caffe base_conv_layers.cpp 学习

##################### In vision_layers.hpp #######################

%%%%%%%%%%%%%%%%%%%%%class BaseConvolutionLayer%%%%%%%%%%%%%%%%%%%%%%
protected数据成员：
/// @brief The spatial dimensions of a filter kernel.
Blob<int> kernel_shape_;
/// @brief The spatial dimensions of the stride.
Blob<int> stride_;
/// @brief The spatial dimensions of the padding.
Blob<int> pad_;
/// @brief The spatial dimensions of the convolution input.
Blob<int> conv_input_shape_;
/// @brief The spatial dimensions of the col_buffer.
vector<int> col_buffer_shape_;
/// @brief The spatial dimensions of the output.
vector<int> output_shape_;
const vector<int>* bottom_shape_;
int num_spatial_axes_;
int bottom_dim_;
int top_dim_;
int channel_axis_;
int num_;
int channels_;
int group_;
int out_spatial_dim_;
int weight_offset_;
int num_output_;
bool bias_term_;
bool is_1x1_;
bool force_nd_im2col_;


private数据成员：
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_;

##################### In im2col.cpp #######################

template <typename Dtype>
void im2col_cpu(const Dtype* data_im, const int channels,
    const int height, const int width, const int kernel_h, const int kernel_w,
    const int pad_h, const int pad_w,
    const int stride_h, const int stride_w,
    Dtype* data_col) {
  const int height_col = (height + 2 * pad_h - kernel_h) / stride_h + 1;
  const int width_col = (width + 2 * pad_w - kernel_w) / stride_w + 1;
  const int channels_col = channels * kernel_h * kernel_w;
  for (int c_col = 0; c_col < channels_col; ++c_col) {
    int w_offset = c_col % kernel_w;
    int h_offset = (c_col / kernel_w) % kernel_h;
    int c_im = c_col / kernel_h / kernel_w;
    for (int h_col = 0; h_col < height_col; ++h_col) {
      for (int w_col = 0; w_col < width_col; ++w_col) {
        int h_im = h_col * stride_h - pad_h + h_offset;
        int w_im = w_col * stride_w - pad_w + w_offset;
        data_col[(c_col * height_col + h_col) * width_col + w_col] =
            (h_im >= 0 && w_im >= 0 && h_im < height && w_im < width) ?
            data_im[(c_im * height + h_im) * width + w_im] : 0;
      }
    }
  }
}
该函数的功能就是将整张图片按照卷积的窗口大小切成子图（按照stride来切，可以有重叠），最后全部元素拉成一列。为啥要怎样做，因为对于这个小窗口内拉成一列的神经元来说来说，它们跟下一层神经元就是全连接了，所以这个小窗口里面的梯度计算就可以按照全连接来计算就可以了。
可以这么想：将图片的通道数与kernel_h、kernel_w的乘积作为子图的channel，即channels_col。由于卷积窗口在输入上按照stride移动，所以总共有height_col×width_col个子图，而每个子图的通道数为channels_col，所以最终拉成的向量的维度是channels_col×height_col×width_col。而c_im, h_im, w_im则用来计算卷积层输入相应元素的位置信息。


template <typename Dtype>
inline void im2col_nd_core_cpu(const Dtype* data_input, const bool im2col,
    const int num_spatial_axes, const int* im_shape, const int* col_shape,
    const int* kernel_shape, const int* pad, const int* stride,
    Dtype* data_output)
该方法是针对输入的spatial dimension 不是二维的情况，但是在一般情况下处理的数据是图像时，其spatial dimension 是二维的，所以这里不细究。


template <typename Dtype>
void col2im_cpu(const Dtype* data_col, const int channels,
    const int height, const int width, const int kernel_h, const int kernel_w,
    const int pad_h, const int pad_w,
    const int stride_h, const int stride_w,
    Dtype* data_im) {
  caffe_set(height * width * channels, Dtype(0), data_im);
  const int height_col = (height + 2 * pad_h - kernel_h) / stride_h + 1;
  const int width_col = (width + 2 * pad_w - kernel_w) / stride_w + 1;
  const int channels_col = channels * kernel_h * kernel_w;
  for (int c_col = 0; c_col < channels_col; ++c_col) {
    int w_offset = c_col % kernel_w;
    int h_offset = (c_col / kernel_w) % kernel_h;
    int c_im = c_col / kernel_h / kernel_w;
    for (int h_col = 0; h_col < height_col; ++h_col) {
      for (int w_col = 0; w_col < width_col; ++w_col) {
        int h_im = h_col * stride_h - pad_h + h_offset;
        int w_im = w_col * stride_w - pad_w + w_offset;
        if (h_im >= 0 && h_im < height && w_im >= 0 && w_im < width)
          data_im[(c_im * height + h_im) * width + w_im] +=
              data_col[(c_col * height_col + h_col) * width_col + w_col];
      }
    }
  }
}
im2col_cpu()的相反过程

####################In caffe.proto#####################

在此文件中，有一段关于axis的注释：
// The axis to interpret as "channels" when performing convolution.
  // Preceding dimensions are treated as independent inputs;
  // succeeding dimensions are treated as "spatial".
  // With (N, C, H, W) inputs, and axis == 1 (the default), we perform
  // N independent 2D convolutions, sliding C-channel (or (C/g)-channels, for
  // groups g>1) filters across the spatial axes (H, W) of the input.
  // With (N, C, D, H, W) inputs, and axis == 1, we perform
  // N independent 3D convolutions, sliding (C/g)-channels
  // filters across the spatial axes (D, H, W) of the input.
  optional int32 axis = 16 [default = 1];

######################In base_conv_layer.cpp###################

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());
  const int first_spatial_axis = channel_axis_ + 1;
  const int num_axes = bottom[0]->num_axes();
  num_spatial_axes_ = num_axes - first_spatial_axis;
  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_).
  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_).
  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.";
  if (reverse_dimensions()) {
    conv_out_channels_ = channels_;
    conv_in_channels_ = num_output_;
  } else {
    conv_out_channels_ = num_output_;
    conv_in_channels_ = channels_;
  }
  // 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) {
      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, 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);//weights <--- blobs_[0]->cpu_data()。类比全连接层，weights为权重，col_buff相当与数据，矩阵相乘weights×col_buff. 其中，weights的维度为(conv_out_channels_ /group_) x kernel_dim_， col_buff的维度为kernel_dim_ x conv_out_spatial_dim_， output的维度为(conv_out_channels_ /group_) x conv_out_spatial_dim_.
  }
}//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) {
  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

##################In conv_layer.cpp#######################

template <typename Dtype>
void ConvolutionLayer<Dtype>::compute_output_shape() {
  const int* kernel_shape_data = this->kernel_shape_.cpu_data();
  const int* stride_data = this->stride_.cpu_data();
  const int* pad_data = this->pad_.cpu_data();
  this->output_shape_.clear();
  for (int i = 0; i < this->num_spatial_axes_; ++i) {
    // i + 1 to skip channel axis
    const int input_dim = this->input_shape(i + 1);
    const int output_dim = (input_dim + 2 * pad_data[i] - kernel_shape_data[i])
        / stride_data[i] + 1;
    this->output_shape_.push_back(output_dim);
  }
}//计算输出feature map 的shape

template <typename Dtype>
void ConvolutionLayer<Dtype>::Forward_cpu(const vector<Blob<Dtype>*>& bottom,
      const vector<Blob<Dtype>*>& top) {
  const Dtype* weight = this->blobs_[0]->cpu_data();
  for (int i = 0; i < bottom.size(); ++i) {
    const Dtype* bottom_data = bottom[i]->cpu_data();//卷积层应该默认有多少个bottom 就有多少个top输出
    Dtype* top_data = top[i]->mutable_cpu_data();
    for (int n = 0; n < this->num_; ++n) {
      this->forward_cpu_gemm(bottom_data + n * this->bottom_dim_, weight,
          top_data + n * this->top_dim_);//说明是一张图像一张图像地进行前向传播，因为：1.num_ 2.top_dim的值等于top blob中一张图像拉成一列的列长。
      if (this->bias_term_) {
        const Dtype* bias = this->blobs_[1]->cpu_data();
        this->forward_cpu_bias(top_data + n * this->top_dim_, bias);
      }
    }
  }
}//卷积层的Forward_cpu方法。

template <typename Dtype>
void ConvolutionLayer<Dtype>::Backward_cpu(const vector<Blob<Dtype>*>& top,
      const vector<bool>& propagate_down, const vector<Blob<Dtype>*>& bottom) {
  const Dtype* weight = this->blobs_[0]->cpu_data();
  Dtype* weight_diff = this->blobs_[0]->mutable_cpu_diff();
  for (int i = 0; i < top.size(); ++i) {
    const Dtype* top_diff = top[i]->cpu_diff();
    const Dtype* bottom_data = bottom[i]->cpu_data();
    Dtype* bottom_diff = bottom[i]->mutable_cpu_diff();
    // Bias gradient, if necessary.
    if (this->bias_term_ && this->param_propagate_down_[1]) {
      Dtype* bias_diff = this->blobs_[1]->mutable_cpu_diff();
      for (int n = 0; n < this->num_; ++n) {
        this->backward_cpu_bias(bias_diff, top_diff + n * this->top_dim_);
      }
    }
    if (this->param_propagate_down_[0] || propagate_down[i]) {
      for (int n = 0; n < this->num_; ++n) {
        // gradient w.r.t. weight. Note that we will accumulate diffs.
        if (this->param_propagate_down_[0]) {
          this->weight_cpu_gemm(bottom_data + n * this->bottom_dim_,
              top_diff + n * this->top_dim_, weight_diff);
        }
        // gradient w.r.t. bottom data, if necessary.
        if (propagate_down[i]) {
          this->backward_cpu_gemm(top_diff + n * this->top_dim_, weight,
              bottom_diff + n * this->bottom_dim_);
        }
      }
    }
  }
}//卷积层的Backward_cpu。