資料層DataLayer正向傳導的目標層是卷積層ConvolutionLayer。卷積層的是用一系列的權重濾波核與輸入影象進行卷積，具體實現是通過將影象展開成向量，作用矩陣乘法實現卷積。

    同樣，首先看一下卷積層的類圖。

    BaseConvolutionLayer類是所有卷積層的基類，它負責初始化濾波核、將影象轉成向量，以及封裝了BLAS庫的矩陣運算函式。Yangqing Jia在Convolution in Caffe: a memo 一文中說明了卷積的實現方式和優缺點：優點是速度快，缺點也很明顯，記憶體開銷大。也還有Alex Krizhevsky等人更好的實現方式，但是由於時間和精力原因並沒有採用，畢竟是不想寫博士論文意外創作的 

    ConvolutionLayer類是卷積層的例項類，如果系統支援cuDNN，則例項類為CuDNNConvolutionLayer。提醒一下，在CUDA計算能力3.0及以上的GPU上才支援cuDNN，這裡CUDA GPUs 可以看到GPU的計算能力。如果當前GPU不支援cuDNN，Caffe又是預設開啟cuDNN的，那麼執行時構造CuDNNConvolutionLayer物件例項時將報錯。這時需要在CommonSettings.props中將<UseCuDNN>標籤改為false，或者在工程屬性“C/C++”->“前處理器”中將USE_CUDNN

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:
  // 一系列BLAS輔助函式
  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];
  }
  // 純虛擬函式，用來識別是卷積(return false)還是反捲積(return true)
  virtual bool reverse_dimensions() = 0;
  // 純虛擬函式，計算卷積後輸出尺寸虛擬函式
  virtual void compute_output_shape() = 0;

  /// 卷積核尺寸
  Blob<int> kernel_shape_;
  /// 卷積核平移步幅
  Blob<int> stride_;
  /// 影象補齊畫素數
  Blob<int> pad_;
  /// 影象膨脹畫素數
  Blob<int> dilation_;
  /// @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_;   // 通道數
  int group_;      // 組數
  int out_spatial_dim_;
  int weight_offset_;    // 權重offset，此處為25*20 = 500
  int num_output_;      // 輸出數
  bool bias_term_;      // 是否包含偏置項
  bool is_1x1_;           // 是否為1x1模式
  bool force_nd_im2col_;

private:
  // 將影象轉成列向量
  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_;    // 卷積操作輸出通道數
  int conv_in_channels_;     // 卷積操作輸入通道數
  int conv_out_spatial_dim_;
  int kernel_dim_;           // 卷積核的尺寸（例如5x5卷積核，kernel_dim_為25）
  int col_offset_;
  int output_offset_;
  Blob<Dtype> col_buffer_;
  Blob<Dtype> bias_multiplier_;
};
 

base_conv_layer.cpp檔案較長

template <typename Dtype>
void BaseConvolutionLayer<Dtype>::LayerSetUp(const vector<Blob<Dtype>*>& bottom,
      const vector<Blob<Dtype>*>& top) {
  // 設定濾波核尺寸等引數
  ConvolutionParameter conv_param = this->layer_param_.convolution_param();
  force_nd_im2col_ = conv_param.force_nd_im2col();
  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));
  // 設定卷積核維度
  kernel_shape_.Reshape(spatial_dim_blob_shape);
  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[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.";
  }
  // 設定卷積核平移步幅
  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.";
    }
  }
  // 設定影象補齊畫素數
  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);
    }
  }
  // 設定影象膨脹畫素數
  dilation_.Reshape(spatial_dim_blob_shape);
  int* dilation_data = dilation_.mutable_cpu_data();
  const int num_dilation_dims = conv_param.dilation_size();
  CHECK(num_dilation_dims == 0 || num_dilation_dims == 1 ||
        num_dilation_dims == num_spatial_axes_)
      << "dilation must be specified once, or once per spatial dimension "
      << "(dilation specified " << num_dilation_dims << " times; "
      << num_spatial_axes_ << " spatial dims).";
  const int kDefaultDilation = 1;
  for (int i = 0; i < num_spatial_axes_; ++i) {
    dilation_data[i] = (num_dilation_dims == 0) ? kDefaultDilation :
                       conv_param.dilation((num_dilation_dims == 1) ? 0 : i);
  }
  // 只有對於尺寸1x1、平移步幅為1、影象不補齊的卷積核才將標誌位1x1置為true
  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; }
  }
  // 配置通道數
  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_;  // 設定卷積操作輸出通道數
    conv_in_channels_ = channels_;     // 設定卷積操作輸入通道數
  }
  // 處理權重引數和偏置引數
  // - 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]);
  }
  // 從配置中讀取是否包含偏置項
  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);  // 如果包含偏置項，則blobs_為兩項
    } else {
      this->blobs_.resize(1);  // 如果不包含偏置項，則blobs_只有一項（權重項）
    }
    // 初始化和填充權重
    // output channels x input channels per-group x kernel height x kernel width
    this->blobs_[0].reset(new Blob<Dtype>(weight_shape));
    shared_ptr<Filler<Dtype> > weight_filler(GetFiller<Dtype>(
        this->layer_param_.convolution_param().weight_filler()));
    // 使用隨機數填充Xavier濾波核
    weight_filler->Fill(this->blobs_[0].get());
    // 如果啟用偏置，則初始化偏置濾波核
    if (bias_term_) {
      this->blobs_[1].reset(new Blob<Dtype>(bias_shape));
      shared_ptr<Filler<Dtype> > bias_filler(GetFiller<Dtype>(
          this->layer_param_.convolution_param().bias_filler()));
      // 使用0填充偏置濾波核
      bias_filler->Fill(this->blobs_[1].get());
    }
  }
  kernel_dim_ = this->blobs_[0]->count(1);
  // 計算權重offset
  weight_offset_ = conv_out_channels_ * kernel_dim_ / group_;
  // Propagate gradients to the parameters (as directed by backward pass).
  this->param_propagate_down_.resize(this->blobs_.size(), true);
}

// 正向傳導矩陣運算函式 
template <typename Dtype>
void BaseConvolutionLayer<Dtype>::forward_cpu_gemm(const Dtype* input,
    const Dtype* weights, Dtype* output, bool skip_im2col) {
  // 先將影象轉為列向量
  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();
  }
  // 矩陣乘法實現卷積運算
  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);
  }
}

// CPU正向傳導偏置（在上一步卷積計算結果上加上偏置）
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);
}

// CPU反向傳導
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);
  }
}

// CPU計算權重的偏導
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);
  }
}

// CPU反向傳導偏置項
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);
}

#ifndef CPU_ONLY
// GPU正向傳導
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);
  }
}

// GPU正向傳導偏置項
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);
}

// GPU計算資料項偏導
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);
  }
}

// GPU計算權重的偏導
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);
  }
}

// GPU反向傳導偏置項
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);
}