import colorsys

from PIL import Image  # type: ignore






def  snake_case  (       snake_case__			:float   ,	snake_case__			:float   ,	snake_case__			:int)						->   float:
       _A        =  x
       _A        =  y
       for step in range(snake_case__):  # noqa: B007
              _A        =  a * a - b * b + x
              _A        =  2 * a * b + y
              _A        =  a_new

              # divergence happens for all complex number with an absolute value
              # greater than 4
              if a * a + b * b > 4:
                     break
       return step / (max_step - 1)






def  snake_case  (       snake_case__			:float)						->   tuple:
       if distance == 1:
              return (0, 0, 0)
       else:
              return (255, 255, 255)






def  snake_case  (       snake_case__			:float)						->   tuple:
       if distance == 1:
              return (0, 0, 0)
       else:
              return tuple(round(i * 255) for i in colorsys.hsv_to_rgb(snake_case__   ,	1   ,	1))






def  snake_case  (       snake_case__			:int = 800   ,	snake_case__			:int = 600   ,	snake_case__			:float = -0.6   ,	snake_case__			:float = 0   ,	snake_case__			:float = 3.2   ,	snake_case__			:int = 50   ,	snake_case__			:bool = True   ,	)						->   Image.Image:
       _A        =  Image.new("""RGB"""   ,	(image_width, image_height))
       _A        =  img.load()

       # loop through the image-coordinates
       for image_x in range(snake_case__):
              for image_y in range(snake_case__):
                     # determine the figure-coordinates based on the image-coordinates
                     _A        =  figure_width / image_width * image_height
                     _A        =  figure_center_x + (image_x / image_width - 0.5) * figure_width
                     _A        =  figure_center_y + (image_y / image_height - 0.5) * figure_height

                     _A        =  get_distance(snake_case__   ,	snake_case__   ,	snake_case__)

                     # color the corresponding pixel based on the selected coloring-function
                     if use_distance_color_coding:
                            _A        =  get_color_coded_rgb(snake_case__)
                     else:
                            _A        =  get_black_and_white_rgb(snake_case__)

       return img


if __name__ == "__main__":
    import doctest

    doctest.testmod()

    # colored version, full figure
    _SCREAMING_SNAKE_CASE										=						get_image()

    # uncomment for colored version, different section, zoomed in
    # img = get_image(figure_center_x = -0.6, figure_center_y = -0.4,
    # figure_width = 0.8)

    # uncomment for black and white version, full figure
    # img = get_image(use_distance_color_coding = False)

    # uncomment to save the image
    # img.save("mandelbrot.png")

    img.show()





import torch
from torch import nn



class 				a							(			nn.Module       ):







 """simple docstring"""






 def __init__(					self		,				lowerCAmelCase_		,				lowerCAmelCase_		,				lowerCAmelCase_		,				lowerCAmelCase_		,				lowerCAmelCase_=1		,				lowerCAmelCase_=False							)  ->					Any:
        super().__init__()

        _A        =  n_token
        _A        =  d_embed
        _A        =  d_proj

        _A        =  cutoffs + [n_token]
        _A        =  [0] + self.cutoffs
        _A        =  div_val

        _A        =  self.cutoffs[0]
        _A        =  len(self.cutoffs							) - 1
        _A        =  self.shortlist_size + self.n_clusters

        if self.n_clusters > 0:
               _A        =  nn.Parameter(torch.zeros(self.n_clusters		,				self.d_embed							)							)
               _A        =  nn.Parameter(torch.zeros(self.n_clusters							)							)

        _A        =  nn.ModuleList()
        _A        =  nn.ParameterList()

        if div_val == 1:
               for i in range(len(self.cutoffs							)							):
                      if d_proj != d_embed:
                             self.out_projs.append(nn.Parameter(torch.FloatTensor(lowerCAmelCase_		,				lowerCAmelCase_							)							)							)
                      else:
                             self.out_projs.append(lowerCAmelCase_							)

               self.out_layers.append(nn.Linear(lowerCAmelCase_		,				lowerCAmelCase_							)							)
        else:
               for i in range(len(self.cutoffs							)							):
                      _A   ,  _A        =  self.cutoff_ends[i], self.cutoff_ends[i + 1]
                      _A        =  d_embed // (div_val**i)

                      self.out_projs.append(nn.Parameter(torch.FloatTensor(lowerCAmelCase_		,				lowerCAmelCase_							)							)							)

                      self.out_layers.append(nn.Linear(lowerCAmelCase_		,				r_idx - l_idx							)							)

        _A        =  keep_order



 def      UpperCAmelCase							(					self		,				lowerCAmelCase_		,				lowerCAmelCase_		,				lowerCAmelCase_		,				lowerCAmelCase_							)  ->					Optional[Any]:
        if proj is None:
               _A        =  nn.functional.linear(lowerCAmelCase_		,				lowerCAmelCase_		,				bias=lowerCAmelCase_							)
        else:
               # if CUDA_MAJOR <= 9 and CUDA_MINOR <= 1:
               _A        =  nn.functional.linear(lowerCAmelCase_		,				proj.t().contiguous()							)
               _A        =  nn.functional.linear(lowerCAmelCase_		,				lowerCAmelCase_		,				bias=lowerCAmelCase_							)
               # else:
               #     logit = torch.einsum('bd,de,ev->bv', (hidden, proj, weight.t()))
               #     if bias is not None:
               #         logit = logit + bias

        return logit



 def      UpperCAmelCase							(					self		,				lowerCAmelCase_		,				lowerCAmelCase_=None		,				lowerCAmelCase_=False							)  ->					List[Any]:

        if labels is not None:
               # Shift so that tokens < n predict n
               _A        =  hidden[..., :-1, :].contiguous()
               _A        =  labels[..., 1:].contiguous()
               _A        =  hidden.view(-1		,				hidden.size(-1							)							)
               _A        =  labels.view(-1							)
               if hidden.size(0							) != labels.size(0							):
                      raise RuntimeError("""Input and labels should have the same size in the batch dimension."""							)
        else:
               _A        =  hidden.view(-1		,				hidden.size(-1							)							)

        if self.n_clusters == 0:
               _A        =  self._compute_logit(lowerCAmelCase_		,				self.out_layers[0].weight		,				self.out_layers[0].bias		,				self.out_projs[0]							)
               if labels is not None:
                      _A        =  labels != -1_00
                      _A        =  torch.zeros_like(lowerCAmelCase_		,				dtype=hidden.dtype		,				device=hidden.device							)
                      _A        =  (
                          -nn.functional.log_softmax(lowerCAmelCase_		,				dim=-1							)[mask].gather(1		,				labels[mask].unsqueeze(1							)							).squeeze(1							)
                      )
               else:
                      _A        =  nn.functional.log_softmax(lowerCAmelCase_		,				dim=-1							)
        else:
               # construct weights and biases
               _A   ,  _A        =  [], []
               for i in range(len(self.cutoffs							)							):
                      if self.div_val == 1:
                             _A   ,  _A        =  self.cutoff_ends[i], self.cutoff_ends[i + 1]
                             _A        =  self.out_layers[0].weight[l_idx:r_idx]
                             _A        =  self.out_layers[0].bias[l_idx:r_idx]
                      else:
                             _A        =  self.out_layers[i].weight
                             _A        =  self.out_layers[i].bias

                      if i == 0:
                             _A        =  torch.cat([weight_i, self.cluster_weight]		,				dim=0							)
                             _A        =  torch.cat([bias_i, self.cluster_bias]		,				dim=0							)

                      weights.append(lowerCAmelCase_							)
                      biases.append(lowerCAmelCase_							)

               _A   ,  _A   ,  _A        =  weights[0], biases[0], self.out_projs[0]

               _A        =  self._compute_logit(lowerCAmelCase_		,				lowerCAmelCase_		,				lowerCAmelCase_		,				lowerCAmelCase_							)
               _A        =  nn.functional.log_softmax(lowerCAmelCase_		,				dim=1							)

               if labels is None:
                      _A        =  hidden.new_empty((head_logit.size(0							), self.n_token)							)
               else:
                      _A        =  torch.zeros_like(lowerCAmelCase_		,				dtype=hidden.dtype		,				device=hidden.device							)

               _A        =  0
               _A        =  [0] + self.cutoffs
               for i in range(len(lowerCAmelCase_							) - 1							):
                      _A   ,  _A        =  cutoff_values[i], cutoff_values[i + 1]

                      if labels is not None:
                             _A        =  (labels >= l_idx) & (labels < r_idx)
                             _A        =  mask_i.nonzero().squeeze()

                             if indices_i.numel() == 0:
                                    continue

                             _A        =  labels.index_select(0		,				lowerCAmelCase_							) - l_idx
                             _A        =  head_logprob.index_select(0		,				lowerCAmelCase_							)
                             _A        =  hidden.index_select(0		,				lowerCAmelCase_							)
                      else:
                             _A        =  hidden

                      if i == 0:
                             if labels is not None:
                                    _A        =  head_logprob_i.gather(1		,				target_i[:, None]							).squeeze(1							)
                             else:
                                    _A        =  head_logprob[:, : self.cutoffs[0]]
                      else:
                             _A   ,  _A   ,  _A        =  weights[i], biases[i], self.out_projs[i]

                             _A        =  self._compute_logit(lowerCAmelCase_		,				lowerCAmelCase_		,				lowerCAmelCase_		,				lowerCAmelCase_							)
                             _A        =  nn.functional.log_softmax(lowerCAmelCase_		,				dim=1							)
                             _A        =  self.cutoffs[0] + i - 1  # No probability for the head cluster
                             if labels is not None:
                                    _A        =  head_logprob_i[:, cluster_prob_idx] + tail_logprob_i.gather(
                                        1		,				target_i[:, None]							).squeeze(1							)
                             else:
                                    _A        =  head_logprob[:, cluster_prob_idx, None] + tail_logprob_i
                                    _A        =  logprob_i

                      if labels is not None:
                             if (hasattr(self		,				"""keep_order"""							) and self.keep_order) or keep_order:
                                    out.index_copy_(0		,				lowerCAmelCase_		,				-logprob_i							)
                             else:
                                    out[offset : offset + logprob_i.size(0							)].copy_(-logprob_i							)
                             offset += logprob_i.size(0							)

        return out



 def      UpperCAmelCase							(					self		,				lowerCAmelCase_							)  ->					int:
        if self.n_clusters == 0:
               _A        =  self._compute_logit(lowerCAmelCase_		,				self.out_layers[0].weight		,				self.out_layers[0].bias		,				self.out_projs[0]							)
               return nn.functional.log_softmax(lowerCAmelCase_		,				dim=-1							)
        else:
               # construct weights and biases
               _A   ,  _A        =  [], []
               for i in range(len(self.cutoffs							)							):
                      if self.div_val == 1:
                             _A   ,  _A        =  self.cutoff_ends[i], self.cutoff_ends[i + 1]
                             _A        =  self.out_layers[0].weight[l_idx:r_idx]
                             _A        =  self.out_layers[0].bias[l_idx:r_idx]
                      else:
                             _A        =  self.out_layers[i].weight
                             _A        =  self.out_layers[i].bias

                      if i == 0:
                             _A        =  torch.cat([weight_i, self.cluster_weight]		,				dim=0							)
                             _A        =  torch.cat([bias_i, self.cluster_bias]		,				dim=0							)

                      weights.append(lowerCAmelCase_							)
                      biases.append(lowerCAmelCase_							)

               _A   ,  _A   ,  _A        =  weights[0], biases[0], self.out_projs[0]
               _A        =  self._compute_logit(lowerCAmelCase_		,				lowerCAmelCase_		,				lowerCAmelCase_		,				lowerCAmelCase_							)

               _A        =  hidden.new_empty((head_logit.size(0							), self.n_token)							)
               _A        =  nn.functional.log_softmax(lowerCAmelCase_		,				dim=1							)

               _A        =  [0] + self.cutoffs
               for i in range(len(lowerCAmelCase_							) - 1							):
                      _A   ,  _A        =  cutoff_values[i], cutoff_values[i + 1]

                      if i == 0:
                             _A        =  head_logprob[:, : self.cutoffs[0]]
                      else:
                             _A   ,  _A   ,  _A        =  weights[i], biases[i], self.out_projs[i]

                             _A        =  self._compute_logit(lowerCAmelCase_		,				lowerCAmelCase_		,				lowerCAmelCase_		,				lowerCAmelCase_							)
                             _A        =  nn.functional.log_softmax(lowerCAmelCase_		,				dim=1							)

                             _A        =  head_logprob[:, -i] + tail_logprob_i
                             _A        =  logprob_i

               return out




