strides() const { return m_in_col_strides; }
  EIGEN_DEVICE_FUNC DenseIndex plane_inflate_strides() const { return m_plane_inflate_strides; }
  EIGEN_DEVICE_FUNC DenseIndex row_inflate_strides() const { return m_row_inflate_strides; }
  EIGEN_DEVICE_FUNC DenseIndex col_inflate_strides() const { return m_col_inflate_strides; }
  EIGEN_DEVICE_FUNC bool padding_explicit() const { return m_padding_explicit; }
  EIGEN_DEVICE_FUNC DenseIndex padding_top_z() const { return m_padding_top_z; }
  EIGEN_DEVICE_FUNC DenseIndex padding_bottom_z() const { return m_padding_bottom_z; }
  EIGEN_DEVICE_FUNC DenseIndex padding_top() const { return m_padding_top; }
  EIGEN_DEVICE_FUNC DenseIndex padding_bottom() const { return m_padding_bottom; }
  EIGEN_DEVICE_FUNC DenseIndex padding_left() const { return m_padding_left; }
  EIGEN_DEVICE_FUNC DenseIndex padding_right() const { return m_padding_right; }
  EIGEN_DEVICE_FUNC PaddingType padding_type() const { return m_padding_type; }
  EIGEN_DEVICE_FUNC Scalar padding_value() const { return m_padding_value; }
 
  EIGEN_DEVICE_FUNC const internal::remove_all_t<typename XprType::Nested>& expression() const { return m_xpr; }
 
 protected:
  typename XprType::Nested m_xpr;
  const DenseIndex m_patch_planes;
  const DenseIndex m_patch_rows;
  const DenseIndex m_patch_cols;
  const DenseIndex m_plane_strides;
  const DenseIndex m_row_strides;
  const DenseIndex m_col_strides;
  const DenseIndex m_in_plane_strides;
  const DenseIndex m_in_row_strides;
  const DenseIndex m_in_col_strides;
  const DenseIndex m_plane_inflate_strides;
  const DenseIndex m_row_inflate_strides;
  const DenseIndex m_col_inflate_strides;
  const bool m_padding_explicit;
  const DenseIndex m_padding_top_z;
  const DenseIndex m_padding_bottom_z;
  const DenseIndex m_padding_top;
  const DenseIndex m_padding_bottom;
  const DenseIndex m_padding_left;
  const DenseIndex m_padding_right;
  const PaddingType m_padding_type;
  const Scalar m_padding_value;
};
 
// Eval as rvalue
template <DenseIndex Planes, DenseIndex Rows, DenseIndex Cols, typename ArgType, typename Device>
struct TensorEvaluator<const TensorVolumePatchOp<Planes, Rows, Cols, ArgType>, Device> {
  typedef TensorVolumePatchOp<Planes, Rows, Cols, ArgType> XprType;
  typedef typename XprType::Index Index;
  static constexpr int NumInputDims =
      internal::array_size<typename TensorEvaluator<ArgType, Device>::Dimensions>::value;
  static constexpr int NumDims = NumInputDims + 1;
  typedef DSizes<Index, NumDims> Dimensions;
  typedef std::remove_const_t<typename XprType::Scalar> Scalar;
  typedef typename XprType::CoeffReturnType CoeffReturnType;
  typedef typename PacketType<CoeffReturnType, Device>::type PacketReturnType;
  static constexpr int PacketSize = PacketType<CoeffReturnType, Device>::size;
  typedef StorageMemory<CoeffReturnType, Device> Storage;
  typedef typename Storage::Type EvaluatorPointerType;
 
  static constexpr int Layout = TensorEvaluator<ArgType, Device>::Layout;
  enum {
    IsAligned = false,
    PacketAccess = TensorEvaluator<ArgType, Device>::PacketAccess,
    BlockAccess = false,
    PreferBlockAccess = TensorEvaluator<ArgType, Device>::PreferBlockAccess,
    CoordAccess = false,
    RawAccess = false
  };
 
  //===- Tensor block evaluation strategy (see TensorBlock.h) -------------===//
  typedef internal::TensorBlockNotImplemented TensorBlock;
  //===--------------------------------------------------------------------===//
 
  EIGEN_STRONG_INLINE TensorEvaluator(const XprType& op, const Device& device) : m_impl(op.expression(), device) {
    EIGEN_STATIC_ASSERT((NumDims >= 5), YOU_MADE_A_PROGRAMMING_MISTAKE);
 
    m_paddingValue = op.padding_value();
 
    const typename TensorEvaluator<ArgType, Device>::Dimensions& input_dims = m_impl.dimensions();
 
    // Cache a few variables.
    if (static_cast<int>(Layout) == static_cast<int>(ColMajor)) {
      m_inputDepth = input_dims[0];
      m_inputPlanes = input_dims[1];
      m_inputRows = input_dims[2];
      m_inputCols = input_dims[3];
    } else {
      m_inputDepth = input_dims[NumInputDims - 1];
      m_inputPlanes = input_dims[NumInputDims - 2];
      m_inputRows = input_dims[NumInputDims - 3];
      m_inputCols = input_dims[NumInputDims - 4];
    }
 
    m_plane_strides = op.plane_strides();
    m_row_strides = op.row_strides();
    m_col_strides = op.col_strides();
 
    // Input strides and effective input/patch size
    m_in_plane_strides = op.in_plane_strides();
    m_in_row_strides = op.in_row_strides();
    m_in_col_strides = op.in_col_strides();
    m_plane_inflate_strides = op.plane_inflate_strides();
    m_row_inflate_strides = op.row_inflate_strides();
    m_col_inflate_strides = op.col_inflate_strides();
 
    // The "effective" spatial size after inflating data with zeros.
    m_input_planes_eff = (m_inputPlanes - 1) * m_plane_inflate_strides + 1;
    m_input_rows_eff = (m_inputRows - 1) * m_row_inflate_strides + 1;
    m_input_cols_eff = (m_inputCols - 1) * m_col_inflate_strides + 1;
    m_patch_planes_eff = op.patch_planes() + (op.patch_planes() - 1) * (m_in_plane_strides - 1);
    m_patch_rows_eff = op.patch_rows() + (op.patch_rows() - 1) * (m_in_row_strides - 1);
    m_patch_cols_eff = op.patch_cols() + (op.patch_cols() - 1) * (m_in_col_strides - 1);
 
    if (op.padding_explicit()) {
      m_outputPlanes =
          numext::ceil((m_input_planes_eff + op.padding_top_z() + op.padding_bottom_z() - m_patch_planes_eff + 1.f) /
                       static_cast<float>(m_plane_strides));
      m_outputRows = numext::ceil((m_input_rows_eff + op.padding_top() + op.padding_bottom() - m_patch_rows_eff + 1.f) /
                                  static_cast<float>(m_row_strides));
      m_outputCols = numext::ceil((m_input_cols_eff + op.padding_left() + op.padding_right() - m_patch_cols_eff + 1.f) /
                                  static_cast<float>(m_col_strides));
      m_planePaddingTop = op.padding_top_z();
      m_rowPaddingTop = op.padding_top();
      m_colPaddingLeft = op.padding_left();
    } else {
      // Computing padding from the type
      switch (op.padding_type()) {
        case PADDING_VALID:
          m_outputPlanes =
              numext::ceil((m_input_planes_eff - m_patch_planes_eff + 1.f) / static_cast<float>(m_plane_strides));
          m_outputRows = numext::ceil((m_input_rows_eff - m_patch_rows_eff + 1.f) / static_cast<float>(m_row_strides));
          m_outputCols = numext::ceil((m_input_cols_eff - m_patch_cols_eff + 1.f) / static_cast<float>(m_col_strides));
          m_planePaddingTop = 0;
          m_rowPaddingTop = 0;
          m_colPaddingLeft = 0;
          break;
        case PADDING_SAME: {
          m_outputPlanes = numext::ceil(m_input_planes_eff / static_cast<float>(m_plane_strides));
          m_outputRows = numext::ceil(m_input_rows_eff / static_cast<float>(m_row_strides));
          m_outputCols = numext::ceil(m_input_cols_eff / static_cast<float>(m_col_strides));
          const Index dz = (m_outputPlanes - 1) * m_plane_strides + m_patch_planes_eff - m_input_planes_eff;
          const Index dy = (m_outputRows - 1) * m_row_strides + m_patch_rows_eff - m_input_rows_eff;
          const Index dx = (m_outputCols - 1) * m_col_strides + m_patch_cols_eff - m_input_cols_eff;
          m_planePaddingTop = dz / 2;
          m_rowPaddingTop = dy / 2;
          m_colPaddingLeft = dx / 2;
          break;
        }
        default: {
          eigen_assert(false && "unexpected padding");
          return;
        }
      }
    }
    eigen_assert(m_outputRows > 0);
    eigen_assert(m_outputCols > 0);
    eigen_assert(m_outputPlanes > 0);
 
    // Dimensions for result of extraction.
    if (static_cast<int>(Layout) == static_cast<int>(ColMajor)) {
      // ColMajor
      // 0: depth
      // 1: patch_planes
      // 2: patch_rows
      // 3: patch_cols
      // 4: number of patches
      // 5 and beyond: anything else (such as batch).
      m_dimensions[0] = input_dims[0];
      m_dimensions[1] = op.patch_planes();
      m_dimensions[2] = op.patch_rows();
      m_dimensions[3] = op.patch_cols();
      m_dimensions[4] = m_outputPlanes * m_outputRows * m_outputCols;
      for (int i = 5; i < NumDims; ++i) {
        m_dimensions[i] = input_dims[i - 1];
      }
    } else {
      // RowMajor
      // NumDims-1: depth
      // NumDims-2: patch_planes
      // NumDims-3: patch_rows
      // NumDims-4: patch_cols
      // NumDims-5: number of patches
      // NumDims-6 and beyond: anything else (such as batch).
      m_dimensions[NumDims - 1] = input_dims[NumInputDims - 1];
      m_dimensions[NumDims - 2] = op.patch_planes();
      m_dimensions[NumDims - 3] = op.patch_rows();
      m_dimensions[NumDims - 4] = op.patch_cols();
      m_dimensions[NumDims - 5] = m_outputPlanes * m_outputRows * m_outputCols;
      for (int i = NumDims - 6; i >= 0; --i) {
        m_dimensions[i] = input_dims[i];
      }
    }
 
    // Strides for the output tensor.
    if (static_cast<int>(Layout) == static_cast<int>(ColMajor)) {
      m_rowStride = m_dimensions[1];
      m_colStride = m_dimensions[2] * m_rowStride;
      m_patchStride = m_colStride * m_dimensions[3] * m_dimensions[0];
      m_otherStride = m_patchStride * m_dimensions[4];
    } else {
      m_rowStride = m_dimensions[NumDims - 2];
      m_colStride = m_dimensions[NumDims - 3] * m_rowStride;
      m_patchStride = m_colStride * m_dimensions[NumDims - 4] * m_dimensions[NumDims - 1];
      m_otherStride = m_patchStride * m_dimensions[NumDims - 5];
    }
 
    // Strides for navigating through the input tensor.
    m_planeInputStride = m_inputDepth;
    m_rowInputStride = m_inputDepth * m_inputPlanes;
    m_colInputStride = m_inputDepth * m_inputRows * m_inputPlanes;
    m_otherInputStride = m_inputDepth * m_inputRows * m_inputCols * m_inputPlanes;
 
    m_outputPlanesRows = m_outputPlanes * m_outputRows;
 
    // Fast representations of different variables.
    m_fastOtherStride = internal::TensorIntDivisor<Index>(m_otherStride);
 
    m_fastPatchStride = internal::TensorIntDivisor<Index>(m_patchStride);
    m_fastColStride = internal::TensorIntDivisor<Index>(m_colStride);
    m_fastRowStride = internal::TensorIntDivisor<Index>(m_rowStride);
    m_fastInputRowStride = internal::TensorIntDivisor<Index>(m_row_inflate_strides);
    m_fastInputColStride = internal::TensorIntDivisor<Index>(m_col_inflate_strides);
    m_fastInputPlaneStride = internal::TensorIntDivisor<Index>(m_plane_inflate_strides);
    m_fastInputColsEff = internal::TensorIntDivisor<Index>(m_input_cols_eff);
    m_fastOutputPlanes = internal::TensorIntDivisor<Index>(m_outputPlanes);
    m_fastOutputPlanesRows = internal::TensorIntDivisor<Index>(m_outputPlanesRows);
 
    if (static_cast<int>(Layout) == static_cast<int>(ColMajor)) {
      m_fastOutputDepth = internal::TensorIntDivisor<Index>(m_dimensions[0]);
    } else {
      m_fastOutputDepth = internal::TensorIntDivisor<Index>(m_dimensions[NumDims - 1]);
    }
  }
 
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Dimensions& dimensions() const { return m_dimensions; }
 
  EIGEN_STRONG_INLINE bool evalSubExprsIfNeeded(EvaluatorPointerType /*data*/) {
    m_impl.evalSubExprsIfNeeded(NULL);
    return true;
  }
 
#ifdef EIGEN_USE_THREADS
  template <typename EvalSubExprsCallback>
  EIGEN_STRONG_INLINE void evalSubExprsIfNeededAsync(EvaluatorPointerType /*data*/, EvalSubExprsCallback done) {
    m_impl.evalSubExprsIfNeededAsync(nullptr, [done](bool) { done(true); });
  }
#endif  // EIGEN_USE_THREADS
 
  EIGEN_STRONG_INLINE void cleanup() { m_impl.cleanup(); }
 
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE CoeffReturnType coeff(Index index) const {
    // Patch index corresponding to the passed in index.
    const Index patchIndex = index / m_fastPatchStride;
 
    // Spatial offset within the patch. This has to be translated into 3D
    // coordinates within the patch.
    const Index patchOffset = (index - patchIndex * m_patchStride) / m_fastOutputDepth;
 
    // Batch, etc.
    const Index otherIndex = (NumDims == 5) ? 0 : index / m_fastOtherStride;
    const Index patch3DIndex = (NumDims == 5) ? patchIndex : (index - otherIndex * m_otherStride) / m_fastPatchStride;
 
    // Calculate column index in the input original tensor.
    const Index colIndex = patch3DIndex / m_fastOutputPlanesRows;
    const Index colOffset = patchOffset / m_fastColStride;
    const Index inputCol = colIndex * m_col_strides + colOffset * m_in_col_strides - m_colPaddingLeft;
    const Index origInputCol =
        (m_col_inflate_strides == 1) ? inputCol : ((inputCol >= 0) ? (inputCol / m_fastInputColStride) : 0);
    if (inputCol < 0 || inputCol >= m_input_cols_eff ||
        ((m_col_inflate_strides != 1) && (inputCol != origInputCol * m_col_inflate_strides))) {
      return Scalar(m_paddingValue);
    }
 
    // Calculate row index in the original input tensor.
    const Index rowIndex = (patch3DIndex - colIndex * m_outputPlanesRows) / m_fastOutputPlanes;
    const Index rowOffset = (patchOffset - colOffset * m_colStride) / m_fastRowStride;
    const Index inputRow = rowIndex * m_row_strides + rowOffset * m_in_row_strides - m_rowPaddingTop;
    const Index origInputRow =
        (m_row_inflate_strides == 1) ? inputRow : ((inputRow >= 0) ? (inputRow / m_fastInputRowStride) : 0);
    if (inputRow < 0 || inputRow >= m_input_rows_eff ||
        ((m_row_inflate_strides != 1) && (inputRow != origInputRow * m_row_inflate_strides))) {
      return Scalar(m_paddingValue);
    }
 
    // Calculate plane index in the original input tensor.
    const Index planeIndex = (patch3DIndex - m_outputPlanes * (colIndex * m_outputRows + rowIndex));
    const Index planeOffset = patchOffset - colOffset * m_colStride - rowOffset * m_rowStride;
    const Index inputPlane = planeIndex * m_plane_strides + planeOffset * m_in_plane_strides - m_planePaddingTop;
    const Index origInputPlane =
        (m_plane_inflate_strides == 1) ? inputPlane : ((inputPlane >= 0) ? (inputPlane / m_fastInputPlaneStride) : 0);
    if (inputPlane < 0 || inputPlane >= m_input_planes_eff ||
        ((m_plane_inflate_strides != 1) && (inputPlane != origInputPlane * m_plane_inflate_strides))) {
      return Scalar(m_paddingValue);
    }
 
    const int depth_index = static_cast<int>(Layout) == static_cast<int>(ColMajor) ? 0 : NumDims - 1;
    const Index depth = index - (index / m_fastOutputDepth) * m_dimensions[depth_index];
 
    const Index inputIndex = depth + origInputRow * m_rowInputStride + origInputCol * m_colInputStride +
                             origInputPlane * m_planeInputStride + otherIndex * m_otherInputStride;
 
    return m_impl.coeff(inputIndex);
  }
 
  template <int LoadMode>
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE PacketReturnType packet(Index index) const {
    eigen_assert(index + PacketSize - 1 < dimensions().TotalSize());
 
    if (m_in_row_strides != 1 || m_in_col_strides != 1 || m_row_inflate_strides != 1 || m_col_inflate_strides != 1 ||
        m_in_plane_strides != 1 || m_plane_inflate_strides != 1) {
      return packetWithPossibleZero(index);
    }
 
    const Index indices[2] = {index, index + PacketSize - 1};
    const Index patchIndex = indices[0] / m_fastPatchStride;
    if (patchIndex != indices[1] / m_fastPatchStride) {
      return packetWithPossibleZero(index);
    }
    const Index otherIndex = (NumDims == 5) ? 0 : indices[0] / m_fastOtherStride;
    eigen_assert(otherIndex == indices[1] / m_fastOtherStride);
 
    // Find the offset of the element wrt the location of the first element.
    Index first_entry = (indices[0] - patchIndex * m_patchStride) / m_fastOutputDepth;
    Index second_entry = PacketSize == 1 ? first_entry : 
                        (indices[1] - patchIndex * m_patchStride) / m_fastOutputDepth;
 
    const Index patchOffsets[2] = {first_entry, second_entry};
 
    const Index patch3DIndex =
        (NumDims == 5) ? patchIndex : (indices[0] - otherIndex * m_otherStride) / m_fastPatchStride;
    eigen_assert(patch3DIndex == (indices[1] - otherIndex * m_otherStride) / m_fastPatchStride);
 
    const Index colIndex = patch3DIndex / m_fastOutputPlanesRows;
    const Index colOffsets[2] = {patchOffsets[0] / m_fastColStride, patchOffsets[1] / m_fastColStride};
 
    // Calculate col indices in the original input tensor.
    const Index inputCols[2] = {colIndex * m_col_strides + colOffsets[0] - m_colPaddingLeft,
                                colIndex * m_col_strides + colOffsets[1] - m_colPaddingLeft};
    if (inputCols[1] < 0 || inputCols[0] >= m_inputCols) {
      return internal::pset1<PacketReturnType>(Scalar(m_paddingValue));
    }
 
    if (inputCols[0] != inputCols[1]) {
      return packetWithPossibleZero(index);
    }
 
    const Index rowIndex = (patch3DIndex - colIndex * m_outputPlanesRows) / m_fastOutputPlanes;
    const Index rowOffsets[2] = {(patchOffsets[0] - colOffsets[0] * m_colStride) / m_fastRowStride,
                                 (patchOffsets[1] - colOffsets[1] * m_colStride) / m_fastRowStride};
    eigen_assert(rowOffsets[0] <= rowOffsets[1]);
    // Calculate col indices in the original input tensor.
    const Index inputRows[2] = {rowIndex * m_row_strides + rowOffsets[0] - m_rowPaddingTop,
                                rowIndex * m_row_strides + rowOffsets[1] - m_rowPaddingTop};
 
    if (inputRows[1] < 0 || inputRows[0] >= m_inputRows) {
      return internal::pset1<PacketReturnType>(Scalar(m_paddingValue));
    }
 
    if (inputRows[0] != inputRows[1]) {
      return packetWithPossibleZero(index);
    }
 
    const Index planeIndex = (patch3DIndex - m_outputPlanes * (colIndex * m_outputRows + rowIndex));
    const Index planeOffsets[2] = {patchOffsets[0] - colOffsets[0] * m_colStride - rowOffsets[0] * m_rowStride,
                                   patchOffsets[1] - colOffsets[1] * m_colStride - rowOffsets[1] * m_rowStride};
    eigen_assert(planeOffsets[0] <= planeOffsets[1]);
    const Index inputPlanes[2] = {planeIndex * m_plane_strides + planeOffsets[0] - m_planePaddingTop,
                                  planeIndex * m_plane_strides + planeOffsets[1] - m_planePaddingTop};
 
    if (inputPlanes[1] < 0 || inputPlanes[0] >= m_inputPlanes) {
      return internal::pset1<PacketReturnType>(Scalar(m_paddingValue));
    }
 
    if (inputPlanes[0] >= 0 && inputPlanes[1] < m_inputPlanes) {
      // no padding
      const int depth_index = static_cast<int>(Layout) == static_cast<int>(ColMajor) ? 0 : NumDims - 1;
      const Index depth = index - (index / m_fastOutputDepth) * m_dimensions[depth_index];
      const Index inputIndex = depth + inputRows[0] * m_rowInputStride + inputCols[0] * m_colInputStride +
                               m_planeInputStride * inputPlanes[0] + otherIndex * m_otherInputStride;
      return m_impl.template packet<Unaligned>(inputIndex);
    }
 
    return packetWithPossibleZero(index);
  }
 
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorOpCost costPerCoeff(bool vectorized) const {
    const double compute_cost =
        10 * TensorOpCost::DivCost<Index>() + 21 * TensorOpCost::MulCost<Index>() + 8 * TensorOpCost::AddCost<Index>();
    return TensorOpCost(0, 0, compute_cost, vectorized, PacketSize);
  }
 
  EIGEN_DEVICE_FUNC EvaluatorPointerType data() const { return NULL; }
 
  const TensorEvaluator<ArgType, Device>& impl() const { return m_impl; }
 
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Index planePaddingTop() const { return m_planePaddingTop; }
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Index rowPaddingTop() const { return m_rowPaddingTop; }
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Index colPaddingLeft() const { return m_colPaddingLeft; }
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Index outputPlanes() const { return m_outputPlanes; }
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Index outputRows() const { return m_outputRows; }
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Index outputCols() const { return m_outputCols; }
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Index userPlaneStride() const { return m_plane_strides; }
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Index userRowStride() const { return m_row_strides; }
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Index userColStride() const { return m_col_strides; }
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Index userInPlaneStride() const { return m_in_plane_strides; }
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Index userInRowStride() const { return m_in_row_strides; }
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Index userInColStride() const { return m_in_col_strides; }
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Index planeInflateStride() const { return m_plane_inflate_strides; }
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Index rowInflateStride() const { return m_row_inflate_strides; }
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Index colInflateStride() const { return m_col_inflate_strides; }
 
 protected:
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE PacketReturnType packetWithPossibleZero(Index index) const {
    EIGEN_ALIGN_MAX std::remove_const_t<CoeffReturnType> values[PacketSize];
    EIGEN_UNROLL_LOOP
    for (int i = 0; i < PacketSize; ++i) {
      values[i] = coeff(index + i);
    }
    PacketReturnType rslt = internal::pload<PacketReturnType>(values);
    return rslt;
  }
 
  Dimensions m_dimensions;
 
  // Parameters passed to the constructor.
  Index m_plane_strides;
  Index m_row_strides;
  Index m_col_strides;
 
  Index m_outputPlanes;
  Index m_outputRows;
  Index m_outputCols;
 
  Index m_planePaddingTop;
  Index m_rowPaddingTop;
  Index m_colPaddingLeft;
 
  Index m_in_plane_strides;
  Index m_in_row_strides;
  Index m_in_col_strides;
 
  Index m_plane_inflate_strides;
  Index m_row_inflate_strides;
  Index m_col_inflate_strides;
 
  // Cached input size.
  Index m_inputDepth;
  Index m_inputPlanes;
  Index m_inputRows;
  Index m_inputCols;
 
  // Other cached variables.
  Index m_outputPlanesRows;
 
  // Effective input/patch post-inflation size.
  Index m_input_planes_eff;
  Index m_input_rows_eff;
  Index m_input_cols_eff;
  Index m_patch_planes_eff;
  Index m_patch_rows_eff;
  Index m_patch_cols_eff;
 
  // Strides for the output tensor.
  Index m_otherStride;
  Index m_patchStride;
  Index m_rowStride;
  Index m_colStride;
 
  // Strides for the input tensor.
  Index m_planeInputStride;
  Index m_rowInputStride;
  Index m_colInputStride;
  Index m_otherInputStride;
 
  internal::TensorIntDivisor<Index> m_fastOtherStride;
  internal::TensorIntDivisor<Index> m_fastPatchStride;
  internal::TensorIntDivisor<Index> m_fastColStride;
  internal::TensorIntDivisor<Index> m_fastRowStride;
  internal::TensorIntDivisor<Index> m_fastInputPlaneStride;
  internal::TensorIntDivisor<Index> m_fastInputRowStride;
  internal::TensorIntDivisor<Index> m_fastInputColStride;
  internal::TensorIntDivisor<Index> m_fastInputColsEff;
  internal::TensorIntDivisor<Index> m_fastOutputPlanesRows;
  internal::TensorIntDivisor<Index> m_fastOutputPlanes;
  internal::TensorIntDivisor<Index> m_fastOutputDepth;
 
  Scalar m_paddingValue;
 
  TensorEvaluator<ArgType, Device> m_impl;
};
 
}  // end namespace Eigen
 
#endif  // EIGEN_CXX11_TENSOR_TENSOR_VOLUME_PATCH_H