text: #include <vector>
  
  #include "caffe/layers/lrn_layer.hpp"
  #include "caffe/util/math_functions.hpp"
  
  namespace caffe {
  
  template <typename Dtype>
  void LRNLayer<Dtype>::LayerSetUp(const vector<Blob<Dtype>*>& bottom,
        const vector<Blob<Dtype>*>& top) {
    size_ = this->layer_param_.lrn_param().local_size();
    CHECK_EQ(size_ % 2, 1) << "LRN only supports odd values for local_size";
    pre_pad_ = (size_ - 1) / 2;
    alpha_ = this->layer_param_.lrn_param().alpha();
    beta_ = this->layer_param_.lrn_param().beta();
    k_ = this->layer_param_.lrn_param().k();
    if (this->layer_param_.lrn_param().norm_region() ==
        LRNParameter_NormRegion_WITHIN_CHANNEL) {
      // Set up split_layer_ to use inputs in the numerator and denominator.
      split_top_vec_.clear();
      split_top_vec_.push_back(&product_input_);
      split_top_vec_.push_back(&square_input_);
      LayerParameter split_param;
      split_layer_.reset(new SplitLayer<Dtype>(split_param));
      split_layer_->SetUp(bottom, split_top_vec_);
      // Set up square_layer_ to square the inputs.
      square_bottom_vec_.clear();
      square_top_vec_.clear();
      square_bottom_vec_.push_back(&square_input_);
      square_top_vec_.push_back(&square_output_);
      LayerParameter square_param;
      square_param.mutable_power_param()->set_power(Dtype(2));
      square_layer_.reset(new PowerLayer<Dtype>(square_param));
      square_layer_->SetUp(square_bottom_vec_, square_top_vec_);
      // Set up pool_layer_ to sum over square neighborhoods of the input.
      pool_top_vec_.clear();
      pool_top_vec_.push_back(&pool_output_);
      LayerParameter pool_param;
      pool_param.mutable_pooling_param()->set_pool(
          PoolingParameter_PoolMethod_AVE);
      pool_param.mutable_pooling_param()->set_pad(pre_pad_);
      pool_param.mutable_pooling_param()->set_kernel_size(size_);
      pool_layer_.reset(new PoolingLayer<Dtype>(pool_param));
      pool_layer_->SetUp(square_top_vec_, pool_top_vec_);
      // Set up power_layer_ to compute (1 + alpha_/N^2 s)^-beta_, where s is
      // the sum of a squared neighborhood (the output of pool_layer_).
      power_top_vec_.clear();
      power_top_vec_.push_back(&power_output_);
      LayerParameter power_param;
      power_param.mutable_power_param()->set_power(-beta_);
      power_param.mutable_power_param()->set_scale(alpha_);
      power_param.mutable_power_param()->set_shift(Dtype(1));
      power_layer_.reset(new PowerLayer<Dtype>(power_param));
      power_layer_->SetUp(pool_top_vec_, power_top_vec_);
      // Set up a product_layer_ to compute outputs by multiplying inputs by the
      // inverse demoninator computed by the power layer.
      product_bottom_vec_.clear();
      product_bottom_vec_.push_back(&product_input_);
      product_bottom_vec_.push_back(&power_output_);
      LayerParameter product_param;
      EltwiseParameter* eltwise_param = product_param.mutable_eltwise_param();
      eltwise_param->set_operation(EltwiseParameter_EltwiseOp_PROD);
      product_layer_.reset(new EltwiseLayer<Dtype>(product_param));
      product_layer_->SetUp(product_bottom_vec_, top);
    }
  }
  
  template <typename Dtype>
  void LRNLayer<Dtype>::Reshape(const vector<Blob<Dtype>*>& bottom,
        const vector<Blob<Dtype>*>& top) {
    CHECK_EQ(4, bottom[0]->num_axes()) << "Input must have 4 axes, "
        << "corresponding to (num, channels, height, width)";
    num_ = bottom[0]->num();
    channels_ = bottom[0]->channels();
    height_ = bottom[0]->height();
    width_ = bottom[0]->width();
    switch (this->layer_param_.lrn_param().norm_region()) {
    case LRNParameter_NormRegion_ACROSS_CHANNELS:
      top[0]->Reshape(num_, channels_, height_, width_);
      scale_.Reshape(num_, channels_, height_, width_);
      break;
    case LRNParameter_NormRegion_WITHIN_CHANNEL:
      split_layer_->Reshape(bottom, split_top_vec_);
      square_layer_->Reshape(square_bottom_vec_, square_top_vec_);
      pool_layer_->Reshape(square_top_vec_, pool_top_vec_);
      power_layer_->Reshape(pool_top_vec_, power_top_vec_);
      product_layer_->Reshape(product_bottom_vec_, top);
      break;
    }
  }
  
  template <typename Dtype>
  void LRNLayer<Dtype>::Forward_cpu(const vector<Blob<Dtype>*>& bottom,
      const vector<Blob<Dtype>*>& top) {
    switch (this->layer_param_.lrn_param().norm_region()) {
    case LRNParameter_NormRegion_ACROSS_CHANNELS:
      CrossChannelForward_cpu(bottom, top);
      break;
    case LRNParameter_NormRegion_WITHIN_CHANNEL:
      WithinChannelForward(bottom, top);
      break;
    default:
      LOG(FATAL) << "Unknown normalization region.";
    }
  }
  
  template <typename Dtype>
  void LRNLayer<Dtype>::CrossChannelForward_cpu(
      const vector<Blob<Dtype>*>& bottom, const vector<Blob<Dtype>*>& top) {
    const Dtype* bottom_data = bottom[0]->cpu_data();
    Dtype* top_data = top[0]->mutable_cpu_data();
    Dtype* scale_data = scale_.mutable_cpu_data();
    // start with the constant value
    for (int i = 0; i < scale_.count(); ++i) {
      scale_data[i] = k_;
    }
    Blob<Dtype> padded_square(1, channels_ + size_ - 1, height_, width_);
    Dtype* padded_square_data = padded_square.mutable_cpu_data();
    caffe_set(padded_square.count(), Dtype(0), padded_square_data);
    Dtype alpha_over_size = alpha_ / size_;
    // go through the images
    for (int n = 0; n < num_; ++n) {
      // compute the padded square
      caffe_sqr(channels_ * height_ * width_,
          bottom_data + bottom[0]->offset(n),
          padded_square_data + padded_square.offset(0, pre_pad_));
      // Create the first channel scale
      for (int c = 0; c < size_; ++c) {
        caffe_axpy<Dtype>(height_ * width_, alpha_over_size,
            padded_square_data + padded_square.offset(0, c),
            scale_data + scale_.offset(n, 0));
      }
      for (int c = 1; c < channels_; ++c) {
        // copy previous scale
        caffe_copy<Dtype>(height_ * width_,
            scale_data + scale_.offset(n, c - 1),
            scale_data + scale_.offset(n, c));
        // add head
        caffe_axpy<Dtype>(height_ * width_, alpha_over_size,
            padded_square_data + padded_square.offset(0, c + size_ - 1),
            scale_data + scale_.offset(n, c));
        // subtract tail
        caffe_axpy<Dtype>(height_ * width_, -alpha_over_size,
            padded_square_data + padded_square.offset(0, c - 1),
            scale_data + scale_.offset(n, c));
      }
    }
  
    // In the end, compute output
    caffe_powx<Dtype>(scale_.count(), scale_data, -beta_, top_data);
    caffe_mul<Dtype>(scale_.count(), top_data, bottom_data, top_data);
  }
  
  template <typename Dtype>
  void LRNLayer<Dtype>::WithinChannelForward(
      const vector<Blob<Dtype>*>& bottom, const vector<Blob<Dtype>*>& top) {
    split_layer_->Forward(bottom, split_top_vec_);
    square_layer_->Forward(square_bottom_vec_, square_top_vec_);
    pool_layer_->Forward(square_top_vec_, pool_top_vec_);
    power_layer_->Forward(pool_top_vec_, power_top_vec_);
    product_layer_->Forward(product_bottom_vec_, top);
  }
  
  template <typename Dtype>
  void LRNLayer<Dtype>::Backward_cpu(const vector<Blob<Dtype>*>& top,
      const vector<bool>& propagate_down, const vector<Blob<Dtype>*>& bottom) {
    switch (this->layer_param_.lrn_param().norm_region()) {
    case LRNParameter_NormRegion_ACROSS_CHANNELS:
      CrossChannelBackward_cpu(top, propagate_down, bottom);
      break;
    case LRNParameter_NormRegion_WITHIN_CHANNEL:
      WithinChannelBackward(top, propagate_down, bottom);
      break;
    default:
      LOG(FATAL) << "Unknown normalization region.";
    }
  }
  
  template <typename Dtype>
  void LRNLayer<Dtype>::CrossChannelBackward_cpu(
      const vector<Blob<Dtype>*>& top, const vector<bool>& propagate_down,
      const vector<Blob<Dtype>*>& bottom) {
    const Dtype* top_diff = top[0]->cpu_diff();
    const Dtype* top_data = top[0]->cpu_data();
    const Dtype* bottom_data = bottom[0]->cpu_data();
    const Dtype* scale_data = scale_.cpu_data();
    Dtype* bottom_diff = bottom[0]->mutable_cpu_diff();
    Blob<Dtype> padded_ratio(1, channels_ + size_ - 1, height_, width_);
    Blob<Dtype> accum_ratio(1, 1, height_, width_);
    Dtype* padded_ratio_data = padded_ratio.mutable_cpu_data();
    Dtype* accum_ratio_data = accum_ratio.mutable_cpu_data();
    // We hack a little bit by using the diff() to store an additional result
    Dtype* accum_ratio_times_bottom = accum_ratio.mutable_cpu_diff();
    caffe_set(padded_ratio.count(), Dtype(0), padded_ratio_data);
    Dtype cache_ratio_value = 2. * alpha_ * beta_ / size_;
  
    caffe_powx<Dtype>(scale_.count(), scale_data, -beta_, bottom_diff);
    caffe_mul<Dtype>(scale_.count(), top_diff, bottom_diff, bottom_diff);
  
    // go through individual data
    int inverse_pre_pad = size_ - (size_ + 1) / 2;
    for (int n = 0; n < num_; ++n) {
      int block_offset = scale_.offset(n);
      // first, compute diff_i * y_i / s_i
      caffe_mul<Dtype>(channels_ * height_ * width_,
          top_diff + block_offset, top_data + block_offset,
          padded_ratio_data + padded_ratio.offset(0, inverse_pre_pad));
      caffe_div<Dtype>(channels_ * height_ * width_,
          padded_ratio_data + padded_ratio.offset(0, inverse_pre_pad),
          scale_data + block_offset,
          padded_ratio_data + padded_ratio.offset(0, inverse_pre_pad));
      // Now, compute the accumulated ratios and the bottom diff
      caffe_set(accum_ratio.count(), Dtype(0), accum_ratio_data);
      for (int c = 0; c < size_ - 1; ++c) {
        caffe_axpy<Dtype>(height_ * width_, 1.,
            padded_ratio_data + padded_ratio.offset(0, c), accum_ratio_data);
      }
      for (int c = 0; c < channels_; ++c) {
        caffe_axpy<Dtype>(height_ * width_, 1.,
            padded_ratio_data + padded_ratio.offset(0, c + size_ - 1),
            accum_ratio_data);
        // compute bottom diff
        caffe_mul<Dtype>(height_ * width_,
            bottom_data + top[0]->offset(n, c),
            accum_ratio_data, accum_ratio_times_bottom);
        caffe_axpy<Dtype>(height_ * width_, -cache_ratio_value,
            accum_ratio_times_bottom, bottom_diff + top[0]->offset(n, c));
        caffe_axpy<Dtype>(height_ * width_, -1.,
            padded_ratio_data + padded_ratio.offset(0, c), accum_ratio_data);
      }
    }
  }
  
  template <typename Dtype>
  void LRNLayer<Dtype>::WithinChannelBackward(
      const vector<Blob<Dtype>*>& top, const vector<bool>& propagate_down,
      const vector<Blob<Dtype>*>& bottom) {
    if (propagate_down[0]) {
      vector<bool> product_propagate_down(2, true);
      product_layer_->Backward(top, product_propagate_down, product_bottom_vec_);
      power_layer_->Backward(power_top_vec_, propagate_down, pool_top_vec_);
      pool_layer_->Backward(pool_top_vec_, propagate_down, square_top_vec_);
      square_layer_->Backward(square_top_vec_, propagate_down,
                              square_bottom_vec_);
      split_layer_->Backward(split_top_vec_, propagate_down, bottom);
    }
  }
  
  #ifdef CPU_ONLY
  STUB_GPU(LRNLayer);
  STUB_GPU_FORWARD(LRNLayer, CrossChannelForward);
  STUB_GPU_BACKWARD(LRNLayer, CrossChannelBackward);
  #endif
  
  INSTANTIATE_CLASS(LRNLayer);
  
  }  // namespace caffe
  