下图是jiayangqing在知乎上的回答,其实过程就是把image转换成矩阵,然后进行矩阵运算
卷积的实现在conv_layer层,conv_layer层继承了base_conv_layer层,base_conv_layer层是卷积操作的基类,包含卷积和反卷积.conv_layer层的前向传播是通过forward_cpu_gemm函数实现,这个函数在vision_layer.hpp里进行了定义,在base_conv_layer.cpp里进行了实现.forward_cpu_gemm函数调用了caffe_cpu_gemm和conv_im2col_cpu,caffe_cpu_gemm的实现在util/math_function.cpp里,conv_im2col_cpu的实现在util/im2col.cpp里
conv_layer层的前向传播代码,先调forward_cpu_gemm函数进行卷积的乘法运算,然后根据是否需要bias项,调用forward_cpu_bias进行加法运算.
templatevoid ConvolutionLayer ::Forward_cpu(const vector *>& bottom, const vector *>& 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(); Dtype* top_data = top[i]->mutable_cpu_data(); for (int n = 0; n < this->num_; ++n) { this->forward_cpu_gemm(bottom_data + bottom[i]->offset(n), weight, top_data + top[i]->offset(n)); if (this->bias_term_) { const Dtype* bias = this->blobs_[1]->cpu_data(); this->forward_cpu_bias(top_data + top[i]->offset(n), bias); } } }}
num_在vision_layers.hpp中的BaseConvolutionLayer类中定义,表示batchsize(https://blog.csdn.net/sinat_22336563/article/details/69808612,这个博客给做了说明).也就是说.每一层卷积是先把一个batch所有的数据计算完才传给下一层,不是把batch中的一个在整个网络中计算一次,再把batch中的下一个传进整个网络进行计算.这里的bottom[i]->offset(n),相当于指向一个batch中下一个图片或者feature map的内存地址,即对batch中下一个进行计算
offset在blob.hpp中定义.bottom、top都是blob类,所以可以去调用blob这个类的属性或者方法,看具体实现的时候直接去看这个类怎么实现的就OK.
inline int offset(const int n, const int c = 0, const int h = 0, const int w = 0) const { CHECK_GE(n, 0); CHECK_LE(n, num()); CHECK_GE(channels(), 0); CHECK_LE(c, channels()); CHECK_GE(height(), 0); CHECK_LE(h, height()); CHECK_GE(width(), 0); CHECK_LE(w, width()); return ((n * channels() + c) * height() + h) * width() + w; } inline int offset(const vector & indices) const { CHECK_LE(indices.size(), num_axes()); int offset = 0; for (int i = 0; i < num_axes(); ++i) { offset *= shape(i); if (indices.size() > i) { CHECK_GE(indices[i], 0); CHECK_LT(indices[i], shape(i)); offset += indices[i]; } } return offset; } 
https://www.cnblogs.com/neopenx/p/5294682.html
forward_cpu_gemm、forward_cpu_bias函数的实现.is_1x1_用来判断是不是1x1的卷积操作,skip_im2col用来判断是不是需要把图片转换成矩阵
templatevoid BaseConvolutionLayer ::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 (CblasNoTrans, CblasNoTrans, conv_out_channels_ / group_, conv_out_spatial_dim_, kernel_dim_ / group_, (Dtype)1., weights + weight_offset_ * g, col_buff + col_offset_ * g, (Dtype)0., output + output_offset_ * g); }}template void BaseConvolutionLayer ::forward_cpu_bias(Dtype* output, const Dtype* bias) { caffe_cpu_gemm (CblasNoTrans, CblasNoTrans, num_output_, height_out_ * width_out_, 1, (Dtype)1., bias, bias_multiplier_.cpu_data(), (Dtype)1., output);}
conv_im2col_cpu
inline void conv_im2col_cpu(const Dtype* data, Dtype* col_buff) { im2col_cpu(data, 1, conv_in_channels_, conv_in_height_, conv_in_width_, kernel_h_, kernel_w_, pad_h_, pad_w_, stride_h_, stride_w_, 1, 1, col_buff); }
templatevoid 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, const int dilation_h, const int dilation_w, Dtype* data_col) { const int output_h = (height + 2 * pad_h - (dilation_h * (kernel_h - 1) + 1)) / stride_h + 1; const int output_w = (width + 2 * pad_w - (dilation_w * (kernel_w - 1) + 1)) / stride_w + 1; const int channel_size = height * width; for (int channel = channels; channel--; data_im += channel_size) { for (int kernel_row = 0; kernel_row < kernel_h; kernel_row++) { for (int kernel_col = 0; kernel_col < kernel_w; kernel_col++) { int input_row = -pad_h + kernel_row * dilation_h; for (int output_rows = output_h; output_rows; output_rows--) { if (!is_a_ge_zero_and_a_lt_b(input_row, height)) { for (int output_cols = output_w; output_cols; output_cols--) { *(data_col++) = 0; } } else { int input_col = -pad_w + kernel_col * dilation_w; for (int output_col = output_w; output_col; output_col--) { if (is_a_ge_zero_and_a_lt_b(input_col, width)) { *(data_col++) = data_im[input_row * width + input_col]; } else { *(data_col++) = 0; } input_col += stride_w; } } input_row += stride_h; } } } }}
caffe_cpu_gemm函数的实现.cblas_sgemm是cblas库的一个函数(# inclue<cblas.h>),
template<>void caffe_cpu_gemm(const CBLAS_TRANSPOSE TransA, const CBLAS_TRANSPOSE TransB, const int M, const int N, const int K, const float alpha, const float* A, const float* B, const float beta, float* C) { int lda = (TransA == CblasNoTrans) ? K : M; int ldb = (TransB == CblasNoTrans) ? N : K; cblas_sgemm(CblasRowMajor, TransA, TransB, M, N, K, alpha, A, lda, B, ldb, beta, C, N); }template<>void caffe_cpu_gemm (const CBLAS_TRANSPOSE TransA, const CBLAS_TRANSPOSE TransB, const int M, const int N, const int K, const double alpha, const double* A, const double* B, const double beta, double* C) { int lda = (TransA == CblasNoTrans) ? K : M; int ldb = (TransB == CblasNoTrans) ? N : K; cblas_dgemm(CblasRowMajor, TransA, TransB, M, N, K, alpha, A, lda, B, ldb, beta, C, N); }template<>void caffe_cpu_gemm (const CBLAS_TRANSPOSE TransA, const CBLAS_TRANSPOSE TransB, const int M, const int N, const int K, const Half alpha, const Half* A, const Half* B, const Half beta, Half* C) { DeviceMemPool& pool = Caffe::Get().cpu_mem_pool(); float* fA = (float*)pool.Allocate(M*K*sizeof(float)); float* fB = (float*)pool.Allocate(K*N*sizeof(float)); float* fC = (float*)pool.Allocate(M*N*sizeof(float)); halves2floats_cpu(A, fA, M*K); halves2floats_cpu(B, fB, K*N); halves2floats_cpu(C, fC, M*N); caffe_cpu_gemm (TransA, TransB, M, N, K, float(alpha), fA, fB, float(beta), fC); floats2halves_cpu(fC, C, M*N); pool.Free((char*)fA); pool.Free((char*)fB); pool.Free((char*)fC);}