fft_convolution.hpp

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#ifndef MLPACK_METHODS_ANN_CONVOLUTION_RULES_FFT_CONVOLUTION_HPP
#define MLPACK_METHODS_ANN_CONVOLUTION_RULES_FFT_CONVOLUTION_HPP

#include <mlpack/prereqs.hpp>
#include "border_modes.hpp"

namespace mlpack {
namespace ann  {

template<typename BorderMode = FullConvolution, const bool padLastDim = false>
class FFTConvolution
{
 public:
  /*
   * Perform a convolution through fft (valid mode). This method only supports
   * input which is even on the last dimension. In case of an odd input width, a
   * user can manually pad the input or specify the padLastDim parameter which
   * takes care of the padding. The filter instead can have any size. When using
   * the valid mode the filter has to be smaller than the input.
   *
   * @param input Input used to perform the convolution.
   * @param filter Filter used to perform the convolution.
   * @param output Output data that contains the results of the convolution.
   */
  template<typename eT, typename Border = BorderMode>
  static typename std::enable_if<
      std::is_same<Border, ValidConvolution>::value, void>::type
  Convolution(const arma::Mat<eT>& input,
              const arma::Mat<eT>& filter,
              arma::Mat<eT>& output)
  {
    arma::Mat<eT> inputPadded = input;
    arma::Mat<eT> filterPadded = filter;

    if (padLastDim)
      inputPadded.resize(inputPadded.n_rows, inputPadded.n_cols + 1);

    // Pad filter and input to the output shape.
    filterPadded.resize(inputPadded.n_rows, inputPadded.n_cols);

    arma::Mat<eT> temp = arma::real(ifft2(arma::fft2(inputPadded) % arma::fft2(
        filterPadded)));

    // Extract the region of interest. We don't need to handle the padLastDim in
    // a special way we just cut it out from the output matrix.
    output = temp.submat(filter.n_rows - 1, filter.n_cols - 1,
        input.n_rows - 1, input.n_cols - 1);
  }

  /*
   * Perform a convolution through fft (full mode). This method only supports
   * input which is even on the last dimension. In case of an odd input width, a
   * user can manually pad the input or specify the padLastDim parameter which
   * takes care of the padding. The filter instead can have any size.
   *
   * @param input Input used to perform the convolution.
   * @param filter Filter used to perform the convolution.
   * @param output Output data that contains the results of the convolution.
   */
  template<typename eT, typename Border = BorderMode>
  static typename std::enable_if<
      std::is_same<Border, FullConvolution>::value, void>::type
  Convolution(const arma::Mat<eT>& input,
              const arma::Mat<eT>& filter,
              arma::Mat<eT>& output)
  {
    // In case of the full convolution outputRows and outputCols doesn't
    // represent the true output size when the padLastDim parameter is set,
    // instead it's the working size.
    const size_t outputRows = input.n_rows + 2 * (filter.n_rows - 1);
    size_t outputCols = input.n_cols + 2 * (filter.n_cols - 1);

    if (padLastDim)
        outputCols++;

    // Pad filter and input to the working output shape.
    arma::Mat<eT> inputPadded = arma::zeros<arma::Mat<eT> >(outputRows,
        outputCols);
    inputPadded.submat(filter.n_rows - 1, filter.n_cols - 1,
          filter.n_rows - 1 + input.n_rows - 1,
          filter.n_cols - 1 + input.n_cols - 1) = input;

    arma::Mat<eT> filterPadded = filter;
    filterPadded.resize(outputRows, outputCols);

    // Perform FFT and IFFT
    arma::Mat<eT> temp = arma::real(ifft2(arma::fft2(inputPadded) % arma::fft2(
        filterPadded)));

    // Extract the region of interest. We don't need to handle the padLastDim
    // parameter in a special way we just cut it out from the output matrix.
    output = temp.submat(filter.n_rows - 1, filter.n_cols - 1,
        2 * (filter.n_rows - 1) + input.n_rows - 1,
        2 * (filter.n_cols - 1) + input.n_cols - 1);
  }

  /*
   * Perform a convolution through fft using 3rd order tensors. This method only
   * supports input which is even on the last dimension. In case of an odd input
   * width, a user can manually pad the input or specify the padLastDim
   * parameter which takes care of the padding. The filter instead can have any
   * size.
   *
   * @param input Input used to perform the convolution.
   * @param filter Filter used to perform the convolution.
   * @param output Output data that contains the results of the convolution.
   */
  template<typename eT>
  static void Convolution(const arma::Cube<eT>& input,
                          const arma::Cube<eT>& filter,
                          arma::Cube<eT>& output)
  {
    arma::Mat<eT> convOutput;
    FFTConvolution<BorderMode>::Convolution(input.slice(0), filter.slice(0),
        convOutput);

    output = arma::Cube<eT>(convOutput.n_rows, convOutput.n_cols,
        input.n_slices);
    output.slice(0) = convOutput;

    for (size_t i = 1; i < input.n_slices; ++i)
    {
      FFTConvolution<BorderMode>::Convolution(input.slice(i), filter.slice(i),
          output.slice(i));
    }
  }

  /*
   * Perform a convolution through fft using dense matrix as input and a 3rd
   * order tensors as filter and output. This method only supports input which
   * is even on the last dimension. In case of an odd input width, a user can
   * manually pad the input or specify the padLastDim parameter which takes care
   * of the padding. The filter instead can have any size.
   *
   * @param input Input used to perform the convolution.
   * @param filter Filter used to perform the convolution.
   * @param output Output data that contains the results of the convolution.
   */
  template<typename eT>
  static void Convolution(const arma::Mat<eT>& input,
                          const arma::Cube<eT>& filter,
                          arma::Cube<eT>& output)
  {
    arma::Mat<eT> convOutput;
    FFTConvolution<BorderMode>::Convolution(input, filter.slice(0),
        convOutput);

    output = arma::Cube<eT>(convOutput.n_rows, convOutput.n_cols,
        filter.n_slices);
    output.slice(0) = convOutput;

    for (size_t i = 1; i < filter.n_slices; ++i)
    {
      FFTConvolution<BorderMode>::Convolution(input, filter.slice(i),
          output.slice(i));
    }
  }

  /*
   * Perform a convolution using a 3rd order tensors as input and output and a
   * dense matrix as filter.
   *
   * @param input Input used to perform the convolution.
   * @param filter Filter used to perform the convolution.
   * @param output Output data that contains the results of the convolution.
   */
  template<typename eT>
  static void Convolution(const arma::Cube<eT>& input,
                          const arma::Mat<eT>& filter,
                          arma::Cube<eT>& output)
  {
    arma::Mat<eT> convOutput;
    FFTConvolution<BorderMode>::Convolution(input.slice(0), filter,
        convOutput);

    output = arma::Cube<eT>(convOutput.n_rows, convOutput.n_cols,
        input.n_slices);
    output.slice(0) = convOutput;

    for (size_t i = 1; i < input.n_slices; ++i)
    {
      FFTConvolution<BorderMode>::Convolution(input.slice(i), filter,
          output.slice(i));
    }
  }
};  // class FFTConvolution

} // namespace ann
} // namespace mlpack

#endif