caffe系列：deeplab中的插值网络层前传和反传的实现分析
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一、前言
最近在torch中实现一个网络，需要用到插值层，索性就看了下deeplab中插值网络层的实现，移植到torch中，废话少说，先粗略地写个放上来。
二、双线性插值理论
暂时没空写那么详细，双线性插值的理论可以看
https://en.wikipedia.org/wiki/Bilinear_interpolation
三、插值层的前向和反向传播的实现分析
插值网络层的实现：
interp_layer.cpp文件
https://bitbucket.org/aquariusjay/deeplab-public-ver2/src/071ef5a59aad8d9e6e1f5b8dff3d7a5c984a3d3a/src/caffe/layers/interp_layer.cpp?at=master&fileviewer=file-view-default
前传和反传的CPU实现interp.cpp
https://bitbucket.org/aquariusjay/deeplab-public-ver2/src/071ef5a59aad8d9e6e1f5b8dff3d7a5c984a3d3a/src/caffe/util/interp.cpp?at=master&fileviewer=file-view-default
我这里只分析CPU的实现，GPU没有时间看
（0）网络层中参数及概览
template <typename Dtype>
void InterpLayer<Dtype>::LayerSetUp(const vector<Blob<Dtype>*>& bottom,
const vector<Blob<Dtype>*>& top)
InterpParameter interp_param = this->layer_param_.interp_param();
pad_beg_ = interp_param.pad_beg();
pad_end_ = interp_param.pad_end();
// pad必须小于等于0,这里实际上是crop
CHECK_LE(pad_beg_, 0) << "Only supports non-pos padding (cropping) for now";
CHECK_LE(pad_end_, 0) << "Only supports non-pos padding (cropping) for now";
template <typename Dtype>
void InterpLayer<Dtype>::Reshape(const vector<Blob<Dtype>*>& bottom,
const vector<Blob<Dtype>*>& top)
num_ = bottom[0]->num();
channels_ = bottom[0]->channels();
height_in_ = bottom[0]->height();
width_in_ = bottom[0]->width();
// crop之后的高度
height_in_eff_ = height_in_ + pad_beg_ + pad_end_;
// crop之后的宽度
width_in_eff_ = width_in_ + pad_beg_ + pad_end_;
InterpParameter interp_param = this->layer_param_.interp_param();
if (interp_param.has_shrink_factor() &&
!interp_param.has_zoom_factor())
// 缩小因子
const int shrink_factor = interp_param.shrink_factor();
// 检查是否大于等于1
CHECK_GE(shrink_factor, 1) << "Shrink factor must be positive";
// 计算缩小之后的大小，宽度和高度， 上取整
height_out_ = (height_in_eff_ - 1) / shrink_factor + 1;
width_out_ = (width_in_eff_ - 1) / shrink_factor + 1;
else if (interp_param.has_zoom_factor() &&
!interp_param.has_shrink_factor())
// 放大因子
const int zoom_factor = interp_param.zoom_factor();
// 检查是否大于等于1
CHECK_GE(zoom_factor, 1) << "Zoom factor must be positive";
// 这是什么鬼，为啥放大因子要减去1
height_out_ = height_in_eff_ + (height_in_eff_ - 1) * (zoom_factor - 1);
width_out_ = width_in_eff_ + (width_in_eff_ - 1) * (zoom_factor - 1);
else if (interp_param.has_height() && interp_param.has_width())
// 如果直接给出输出大小
height_out_ = interp_param.height();
width_out_ = interp_param.width();
else if (interp_param.has_shrink_factor() &&
interp_param.has_zoom_factor())
// 如果给出缩放因子和放大因子
const int shrink_factor = interp_param.shrink_factor();
const int zoom_factor = interp_param.zoom_factor();
CHECK_GE(shrink_factor, 1) << "Shrink factor must be positive";
CHECK_GE(zoom_factor, 1) << "Zoom factor must be positive";
// 先缩放，再放大之后的大小
height_out_ = (height_in_eff_ - 1) / shrink_factor + 1;
width_out_ = (width_in_eff_ - 1) / shrink_factor + 1;
height_out_ = height_out_ + (height_out_ - 1) * (zoom_factor - 1);
width_out_ = width_out_ + (width_out_ - 1) * (zoom_factor - 1);
else
LOG(FATAL);
CHECK_GT(height_in_eff_, 0) << "height should be positive";
CHECK_GT(width_in_eff_, 0) << "width should be positive";
CHECK_GT(height_out_, 0) << "height should be positive";
CHECK_GT(width_out_, 0) << "width should be positive";
// reshape输出的blob
top[0]->Reshape(num_, channels_, height_out_, width_out_);
template <typename Dtype>
void InterpLayer<Dtype>::Forward_cpu(const vector<Blob<Dtype>*>& bottom,
const vector<Blob<Dtype>*>& top)
// 调用具体的实现
caffe_cpu_interp2<Dtype,false>(num_ * channels_,
bottom[0]->cpu_data(), - pad_beg_, - pad_beg_, height_in_eff_, width_in_eff_, height_in_, width_in_,
top[0]->mutable_cpu_data(), 0, 0, height_out_, width_out_, height_out_, width_out_);
template <typename Dtype>
void InterpLayer<Dtype>::Backward_cpu(const vector<Blob<Dtype>*>& top,
const vector<bool>& propagate_down, const vector<Blob<Dtype>*>& bottom)
if (!propagate_down[0]) return;
// 调用具体的实现
caffe_set(bottom[0]->count(), Dtype(0), bottom[0]->mutable_cpu_diff());
caffe_cpu_interp2_backward<Dtype,false>(num_ * channels_,
bottom[0]->mutable_cpu_diff(), - pad_beg_, - pad_beg_, height_in_eff_, width_in_eff_, height_in_, width_in_,
top[0]->cpu_diff(), 0, 0, height_out_, width_out_, height_out_, width_out_);
（1）前向
注释有部分是英文的，先贴上来，后面有空再解释
// Bi-linear interpolation
// https://en.wikipedia.org/wiki/Bilinear_interpolation
// IN : [channels height1 width1] cropped from a bigger [Height1 Width1] image
// OUT: [channels height2 width2] cropped from a bigger [Height2 Width2] image
template <typename Dtype, bool packed>
void caffe_cpu_interp2(const int channels,
const Dtype *data1, const int x1, const int y1, const int height1, const int width1, const int Height1, const int Width1,
Dtype *data2, const int x2, const int y2, const int height2, const int width2, const int Height2, const int Width2)
// 检查是否合法
CHECK(x1 >= 0 && y1 >= 0 && height1 > 0 && width1 > 0 && x2 >= 0 && y2 >= 0 && height2 > 0 && width2 > 0);
CHECK(Width1 >= width1 + x1 && Height1 >= height1 + y1 && Width2 >= width2 + x2 && Height2 >= height2 + y2);
// 参数解释
// channels 输入数据的个数
// data1 输入数据指针
// x1 输入数据w偏移量
// y1 输入数据h偏移量
// height1 输入数据crop之后的高度
// width1 输入数据crop之后的宽度
// Height1 输入数据的原始高度
// Width1 输入数据的原始宽度
// data2 输出的数据指针
// x2 输出数据w偏移
// y2 输出数据h偏移
// height2 输出数据crop之后的高度
// width2 输出数据crop之后的宽度
// Height2 输出数据的原始高度
// Width2 输出数据的原始宽度
// special case: just copy
if (height1 == height2 && width1 == width2)
// 输入和输出一样大小的
for (int h2 = 0; h2 < height2; ++h2)
const int h1 = h2;
for (int w2 = 0; w2 < width2; ++w2)
const int w1 = w2;
if (packed)
// what is packed?
const Dtype* pos1 = &data1[channels * ((y1 + h1) * Width1 + (x1 + w1))];
Dtype* pos2 = &data2[channels * ((y2 + h2) * Width2 + (x2 + w2))];
for (int c = 0; c < channels; ++c)
pos2[0] = pos1[0];
pos1++;
pos2++;
else
// normal situation
const Dtype* pos1 = &data1[(y1 + h1) * Width1 + (x1 + w1)];
Dtype* pos2 = &data2[(y2 + h2) * Width2 + (x2 + w2)];
for (int c = 0; c < channels; ++c)
pos2[0] = pos1[0];
pos1 += Width1 * Height1;
pos2 += Width2 * Height2;
return;
// calculate height factor and width factor
// input / output
const float rheight = (height2 > 1) ? static_cast<float>(height1 - 1) / (height2 - 1) : 0.f;
const float rwidth = (width2 > 1) ? static_cast<float>(width1 - 1) / (width2 - 1) : 0.f;
for (int h2 = 0; h2 < height2; ++h2) // calculate h1 and w1 according to h2 and w2
// calculate height in the input image according to h factor
const float h1r = rheight * h2;
// convert h1r to int
const int h1 = h1r;
// h1p indicates whether the pos is valid
const int h1p = (h1 < height1 - 1) ? 1 : 0;
// h0lambda and h1lambda indicate two residuals in wiki equation
const Dtype h1lambda = h1r - h1;
const Dtype h0lambda = Dtype(1.) - h1lambda;
for (int w2 = 0; w2 < width2; ++w2)
// calculate width in the input image according to w factor
const float w1r = rwidth * w2;
// convert w1r to int
const int w1 = w1r;
// w1p indicates whether the pos is valid
const int w1p = (w1 < width1 - 1) ? 1 : 0;
// w0lambda and w1lambda indicate two residuals in wiki equation
const Dtype w1lambda = w1r - w1;
const Dtype w0lambda = Dtype(1.) - w1lambda;
if (packed)
const Dtype* pos1 = &data1[channels * ((y1 + h1) * Width1 + (x1 + w1))];
Dtype* pos2 = &data2[channels * ((y2 + h2) * Width2 + (x2 + w2))];
for (int c = 0; c < channels; ++c)
pos2[0] =
h0lambda * (w0lambda * pos1[0] + w1lambda * pos1[channels * w1p]) +
h1lambda * (w0lambda * pos1[channels * h1p * Width1] + w1lambda * pos1[channels * (h1p * Width1 + w1p)]);
pos1++;
pos2++;
else
const Dtype* pos1 = &data1[(y1 + h1) * Width1 + (x1 + w1)];
Dtype* pos2 = &data2[(y2 + h2) * Width2 + (x2 + w2)];
for (int c = 0; c < channels; ++c) // visit all channels
// calculate bi-linear interpolation according to wiki
pos2[0] =
h0lambda * (w0lambda * pos1[0] + w1lambda * pos1[w1p]) +
h1lambda * (w0lambda * pos1[h1p * Width1] + w1lambda * pos1[h1p * Width1 + w1p]);
pos1 += Width1 * Height1;
pos2 += Width2 * Height2;
（2）反向
// Backward (adjoint) operation 1 <- 2 (accumulates)
template <typename Dtype, bool packed>
void caffe_cpu_interp2_backward(const int channels,
Dtype *data1, const int x1, const int y1, const int height1, const int width1, const int Height1, const int Width1,
const Dtype *data2, const int x2, const int y2, const int height2, const int width2, const int Height2, const int Width2)
// check parameters
CHECK(x1 >= 0 && y1 >= 0 && height1 > 0 && width1 > 0 && x2 >= 0 && y2 >= 0 && height2 > 0 && width2 > 0);
CHECK(Width1 >= width1 + x1 && Height1 >= height1 + y1 && Width2 >= width2 + x2 && Height2 >= height2 + y2);
// special case: same-size matching grids
if (height1 == height2 && width1 == width2)
for (int h2 = 0; h2 < height2; ++h2)
const int h1 = h2;
for (int w2 = 0; w2 < width2; ++w2)
const int w1 = w2;
if (packed)
Dtype* pos1 = &data1[channels * ((y1 + h1) * Width1 + (x1 + w1))];
const Dtype* pos2 = &data2[channels * ((y2 + h2) * Width2 + (x2 + w2))];
for (int c = 0; c < channels; ++c)
pos1[0] += pos2[0];
pos1++;
pos2++;
else
Dtype* pos1 = &data1[(y1 + h1) * Width1 + (x1 + w1)];
const Dtype* pos2 = &data2[(y2 + h2) * Width2 + (x2 + w2)];
for (int c = 0; c < channels; ++c)
// acumulate gradients
pos1[0] += pos2[0];
pos1 += Width1 * Height1;
pos2 += Width2 * Height2;
return;
// calculate w/h factor
// input image / output image
const float rheight = (height2 > 1) ? static_cast<float>(height1 - 1) / (height2 - 1) : 0.f;
const float rwidth = (width2 > 1) ? static_cast<float>(width1 - 1) / (width2 - 1) : 0.f;
for (int h2 = 0; h2 < height2; ++h2)
const float h1r = rheight * h2;
const int h1 = h1r;
const int h1p = (h1 < height1 - 1) ? 1 : 0;
const Dtype h1lambda = h1r - h1;
const Dtype h0lambda = Dtype(1.) - h1lambda;
for (int w2 = 0; w2 < width2; ++w2)
const float w1r = rwidth * w2;
const int w1 = w1r;
const int w1p = (w1 < width1 - 1) ? 1 : 0;
const Dtype w1lambda = w1r - w1;
const Dtype w0lambda = Dtype(1.) - w1lambda;
if (packed)
Dtype* pos1 = &data1[channels * ((y1 + h1) * Width1 + (x1 + w1))];
const Dtype* pos2 = &data2[channels * ((y2 + h2) * Width2 + (x2 + w2))];
for (int c = 0; c < channels; ++c)
pos1[0] += h0lambda * w0lambda * pos2[0];
pos1[channels * w1p] += h0lambda * w1lambda * pos2[0];
pos1[channels * h1p * Width1] += h1lambda * w0lambda * pos2[0];
pos1[channels * (h1p * Width1 + w1p)] += h1lambda * w1lambda * pos2[0];
pos1++;
pos2++;
else
Dtype* pos1 = &data1[(y1 + h1) * Width1 + (x1 + w1)];
const Dtype* pos2 = &data2[(y2 + h2) * Width2 + (x2 + w2)];
for (int c = 0; c < channels; ++c)
// acumulate gradients from scaled pixels
pos1[0] += h0lambda * w0lambda * pos2[0];
pos1[w1p] += h0lambda * w1lambda * pos2[0];
pos1[h1p * Width1] += h1lambda * w0lambda * pos2[0];
pos1[h1p * Width1 + w1p] += h1lambda * w1lambda * pos2[0];
pos1 += Width1 * Height1;
pos2 += Width2 * Height2;
四、总结：
实际上这里实现的双线性插值还挺简单的，就是根据维基百科上面的实现来实现前传的，另外，前传的时候需要注意边界问题
此外反传则是将进行插值后之后的像素值反传到插值之前的位置，进行累加来实现的。
有不懂的可以留言
后来发现torch里面已经有人移植过去了，干脆帖进来
五、torch中的实现
https://github.com/torch/nn/blob/master/SpatialUpSamplingBilinear.lua
lua的接口
require 'nn.THNN'
local SpatialUpSamplingBilinear, parent =
torch.class('nn.SpatialUpSamplingBilinear', 'nn.Module')
--[[
Applies a 2D bilinear up-sampling over an input image composed of several
input planes.
The Y and X dimensions are assumed to be the last 2 tensor dimensions. For
instance, if the tensor is 4D, then dim 3 is the y dimension and dim 4 is the x.
scale_factor is assumed to be a positive integer.
owidth = (width-1)*(scale_factor-1) + width
oheight = (height-1)*(scale_factor-1) + height
Alternatively, owidth and oheight can be directly provided as input.
--]]
function SpatialUpSamplingBilinear:__init(params)
parent.__init(self)
self.owidth, self.oheight, self.scale_factor = nil, nil, nil
if torch.type(params) == 'table' then
self.owidth, self.oheight = params.owidth, params.oheight
else
self.scale_factor = params
if self.scale_factor < 1 then
error('scale_factor must be greater than 1')
end
if math.floor(self.scale_factor) ~= self.scale_factor then
error('scale_factor must be integer')
end
end
self.inputSize = torch.LongStorage(4)
self.outputSize = torch.LongStorage(4)
end
local function makeContiguous(self, input, gradOutput)
if not input:isContiguous() then
self._input = self._input or input.new()
self._input:resizeAs(input):copy(input)
input = self._input
end
if gradOutput then
if not gradOutput:isContiguous() then
self._gradOutput = self._gradOutput or gradOutput.new()
self._gradOutput:resizeAs(gradOutput):copy(gradOutput)
gradOutput = self._gradOutput
end
end
return input, gradOutput
end
function SpatialUpSamplingBilinear:setSize(input)
local xdim = input:dim()
local ydim = xdim - 1
for i = 1, input:dim() do
self.inputSize[i] = input:size(i)
self.outputSize[i] = input:size(i)
end
if self.scale_factor ~= nil then
self.outputSize[ydim] = self.outputSize[ydim] * self.scale_factor
self.outputSize[xdim] = self.outputSize[xdim] * self.scale_factor
else
self.outputSize[ydim] = self.oheight
self.outputSize[xdim] = self.owidth
end
end
function SpatialUpSamplingBilinear:updateOutput(input)
assert(input:dim() == 4 or input:dim()==3,
'SpatialUpSamplingBilinear only supports 3D or 4D tensors' )
input = makeContiguous(self, input)
local inputwas3D = false
if input:dim() == 3 then
input=input:view(-1, input:size(1), input:size(2), input:size(3))
inputwas3D = true
end
local xdim = input:dim()
local ydim = xdim - 1
self:setSize(input)
input.THNN.SpatialUpSamplingBilinear_updateOutput(
input:cdata(),
self.output:cdata(),
self.outputSize[ydim],
self.outputSize[xdim]
)
if inputwas3D then
input = input:squeeze(1)
self.output = self.output:squeeze(1)
end
return self.output
end
function SpatialUpSamplingBilinear:updateGradInput(input, gradOutput)
assert(input:dim() == 4 or input:dim()==3,
'SpatialUpSamplingBilinear only support 3D or 4D tensors' )
assert(input:dim() == gradOutput:dim(),
'Input and gradOutput should be of same dimension' )
input, gradOutput = makeContiguous(self, input, gradOutput)
local inputwas3D = false
if input:dim() == 3 then
input = input:view(-1, input:size(1), input:size(2), input:size(3))
gradOutput = gradOutput:view(-1, gradOutput:size(1), gradOutput:size(2),
gradOutput:size(3))
inputwas3D = true
end
local xdim = input:dim()
local ydim = xdim - 1
self.gradInput:resizeAs(input)
input.THNN.SpatialUpSamplingBilinear_updateGradInput(
gradOutput:cdata(),
self.gradInput:cdata(),
input:size(1),
input:size(2),
input:size(3),
input:size(4),
self.outputSize[ydim],
self.outputSize[xdim]
)
if inputwas3D then
input = input:squeeze(1)
gradOutput = gradOutput:squeeze(1)
self.gradInput = self.gradInput:squeeze(1)
end
return self.gradInput
end
function SpatialUpSamplingBilinear:__tostring__()
local s
if self.scale_factor ~= nil then
s = string.format('%s(%d)', torch.type(self), self.scale_factor)
else
s = string.format('%s(%d, %d)',
torch.type(self), self.oheight, self.owidth)
end
return s
end
底层的c实现
https://raw.githubusercontent.com/torch/nn/master/lib/THNN/generic/SpatialUpSamplingBilinear.c
// Adapted from interp.cpp from Caffe util by Pauline Luc
// Originally developed by George Papandreou
#ifndef TH_GENERIC_FILE
#define TH_GENERIC_FILE "generic/SpatialUpSamplingBilinear.c"
#else
static inline void THNN_(SpatialUpSamplingBilinear_shapeCheck)
(THTensor *input, THTensor *gradOutput,
int nBatch, int nChannels,
int inputHeight, int inputWidth,
int outputHeight, int outputWidth)
THArgCheck(inputHeight > 0 && inputWidth > 0
&& outputHeight > 0 && outputWidth > 0, 2,
"input and output sizes should be greater than 0,"
" but got input (H: %d, W: %d) output (H: %d, W: %d)",
inputHeight, inputWidth, outputHeight, outputWidth);
if (input != NULL)
THNN_ARGCHECK(input->nDimension == 4, 2, input,
"4D input tensor expected but got: %s");
if (gradOutput != NULL)
THNN_CHECK_DIM_SIZE(gradOutput, 4, 0, nBatch);
THNN_CHECK_DIM_SIZE(gradOutput, 4, 1, nChannels);
THNN_CHECK_DIM_SIZE(gradOutput, 4, 2, outputHeight);
THNN_CHECK_DIM_SIZE(gradOutput, 4, 3, outputWidth);
void THNN_(SpatialUpSamplingBilinear_updateOutput)(
THNNState *state,
THTensor *input,
THTensor *output,
int outputHeight,
int outputWidth)
int nbatch = THTensor_(size)(input, 0);
int channels = THTensor_(size)(input, 1);
int inputHeight = THTensor_(size)(input, 2);
int inputWidth = THTensor_(size)(input, 3);
THNN_(SpatialUpSamplingBilinear_shapeCheck)
(input, NULL,
nbatch, channels,
inputHeight, inputWidth,
outputHeight, outputWidth);
input = THTensor_(newContiguous)(input);
THTensor_(resize4d)(output,
THTensor_(size)(input, 0),
THTensor_(size)(input, 1),
outputHeight, outputWidth);
THTensor_(zero)(output);
real *idata = THTensor_(data)(input);
real *odata = THTensor_(data)(output);
channels = nbatch * channels;
THAssert(inputHeight > 0 && inputWidth > 0 && outputHeight > 0 && outputWidth > 0);
// special case: just copy
if (inputHeight == outputHeight && inputWidth == outputWidth)
for (int h2 = 0; h2 < outputHeight; ++h2)
const int h1 = h2;
for (int w2 = 0; w2 < outputWidth; ++w2)
const int w1 = w2;
const real* pos1 = &idata[h1 * inputWidth + w1];
real* pos2 = &odata[h2 * outputWidth + w2];
for (int c = 0; c < channels; ++c)
pos2[0] = pos1[0];
pos1 += inputWidth * inputHeight;
pos2 += outputWidth * outputHeight;
return;
const float rheight =(outputHeight > 1) ? (float)(inputHeight - 1)/(outputHeight - 1) : 0.f;
const float rwidth = (outputWidth > 1) ? (float)(inputWidth - 1) / (outputWidth - 1) : 0.f;
for (int h2 = 0; h2 < outputHeight; ++h2)
const float h1r = rheight * h2;
const int h1 = h1r;
const int h1p = (h1 < inputHeight - 1) ? 1 : 0;
const real h1lambda = h1r - h1;
const real h0lambda = (real)1. - h1lambda;
for (int w2 = 0; w2 < outputWidth; ++w2)
const float w1r = rwidth * w2;
const int w1 = w1r;
const int w1p = (w1 < inputWidth - 1) ? 1 : 0;
const real w1lambda = w1r - w1;
const real w0lambda = (real)1. - w1lambda;
const real* pos1 = &idata[h1 * inputWidth + w1];
real* pos2 = &odata[h2 * outputWidth + w2];
for (int c = 0; c < channels; ++c)
pos2[0] = h0lambda * (w0lambda * pos1[0]+ w1lambda * pos1[w1p])
+ h1lambda * (w0lambda * pos1[h1p * inputWidth]
+ w1lambda * pos1[h1p * inputWidth + w1p]);
pos1 += inputWidth * inputHeight;
pos2 += outputWidth * outputHeight;
THTensor_(free)(input);
void THNN_(SpatialUpSamplingBilinear_updateGradInput)(
THNNState *state,
THTensor *gradOutput,
THTensor *gradInput,
int nbatch,
int channels,
int inputHeight,
int inputWidth,
int outputHeight,
int outputWidth)
THNN_(SpatialUpSamplingBilinear_shapeCheck)
(NULL, gradOutput,
nbatch, channels,
inputHeight, inputWidth,
outputHeight, outputWidth);
THTensor_(resize4d)(gradInput, nbatch, channels, inputHeight, inputWidth);
THTensor_(zero)(gradInput);
gradOutput = THTensor_(newContiguous)(gradOutput);
real *data1 = THTensor_(data)(gradInput);
real *data2 = THTensor_(data)(gradOutput);
channels = nbatch * channels;
// special case: same-size matching grids
if (inputHeight == outputHeight && inputWidth == outputWidth)
for (int h2 = 0; h2 < outputHeight; ++h2)
const int h1 = h2;
for (int w2 = 0; w2 < outputWidth; ++w2)
const int w1 = w2;
real* pos1 = &data1[h1 * inputWidth + w1];
const real* pos2 = &data2[h2 * outputWidth + w2];
for (int c = 0; c < channels; ++c)
pos1[0] += pos2[0];
pos1 += inputWidth * inputHeight;
pos2 += outputWidth * outputHeight;
return;
const float rheight =(outputHeight > 1) ? (float)(inputHeight - 1)/(outputHeight - 1) : 0.f;
const float rwidth = (outputWidth > 1) ? (float)(inputWidth - 1)/(outputWidth - 1) : 0.f;
for (int h2 = 0; h2 < outputHeight; ++h2)
const float h1r = rheight * h2;
const int h1 = h1r;
const int h1p = (h1 < inputHeight - 1) ? 1 : 0;
const real h1lambda = h1r - h1;
const real h0lambda = (real)1. - h1lambda;
for (int w2 = 0; w2 < outputWidth; ++w2)
const float w1r = rwidth * w2;
const int w1 = w1r;
const int w1p = (w1 < inputWidth - 1) ? 1 : 0;
const real w1lambda = w1r - w1;
const real w0lambda = (real)1. - w1lambda;
real* pos1 = &data1[h1 * inputWidth + w1];
const real* pos2 = &data2[h2 * outputWidth + w2];
for (int c = 0; c < channels; ++c)
pos1[0] += h0lambda * w0lambda * pos2[0];
pos1[w1p] += h0lambda * w1lambda * pos2[0];
pos1[h1p * inputWidth] += h1lambda * w0lambda * pos2[0];
pos1[h1p * inputWidth + w1p] += h1lambda * w1lambda * pos2[0];
pos1 += inputWidth * inputHeight;
pos2 += outputWidth * outputHeight;
THTensor_(free)(gradOutput);
#endif
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