Propagation.hxx

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// @(#)root/tmva/tmva/dnn:$Id$
// Author: Simon Pfreundschuh 10/07/16
 
/*************************************************************************
 * Copyright (C) 2016, Simon Pfreundschuh                                *
 * All rights reserved.                                                  *
 *                                                                       *
 * For the licensing terms see $ROOTSYS/LICENSE.                         *
 * For the list of contributors see $ROOTSYS/README/CREDITS.             *
 *************************************************************************/
 
//////////////////////////////////////////////////////////////////////
// Implementation of the functions required for the forward and     //
// backward propagation of activations through a neural network for //
// the reference implementation.                                    //
//////////////////////////////////////////////////////////////////////
 
#include "TMVA/DNN/Architectures/Cpu.h"
 
 
#ifdef R__HAS_TMVACPU
#include "Blas.h"
#else
#include "TMVA/DNN/Architectures/Reference.h"
#endif
 
namespace TMVA {
namespace DNN {
 
 
 
template <typename AFloat>
void TCpu<AFloat>::MultiplyTranspose(TCpu<AFloat>::Matrix_t &output, const TCpu<AFloat>::Matrix_t &input,
                                     const TCpu<AFloat>::Matrix_t &Weights)
{
 
   int m = (int)input.GetNrows();
   int k = (int)input.GetNcols();
   int n = (int)Weights.GetNrows();
 
   if ((int)output.GetNrows() != m) {
      Error("MultiplyTranspose","Invalid input - output  rows  - input:  %d != output : %d",m, (int) output.GetNrows());
      R__ASSERT((int) output.GetNrows() == m);
   }
   if ((int)output.GetNcols() != n) {
      Error("MultiplyTranspose","Invalid output cols or weight  rows  - output cols:  %d != weight rows : %d",(int) output.GetNcols(),n);
      R__ASSERT((int) output.GetNcols() == n);
   }
   if ((int)Weights.GetNcols() != k) {
      Error("MultiplyTranspose","Invalid input cols or weight cols  - input cols:  %d != weight cols : %d", k, (int) Weights.GetNcols());
      R__ASSERT((int) Weights.GetNcols() == k);
   }
 
#ifdef R__HAS_TMVACPU
 
   char transa = 'N';
   char transb = 'T';
 
   AFloat alpha = 1.0;
   AFloat beta = 0.0;
 
   const AFloat *A = input.GetRawDataPointer();
   const AFloat *B = Weights.GetRawDataPointer();
   AFloat *C = output.GetRawDataPointer();
 
   ::TMVA::DNN::Blas::Gemm(&transa, &transb, &m, &n, &k, &alpha, A, &m, B, &n, &beta, C, &m);
#else
   TMatrixT<AFloat> tmp(output.GetNrows(), output.GetNcols());
   tmp.MultT(input, Weights);
   output = tmp;
#endif
}
 
template <typename AFloat>
void TCpu<AFloat>::AddRowWise(TCpu<AFloat>::Matrix_t &output, const TCpu<AFloat>::Matrix_t &biases)
{
#ifdef R__HAS_TMVACPU
   int m = (int)output.GetNrows();
   int n = (int)output.GetNcols();
 
   int inc = 1.0;
   AFloat alpha = 1.0;
 
   AFloat *A = output.GetRawDataPointer();
   const AFloat *x = TCpuMatrix<AFloat>::GetOnePointer();
   const AFloat *y = biases.GetRawDataPointer();
 
   R__ASSERT(m <= (int)TCpuMatrix<AFloat>::GetOnePointerSize());
   R__ASSERT(n <= (int)(biases.GetNcols()*biases.GetNrows()));
 
   ::TMVA::DNN::Blas::Ger(&m, &n, &alpha, x, &inc, y, &inc, A, &m);
#else
   TMatrixT<AFloat> tmp = output;
   TReference<AFloat>::AddRowWise(tmp, biases);
   output = tmp;
#endif
}
 
template <typename AFloat>
void TCpu<AFloat>::Backward(TCpuTensor<AFloat> &activationGradientsBackward, TCpuMatrix<AFloat> &weightGradients,
                            TCpuMatrix<AFloat> &biasGradients, const TCpuTensor<AFloat> &df,
                            const TCpuTensor<AFloat> &/*activationGradients*/, const TCpuMatrix<AFloat> &weights,
                            const TCpuTensor<AFloat> &activationsBackward)
{
   // Compute element-wise product.
   //Hadamard(df, activationGradients);
 
   Matrix_t df_m = df.GetMatrix();
 
   // Activation gradients (exclude if it is first layer)
   if (activationGradientsBackward.GetSize() > 0 ) {
 
      Matrix_t  activationGradientsBackward_m = activationGradientsBackward.GetMatrix();
 
      Multiply(activationGradientsBackward_m, df_m, weights);
   }
 
   // Weight gradients.
   if (weightGradients.GetNoElements() > 0) TransposeMultiply(weightGradients, df_m, activationsBackward.GetMatrix());
 
   // PrintTensor(activationsBackward,"activ backward");
   //PrintTensor(Tensor_t(weightGradients),"weight gradients");
 
   // Bias gradients.
   if (biasGradients.GetNoElements() > 0) SumColumns(biasGradients, df_m);
}
 
 
 
//____________________________________________________________________________
template <typename AFloat>
void TCpu<AFloat>::Im2col(TCpuMatrix<AFloat> &A, const TCpuMatrix<AFloat> &B, size_t imgHeight, size_t imgWidth,
                          size_t fltHeight, size_t fltWidth, size_t strideRows, size_t strideCols,
                          size_t zeroPaddingHeight, size_t zeroPaddingWidth)
{
 
   // image boudaries
   int imgHeightBound = imgHeight + zeroPaddingHeight - (fltHeight - 1) / 2 - 1;
   int imgWidthBound = imgWidth + zeroPaddingWidth - (fltWidth - 1) / 2 - 1;
   size_t currLocalView = 0;
 
   const int halfFltHeight =  fltHeight / 2;
   const int halfFltWidth =  fltWidth / 2;
   const int halfFltHeightM1 = (fltHeight - 1) / 2;
   const int halfFltWidthM1 = (fltWidth - 1) / 2;
   const int nRowsInput = B.GetNrows();
   const int nColsInput = B.GetNcols();
   const int nRowsOutput = A.GetNrows();
   const int nColsOutput = A.GetNcols();
 
   // convolution centers
   for (int i = halfFltHeight -zeroPaddingHeight; i <= imgHeightBound; i += strideRows) {
      for (int j = halfFltWidth -zeroPaddingWidth ; j <= imgWidthBound; j += strideCols) {
         size_t currLocalViewPixel = 0;
 
         // within the local view
         R__ASSERT((int) currLocalView < nRowsOutput );
 
         for (int m = 0; m < nRowsInput; m++) {
            for (int k = i - halfFltHeight  ; k <= Int_t(i + halfFltHeightM1 ); k++) {
               int kstep = k * imgWidth;
               for (int l = j - halfFltWidth ; l <= Int_t(j + halfFltWidthM1); l++) {
 
                  // Check the boundaries
                  R__ASSERT((int) currLocalViewPixel < nColsOutput );
                  //R__ASSERT(k * imgWidth + l < B.GetNcols());
                  if (k < 0 || k >= (Int_t)imgHeight || l < 0 || l >= (Int_t)imgWidth || kstep + l >=  nColsInput)
                     A(currLocalView, currLocalViewPixel++) = 0;
                  else
                     A(currLocalView, currLocalViewPixel++) = B(m, kstep + l);
               }
            }
         }
         //std::cout << " i " << i << "  " << j << " increment currLocalView " << currLocalView << std::endl;
         currLocalView++;
      }
   }
   //TMVA_DNN_PrintTCpuMatrix(A,"FromIm2Col");
}
 
//____________________________________________________________________________
template <typename AFloat>
void TCpu<AFloat>::Im2colIndices(std::vector<int> &V, const TCpuMatrix<AFloat> &B, size_t nLocalViews, size_t imgHeight, size_t imgWidth,
                          size_t fltHeight, size_t fltWidth, size_t strideRows, size_t strideCols,
                           size_t zeroPaddingHeight, size_t zeroPaddingWidth)
{
 
   // image boudaries
   int imgHeightBound = imgHeight + zeroPaddingHeight - (fltHeight - 1) / 2 - 1;
   int imgWidthBound = imgWidth + zeroPaddingWidth - (fltWidth - 1) / 2 - 1;
   size_t currLocalView = 0;
 
   const int halfFltHeight =  fltHeight / 2;
   const int halfFltWidth =  fltWidth / 2;
   const int halfFltHeightM1 = (fltHeight - 1) / 2;
   const int halfFltWidthM1 = (fltWidth - 1) / 2;
   const int nRowsInput = B.GetNrows();
   const int nColsInput = B.GetNcols();
   const size_t nSizeOutput = V.size();
   const int npixels =  nRowsInput * fltHeight * fltWidth;
   // const int nRowsOutput = A.GetNrows();
   // const int nColsOutput = A.GetNcols();
 
   // convolution centers
   for (int i = halfFltHeight -zeroPaddingHeight; i <= imgHeightBound; i += strideRows) {
      for (int j = halfFltWidth -zeroPaddingWidth ; j <= imgWidthBound; j += strideCols) {
         size_t currLocalViewPixel = 0;
 
         // within the local view
         //R__ASSERT((int) currLocalView < nRowsOutput );
 
         for (int m = 0; m < nRowsInput; m++) {
            for (int k = i - halfFltHeight  ; k <= Int_t(i + halfFltHeightM1 ); k++) {
               int kstep = k * imgWidth;
               for (int l = j - halfFltWidth ; l <= Int_t(j + halfFltWidthM1); l++) {
 
                  // Check the boundaries
                  //R__ASSERT(currLocalViewPixel < nColsOutput );
                  R__ASSERT(currLocalView * npixels + currLocalViewPixel < nSizeOutput );
                  if (k < 0 || k >= (Int_t)imgHeight || l < 0 || l >= (Int_t)imgWidth || kstep + l >=  nColsInput)
                     //V[currLocalView * npixels + currLocalViewPixel]=-1;
                     V[currLocalViewPixel * nLocalViews + currLocalView] = -1;
                  else
                     V[currLocalViewPixel * nLocalViews + currLocalView]= ( kstep + l) * nRowsInput + m;
 
                  currLocalViewPixel++;
               }
            }
         }
         currLocalView++;
      }
   }
}
template <typename AFloat>
void TCpu<AFloat>::Im2colFast(TCpuMatrix<AFloat> &A, const TCpuMatrix<AFloat> &B, const std::vector<int> &V)
{
   size_t  n = V.size();
   R__ASSERT( n == A.GetNcols() * A.GetNrows() );
   AFloat *  a = A.GetRawDataPointer();
   const AFloat *  b = B.GetRawDataPointer();
 
//#define DL_USE_MTE
   // parallel execution
#ifdef DL_USE_MTE
   const size_t nsteps = TCpuMatrix<AFloat>::GetNWorkItems(n);
 
   auto f = [&](UInt_t workerID)
   {
      for (size_t j = 0; j < nsteps; ++j) {
         size_t ii = workerID+j;
         if (ii >= n) break;
         int idx = V[ii];
         if (idx >= 0) a[ii] = b[idx];
         else a[ii] = 0;
      }
      return 0;
   };
 
   A.GetThreadExecutor().Foreach(f, ROOT::TSeqI(0,n,nsteps) );
 
#else
   //serial execution
   for (size_t ii = 0; ii < n; ++ii) {
      int idx = V[ii];
      if (idx >= 0) a[ii] = b[idx];
      else a[ii] = 0;
   }
 
#endif
}
//____________________________________________________________________________
template <typename AFloat>
void TCpu<AFloat>::RotateWeights(TCpuMatrix<AFloat> &A, const TCpuMatrix<AFloat> &B, size_t filterDepth,
                                 size_t filterHeight, size_t filterWidth, size_t numFilters)
{
   size_t jump = filterHeight * filterWidth;
   for (size_t j = 0; j < filterDepth; j++) {
      for (size_t k = 0; k < numFilters; k++) {
         for (size_t i = 0; i < jump; i++) {
            A(j, k * jump + i) = B(k, ((j + 1) * jump - 1) - i);
            //A(j, k * jump + i) = B(k, j * jump + i);
         }
      }
   }
}
 
//____________________________________________________________________________
template <typename AFloat>
void TCpu<AFloat>::AddConvBiases(TCpuMatrix<AFloat> &output, const TCpuMatrix<AFloat> &biases)
{
#ifdef R__HAS_TMVACPU
   int m = (int)output.GetNrows();
   int n = (int)output.GetNcols();
 
   int inc = 1.0;
   AFloat alpha = 1.0;
 
   AFloat *A = output.GetRawDataPointer();
   const AFloat *x = biases.GetRawDataPointer();
   const AFloat *y = TCpuMatrix<AFloat>::GetOnePointer();
 
   R__ASSERT(m <= (int)biases.GetNoElements() );
   R__ASSERT(n <= (int)TCpuMatrix<AFloat>::GetOnePointerSize() );
 
   ::TMVA::DNN::Blas::Ger(&m, &n, &alpha, x, &inc, y, &inc, A, &m);
#else
   TMatrixT<AFloat> tmp;
   TReference<AFloat>::AddConvBiases(tmp, biases);
   output = tmp;
#endif
}
 
template<typename AFloat>
size_t TCpu<AFloat>::calculateDimension(size_t imgDim, size_t fltDim, size_t padding, size_t stride)
{
   size_t temp = imgDim - fltDim + 2 * padding;
   if (temp % stride || temp + stride <= 0) {
      Fatal("calculateDimension", "Not compatible hyper parameters for layer - (imageDim, filterDim, padding, stride) "
            "%zu, %zu, %zu, %zu", imgDim, fltDim, padding, stride);
   }
   return temp / stride + 1;
}
 
//____________________________________________________________________________
template <typename AFloat>
void TCpu<AFloat>::ConvLayerForward(TCpuTensor<AFloat> & output,
                                    TCpuTensor<AFloat> & inputActivationFunc,
                                    const TCpuTensor<AFloat> &input,
                                    const TCpuMatrix<AFloat> &weights, const TCpuMatrix<AFloat> & biases,
                                    const DNN::CNN::TConvParams & params, EActivationFunction activFunc,
                                    TCpuTensor<AFloat> & /*  */,
                                    const ConvDescriptors_t & /*descriptors*/,
                                    ConvWorkspace_t & /*workspace*/)
{
   size_t height = calculateDimension(params.inputHeight, params.filterHeight, params.paddingHeight, params.strideRows);
   size_t width = calculateDimension(params.inputWidth, params.filterWidth, params.paddingWidth, params.strideCols);
   size_t nLocalViews = height * width;
   size_t nLocalViewPixels = params.inputDepth * params.filterHeight * params.filterWidth;
 
   R__ASSERT( input.GetSize() > 0);
   std::vector<int> forwardIndices(nLocalViews * nLocalViewPixels);
   Im2colIndices(forwardIndices, input.At(0).GetMatrix(), nLocalViews, params.inputHeight, params.inputWidth, params.filterHeight,
                 params.filterWidth, params.strideRows, params.strideCols, params.paddingHeight, params.paddingWidth);
 
   //this should fix multi-thread inizializations of arrays
   TCpuMatrix<AFloat>::InitializeOneVector(nLocalViews);
   TCpuMatrix<AFloat>::InitializeOneVector(output.GetWSize());   // since it is used in AddCOnvBiases
 
 
   auto f = [&] (UInt_t i)
   {
       // dropout not yet implemented for CNN
       // if (applyDropout && (dropoutProbability != 1.0)) {
       //    Dropout(input[i], dropoutProbability);
       // }
 
       TCpuMatrix<AFloat> inputTr(nLocalViews, nLocalViewPixels);
       //inputTr.Zero();   // this is not thread safe
 
       Im2colFast(inputTr, input.At(i).GetMatrix(), forwardIndices);
 
       Matrix_t output_m = output.At(i).GetMatrix();
       MultiplyTranspose(output_m, weights, inputTr);
       AddConvBiases(output_m, biases);
 
   };
 
   TCpuMatrix<AFloat>::GetThreadExecutor().Foreach(f, ROOT::TSeqI(input.GetFirstSize()));
 
   //evaluateDerivative<TCpu<AFloat>>(derivatives, activFunc, output);
   // need to save output of convolution (input to activation function)
   Copy(inputActivationFunc, output);
 
   //evaluate<TCpu<AFloat>>(output, activFunc);
   ActivationFunctionForward(output, activFunc, ActivationDescriptor_t());
}
 
//____________________________________________________________________________
template <typename AFloat>
void TCpu<AFloat>::ConvLayerBackward(TCpuTensor<AFloat> &activationGradientsBackward,
                                     TCpuMatrix<AFloat> &weightGradients, TCpuMatrix<AFloat> &biasGradients,
                                     TCpuTensor<AFloat> &inputActivationFunc,
                                     TCpuTensor<AFloat> &activationGradients,
                                     const TCpuMatrix<AFloat> &weights,
                                     const TCpuTensor<AFloat> &activationsBackward,
                                     const Tensor_t & outputTensor,
                                     EActivationFunction activFunc,
                                     const ConvDescriptors_t & /*descriptors*/,
                                     ConvWorkspace_t & /*workspace*/,
                                     size_t batchSize,   size_t inputHeight,
                                     size_t inputWidth,  size_t depth,
                                     size_t height,      size_t width,
                                     size_t filterDepth, size_t filterHeight,
                                     size_t filterWidth, size_t nLocalViews)
{
   // Update derivatives
   //    size_t m, n;
   //    m = activationGradients[0].GetNrows();
   //    n = activationGradients[0].GetNcols();
 
 
   // Compute activation backward pass  dx = f'(x) * dy
   //  put resulting dx of activation in activationgradients
   Tensor_t df(activationGradients.GetShape() );   // this is a deep copy, could be put as data member of class
   ActivationFunctionBackward(df, outputTensor, activationGradients, inputActivationFunc,
                              activFunc, ActivationDescriptor_t() );
 
   // Hadamard(df, activationGradients);
 
 
   // Calculate the activation gradients of the previous layer
   CalculateConvActivationGradients(activationGradientsBackward, df, weights, batchSize, inputHeight, inputWidth, depth,
                                    height, width, filterDepth, filterHeight, filterWidth);
 
   // Calculate the weight gradients
   CalculateConvWeightGradients(weightGradients, df, activationsBackward, batchSize, inputHeight, inputWidth, depth,
                                height, width, filterDepth, filterHeight, filterWidth, nLocalViews);
 
   // Calculate the bias gradients
   CalculateConvBiasGradients(biasGradients, df, batchSize, depth, nLocalViews);
}
 
//____________________________________________________________________________
template <typename AFloat>
void TCpu<AFloat>::CalculateConvActivationGradients(TCpuTensor<AFloat> &activationGradientsBackward,
                                                    const TCpuTensor<AFloat> &df,
                                                    const TCpuMatrix<AFloat> &weights, size_t batchSize,
                                                    size_t inputHeight, size_t inputWidth, size_t depth, size_t height,
                                                    size_t width, size_t filterDepth, size_t filterHeight,
                                                    size_t filterWidth)
{
   if (activationGradientsBackward.GetSize() == 0) return;
 
 
   activationGradientsBackward.Zero();
 
 
   // Transform the weights
 
   //TMVA_DNN_PrintTCpuMatrix(weights,"weights");
   // filter depth must be same as input depth
   TCpuMatrix<AFloat> rotWeights(filterDepth, depth * filterHeight * filterWidth);
   RotateWeights(rotWeights, weights, filterDepth, filterHeight, filterWidth, weights.GetNrows());
   //TMVA_DNN_PrintTCpuMatrix(rotWeights,"rot-weights");
 
   // Calculate the zero paddings
   size_t tempZeroPaddingHeight = (size_t)(floor((inputHeight - height + filterHeight - 1) / 2));
   size_t tempZeroPaddingWidth = (size_t)(floor((inputWidth - width + filterWidth - 1) / 2));
 
   // size_t tempZeroPaddingHeight = 1;
   // size_t tempZeroPaddingWidth = 1;
 
   // Calculate the number of local views and the number of pixles in each view
   size_t tempNLocalViews = inputHeight * inputWidth;
   size_t tempNLocalViewPixels = depth * filterHeight * filterWidth;
 
   size_t tempStrideRows = 1;
   size_t tempStrideCols = 1;
 
   // An entire convolution follows
 
    std::vector<int> vIndices( tempNLocalViews * tempNLocalViewPixels );
    Im2colIndices(vIndices, df.At(0).GetMatrix(), tempNLocalViews, height, width, filterHeight, filterWidth, tempStrideRows, tempStrideCols,
             tempZeroPaddingHeight, tempZeroPaddingWidth);
 
 
    //for (size_t i = 0; i < batchSize; i++) {
    R__ASSERT(batchSize == df.GetFirstSize() );
    R__ASSERT(batchSize == activationGradientsBackward.GetFirstSize() );
    auto f = [&] (UInt_t i)
   {
       // Im2col(dfTr, df[i], height, width, filterHeight, filterWidth, tempStrideRows, tempStrideCols,
       //       tempZeroPaddingHeight, tempZeroPaddingWidth);
 
      TCpuMatrix<AFloat> dfTr(tempNLocalViews, tempNLocalViewPixels);
 
      Im2colFast(dfTr, df.At(i).GetMatrix(), vIndices);
 
       //TMVA_DNN_PrintTCpuMatrix(df[i],"df[i]");
       //TMVA_DNN_PrintTCpuMatrix(dfTr,"dfTr");
 
      Matrix_t agb_m = activationGradientsBackward.At(i).GetMatrix();
      MultiplyTranspose(agb_m, rotWeights, dfTr);
 
       //TMVA_DNN_PrintTCpuMatrix(activationGradientsBackward[i],"activGrad-result");
 
   };
 
    TCpuMatrix<AFloat>::GetThreadExecutor().Foreach(f, ROOT::TSeqI( batchSize ) );
}
 
//____________________________________________________________________________
template <typename AFloat>
void TCpu<AFloat>::CalculateConvWeightGradients(TCpuMatrix<AFloat> &weightGradients,
                                                const TCpuTensor<AFloat> &df,
                                                const TCpuTensor<AFloat> &activationsBackward,
                                                size_t batchSize, size_t inputHeight, size_t inputWidth, size_t depth,
                                                size_t height, size_t width, size_t filterDepth, size_t filterHeight,
                                                size_t filterWidth, size_t nLocalViews)
{
   // reinitialize the weight gradients to 0
   weightGradients.Zero();
 
   const size_t filterSize = filterHeight * filterWidth;
   const size_t nLocalViewPixels = filterDepth * filterHeight * filterWidth;
   R__ASSERT( weightGradients.GetNcols() == filterDepth * filterHeight * filterWidth);
 
   const size_t tempStrideRows = 1;
   const size_t tempStrideCols = 1;
 
      // Calculate the zero paddings from the input height and width (assume stride =1 )
   const size_t tempZeroPaddingHeight = (height - inputHeight + filterHeight - 1) / 2;
   const size_t tempZeroPaddingWidth = (width - inputWidth + filterWidth - 1) / 2;
 
 
   // convolution
 
 
 
   std::vector<int> vIndices(nLocalViews * nLocalViewPixels );
   Im2colIndices(vIndices, activationsBackward.At(0).GetMatrix(), nLocalViews, inputHeight, inputWidth, filterHeight , filterWidth,
             tempStrideRows, tempStrideCols, tempZeroPaddingHeight, tempZeroPaddingWidth);
 
   //std::cout << "do back-propagation in conv layer - compute weight gradient" << std::endl;
 
   // std::vector< TCpuMatrix<AFloat> > vres;//(batchSize);
   // for (size_t i = 0; i < batchSize; i++) {
   //    vres.emplace_back(depth, nLocalViewPixels);
   //    //TMVA_DNN_PrintTCpuMatrix(df[i],"df");
   //    //TMVA_DNN_PrintTCpuMatrix(activationsBackward[i],"df");
 
   //}
   //TCpuTensor<AFloat> vres( { batchSize, depth, nLocalViewPIxels} );
   TCpuTensor<AFloat> vres( batchSize, depth, nLocalViewPixels);
 
   auto fmap = [&](int i) {
 
      //TMVA_DNN_PrintTCpuMatrix(df[i],"df-i");
      TCpuMatrix<AFloat> xTr(nLocalViews, nLocalViewPixels);
      TCpuMatrix<AFloat> res(depth, nLocalViewPixels);
 
      //computing t he gradient is equivalent of doing a convolution of the input using as conv kernel the delta's (the df[] values)
      //N.B. only stride values=1 are now supported
 
      //xTr.Zero();
      // Im2col(xTr, const_cast<TCpuMatrix<AFloat> &>(activationsBackward[i]), inputHeight, inputWidth, filterHeight , filterWidth,
      //        tempStrideRows, tempStrideCols, tempZeroPaddingHeight, tempZeroPaddingWidth);
      Im2colFast(xTr, activationsBackward.At(i).GetMatrix(), vIndices);
 
      //std::cout << "doing im2colfast" << std::endl;
      //TMVA_DNN_PrintTCpuMatrix(xTr,"xTr-i");
      //TMVA_DNN_PrintTCpuMatrix(activationsBackward[i],"actbackward-i");
      Matrix_t mres = vres.At(i).GetMatrix();
      Multiply( mres, df.At(i).GetMatrix(), xTr);
      //TMVA_DNN_PrintTCpuMatrix(vres[i],"res_ofMT");
 
      return;
      //return res;
   };
 
   TCpuMatrix<AFloat>::GetThreadExecutor().Foreach(fmap, ROOT::TSeqI( batchSize ) );
 
//   auto freduce = [&](const TCpuTensor<AFloat> & vres) {
      R__ASSERT(vres.GetFirstSize() == batchSize);
      for (size_t i = 0; i < batchSize; i++) {
         //TMVA_DNN_PrintTCpuMatrix(vres[i],"res");
         Matrix_t vres_m = vres.At(i).GetMatrix();
         for (size_t j = 0; j < depth; j++) {
            for (size_t k = 0; k < filterDepth; k++) {
               size_t kOffset = k * filterSize;
               for (size_t l = 0; l < filterSize; l++) {
                  //weightGradients(j, k * (filterHeight * filterWidth) + l) += res(k, (tempNLocalViews - 1) - l);
                  weightGradients(j, kOffset + l) += vres_m(j,  kOffset + l);
               }
            }
         }
         // TMVA_DNN_PrintTCpuMatrix(weightGradients,"weights_i");
      }
      //  };
 
   //TCpuMatrix<AFloat>::GetThreadExecutor().MapReduce(fmap, ROOT::TSeqI( batchSize ) , freduce);
   //TMVA_DNN_PrintTCpuMatrix(weightGradients,"W-Grad");
}
 
//____________________________________________________________________________
template <typename AFloat>
void TCpu<AFloat>::CalculateConvBiasGradients(TCpuMatrix<AFloat> &biasGradients, const TCpuTensor<AFloat> &df,
                                              size_t batchSize, size_t depth, size_t nLocalViews)
{
   biasGradients.Zero();
   for (size_t i = 0; i < depth; i++) {
      AFloat sum = 0;
      for (size_t j = 0; j < nLocalViews; j++) {
         for (size_t k = 0; k < batchSize; k++) {
            sum += df(k,i,j);
            //sum += df[k](i, j);
         }
      }
      biasGradients(i, 0) = sum;
   }
}
 
//____________________________________________________________________________
template <typename AFloat>
void TCpu<AFloat>::Downsample(TCpuTensor<AFloat> &tA, TCpuTensor<AFloat> &tB, const TCpuTensor<AFloat> &tC,
                              const PoolingDescriptors_t & /*descriptors*/,
                              PoolingWorkspace_t & /*workspace*/,
                              size_t imgHeight, size_t imgWidth, size_t fltHeight, size_t fltWidth, size_t strideRows,
                              size_t strideCols)
{
   // A is output , B is a cached index tensor used for backward pass and C is the input
 
   assert( tA.GetFirstSize() == tC.GetFirstSize());
   for (size_t ifirst = 0; ifirst < tC.GetFirstSize(); ++ifirst) {
 
      Matrix_t A = tA.At(ifirst).GetMatrix();
      Matrix_t B = tB.At(ifirst).GetMatrix();
      Matrix_t C = tC.At(ifirst).GetMatrix();
 
      // image boudaries
      int imgHeightBound = imgHeight - (fltHeight - 1) / 2 - 1;
      int imgWidthBound = imgWidth - (fltWidth - 1) / 2 - 1;
      size_t currLocalView = 0;
 
      // centers
      for (int i = fltHeight / 2; i <= imgHeightBound; i += strideRows) {
         for (int j = fltWidth / 2; j <= imgWidthBound; j += strideCols) {
            // within local views
            for (int m = 0; m < (Int_t)C.GetNrows(); m++) {
               AFloat value = -std::numeric_limits<AFloat>::max();
 
               for (int k = i - fltHeight / 2; k <= Int_t(i + (fltHeight - 1) / 2); k++) {
                  for (int l = j - fltWidth / 2; l <= Int_t(j + (fltWidth - 1) / 2); l++) {
                     if (C(m, k * imgWidth + l) > value) {
                        value = C(m, k * imgWidth + l);
                        B(m, currLocalView) = k * imgWidth + l;
                     }
                  }
               }
               A(m, currLocalView) = value;
            }
            currLocalView++;
         }
      }
   }
}
 
//____________________________________________________________________________
template <typename AFloat>
void TCpu<AFloat>::MaxPoolLayerBackward(TCpuTensor<AFloat> &activationGradientsBackward,
                                        const TCpuTensor<AFloat> &activationGradients,
                                        const TCpuTensor<AFloat> &indexMatrix,
                                        const TCpuTensor<AFloat> & /*inputActivation*/,
                                        const TCpuTensor<AFloat> & /*outputTensor*/,
                                        const PoolingDescriptors_t & /*descriptors*/,
                                        PoolingWorkspace_t & /*workspace*/,
                                        size_t /* imgHeight */,
                                        size_t /* imgWidth */,
                                        size_t /* fltHeight */,
                                        size_t /* fltWidth */,
                                        size_t /* strideRows */,
                                        size_t /* strideCols */,
                                        size_t nLocalViews)
{
 
   assert( activationGradientsBackward.GetFirstSize() == activationGradients.GetFirstSize());
   for (size_t l = 0; l < activationGradients.GetFirstSize(); ++l) {
 
      Matrix_t activationGradientsBackward_m = activationGradientsBackward.At(l).GetMatrix();
      Matrix_t activationGradients_m = activationGradients.At(l).GetMatrix();
      Matrix_t indexMatrix_m = indexMatrix.At(l).GetMatrix();
 
      size_t depth = activationGradientsBackward_m.GetNrows();
 
      for (size_t j = 0; j < depth; j++) {
         // initialize to zeros
         for (size_t t = 0; t < (size_t)activationGradientsBackward_m.GetNcols(); t++) {
            activationGradientsBackward_m(j, t) = 0;
         }
 
         // set values
         for (size_t k = 0; k < nLocalViews; k++) {
            AFloat grad = activationGradients_m(j, k);
            size_t winningIdx = indexMatrix_m(j, k);
            activationGradientsBackward_m(j, winningIdx) += grad;
         }
      }
   }
}
 
//____________________________________________________________________________
template <typename AFloat>
TCpuTensor<AFloat> TCpu<AFloat>::BatchNormLayerReshapeTensor(int axis, const TCpuTensor<AFloat> &x) {
   // reshape tensor for batch norm layer according to normalization axis
   // input x - output reshpe of X
   if (axis == 1) {
      // reshape to a RowMajor tensor so I can use same indices, in this case channel
      typename TCpuTensor<AFloat>::Shape_t newShape = { x.GetSize() / x.GetShape().front() , x.GetShape().front() }; // shape is HXWXB , C
      TCpuTensor<AFloat> xtmp(x.GetDeviceBuffer(), newShape, TCpuTensor<AFloat>::MemoryLayout::RowMajor);
      return xtmp;
   }
   // dense layer case (axis == -1)
   return  x.Reshape( { x.GetShape().front(), x.GetSize()/ x.GetShape().front()});
   // what to do with time layer ?
}
 
//____________________________________________________________________________
template <typename AFloat>
void TCpu<AFloat>::BatchNormLayerForwardTraining(int axis, const TCpuTensor<AFloat> &x,
                                                 TCpuTensor<AFloat> & y,
                                                 Matrix_t &gamma, Matrix_t &beta,
                                                 Matrix_t & mean,
                                                 Matrix_t & variance,
                                                 Matrix_t & iVariance,
                                                 Matrix_t & runningMeans,
                                                 Matrix_t & runningVars,
                                                 Scalar_t nTrainedBatches,
                                                 Scalar_t momentum, Scalar_t epsilon,
                                                 const TensorDescriptor_t &  )
                                                 //BNormWorkspace_t * workspace )
{
   // the tensor are reshaped in order to
   // have a first coordinate the normalized coordinates and second the feature we are computing the norm
   // e.g. batch size , number of features  or
   //  B x H x W , C
 
   TCpuTensor<AFloat> input = BatchNormLayerReshapeTensor(axis,x);
   TCpuTensor<AFloat> output = BatchNormLayerReshapeTensor(axis,y);
 
   assert (input.GetShape().size() == 2);
   size_t n = input.GetShape()[0];   // size of coordinates we are normalizing (e.g batch size)
   size_t d = input.GetShape()[1];   // size of the coordinate we are not normalizing (e.g. feature size)
 
   TCpuBuffer<AFloat> &inputBuffer = input.GetDeviceBuffer();
   TCpuBuffer<AFloat> &outputBuffer = output.GetDeviceBuffer();
 
 
   // lambda implementing computation for each single component k we need to normalize
   auto f = [&] (size_t k)
   {
 
      auto inputK = inputBuffer.GetSubBuffer(k * n, n);
      auto outputK = outputBuffer.GetSubBuffer(k * n, n);
 
      double  meanK = 0;
      meanK = 0;
      for (size_t i = 0; i < n; i++) {
         AFloat xi = inputK[i];
         meanK += xi;
      }
      meanK = meanK/ n;
 
      double sq = 0;
      for (size_t i = 0; i < n; i++) {
         AFloat xi = inputK[i];
         double xmu = xi - meanK;
         sq = sq + (xmu * xmu);
         outputK[i] = AFloat(xmu);
      }
      mean(0,k) = meanK;
      variance(0,k) = sq / n;
      iVariance(0,k) = 1. / std::sqrt(variance(0,k) + epsilon);
 
      double iVK = iVariance(0, k);
      double gK = gamma(0, k);
      double bK = beta(0, k);
      for (size_t i = 0; i < n; i++) {
         AFloat yi = outputK[i] ;
         outputK[i] = AFloat( gK * iVK * yi  + bK );
      }
 
 
      // fVar(0,k) -= epsilon;
 
      if (nTrainedBatches == 0) {
         runningMeans(0,k) = mean(0,k);
         runningVars(0,k) = variance(0,k) * (n) / (Scalar_t(n - 1) + epsilon);
      } else {
         double decay = momentum;
         if (momentum < 0) decay = nTrainedBatches/Scalar_t(nTrainedBatches+1);
         runningMeans(0,k) = decay * runningMeans(0,k) + (1. - decay) * mean(0,k);
         runningVars(0,k) = decay * runningVars(0,k) + (1.-decay) * variance(0,k) * (n) / (Scalar_t(n - 1) + epsilon);
      }
      // std::cout << " training batch " << nTrainedBatches << " estimated mu : " << runningMeans(0, k)
      // << " estimated var " << runningVars(0,k) << std::endl;
 
   }; // end f(k) definition
 
   TCpuMatrix<AFloat>::GetThreadExecutor().Foreach(f, ROOT::TSeqI(d) );
}
 
//____________________________________________________________________________
template <typename AFloat>
void TCpu<AFloat>::BatchNormLayerForwardInference(int axis, const TCpuTensor<AFloat> &x,
                                                  Matrix_t & gamma,
                                                  Matrix_t & beta,
                                                  TCpuTensor<AFloat> &y,
                                                  const Matrix_t & runningMeans,
                                                  const Matrix_t & runningVars,
                                                  Scalar_t epsilon,
                                                  const TensorDescriptor_t & )
{
   TCpuTensor<AFloat> input = BatchNormLayerReshapeTensor(axis,x);
   TCpuTensor<AFloat> output = BatchNormLayerReshapeTensor(axis,y);
 
   assert (input.GetShape().size() == 2);
   size_t n = input.GetShape()[0];   // size of coordinates we are normalizing (e.g batch size)
   size_t d = input.GetShape()[1];
 
   TCpuBuffer<AFloat> &inputBuffer = input.GetDeviceBuffer();
   TCpuBuffer<AFloat> &outputBuffer = output.GetDeviceBuffer();
 
   auto f = [&] (size_t k) {
 
      auto inputK = inputBuffer.GetSubBuffer(k * n, n);
      auto outputK = outputBuffer.GetSubBuffer(k * n, n);
 
      double gK = gamma(0, k);
      double bK = beta(0, k);
      double mK = runningMeans(0, k);
      double vK = 1. / (sqrt(runningVars(0, k) + epsilon));
 
      // during inference just use stored mu and variance
      for (size_t i = 0; i < n; i++) {
         AFloat xi = inputK[i];
         outputK[i] = AFloat( gK * (xi - mK) * vK + bK );
      }
   };  // end definition of f(k)
 
   TCpuMatrix<AFloat>::GetThreadExecutor().Foreach(f, ROOT::TSeqI(d) );
}
 
//____________________________________________________________________________
template <typename AFloat>
void TCpu<AFloat>::BatchNormLayerBackward(int axis, const TCpuTensor<AFloat> &x,
                                                 const TCpuTensor<AFloat> &dy,
                                                 TCpuTensor<AFloat> &dx,
                                                 Matrix_t &gamma, //  Matrix_t &beta, (not needed)
                                                 Matrix_t &dgamma, Matrix_t &dbeta,
                                                 const Matrix_t & mean,
                                                 const Matrix_t & variance,
                                                 const Matrix_t & iVariance,
                                                 Scalar_t epsilon,
                                                 const TensorDescriptor_t & )
{
   TCpuTensor<AFloat> input = BatchNormLayerReshapeTensor(axis,x);
   TCpuTensor<AFloat> inputGrad = BatchNormLayerReshapeTensor(axis,dx);
   TCpuTensor<AFloat> outputGrad = BatchNormLayerReshapeTensor(axis,dy);
 
   assert (outputGrad.GetShape().size() == 2);
   size_t n = outputGrad.GetShape()[0];   // size of coordinates we are normalizing (e.g batch size)
   size_t d = outputGrad.GetShape()[1];
 
   TCpuBuffer<AFloat> & inputBuffer = input.GetDeviceBuffer();
   TCpuBuffer<AFloat> & dyBuffer = outputGrad.GetDeviceBuffer();
   TCpuBuffer<AFloat> & dxBuffer = inputGrad.GetDeviceBuffer();
 
 
   // compute first gradients for gamma and beta
   auto f = [&] (size_t k) {
      dgamma(0, k) = 0;
      dbeta(0, k) = 0;
      auto inputK = inputBuffer.GetSubBuffer(k * n, n);
      auto outputGradK = dyBuffer.GetSubBuffer(k * n, n);
      auto inputGradK = dxBuffer.GetSubBuffer(k * n, n);
      auto meanK = mean(0, k);
      for (size_t i = 0; i < n; i++) {
         AFloat xi = inputK[i];
         double xhat = xi - meanK;
         dbeta(0, k) += outputGradK[i];
         dgamma(0, k) += outputGradK[i] * xhat;
      }
      double npSumDy = dbeta(0, k);
      double npSumDyHMu = dgamma(0, k);
      dgamma(0, k) *= iVariance(0, k);
 
      // compute gradients with respect to input
      double bterm = npSumDyHMu / (variance(0, k) + epsilon);
      double aterm = (1. / double(n) * gamma(0, k) * iVariance(0, k));
      for (size_t i = 0; i < n; i++) {
         AFloat xi = inputK[i];
         AFloat dyi = outputGradK[i];
         double xmu = xi - meanK;
         inputGradK[i] = AFloat( aterm * (n * dyi - npSumDy - xmu * bterm) );
      }
   };
 
   TCpuMatrix<AFloat>::GetThreadExecutor().Foreach(f, ROOT::TSeqI(d) );
}
 
//____________________________________________________________________________
template <typename AFloat>
void TCpu<AFloat>::Reshape(TCpuMatrix<AFloat> &A, const TCpuMatrix<AFloat> &B)
{
   size_t nColsA = A.GetNcols();
   size_t nColsB = B.GetNcols();
 
   for (size_t i = 0; i < A.GetNrows(); i++) {
      for (size_t j = 0; j < A.GetNcols(); j++) {
         size_t nElem = i * nColsA + j;
         A(i, j) = B(nElem / nColsB, nElem % nColsB);
      }
   }
}
 
//____________________________________________________________________________
template <typename AFloat>
void TCpu<AFloat>::Flatten(TCpuTensor<AFloat> &A, const TCpuTensor<AFloat> &B )
{
 
   //printf ( "input tensor %f \n",B(0,0,0));
   //std::cout << "Flatten CPU arch " << std::endl;
 
   assert( B.GetShape().size() == 3  );
   assert( A.GetShape().size() == 3  );
 
 
   size_t bsize = B.GetFirstSize();
   size_t nRows = B.GetHSize();
   size_t nCols = B.GetWSize();
 
   assert (  A.GetFirstSize() == 1);
   assert (  A.GetHSize() == bsize);
   assert (  A.GetWSize() == nRows*nCols);
 
   for (size_t i = 0; i < bsize; i++) {
      for (size_t j = 0; j < nRows; j++) {
         for (size_t k = 0; k < nCols; k++) {
            A( 0, i, j * nCols + k) = B(i, j, k);
         }
      }
   }
 
   // size_t bsize = B.GetFirstSize();
   // size_t n = B.GetSize()/bsize;
   // if (B.GetLayout() == TCpuTensor<AFloat>::MemoryLayout::ColumnMajor ) {
 
   // }
   // A = B.Reshape(bsize, n)
}
 
//____________________________________________________________________________
template <typename AFloat>
void TCpu<AFloat>::Deflatten(TCpuTensor<AFloat> &A, const TCpuTensor<AFloat> &B )
{
 
   assert( B.GetShape().size() == 3  );
   assert( A.GetShape().size() == 3  );
 
   size_t size = A.GetFirstSize();
   size_t nRows = A.GetHSize();
   size_t nCols = A.GetWSize();
 
   assert (  B.GetFirstSize() == 1);
   assert (  B.GetHSize() == size);
   assert (  B.GetWSize() == nRows*nCols);
   for (size_t i = 0; i < (size_t)size; i++) {
      for (size_t j = 0; j < (size_t)nRows; j++) {
         for (size_t k = 0; k < (size_t)nCols; k++) {
               A(i, j, k) = B(0, i, j * nCols + k);
         }
      }
   }
}
 
//______________________________________________________________________________
template <typename AFloat>
void TCpu<AFloat>::Rearrange(Tensor_t &out, const Tensor_t &in)
{
   // B x T x D out --- T x B x D in*/
   assert ( out.GetShape().size() == 3 && in.GetShape().size() == 3);
 
 
   size_t B = out.GetFirstSize();
   size_t T = out.GetCSize();  //1 for row-major
   size_t D = out.GetWSize();  // 2 for row-major
   if ((T != in.GetFirstSize()) || (B != in.GetCSize()) || (D != in.GetWSize()) ) {
      std::cout << "Incompatible Dimensions\n"
                << in.GetFirstSize() << "x" << in.GetCSize() << "x" << in.GetWSize() << " --> " << B << "x" << T << "x"
                << D << "\n";
      assert(false);
      return;
   }
   for (size_t i = 0; i < B; ++i) {
      for (size_t j = 0; j < T; ++j) {
         for (size_t k = 0; k < D; ++k) {
            out( i, j, k ) = in( j, i, k);
         }
      }
   }
   return;
}
 
} // namespace DNN
} // namespace TMVA