梳理caffe代码base_conv_layer（十八）

这个是实现卷积的基类。

base_conv_layer.hpp

#ifndef CAFFE_BASE_CONVOLUTION_LAYER_HPP_
#define CAFFE_BASE_CONVOLUTION_LAYER_HPP_

#include <vector>

#include "caffe/blob.hpp"
#include "caffe/layer.hpp"
#include "caffe/proto/caffe.pb.h"
#include "caffe/util/im2col.hpp"

namespace caffe {

/**
 * @brief Abstract base class that factors out the BLAS code common to
 *        ConvolutionLayer and DeconvolutionLayer.
 */
template <typename Dtype>
class BaseConvolutionLayer : public Layer<Dtype> {
 public:
  explicit BaseConvolutionLayer(const LayerParameter& param)
      : Layer<Dtype>(param) {}
  virtual void LayerSetUp(const vector<Blob<Dtype>*>& bottom,
      const vector<Blob<Dtype>*>& top);
  virtual void Reshape(const vector<Blob<Dtype>*>& bottom,
      const vector<Blob<Dtype>*>& top);

  virtual inline int MinBottomBlobs() const { return 1; }
  virtual inline int MinTopBlobs() const { return 1; }
  virtual inline bool EqualNumBottomTopBlobs() const { return true; }

 protected:
  // Helper functions that abstract away the column buffer and gemm arguments.
  // The last argument in forward_cpu_gemm is so that we can skip the im2col if
  // we just called weight_cpu_gemm with the same input.
  void forward_cpu_gemm(const Dtype* input, const Dtype* weights,
      Dtype* output, bool skip_im2col = false);
  void forward_cpu_bias(Dtype* output, const Dtype* bias);
  void backward_cpu_gemm(const Dtype* input, const Dtype* weights,
      Dtype* output);
  void weight_cpu_gemm(const Dtype* input, const Dtype* output, Dtype*
      weights);
  void backward_cpu_bias(Dtype* bias, const Dtype* input);

#ifndef CPU_ONLY
  void forward_gpu_gemm(const Dtype* col_input, const Dtype* weights,
      Dtype* output, bool skip_im2col = false);
  void forward_gpu_bias(Dtype* output, const Dtype* bias);
  void backward_gpu_gemm(const Dtype* input, const Dtype* weights,
      Dtype* col_output);
  void weight_gpu_gemm(const Dtype* col_input, const Dtype* output, Dtype*
      weights);
  void backward_gpu_bias(Dtype* bias, const Dtype* input);
#endif

  /// @brief The spatial dimensions of the input.
  inline int input_shape(int i) {
    return (*bottom_shape_)[channel_axis_ + i];
  }
  // reverse_dimensions should return true iff we are implementing deconv, so
  // that conv helpers know which dimensions are which.
  virtual bool reverse_dimensions() = 0;
  // Compute height_out_ and width_out_ from other parameters.
  virtual void compute_output_shape() = 0;

  /// @brief The spatial dimensions of a filter kernel.
  // kernel的形状 = [kernel_h, kernel_w]
  Blob<int> kernel_shape_;
  /// @brief The spatial dimensions of the stride.
  // 步长形状 = [stride_h, stride_w]
  Blob<int> stride_;
  /// @brief The spatial dimensions of the padding.
  // pad的形状 = [pad_h, pad_w]
  Blob<int> pad_;
  /// @brief The spatial dimensions of the convolution input.
  // 卷积的输入形状 = [输入图像通道数, 输入图像h,    输入图像w]
  Blob<int> conv_input_shape_;
  /// @brief The spatial dimensions of the col_buffer.
  // col_buffer的形状 = [kernel_dim_, conv_out_spatial_dim_ ]
  vector<int> col_buffer_shape_;
  /// @brief The spatial dimensions of the output.
  // 输出的形状
  vector<int> output_shape_;
  // 输入的形状
  const vector<int>* bottom_shape_;
  // 空间轴个数
  int num_spatial_axes_;
  // 输入度维度 = 输入图像通道数*输入图像的h*输入图像w
  int bottom_dim_;
  // 输出维度 = 输出通道数*输出h*输出w
  int top_dim_;
  // 输入图像的第几个轴是通道
  int channel_axis_;
  // batchsize
  int num_;
  // 输入图像的通道数
  int channels_;
  // 卷积组的大小
  int group_;
  // 输出空间维度 = 卷积之后的图像长*卷积之后图像的宽
  int out_spatial_dim_;
  // 使用卷积组用到的
  int weight_offset_;
  // 卷积后的图像的通道数
  int num_output_;
  // 是否启用偏置
  bool bias_term_;
  // 是不是1x1卷积
  bool is_1x1_;
  // 强制使用n维通用卷积
  bool force_nd_im2col_;
  // conv_in_channels_ * conv_out_spatial_dim_
  int num_kernels_im2col_;
  // num_kernels_col2im_ = reverse_dimensions() ? top_dim_ : bottom_dim_
  int num_kernels_col2im_;
  // 卷积的输出通道数 ,在参数配置文件中设置
  int conv_out_channels_;
  // 卷积的输入通道数 （即输入图像的通道数）
  int conv_in_channels_;
  // 卷积的输出的空间维度 = 卷积后图像h*卷积后图像w
  int conv_out_spatial_dim_;
  // 卷积核的维度 = 输入图像的维度*卷积核的h*卷积核的w
  int kernel_dim_;
  // 在使用gropu参数的时候使用的offset
  int col_offset_;
  int output_offset_;
  // im2col的时候使用的存储空间
  Blob<Dtype> col_buffer_;
  // 将偏置扩展成矩阵的东东
  Blob<Dtype> bias_multiplier_;

 private:
  // wrap im2col/col2im so we don't have to remember the (long) argument lists
  inline void conv_im2col_cpu(const Dtype* data, Dtype* col_buff) {
    if (!force_nd_im2col_ && num_spatial_axes_ == 2) {
      im2col_cpu(data, conv_in_channels_,
          conv_input_shape_.cpu_data()[1], conv_input_shape_.cpu_data()[2],
          kernel_shape_.cpu_data()[0], kernel_shape_.cpu_data()[1],
          pad_.cpu_data()[0], pad_.cpu_data()[1],
          stride_.cpu_data()[0], stride_.cpu_data()[1],
          dilation_.cpu_data()[0], dilation_.cpu_data()[1], col_buff);
    } else {
      im2col_nd_cpu(data, num_spatial_axes_, conv_input_shape_.cpu_data(),
          col_buffer_shape_.data(), kernel_shape_.cpu_data(),
          pad_.cpu_data(), stride_.cpu_data(), dilation_.cpu_data(), col_buff);
    }
  }
  inline void conv_col2im_cpu(const Dtype* col_buff, Dtype* data) {
    if (!force_nd_im2col_ && num_spatial_axes_ == 2) {
      col2im_cpu(col_buff, conv_in_channels_,
          conv_input_shape_.cpu_data()[1], conv_input_shape_.cpu_data()[2],
          kernel_shape_.cpu_data()[0], kernel_shape_.cpu_data()[1],
          pad_.cpu_data()[0], pad_.cpu_data()[1],
          stride_.cpu_data()[0], stride_.cpu_data()[1],
          dilation_.cpu_data()[0], dilation_.cpu_data()[1], data);
    } else {
      col2im_nd_cpu(col_buff, num_spatial_axes_, conv_input_shape_.cpu_data(),
          col_buffer_shape_.data(), kernel_shape_.cpu_data(),
          pad_.cpu_data(), stride_.cpu_data(), dilation_.cpu_data(), data);
    }
  }
#ifndef CPU_ONLY
  inline void conv_im2col_gpu(const Dtype* data, Dtype* col_buff) {
    if (!force_nd_im2col_ && num_spatial_axes_ == 2) {
      im2col_gpu(data, conv_in_channels_,
          conv_input_shape_.cpu_data()[1], conv_input_shape_.cpu_data()[2],
          kernel_shape_.cpu_data()[0], kernel_shape_.cpu_data()[1],
          pad_.cpu_data()[0], pad_.cpu_data()[1],
          stride_.cpu_data()[0], stride_.cpu_data()[1],
          dilation_.cpu_data()[0], dilation_.cpu_data()[1], col_buff);
    } else {
      im2col_nd_gpu(data, num_spatial_axes_, num_kernels_im2col_,
          conv_input_shape_.gpu_data(), col_buffer_.gpu_shape(),
          kernel_shape_.gpu_data(), pad_.gpu_data(),
          stride_.gpu_data(), dilation_.gpu_data(), col_buff);
    }
  }
  inline void conv_col2im_gpu(const Dtype* col_buff, Dtype* data) {
    if (!force_nd_im2col_ && num_spatial_axes_ == 2) {
      col2im_gpu(col_buff, conv_in_channels_,
          conv_input_shape_.cpu_data()[1], conv_input_shape_.cpu_data()[2],
          kernel_shape_.cpu_data()[0], kernel_shape_.cpu_data()[1],
          pad_.cpu_data()[0], pad_.cpu_data()[1],
          stride_.cpu_data()[0], stride_.cpu_data()[1],
          dilation_.cpu_data()[0], dilation_.cpu_data()[1], data);
    } else {
      col2im_nd_gpu(col_buff, num_spatial_axes_, num_kernels_col2im_,
          conv_input_shape_.gpu_data(), col_buffer_.gpu_shape(),
          kernel_shape_.gpu_data(), pad_.gpu_data(), stride_.gpu_data(),
          dilation_.gpu_data(), data);
    }
  }
#endif

  int num_kernels_im2col_;
  int num_kernels_col2im_;
  int conv_out_channels_;
  int conv_in_channels_;
  int conv_out_spatial_dim_;
  int kernel_dim_;
  int col_offset_;
  int output_offset_;

  Blob<Dtype> col_buffer_;
  Blob<Dtype> bias_multiplier_;
};

}  // namespace caffe

#endif  // CAFFE_BASE_CONVOLUTION_LAYER_HPP_

实现部分：

#include <algorithm>
#include <vector>

#include "caffe/filler.hpp"
#include "caffe/layers/base_conv_layer.hpp"
#include "caffe/util/im2col.hpp"
#include "caffe/util/math_functions.hpp"

namespace caffe {

template <typename Dtype>
void BaseConvolutionLayer<Dtype>::LayerSetUp(const vector<Blob<Dtype>*>& bottom,
      const vector<Blob<Dtype>*>& top) {
  // Configure the kernel size, padding, stride, and inputs.
  ConvolutionParameter conv_param = this->layer_param_.convolution_param();
  force_nd_im2col_ = conv_param.force_nd_im2col();//im2col,一般情况下num_spatial_axes_==2,即将2维图像拉成向量，但force_nd_im2col_针对的是更general的情况n-d“图像”
  channel_axis_ = bottom[0]->CanonicalAxisIndex(conv_param.axis());//获取channel的axis
  const int first_spatial_axis = channel_axis_ + 1;//chanel_axis是从零开始
  const int num_axes = bottom[0]->num_axes();//数据的axis数量
  num_spatial_axes_ = num_axes - first_spatial_axis;//空间轴的个数
  CHECK_GE(num_spatial_axes_, 0);
  vector<int> bottom_dim_blob_shape(1, num_spatial_axes_ + 1);
  vector<int> spatial_dim_blob_shape(1, std::max(num_spatial_axes_, 1));//当num_spatial_axes_==2时，spatial_dim_blob_shape这个vector只包含一个元素且值为2
  // Setup filter kernel dimensions (kernel_shape_).
  // 设置kernel的dimensions
  kernel_shape_.Reshape(spatial_dim_blob_shape);//以spatial_dim_blob_shape为参数来构造一个Blob，即kernel_shape_，则这个Blob的维度信息只包含一个维度，值为2,也就是说这个Blob的count_==2。尽管这个Blob的维度信息只包含一个维度，因为在后续的计算（Im2col）中，我只关心这个Blob中的数据的值，而不关心这个Blob的shape信息，例如在Im2col()中，只要取出相应数值即可kernel_shape_.cpu_data()[0], kernel_shape_.cpu_data()[1],pad_.cpu_data()[0], pad_.cpu_data()[1]。
  int* kernel_shape_data = kernel_shape_.mutable_cpu_data();
  if (conv_param.has_kernel_h() || conv_param.has_kernel_w()) {
    CHECK_EQ(num_spatial_axes_, 2)
        << "kernel_h & kernel_w can only be used for 2D convolution.";
    CHECK_EQ(0, conv_param.kernel_size_size())
        << "Either kernel_size or kernel_h/w should be specified; not both.";
    kernel_shape_data[0] = conv_param.kernel_h();//kernel_shape_data是一个二维数组
    kernel_shape_data[1] = conv_param.kernel_w();
  } else {
    const int num_kernel_dims = conv_param.kernel_size_size();
    CHECK(num_kernel_dims == 1 || num_kernel_dims == num_spatial_axes_)
        << "kernel_size must be specified once, or once per spatial dimension "
        << "(kernel_size specified " << num_kernel_dims << " times; "
        << num_spatial_axes_ << " spatial dims);";
      for (int i = 0; i < num_spatial_axes_; ++i) {
        kernel_shape_data[i] =
            conv_param.kernel_size((num_kernel_dims == 1) ? 0 : i);
      }
  }
  for (int i = 0; i < num_spatial_axes_; ++i) {
    CHECK_GT(kernel_shape_data[i], 0) << "Filter dimensions must be nonzero.";
  }
  // Setup stride dimensions (stride_).
  stride_.Reshape(spatial_dim_blob_shape);
  int* stride_data = stride_.mutable_cpu_data();
  if (conv_param.has_stride_h() || conv_param.has_stride_w()) {
    CHECK_EQ(num_spatial_axes_, 2)
        << "stride_h & stride_w can only be used for 2D convolution.";
    CHECK_EQ(0, conv_param.stride_size())
        << "Either stride or stride_h/w should be specified; not both.";
    stride_data[0] = conv_param.stride_h();
    stride_data[1] = conv_param.stride_w();
  } else {
    const int num_stride_dims = conv_param.stride_size();
    CHECK(num_stride_dims == 0 || num_stride_dims == 1 ||
          num_stride_dims == num_spatial_axes_)
        << "stride must be specified once, or once per spatial dimension "
        << "(stride specified " << num_stride_dims << " times; "
        << num_spatial_axes_ << " spatial dims);";
    const int kDefaultStride = 1;
    for (int i = 0; i < num_spatial_axes_; ++i) {
      stride_data[i] = (num_stride_dims == 0) ? kDefaultStride :
          conv_param.stride((num_stride_dims == 1) ? 0 : i);
      CHECK_GT(stride_data[i], 0) << "Stride dimensions must be nonzero.";
    }
  }
  // Setup pad dimensions (pad_).
  //设置相应的stride dimensions，
  pad_.Reshape(spatial_dim_blob_shape);
  int* pad_data = pad_.mutable_cpu_data();
  if (conv_param.has_pad_h() || conv_param.has_pad_w()) {
    CHECK_EQ(num_spatial_axes_, 2)
        << "pad_h & pad_w can only be used for 2D convolution.";
    CHECK_EQ(0, conv_param.pad_size())
        << "Either pad or pad_h/w should be specified; not both.";
    pad_data[0] = conv_param.pad_h();
    pad_data[1] = conv_param.pad_w();
  } else {
    const int num_pad_dims = conv_param.pad_size();
    CHECK(num_pad_dims == 0 || num_pad_dims == 1 ||
          num_pad_dims == num_spatial_axes_)
        << "pad must be specified once, or once per spatial dimension "
        << "(pad specified " << num_pad_dims << " times; "
        << num_spatial_axes_ << " spatial dims);";
    const int kDefaultPad = 0;
    for (int i = 0; i < num_spatial_axes_; ++i) {
      pad_data[i] = (num_pad_dims == 0) ? kDefaultPad :
          conv_param.pad((num_pad_dims == 1) ? 0 : i);
    }
  }
  // Special case: im2col is the identity for 1x1 convolution with stride 1
  // and no padding, so flag for skipping the buffer and transformation.
  is_1x1_ = true;
  for (int i = 0; i < num_spatial_axes_; ++i) {
    is_1x1_ &=
        kernel_shape_data[i] == 1 && stride_data[i] == 1 && pad_data[i] == 0;
    if (!is_1x1_) { break; }
  }
  // Configure output channels and groups.
  channels_ = bottom[0]->shape(channel_axis_);
  num_output_ = this->layer_param_.convolution_param().num_output();
  CHECK_GT(num_output_, 0);
  group_ = this->layer_param_.convolution_param().group();
  CHECK_EQ(channels_ % group_, 0);
  CHECK_EQ(num_output_ % group_, 0)
      << "Number of output should be multiples of group.";
  //channel 和 输出 feature map 个数必须为group的整数倍，每个group中只用本group的featrue map
  if (reverse_dimensions()) {
    conv_out_channels_ = channels_;
    conv_in_channels_ = num_output_;
  } else {
    conv_out_channels_ = num_output_;//输出图像的通道数
    conv_in_channels_ = channels_;//输入图像的通道数
  }
  // Handle the parameters: weights and biases.
  // - blobs_[0] holds the filter weights
  // - blobs_[1] holds the biases (optional)
  vector<int> weight_shape(2);
  weight_shape[0] = conv_out_channels_;
  weight_shape[1] = conv_in_channels_ / group_;
  for (int i = 0; i < num_spatial_axes_; ++i) {
    weight_shape.push_back(kernel_shape_data[i]);
  }
  bias_term_ = this->layer_param_.convolution_param().bias_term();
  vector<int> bias_shape(bias_term_, num_output_);
  if (this->blobs_.size() > 0) {
    CHECK_EQ(1 + bias_term_, this->blobs_.size())
        << "Incorrect number of weight blobs.";
    if (weight_shape != this->blobs_[0]->shape()) {
      Blob<Dtype> weight_shaped_blob(weight_shape);
      LOG(FATAL) << "Incorrect weight shape: expected shape "
          << weight_shaped_blob.shape_string() << "; instead, shape was "
          << this->blobs_[0]->shape_string();
    }
    if (bias_term_ && bias_shape != this->blobs_[1]->shape()) {
      Blob<Dtype> bias_shaped_blob(bias_shape);
      LOG(FATAL) << "Incorrect bias shape: expected shape "
          << bias_shaped_blob.shape_string() << "; instead, shape was "
          << this->blobs_[1]->shape_string();
    }
    LOG(INFO) << "Skipping parameter initialization";
  } else {
    if (bias_term_) {
      this->blobs_.resize(2);
    } else {
      this->blobs_.resize(1);
    }
    // Initialize and fill the weights:
    // output channels x input channels per-group x kernel height x kernel width
    this->blobs_[0].reset(new Blob<Dtype>(weight_shape));//blobs_[0]的维度信息是四个维度，count_为四个维度的值相乘
    shared_ptr<Filler<Dtype> > weight_filler(GetFiller<Dtype>(
        this->layer_param_.convolution_param().weight_filler()));
    weight_filler->Fill(this->blobs_[0].get());
    // If necessary, initialize and fill the biases.
    if (bias_term_) {
      this->blobs_[1].reset(new Blob<Dtype>(bias_shape));//blobs_[1]的维度信息是1个维度，count_为num_output_
      shared_ptr<Filler<Dtype> > bias_filler(GetFiller<Dtype>(
          this->layer_param_.convolution_param().bias_filler()));
      bias_filler->Fill(this->blobs_[1].get());
    }
  }
  kernel_dim_ = this->blobs_[0]->count(1);//是一个三维维度的乘积
  weight_offset_ = conv_out_channels_ * kernel_dim_ / group_;//写成(conv_out_channels_ / group_) * kernel_dim_更直观。这个offset是相对group分组来讲的。
  // Propagate gradients to the parameters (as directed by backward pass).
  this->param_propagate_down_.resize(this->blobs_.size(), true);
}


template <typename Dtype>
void BaseConvolutionLayer<Dtype>::Reshape(const vector<Blob<Dtype>*>& bottom,
      const vector<Blob<Dtype>*>& top) {
  const int first_spatial_axis = channel_axis_ + 1;
  CHECK_EQ(bottom[0]->num_axes(), first_spatial_axis + num_spatial_axes_)
      << "bottom num_axes may not change.";
  num_ = bottom[0]->count(0, channel_axis_);
  CHECK_EQ(bottom[0]->shape(channel_axis_), channels_)
      << "Input size incompatible with convolution kernel.";
  // TODO: generalize to handle inputs of different shapes.所有的输入bottom都必须有相同的shape
  for (int bottom_id = 1; bottom_id < bottom.size(); ++bottom_id) {
    CHECK(bottom[0]->shape() == bottom[bottom_id]->shape())
        << "All inputs must have the same shape.";
  }
  // Shape the tops.卷积层应该默认有多少个bottom 就有多少个top输出
  bottom_shape_ = &bottom[0]->shape();
  compute_output_shape();
  vector<int> top_shape(bottom[0]->shape().begin(),
      bottom[0]->shape().begin() + channel_axis_);
  top_shape.push_back(num_output_);
  for (int i = 0; i < num_spatial_axes_; ++i) {
    top_shape.push_back(output_shape_[i]);
  }
  for (int top_id = 0; top_id < top.size(); ++top_id) {
    top[top_id]->Reshape(top_shape);
  }
  if (reverse_dimensions()) {
    conv_out_spatial_dim_ = bottom[0]->count(first_spatial_axis);
  } else {
    conv_out_spatial_dim_ = top[0]->count(first_spatial_axis);
  }
  //group分，对conv_in_channels分组; 卷积窗口在输入“图像”上按步长滑动，（可以想象）形成了多个子图;然后将所有子图拉成一列，列的长度就是col_offset_。
  col_offset_ = kernel_dim_ * conv_out_spatial_dim_;//col_offset_与im2col_cpu()函数中channels_col的计算是相似的，但是值并不相等，原因在于：channels_col是将卷积层输入的通道数conv_in_channels_用于相乘，但kernel_dim_只用到了一部分channel,即conv_in_channels_/group_ 。
  output_offset_ = conv_out_channels_ * conv_out_spatial_dim_ / group_;//卷积层的输出特征图也要分组，当然group_默认为1。写成(conv_out_channels_ / group_) * conv_out_spatial_dim_更直观
  // Setup input dimensions (conv_input_shape_).
  vector<int> bottom_dim_blob_shape(1, num_spatial_axes_ + 1);
  conv_input_shape_.Reshape(bottom_dim_blob_shape);//与pad_、 stride_类似
  int* conv_input_shape_data = conv_input_shape_.mutable_cpu_data();
  for (int i = 0; i < num_spatial_axes_ + 1; ++i) {
    if (reverse_dimensions()) {
      conv_input_shape_data[i] = top[0]->shape(channel_axis_ + i);
    } else {
      conv_input_shape_data[i] = bottom[0]->shape(channel_axis_ + i);
    }
  }
  // The im2col result buffer will only hold one image at a time to avoid
  // overly large memory usage. In the special case of 1x1 convolution
  // it goes lazily unused to save memory.
  col_buffer_shape_.clear();//col_buffer_shape_是一个vector
  col_buffer_shape_.push_back(kernel_dim_ * group_);//所有conv_in_channels_个输入的channels都包含其中。
  for (int i = 0; i < num_spatial_axes_; ++i) {
    if (reverse_dimensions()) {
      col_buffer_shape_.push_back(input_shape(i + 1));
    } else {
      col_buffer_shape_.push_back(output_shape_[i]);
    }
  }
  col_buffer_.Reshape(col_buffer_shape_);//一般情况下，col_buffer_的维度信息为三个维度。col_buffer_shape_的存储的元素为：kernel_dim_ * group_， 输出特征图的H， 输出特征图的W。可以认为col_buffer_内所存储的数据的维度为：(kernel_dim_ * group_) × H × W，且与kernel_dim_ x conv_out_spatial_dim_有密切关系.
  bottom_dim_ = bottom[0]->count(channel_axis_);
  top_dim_ = top[0]->count(channel_axis_);
  num_kernels_im2col_ = conv_in_channels_ * conv_out_spatial_dim_;
  num_kernels_col2im_ = reverse_dimensions() ? top_dim_ : bottom_dim_;
  // Set up the all ones "bias multiplier" for adding biases by BLAS
  out_spatial_dim_ = top[0]->count(first_spatial_axis);//out_spatial_dim_ == conv_out_spatial_dim_
  if (bias_term_) {
    vector<int> bias_multiplier_shape(1, out_spatial_dim_);
    bias_multiplier_.Reshape(bias_multiplier_shape);//bias_multiplier_这个Blob的count_为out_spatial_dim_，是输出特征图的H×W
    caffe_set(bias_multiplier_.count(), Dtype(1),
        bias_multiplier_.mutable_cpu_data());
  }
}
//////////////////////注意： col_offset_ output_offset_ weight_offet 都是因为group_分组而存在的\\\\\\\\\\\\\\\\\\\\\\\\\\\\\


template <typename Dtype>
void BaseConvolutionLayer<Dtype>::forward_cpu_gemm(const Dtype* input,
    const Dtype* weights, Dtype* output, bool skip_im2col) {
  const Dtype* col_buff = input;
  if (!is_1x1_) {
    if (!skip_im2col) {
      // 如果没有1x1卷积，也没有skip_im2col  
      // 则使用conv_im2col_cpu对使用卷积核滑动过程中的每一个kernel大小的图像块  
      // 变成一个列向量，形成一个height=kernel_dim_的  
      // width = 卷积后图像heght*卷积后图像width 
      conv_im2col_cpu(input, col_buffer_.mutable_cpu_data());
    }
    col_buff = col_buffer_.cpu_data();
  }
  // 使用caffe的cpu_gemm来进行计算
  for (int g = 0; g < group_; ++g) {
      // conv_out_channels_ / group_是每个卷积组的输出的channel  
      // kernel_dim_ = input channels per-group x kernel height x kernel width  
      // 计算的是output[output_offset_ * g] =  
      // weights[weight_offset_ * g] X col_buff[col_offset_ * g]
      // weights的维度为(conv_out_channels_ /group_) x kernel_dim_ 
      // weights的形状是 [conv_out_channel x kernel_dim_]  
      // col_buff相当于数据，它的形状是[kernel_dim_ x (卷积后图像高度乘以卷积后图像宽度)]=
      //	kernel_dim_ x conv_out_spatial_dim_  
      // 所以output的形状自然就是conv_out_channel X (卷积后图像高度乘以卷积后图像宽度)=
      //       (conv_out_channels_ /group_) x conv_out_spatial_dim_
    caffe_cpu_gemm<Dtype>(CblasNoTrans, CblasNoTrans, conv_out_channels_ /
        group_, conv_out_spatial_dim_, kernel_dim_,
        (Dtype)1., weights + weight_offset_ * g, col_buff + col_offset_ * g,
        (Dtype)0., output + output_offset_ * g);
  }
}//只是对一张图像进行前向传播！与全连接层类比，conv_out_channels_ / group_相当与全连接层的输出神经元个数;conv_out_spatial_dim_相当于全连接层中的样本个数;kernel_dim_相当与全连接层中每个样本特征向量的维数。

template <typename Dtype>
void BaseConvolutionLayer<Dtype>::forward_cpu_bias(Dtype* output,
    const Dtype* bias) {
  // output = bias * bias_multiplier_  
  // num_output 与 conv_out_channel是一样的  
  // num_output_ X out_spatial_dim_ = num_output_ X 1    1 X out_spatial_dim_  
  caffe_cpu_gemm<Dtype>(CblasNoTrans, CblasNoTrans, num_output_,
      out_spatial_dim_, 1, (Dtype)1., bias, bias_multiplier_.cpu_data(),
      (Dtype)1., output);
}//卷积后加bias 

template <typename Dtype>
void BaseConvolutionLayer<Dtype>::backward_cpu_gemm(const Dtype* output,
    const Dtype* weights, Dtype* input) {
  Dtype* col_buff = col_buffer_.mutable_cpu_data();
  if (is_1x1_) {
    col_buff = input;
  }
  for (int g = 0; g < group_; ++g) {
    caffe_cpu_gemm<Dtype>(CblasTrans, CblasNoTrans, kernel_dim_,
        conv_out_spatial_dim_, conv_out_channels_ / group_,
        (Dtype)1., weights + weight_offset_ * g, output + output_offset_ * g,
        (Dtype)0., col_buff + col_offset_ * g);
  }
  if (!is_1x1_) {
    conv_col2im_cpu(col_buff, input);
  }
}//计算关于bottom data的导数以便传给下一层

template <typename Dtype>
void BaseConvolutionLayer<Dtype>::weight_cpu_gemm(const Dtype* input,
    const Dtype* output, Dtype* weights) {
  const Dtype* col_buff = input;
  if (!is_1x1_) {
    conv_im2col_cpu(input, col_buffer_.mutable_cpu_data());
    col_buff = col_buffer_.cpu_data();
  }
  for (int g = 0; g < group_; ++g) {
    caffe_cpu_gemm<Dtype>(CblasNoTrans, CblasTrans, conv_out_channels_ / group_,
        kernel_dim_, conv_out_spatial_dim_,
        (Dtype)1., output + output_offset_ * g, col_buff + col_offset_ * g,
        (Dtype)1., weights + weight_offset_ * g);
  }
}//计算关于weight的导数用于更新。

template <typename Dtype>
void BaseConvolutionLayer<Dtype>::backward_cpu_bias(Dtype* bias,
    const Dtype* input) {
  caffe_cpu_gemv<Dtype>(CblasNoTrans, num_output_, out_spatial_dim_, 1.,
      input, bias_multiplier_.cpu_data(), 1., bias);
}//计算关于bias的导数

#ifndef CPU_ONLY

template <typename Dtype>
void BaseConvolutionLayer<Dtype>::forward_gpu_gemm(const Dtype* input,
    const Dtype* weights, Dtype* output, bool skip_im2col) {
  const Dtype* col_buff = input;
  if (!is_1x1_) {
    if (!skip_im2col) {
      conv_im2col_gpu(input, col_buffer_.mutable_gpu_data());
    }
    col_buff = col_buffer_.gpu_data();
  }
  for (int g = 0; g < group_; ++g) {
    caffe_gpu_gemm<Dtype>(CblasNoTrans, CblasNoTrans, conv_out_channels_ /
        group_, conv_out_spatial_dim_, kernel_dim_,
        (Dtype)1., weights + weight_offset_ * g, col_buff + col_offset_ * g,
        (Dtype)0., output + output_offset_ * g);
  }
}

template <typename Dtype>
void BaseConvolutionLayer<Dtype>::forward_gpu_bias(Dtype* output,
    const Dtype* bias) {
  caffe_gpu_gemm<Dtype>(CblasNoTrans, CblasNoTrans, num_output_,
      out_spatial_dim_, 1, (Dtype)1., bias, bias_multiplier_.gpu_data(),
      (Dtype)1., output);
}

template <typename Dtype>
void BaseConvolutionLayer<Dtype>::backward_gpu_gemm(const Dtype* output,
    const Dtype* weights, Dtype* input) {
  Dtype* col_buff = col_buffer_.mutable_gpu_data();
  if (is_1x1_) {
    col_buff = input;
  }
  for (int g = 0; g < group_; ++g) {
    caffe_gpu_gemm<Dtype>(CblasTrans, CblasNoTrans, kernel_dim_,
        conv_out_spatial_dim_, conv_out_channels_ / group_,
        (Dtype)1., weights + weight_offset_ * g, output + output_offset_ * g,
        (Dtype)0., col_buff + col_offset_ * g);
  }
  if (!is_1x1_) {
    conv_col2im_gpu(col_buff, input);
  }
}

template <typename Dtype>
void BaseConvolutionLayer<Dtype>::weight_gpu_gemm(const Dtype* input,
    const Dtype* output, Dtype* weights) {
  const Dtype* col_buff = input;
  if (!is_1x1_) {
    conv_im2col_gpu(input, col_buffer_.mutable_gpu_data());
    col_buff = col_buffer_.gpu_data();
  }
  for (int g = 0; g < group_; ++g) {
    caffe_gpu_gemm<Dtype>(CblasNoTrans, CblasTrans, conv_out_channels_ / group_,
        kernel_dim_, conv_out_spatial_dim_,
        (Dtype)1., output + output_offset_ * g, col_buff + col_offset_ * g,
        (Dtype)1., weights + weight_offset_ * g);
  }
}

template <typename Dtype>
void BaseConvolutionLayer<Dtype>::backward_gpu_bias(Dtype* bias,
    const Dtype* input) {
  caffe_gpu_gemv<Dtype>(CblasNoTrans, num_output_, out_spatial_dim_, 1.,
      input, bias_multiplier_.gpu_data(), 1., bias);
}

#endif  // !CPU_ONLY

INSTANTIATE_CLASS(BaseConvolutionLayer);

}  // namespace caffe