code: '''
  Code courtesy of Ben Feinstein & Assaf Shocher
  Please see their work:
  https://github.com/assafshocher/PyTorch-Resizer
  https://github.com/feinsteinben
  '''
  import numpy as np
  import torch
  from math import pi
  from torch import nn
  
  
  class Resizer(nn.Module):
      def __init__(self, in_shape, scale_factor=None, output_shape=None, kernel=None, antialiasing=True, device=None, dtype=None):
          super(Resizer, self).__init__()
          # First standardize values and fill missing arguments (if needed) by deriving scale from output shape or vice versa
          scale_factor, output_shape = self.fix_scale_and_size(in_shape, output_shape, scale_factor)
          self.device = device
          # Choose interpolation method, each method has the matching kernel size
          method, kernel_width = {
              "cubic": (cubic, 4.0),
              "lanczos2": (lanczos2, 4.0),
              "lanczos3": (lanczos3, 6.0),
              "box": (box, 1.0),
              "linear": (linear, 2.0),
              None: (cubic, 6.0)  # set default interpolation method as cubic
          }.get(kernel)
  
          # Antialiasing is only used when downscaling
          antialiasing *= (np.any(np.array(scale_factor) < 1))
  
          # Sort indices of dimensions according to scale of each dimension. since we are going dim by dim this is efficient
          sorted_dims = np.argsort(np.array(scale_factor))
          self.sorted_dims = [int(dim) for dim in sorted_dims if scale_factor[dim] != 1]
  
          # Iterate over dimensions to calculate local weights for resizing and resize each time in one direction
          field_of_view_list = []
          weights_list = []
          for dim in self.sorted_dims:
              # for each coordinate (along 1 dim), calculate which coordinates in the input image affect its result and the
              # weights that multiply the values there to get its result.
              weights, field_of_view = self.contributions(in_shape[dim], output_shape[dim], scale_factor[dim], method, kernel_width, antialiasing)
  
              # convert to torch tensor
              if dtype is not None:
                  weights = torch.tensor(weights.T, dtype=dtype, device=device)
              else:
                  weights = torch.tensor(weights.T, dtype=torch.float32, device=device)
              # We add singleton dimensions to the weight matrix so we can multiply it with the big tensor we get for
              # tmp_im[field_of_view.T], (bsxfun style)
              weights_list.append(nn.Parameter(torch.reshape(weights, list(weights.shape) + (len(scale_factor) - 1) * [1]), requires_grad=False))
              field_of_view_list.append(nn.Parameter(torch.tensor(field_of_view.T.astype(np.int32), dtype=torch.long, device=device), requires_grad=False))
  
          self.field_of_view = nn.ParameterList(field_of_view_list)
          self.weights = nn.ParameterList(weights_list)
          self.in_shape = in_shape
  
      def forward(self, in_tensor):
          x = in_tensor
  
          # make sure input is in the correct size
          assert list(self.in_shape[1:]) == list(x.shape[1:]), 'wrong input shape: %s, expected %s' % (str(x.shape), str(self.in_shape))
  
          # Use the affecting position values and the set of weights to calculate the result of resizing along this 1 dim
          for dim, fov, w in zip(self.sorted_dims, self.field_of_view, self.weights):
              # To be able to act on each dim, we swap so that dim 0 is the wanted dim to resize
              x = torch.transpose(x, dim, 0)
  
              # This is a bit of a complicated multiplication: x[field_of_view] is a tensor of order image_dims+1.
              # for each pixel in the output-image it matches the positions the influence it from the input image (along 1 dim
              # only, this is why it only adds 1 dim to 5the shape). We then multiply, for each pixel, its set of positions with
              # the matching set of weights. we do this by this big tensor element-wise multiplication (MATLAB bsxfun style:
              # matching dims are multiplied element-wise while singletons mean that the matching dim is all multiplied by the
              # same number
              x = torch.sum(x[fov] * w, dim=0).to(self.device)
  
              # Finally we swap back the axes to the original order
              x = torch.transpose(x, dim, 0)
  
          return x
  
      def fix_scale_and_size(self, input_shape, output_shape, scale_factor):
          # First fixing the scale-factor (if given) to be standardized the function expects (a list of scale factors in the
          # same size as the number of input dimensions)
          if scale_factor is not None:
              # By default, if scale-factor is a scalar we assume 2d resizing and duplicate it.
              if np.isscalar(scale_factor) and len(input_shape) > 1:
                  scale_factor = [scale_factor, scale_factor]
  
              # We extend the size of scale-factor list to the size of the input by assigning 1 to all the unspecified scales
              scale_factor = list(scale_factor)
              scale_factor = [1] * (len(input_shape) - len(scale_factor)) + scale_factor
  
          # Fixing output-shape (if given): extending it to the size of the input-shape, by assigning the original input-size
          # to all the unspecified dimensions
          if output_shape is not None:
              output_shape = list(input_shape[len(output_shape):]) + list(np.uint(np.array(output_shape)))
  
          # Dealing with the case of non-give scale-factor, calculating according to output-shape. note that this is
          # sub-optimal, because there can be different scales to the same output-shape.
          if scale_factor is None:
              scale_factor = np.array(output_shape) / np.array(input_shape)
  
          # Dealing with missing output-shape. calculating according to scale-factor
          if output_shape is None:
              output_shape = np.uint(np.ceil(np.array(input_shape) * np.array(scale_factor)))
  
          return scale_factor, output_shape
  
      def contributions(self, in_length, out_length, scale, kernel, kernel_width, antialiasing):
          # This function calculates a set of 'filters' and a set of field_of_view that will later on be applied
          # such that each position from the field_of_view will be multiplied with a matching filter from the
          # 'weights' based on the interpolation method and the distance of the sub-pixel location from the pixel centers
          # around it. This is only done for one dimension of the image.
  
          # When anti-aliasing is activated (default and only for downscaling) the receptive field is stretched to size of
          # 1/sf. this means filtering is more 'low-pass filter'.
          fixed_kernel = (lambda arg: scale * kernel(scale * arg)) if antialiasing and scale < 1.0 else kernel
          kernel_width *= 1.0 / scale if antialiasing and scale < 1.0 else 1.0
  
          # These are the coordinates of the output image
          out_coordinates = np.arange(1, out_length+1)
  
          # since both scale-factor and output size can be provided simulatneously, perserving the center of the image requires shifting
          # the output coordinates. the deviation is because out_length doesn't necesary equal in_length*scale.
          # to keep the center we need to subtract half of this deivation so that we get equal margins for boths sides and center is preserved.
          shifted_out_coordinates = out_coordinates - (out_length - in_length*scale)/2
  
          # These are the matching positions of the output-coordinates on the input image coordinates.
          # Best explained by example: say we have 4 horizontal pixels for HR and we downscale by SF=2 and get 2 pixels:
          # [1,2,3,4] -> [1,2]. Remember each pixel number is the middle of the pixel.
          # The scaling is done between the distances and not pixel numbers (the right boundary of pixel 4 is transformed to
          # the right boundary of pixel 2. pixel 1 in the small image matches the boundary between pixels 1 and 2 in the big
          # one and not to pixel 2. This means the position is not just multiplication of the old pos by scale-factor).
          # So if we measure distance from the left border, middle of pixel 1 is at distance d=0.5, border between 1 and 2 is
          # at d=1, and so on (d = p - 0.5).  we calculate (d_new = d_old / sf) which means:
          # (p_new-0.5 = (p_old-0.5) / sf)     ->          p_new = p_old/sf + 0.5 * (1-1/sf)
          match_coordinates = shifted_out_coordinates / scale + 0.5 * (1 - 1 / scale)
  
          # This is the left boundary to start multiplying the filter from, it depends on the size of the filter
          left_boundary = np.floor(match_coordinates - kernel_width / 2)
  
          # Kernel width needs to be enlarged because when covering has sub-pixel borders, it must 'see' the pixel centers
          # of the pixels it only covered a part from. So we add one pixel at each side to consider (weights can zeroize them)
          expanded_kernel_width = np.ceil(kernel_width) + 2
  
          # Determine a set of field_of_view for each each output position, these are the pixels in the input image
          # that the pixel in the output image 'sees'. We get a matrix whos horizontal dim is the output pixels (big) and the
          # vertical dim is the pixels it 'sees' (kernel_size + 2)
          field_of_view = np.squeeze(np.int16(np.expand_dims(left_boundary, axis=1) + np.arange(expanded_kernel_width) - 1))
  
          # Assign weight to each pixel in the field of view. A matrix whos horizontal dim is the output pixels and the
          # vertical dim is a list of weights matching to the pixel in the field of view (that are specified in
          # 'field_of_view')
          weights = fixed_kernel(1.0 * np.expand_dims(match_coordinates, axis=1) - field_of_view - 1)
  
          # Normalize weights to sum up to 1. be careful from dividing by 0
          sum_weights = np.sum(weights, axis=1)
          sum_weights[sum_weights == 0] = 1.0
          weights = 1.0 * weights / np.expand_dims(sum_weights, axis=1)
  
          # We use this mirror structure as a trick for reflection padding at the boundaries
          mirror = np.uint(np.concatenate((np.arange(in_length), np.arange(in_length - 1, -1, step=-1))))
          field_of_view = mirror[np.mod(field_of_view, mirror.shape[0])]
  
          # Get rid of  weights and pixel positions that are of zero weight
          non_zero_out_pixels = np.nonzero(np.any(weights, axis=0))
          weights = np.squeeze(weights[:, non_zero_out_pixels])
          field_of_view = np.squeeze(field_of_view[:, non_zero_out_pixels])
  
          # Final products are the relative positions and the matching weights, both are output_size X fixed_kernel_size
          return weights, field_of_view
  
  
  # These next functions are all interpolation methods. x is the distance from the left pixel center
  
  
  def cubic(x):
      absx = np.abs(x)
      absx2 = absx ** 2
      absx3 = absx ** 3
      return ((1.5*absx3 - 2.5*absx2 + 1) * (absx <= 1) +
              (-0.5*absx3 + 2.5*absx2 - 4*absx + 2) * ((1 < absx) & (absx <= 2)))
  
  
  def lanczos2(x):
      return (((np.sin(pi*x) * np.sin(pi*x/2) + np.finfo(np.float32).eps) /
               ((pi**2 * x**2 / 2) + np.finfo(np.float32).eps))
              * (abs(x) < 2))
  
  
  def box(x):
      return ((-0.5 <= x) & (x < 0.5)) * 1.0
  
  
  def lanczos3(x):
      return (((np.sin(pi*x) * np.sin(pi*x/3) + np.finfo(np.float32).eps) /
              ((pi**2 * x**2 / 3) + np.finfo(np.float32).eps))
              * (abs(x) < 3))
  
  
  def linear(x):
      return (x + 1) * ((-1 <= x) & (x < 0)) + (1 - x) * ((0 <= x) & (x <= 1))
  
apis: torch.sum numpy.sum numpy.ceil numpy.squeeze numpy.any torch.nn.ParameterList numpy.floor numpy.abs torch.tensor numpy.arange numpy.mod numpy.expand_dims numpy.array numpy.sin numpy.finfo numpy.isscalar torch.transpose