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 *
 *  Copyright NumFOCUS
 *
 *  Licensed under the Apache License, Version 2.0 (the "License");
 *  you may not use this file except in compliance with the License.
 *  You may obtain a copy of the License at
 *
 *         https://www.apache.org/licenses/LICENSE-2.0.txt
 *
 *  Unless required by applicable law or agreed to in writing, software
 *  distributed under the License is distributed on an "AS IS" BASIS,
 *  WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 *  See the License for the specific language governing permissions and
 *  limitations under the License.
 *
 *=========================================================================*/
#ifndef itkFrequencyHalfHermitianFFTLayoutImageRegionConstIteratorWithIndex_h
#define itkFrequencyHalfHermitianFFTLayoutImageRegionConstIteratorWithIndex_h

#include "itkImageRegionConstIteratorWithIndex.h"

namespace itk
{
/**
 * \class FrequencyHalfHermitianFFTLayoutImageRegionConstIteratorWithIndex
 * \brief A multi-dimensional iterator templated over image type that walks
 * pixels within a region and is specialized to keep track of its image index
 * location.
 *
 * This class is a specialization of ImageRegionConstIteratorWithIndex,
 * adding method GetFrequencyBins to give the frequency bins corresponding to image indices, and GetFrequency to get the
 * frequency of the bin. The frequency bins depends on the image size.
 *
 * The default assumes that the image to iterate over is
 * the output of a forward FFT filter, where the first index corresponds to 0 frequency, and Nyquist Frequencies are
 * in the middle, between positive and negative frequencies.
 *
 * This class is specialized to iterate over the frequency
 * layout that result after applying a \see RealToHalfHermitianFFTForwardFFTImageFilter
 * For different layouts, use other frequency iterator.
 * \sa itkFrequencyFFTLayoutImageRegionConstIteratorWithIndex
 * \sa itkFrequencyShiftedFFTLayoutImageRegionConstIteratorWithIndex
 *
 * This iterator is for the frequency layout that results from applying a FFT (vnl or fftw) to an image.
 * The default ImageInformation is: Origin = {{0}}, Spacing = {{1}}.
 * In this case the frequency values will be in the range: [-1/2, 1/2] Hz
 * Or [-pi, pi] rad/s
 * To modify those ranges:
 * a) Avoid modifying the origin. The origin index always corresponds to zero frequency after a FFT.
 *    The range should be always centered around zero.
 * b) The spacing control the range of frequencies (always around zero).
 *    If the spacing is = {{0.5}} we get a frequency range of [-1/4, 1/4] or [-pi/2, pi/2].
 *
 * The frequency layout is assumed to be: where fs is frequency sampling, or frequency spacing (1.0 by default).
 * If N is even:
 * <------------ Frequencies --------------->
 * 0(DC) fs/N 2*fs/N  ... (N/2 -1)*fs/N  fs/2
 * <------------ Indices ------------------->
 *   0    1     2     ...     (N/2-1)     N/2
 *
 * Example: Size 6:
 * ------------
 * 0 <-- DC Component (0 freq)
 * 1
 * 2
 * 3 <-- Nyquist.
 *
 * If N is odd:
 * Nyquist frequency is not represented but there are symmetric largest frequencies at index=N/2, N/2 +1
 * <----------positive f ------------------>
 * 0(DC) fs/N  ......  fs/2*(N-2)/N   fs/2*(N-1)/N
 * <------------ Indices ------------------>
 *   0    1    ......    (N-1)/2 -1       N/2(rounded down, i.e (N-1)/2)
 *
 * Example: Size 5:
 * ------------
 * 0 <-- DC Component (0 freq)
 * 1
 * 2 <-- Largest Frequency bins
 *
 * Please see ImageRegionConstIteratorWithIndex for more information.
 * \sa RealToHalfHermitianFFTForwardFFTImageFilter
 *
 * \par MORE INFORMATION
 * For a complete description of the ITK Image Iterators and their API, please
 * see the Iterators chapter in the ITK Software Guide.  The ITK Software Guide
 * is available in print and as a free .pdf download from https://www.itk.org.
 *
 * \ingroup ImageIterators
 *
 * \sa ImageRegionIteratorWithIndex
 * \sa ImageConstIterator \sa ConditionalConstIterator
 * \sa ConstNeighborhoodIterator \sa ConstShapedNeighborhoodIterator
 * \sa ConstSliceIterator  \sa CorrespondenceDataStructureIterator
 * \sa FloodFilledFunctionConditionalConstIterator
 * \sa FloodFilledImageFunctionConditionalConstIterator
 * \sa FloodFilledImageFunctionConditionalIterator
 * \sa FloodFilledSpatialFunctionConditionalConstIterator
 * \sa FloodFilledSpatialFunctionConditionalIterator
 * \sa ImageConstIterator \sa ImageConstIteratorWithIndex
 * \sa ImageIterator \sa ImageIteratorWithIndex
 * \sa ImageLinearConstIteratorWithIndex  \sa ImageLinearIteratorWithIndex
 * \sa ImageRandomConstIteratorWithIndex  \sa ImageRandomIteratorWithIndex
 * \sa ImageRegionConstIterator \sa ImageRegionConstIteratorWithIndex
 * \sa ImageRegionExclusionConstIteratorWithIndex
 * \sa ImageRegionExclusionIteratorWithIndex
 * \sa ImageRegionIterator  \sa ImageRegionIteratorWithIndex
 * \sa ImageRegionReverseConstIterator  \sa ImageRegionReverseIterator
 * \sa ImageReverseConstIterator  \sa ImageReverseIterator
 * \sa ImageSliceConstIteratorWithIndex  \sa ImageSliceIteratorWithIndex
 * \sa NeighborhoodIterator \sa PathConstIterator  \sa PathIterator
 * \sa ShapedNeighborhoodIterator  \sa SliceIterator
 * \sa ImageConstIteratorWithIndex
 *
 * \ingroup ITKImageFrequency
 *
 */
template <typename TImage>
class FrequencyHalfHermitianFFTLayoutImageRegionConstIteratorWithIndex
  : public ImageRegionConstIteratorWithIndex<TImage>
{
public:
  /** Standard class type alias. */
  using Self = FrequencyHalfHermitianFFTLayoutImageRegionConstIteratorWithIndex;
  using Superclass = ImageRegionConstIteratorWithIndex<TImage>;

  /** Types inherited from the Superclass */
  using typename Superclass::IndexType;
  using typename Superclass::SizeType;
  using typename Superclass::OffsetType;
  using typename Superclass::RegionType;
  using typename Superclass::ImageType;
  using typename Superclass::PixelContainer;
  using typename Superclass::PixelContainerPointer;
  using typename Superclass::InternalPixelType;
  using typename Superclass::PixelType;
  using typename Superclass::AccessorType;

  using FrequencyType = typename ImageType::SpacingType;
  using FrequencyValueType = typename ImageType::SpacingValueType;
  /** Default constructor. Needed since we provide a cast constructor. */
  FrequencyHalfHermitianFFTLayoutImageRegionConstIteratorWithIndex()
    : ImageRegionConstIteratorWithIndex<TImage>()

  {
    this->Init();
  }

  /** Constructor establishes an iterator to walk a particular image and a
   * particular region of that image. */
  FrequencyHalfHermitianFFTLayoutImageRegionConstIteratorWithIndex(const TImage * ptr, const RegionType & region)
    : ImageRegionConstIteratorWithIndex<TImage>(ptr, region)
  {
    this->Init();
  }

  /** Constructor that can be used to cast from an ImageIterator to an
   * ImageRegionIteratorWithIndex. Many routines return an ImageIterator, but for a
   * particular task, you may want an ImageRegionIteratorWithIndex.  Rather than
   * provide overloaded APIs that return different types of Iterators, itk
   * returns ImageIterators and uses constructors to cast from an
   * ImageIterator to a ImageRegionIteratorWithIndex. */
  explicit FrequencyHalfHermitianFFTLayoutImageRegionConstIteratorWithIndex(const Superclass & it)
    : ImageRegionConstIteratorWithIndex<TImage>(it)
  {
    this->Init();
  }

  /*
   * Image Index [0, N - 1] returns [0 to N/2] (positive) union [-N/2 + 1, -1] (negative).
   * So index N/2 + 1 returns the bin -N/2 + 1.
   * If first index of the image is not zero, it stills returns values in the same range.
   * f = [0, 1, ...,   N/2-1,     -N/2, ..., -1]  if N is even
   * f = [0, 1, ..., (N-1)/2, -(N-1)/2, ..., -1]  if N is odd
   */
  IndexType
  GetFrequencyBin() const
  {
    IndexType freqInd;
    freqInd.Fill(0);
    for (unsigned int dim = 0; dim < TImage::ImageDimension; ++dim)
    {
      if (this->m_PositionIndex[dim] <= m_LargestPositiveFrequencyIndex[dim])
      {
        freqInd[dim] = this->m_PositionIndex[dim] - this->m_MinIndex[dim];
      }
      else //  -. From -N/2 + 1 (Nyquist if even) to -1 (-df in frequency)
      {
        freqInd[dim] = this->m_PositionIndex[dim] - (this->m_MaxIndex[dim] + 1);
      }
    }
    return freqInd;
  }

  /** Note that this method is independent of the region in the constructor.
   * It takes into account the ImageInformation of the Image in the frequency domain.
   * This iterator is for the frequency layout that results from applying a FFT (vnl or fftw) to an image.
   * If your image has a different layout, use other frequency iterator.
   * The default ImageInformation is: Origin = {{0}}, Spacing = {{1}}.
   * In this case the frequency values will be in the range: [-1/2, 1/2] Hz
   * Or [-pi, pi] rad/s
   * To modify those ranges:
   * a) Avoid modifying the origin. The origin index always corresponds to zero frequency after a FFT.
   *    The range should be always centered around zero.
   * b) The spacing control the range of frequencies (always around zero).
   *    If the spacing is = {{0.5}} we get a frequency range of [-1/4, 1/4] or [-pi/2, pi/2].
   *
   * f = [0, 1, ...,   N/2-1,     -N/2, ..., -1] * FrequencySpacing   if N is even
   * f = [0, 1, ..., (N-1)/2, -(N-1)/2, ..., -1] * FrequencySpacing   if N is odd
   *
   * Where FrequencySpacing = samplingFrequency / N;
   *   and samplingFrequency = 1.0 / inputImageSpatialDomainSpacing;
   */
  FrequencyType
  GetFrequency() const
  {
    FrequencyType freq;
    IndexType     freqInd = this->GetFrequencyBin();

    for (unsigned int dim = 0; dim < TImage::ImageDimension; ++dim)
    {
      freq[dim] = this->m_FrequencyOrigin[dim] + this->m_FrequencySpacing[dim] * freqInd[dim];
    }
    return freq;
  }

  FrequencyValueType
  GetFrequencyModuloSquare() const
  {
    FrequencyValueType w2(0);
    FrequencyType      w(this->GetFrequency());

    for (unsigned int dim = 0; dim < TImage::ImageDimension; ++dim)
    {
      w2 += w[dim] * w[dim];
    }
    return w2;
  }

  /**
   * Index corresponding to the first highest frequency (Nyquist) after a FFT transform.
   * If the size of the image is even, the Nyquist frequency = fs/2 is unique and shared
   * between positive and negative frequencies.
   * (Even Size) LargestPositiveFrequencyIndex = originIndex + N / 2
   * If odd, Nyquist frequency is not represented, but there is still a largest frequency at this index
   * = fs/2 * (N-1)/N.
   * (Odd Size) LargestPositiveFrequencyIndex = originIndex + (N + 1) / 2
   */
  itkGetConstReferenceMacro(LargestPositiveFrequencyIndex, IndexType);
  /** Default to first index of the largest possible Region. */
  itkGetConstReferenceMacro(MinIndex, IndexType);
  /** Default to UpperIndex of the largest possible Region. */
  itkGetConstReferenceMacro(MaxIndex, IndexType);

  /** Origin of frequencies is zero for FFT output. */
  itkGetConstReferenceMacro(FrequencyOrigin, FrequencyType);

  /** This is the pixel width, or the bin size of the frequency in physical or world coordinates.
   * SamplingFrequency = 1.0 / SpatialImageSpacing
   * FrequencySpacing  = SamplingFrequency / ImageSize
   * FrequencySpacing  = 1.0 / (SpatialImageSpacing * ImageSize)
   * FrequencySpacing is computed at construction from the spacing of the
   * input image, and cannot be modified. */
  itkGetConstReferenceMacro(FrequencySpacing, FrequencyType);

  /** In images resulting from itkRealToHalfHermitianForwardFFT
   * the size in the fastest dimension (0) is n/2 + 1.
   * To compute the right frequency spacing and the original size,
   * this information has to be provided.
   */
  void
  SetActualXDimensionIsOdd(bool value)
  {
    this->m_ActualXDimensionIsOdd = value;
    SizeType sizeImage = this->m_Image->GetLargestPossibleRegion().GetSize();
    auto     size_estimated = 2 * (sizeImage[0] - 1);
    size_estimated += this->GetActualXDimensionIsOdd() ? 1 : 0;
    this->m_FrequencySpacing[0] = 1.0 / (this->m_Image->GetSpacing()[0] * size_estimated);
  }
  itkGetMacro(ActualXDimensionIsOdd, bool);
  itkBooleanMacro(ActualXDimensionIsOdd);

private:
  /** Calculate Nyquist frequency index (m_LargestPositiveFrequencyIndex), Min/Max indices from LargestPossibleRegion.
   * Also sets FrequencySpacing and FrequencyOrigin.
   * Called by constructors.  */
  void
  Init()
  {
    SizeType sizeImage = this->m_Image->GetLargestPossibleRegion().GetSize();
    this->m_MinIndex = this->m_Image->GetLargestPossibleRegion().GetIndex();
    this->m_MaxIndex = this->m_Image->GetLargestPossibleRegion().GetUpperIndex();
    for (unsigned int dim = 0; dim < ImageType::ImageDimension; ++dim)
    {
      this->m_LargestPositiveFrequencyIndex[dim] =
        static_cast<FrequencyValueType>(this->m_MinIndex[dim] + sizeImage[dim] / 2);
      // Set frequency metadata.
      // Origin of frequencies is zero after a FFT.
      this->m_FrequencyOrigin[dim] = 0.0;
      // SamplingFrequency = 1.0 / SpatialImageSpacing
      // Freq_BinSize = SamplingFrequency / Size
      this->m_FrequencySpacing[dim] = 1.0 / (this->m_Image->GetSpacing()[dim] * sizeImage[dim]);
    }
    // Corrections for Hermitian
    // The fastest index has no negative frequencies.
    this->m_LargestPositiveFrequencyIndex[0] = static_cast<FrequencyValueType>(this->m_MaxIndex[0]);
    // In fastest dimension only:
    // Size_estimated_original = 2 * (Size_current - 1 )
    // Where size_current is the size of the output of RealToHalfHermitianFFT
    // Ex: Size Original = 10, Current = 6, Estimated = 10.
    //     Size Original = 11, Current = 6, Estimated = 10.
    auto size_estimated = 2 * (sizeImage[0] - 1);
    size_estimated += this->GetActualXDimensionIsOdd() ? 1 : 0;
    this->m_FrequencySpacing[0] = 1.0 / (this->m_Image->GetSpacing()[0] * size_estimated);
  }

  IndexType     m_LargestPositiveFrequencyIndex;
  IndexType     m_MinIndex;
  IndexType     m_MaxIndex;
  FrequencyType m_FrequencyOrigin;
  FrequencyType m_FrequencySpacing;
  bool          m_ActualXDimensionIsOdd{ false };
};
} // end namespace itk
#endif
