code: 
  
  
  
  import math
  from typing import Optional
  
  import numpy as np
  import torch
  from torch import nn
  
  from .activations import get_activation
  
  
  
  
  
  
  def 			__lowercase     (				a__							,     a__							,     a__ = False							,     a__ = 1							,     a__ = 1							,     a__ = 1_00_00							,     )       ->				Optional[int]:
  							assert len(timesteps.shape     ) == 1, "Timesteps should be a 1d-array"
  
  							__SCREAMING_SNAKE_CASE								=      embedding_dim // 2
  							__SCREAMING_SNAKE_CASE								=      -math.log(a__     ) * torch.arange(
  							    start=0							,     end=a__							,     dtype=torch.floataa							,     device=timesteps.device     )
  							__SCREAMING_SNAKE_CASE								=      exponent / (half_dim - downscale_freq_shift)
  
  							__SCREAMING_SNAKE_CASE								=      torch.exp(a__     )
  							__SCREAMING_SNAKE_CASE								=      timesteps[:, None].float() * emb[None, :]
  
  							# scale embeddings
  							__SCREAMING_SNAKE_CASE								=      scale * emb
  
  							# concat sine and cosine embeddings
  							__SCREAMING_SNAKE_CASE								=      torch.cat([torch.sin(a__     ), torch.cos(a__     )]							,     dim=-1     )
  
  							# flip sine and cosine embeddings
  							if flip_sin_to_cos:
  														__SCREAMING_SNAKE_CASE								=      torch.cat([emb[:, half_dim:], emb[:, :half_dim]]							,     dim=-1     )
  
  							# zero pad
  							if embedding_dim % 2 == 1:
  														__SCREAMING_SNAKE_CASE								=      torch.nn.functional.pad(a__							,     (0, 1, 0, 0)     )
  							return emb
  
  
  
  
  
  
  def 			__lowercase     (				a__							,     a__							,     a__=False							,     a__=0     )       ->				int:
  							__SCREAMING_SNAKE_CASE								=      np.arange(a__							,     dtype=np.floataa     )
  							__SCREAMING_SNAKE_CASE								=      np.arange(a__							,     dtype=np.floataa     )
  							__SCREAMING_SNAKE_CASE								=      np.meshgrid(a__							,     a__     )  # here w goes first
  							__SCREAMING_SNAKE_CASE								=      np.stack(a__							,     axis=0     )
  
  							__SCREAMING_SNAKE_CASE								=      grid.reshape([2, 1, grid_size, grid_size]     )
  							__SCREAMING_SNAKE_CASE								=      get_ad_sincos_pos_embed_from_grid(a__							,     a__     )
  							if cls_token and extra_tokens > 0:
  														__SCREAMING_SNAKE_CASE								=      np.concatenate([np.zeros([extra_tokens, embed_dim]     ), pos_embed]							,     axis=0     )
  							return pos_embed
  
  
  
  
  
  
  def 			__lowercase     (				a__							,     a__     )       ->				List[Any]:
  							if embed_dim % 2 != 0:
  														raise ValueError('embed_dim must be divisible by 2'     )
  
  							# use half of dimensions to encode grid_h
  							__SCREAMING_SNAKE_CASE								=      get_ad_sincos_pos_embed_from_grid(embed_dim // 2							,     grid[0]     )  # (H*W, D/2)
  							__SCREAMING_SNAKE_CASE								=      get_ad_sincos_pos_embed_from_grid(embed_dim // 2							,     grid[1]     )  # (H*W, D/2)
  
  							__SCREAMING_SNAKE_CASE								=      np.concatenate([emb_h, emb_w]							,     axis=1     )  # (H*W, D)
  							return emb
  
  
  
  
  
  
  def 			__lowercase     (				a__							,     a__     )       ->				Optional[Any]:
  							if embed_dim % 2 != 0:
  														raise ValueError('embed_dim must be divisible by 2'     )
  
  							__SCREAMING_SNAKE_CASE								=      np.arange(embed_dim // 2							,     dtype=np.floataa     )
  							omega /= embed_dim / 2.0
  							__SCREAMING_SNAKE_CASE								=      1.0 / 1_00_00**omega  # (D/2,)
  
  							__SCREAMING_SNAKE_CASE								=      pos.reshape(-1     )  # (M,)
  							__SCREAMING_SNAKE_CASE								=      np.einsum('m,d->md'							,     a__							,     a__     )  # (M, D/2), outer product
  
  							__SCREAMING_SNAKE_CASE								=      np.sin(a__     )  # (M, D/2)
  							__SCREAMING_SNAKE_CASE								=      np.cos(a__     )  # (M, D/2)
  
  							__SCREAMING_SNAKE_CASE								=      np.concatenate([emb_sin, emb_cos]							,     axis=1     )  # (M, D)
  							return emb
  
  class      UpperCAmelCase_						(     nn.Module ):
  
  						'''simple docstring'''
  
  
  
  
  						def __init__(					self   ,							_A=224   ,							_A=224   ,							_A=16   ,							_A=3   ,							_A=768   ,							_A=False   ,							_A=True   ,							_A=True   ,							):
  
  
  
  
  
  
  
  													'''simple docstring'''
  
  													super().__init__()
  
  													__SCREAMING_SNAKE_CASE								=      (height // patch_size) * (width // patch_size)
  													__SCREAMING_SNAKE_CASE								=      flatten
  													__SCREAMING_SNAKE_CASE								=      layer_norm
  
  													__SCREAMING_SNAKE_CASE								=      nn.Convad(
  													    _A   ,							_A   ,							kernel_size=(patch_size, patch_size)   ,							stride=_A   ,							bias=_A	)
  													if layer_norm:
  																				__SCREAMING_SNAKE_CASE								=      nn.LayerNorm(_A   ,							elementwise_affine=_A   ,							eps=1e-6	)
  													else:
  																				__SCREAMING_SNAKE_CASE								=      None
  
  													__SCREAMING_SNAKE_CASE								=      get_ad_sincos_pos_embed(_A   ,							int(num_patches**0.5	)	)
  													self.register_buffer('pos_embed'   ,							torch.from_numpy(_A	).float().unsqueeze(0	)   ,							persistent=_A	)
  
  
  
  
  
  
  						def  _A			(					self   ,							_A	):
  
  
  
  
  
  
  
  													'''simple docstring'''
  
  													__SCREAMING_SNAKE_CASE								=      self.proj(_A	)
  													if self.flatten:
  																				__SCREAMING_SNAKE_CASE								=      latent.flatten(2	).transpose(1   ,							2	)  # BCHW -> BNC
  													if self.layer_norm:
  																				__SCREAMING_SNAKE_CASE								=      self.norm(_A	)
  													return latent + self.pos_embed
  
  
  
  
  
  
  
  class      UpperCAmelCase_						(     nn.Module ):
  
  						'''simple docstring'''
  
  
  
  
  						def __init__(					self   ,							_A   ,							_A   ,							_A = "silu"   ,							_A = None   ,							_A = None   ,							_A=None   ,							):
  
  
  
  
  
  
  
  													'''simple docstring'''
  
  													super().__init__()
  
  													__SCREAMING_SNAKE_CASE								=      nn.Linear(_A   ,							_A	)
  
  													if cond_proj_dim is not None:
  																				__SCREAMING_SNAKE_CASE								=      nn.Linear(_A   ,							_A   ,							bias=_A	)
  													else:
  																				__SCREAMING_SNAKE_CASE								=      None
  
  													__SCREAMING_SNAKE_CASE								=      get_activation(_A	)
  
  													if out_dim is not None:
  																				__SCREAMING_SNAKE_CASE								=      out_dim
  													else:
  																				__SCREAMING_SNAKE_CASE								=      time_embed_dim
  													__SCREAMING_SNAKE_CASE								=      nn.Linear(_A   ,							_A	)
  
  													if post_act_fn is None:
  																				__SCREAMING_SNAKE_CASE								=      None
  													else:
  																				__SCREAMING_SNAKE_CASE								=      get_activation(_A	)
  
  
  
  
  
  
  						def  _A			(					self   ,							_A   ,							_A=None	):
  
  
  
  
  
  
  
  													'''simple docstring'''
  
  													if condition is not None:
  																				__SCREAMING_SNAKE_CASE								=      sample + self.cond_proj(_A	)
  													__SCREAMING_SNAKE_CASE								=      self.linear_a(_A	)
  
  													if self.act is not None:
  																				__SCREAMING_SNAKE_CASE								=      self.act(_A	)
  
  													__SCREAMING_SNAKE_CASE								=      self.linear_a(_A	)
  
  													if self.post_act is not None:
  																				__SCREAMING_SNAKE_CASE								=      self.post_act(_A	)
  													return sample
  
  
  
  
  
  
  
  class      UpperCAmelCase_						(     nn.Module ):
  
  						'''simple docstring'''
  
  
  
  
  						def __init__(					self   ,							_A   ,							_A   ,							_A	):
  
  
  
  
  
  
  
  													'''simple docstring'''
  
  													super().__init__()
  													__SCREAMING_SNAKE_CASE								=      num_channels
  													__SCREAMING_SNAKE_CASE								=      flip_sin_to_cos
  													__SCREAMING_SNAKE_CASE								=      downscale_freq_shift
  
  
  
  
  
  
  						def  _A			(					self   ,							_A	):
  
  
  
  
  
  
  
  													'''simple docstring'''
  
  													__SCREAMING_SNAKE_CASE								=      get_timestep_embedding(
  													    _A   ,							self.num_channels   ,							flip_sin_to_cos=self.flip_sin_to_cos   ,							downscale_freq_shift=self.downscale_freq_shift   ,							)
  													return t_emb
  
  
  
  
  
  
  
  class      UpperCAmelCase_						(     nn.Module ):
  
  						'''simple docstring'''
  
  
  
  
  						def __init__(					self   ,							_A = 256   ,							_A = 1.0   ,							_A=True   ,							_A=True   ,							_A=False	):
  
  
  
  
  
  
  
  													'''simple docstring'''
  
  													super().__init__()
  													__SCREAMING_SNAKE_CASE								=      nn.Parameter(torch.randn(_A	) * scale   ,							requires_grad=_A	)
  													__SCREAMING_SNAKE_CASE								=      log
  													__SCREAMING_SNAKE_CASE								=      flip_sin_to_cos
  
  													if set_W_to_weight:
  																				# to delete later
  																				__SCREAMING_SNAKE_CASE								=      nn.Parameter(torch.randn(_A	) * scale   ,							requires_grad=_A	)
  
  																				__SCREAMING_SNAKE_CASE								=      self.W
  
  
  
  
  
  
  						def  _A			(					self   ,							_A	):
  
  
  
  
  
  
  
  													'''simple docstring'''
  
  													if self.log:
  																				__SCREAMING_SNAKE_CASE								=      torch.log(_A	)
  
  													__SCREAMING_SNAKE_CASE								=      x[:, None] * self.weight[None, :] * 2 * np.pi
  
  													if self.flip_sin_to_cos:
  																				__SCREAMING_SNAKE_CASE								=      torch.cat([torch.cos(_A	), torch.sin(_A	)]   ,							dim=-1	)
  													else:
  																				__SCREAMING_SNAKE_CASE								=      torch.cat([torch.sin(_A	), torch.cos(_A	)]   ,							dim=-1	)
  													return out
  
  
  
  
  
  
  
  class      UpperCAmelCase_						(     nn.Module ):
  
  						'''simple docstring'''
  
  
  
  
  						def __init__(					self   ,							_A   ,							_A   ,							_A   ,							_A   ,							):
  
  
  
  
  
  
  
  													'''simple docstring'''
  
  													super().__init__()
  
  													__SCREAMING_SNAKE_CASE								=      height
  													__SCREAMING_SNAKE_CASE								=      width
  													__SCREAMING_SNAKE_CASE								=      num_embed
  													__SCREAMING_SNAKE_CASE								=      embed_dim
  
  													__SCREAMING_SNAKE_CASE								=      nn.Embedding(self.num_embed   ,							_A	)
  													__SCREAMING_SNAKE_CASE								=      nn.Embedding(self.height   ,							_A	)
  													__SCREAMING_SNAKE_CASE								=      nn.Embedding(self.width   ,							_A	)
  
  
  
  
  
  
  						def  _A			(					self   ,							_A	):
  
  
  
  
  
  
  
  													'''simple docstring'''
  
  													__SCREAMING_SNAKE_CASE								=      self.emb(_A	)
  
  													__SCREAMING_SNAKE_CASE								=      self.height_emb(torch.arange(self.height   ,							device=index.device	).view(1   ,							self.height	)	)
  
  													# 1 x H x D -> 1 x H x 1 x D
  													__SCREAMING_SNAKE_CASE								=      height_emb.unsqueeze(2	)
  
  													__SCREAMING_SNAKE_CASE								=      self.width_emb(torch.arange(self.width   ,							device=index.device	).view(1   ,							self.width	)	)
  
  													# 1 x W x D -> 1 x 1 x W x D
  													__SCREAMING_SNAKE_CASE								=      width_emb.unsqueeze(1	)
  
  													__SCREAMING_SNAKE_CASE								=      height_emb + width_emb
  
  													# 1 x H x W x D -> 1 x L xD
  													__SCREAMING_SNAKE_CASE								=      pos_emb.view(1   ,							self.height * self.width   ,							-1	)
  
  													__SCREAMING_SNAKE_CASE								=      emb + pos_emb[:, : emb.shape[1], :]
  
  													return emb
  
  
  
  
  
  
  
  class      UpperCAmelCase_						(     nn.Module ):
  
  						'''simple docstring'''
  
  
  
  
  						def __init__(					self   ,							_A   ,							_A   ,							_A	):
  
  
  
  
  
  
  
  													'''simple docstring'''
  
  													super().__init__()
  													__SCREAMING_SNAKE_CASE								=      dropout_prob > 0
  													__SCREAMING_SNAKE_CASE								=      nn.Embedding(num_classes + use_cfg_embedding   ,							_A	)
  													__SCREAMING_SNAKE_CASE								=      num_classes
  													__SCREAMING_SNAKE_CASE								=      dropout_prob
  
  
  
  
  
  
  						def  _A			(					self   ,							_A   ,							_A=None	):
  
  
  
  
  
  
  
  													'''simple docstring'''
  
  													if force_drop_ids is None:
  																				__SCREAMING_SNAKE_CASE								=      torch.rand(labels.shape[0]   ,							device=labels.device	) < self.dropout_prob
  													else:
  																				__SCREAMING_SNAKE_CASE								=      torch.tensor(force_drop_ids == 1	)
  													__SCREAMING_SNAKE_CASE								=      torch.where(_A   ,							self.num_classes   ,							_A	)
  													return labels
  
  
  
  
  
  
  						def  _A			(					self   ,							_A   ,							_A=None	):
  
  
  
  
  
  
  
  													'''simple docstring'''
  
  													__SCREAMING_SNAKE_CASE								=      self.dropout_prob > 0
  													if (self.training and use_dropout) or (force_drop_ids is not None):
  																				__SCREAMING_SNAKE_CASE								=      self.token_drop(_A   ,							_A	)
  													__SCREAMING_SNAKE_CASE								=      self.embedding_table(_A	)
  													return embeddings
  
  
  
  
  
  
  
  class      UpperCAmelCase_						(     nn.Module ):
  
  						'''simple docstring'''
  
  
  
  
  						def __init__(					self   ,							_A = 1_024   ,							_A = 768   ,							_A = 768   ,							_A = 10   ,							):
  
  
  
  
  
  
  
  													'''simple docstring'''
  
  													super().__init__()
  
  													__SCREAMING_SNAKE_CASE								=      num_image_text_embeds
  													__SCREAMING_SNAKE_CASE								=      nn.Linear(_A   ,							self.num_image_text_embeds * cross_attention_dim	)
  													__SCREAMING_SNAKE_CASE								=      nn.Linear(_A   ,							_A	)
  
  
  
  
  
  
  						def  _A			(					self   ,							_A   ,							_A	):
  
  
  
  
  
  
  
  													'''simple docstring'''
  
  													__SCREAMING_SNAKE_CASE								=      text_embeds.shape[0]
  
  													# image
  													__SCREAMING_SNAKE_CASE								=      self.image_embeds(_A	)
  													__SCREAMING_SNAKE_CASE								=      image_text_embeds.reshape(_A   ,							self.num_image_text_embeds   ,							-1	)
  
  													# text
  													__SCREAMING_SNAKE_CASE								=      self.text_proj(_A	)
  
  													return torch.cat([image_text_embeds, text_embeds]   ,							dim=1	)
  
  
  
  
  
  
  
  class      UpperCAmelCase_						(     nn.Module ):
  
  						'''simple docstring'''
  
  
  
  
  						def __init__(					self   ,							_A = 768   ,							_A = 768   ,							_A = 32   ,							):
  
  
  
  
  
  
  
  													'''simple docstring'''
  
  													super().__init__()
  
  													__SCREAMING_SNAKE_CASE								=      num_image_text_embeds
  													__SCREAMING_SNAKE_CASE								=      nn.Linear(_A   ,							self.num_image_text_embeds * cross_attention_dim	)
  													__SCREAMING_SNAKE_CASE								=      nn.LayerNorm(_A	)
  
  
  
  
  
  
  						def  _A			(					self   ,							_A	):
  
  
  
  
  
  
  
  													'''simple docstring'''
  
  													__SCREAMING_SNAKE_CASE								=      image_embeds.shape[0]
  
  													# image
  													__SCREAMING_SNAKE_CASE								=      self.image_embeds(_A	)
  													__SCREAMING_SNAKE_CASE								=      image_embeds.reshape(_A   ,							self.num_image_text_embeds   ,							-1	)
  													__SCREAMING_SNAKE_CASE								=      self.norm(_A	)
  													return image_embeds
  
  
  
  
  
  
  
  class      UpperCAmelCase_						(     nn.Module ):
  
  						'''simple docstring'''
  
  
  
  
  						def __init__(					self   ,							_A   ,							_A   ,							_A=0.1	):
  
  
  
  
  
  
  
  													'''simple docstring'''
  
  													super().__init__()
  
  													__SCREAMING_SNAKE_CASE								=      Timesteps(num_channels=256   ,							flip_sin_to_cos=_A   ,							downscale_freq_shift=1	)
  													__SCREAMING_SNAKE_CASE								=      TimestepEmbedding(in_channels=256   ,							time_embed_dim=_A	)
  													__SCREAMING_SNAKE_CASE								=      LabelEmbedding(_A   ,							_A   ,							_A	)
  
  
  
  
  
  
  						def  _A			(					self   ,							_A   ,							_A   ,							_A=None	):
  
  
  
  
  
  
  
  													'''simple docstring'''
  
  													__SCREAMING_SNAKE_CASE								=      self.time_proj(_A	)
  													__SCREAMING_SNAKE_CASE								=      self.timestep_embedder(timesteps_proj.to(dtype=_A	)	)  # (N, D)
  
  													__SCREAMING_SNAKE_CASE								=      self.class_embedder(_A	)  # (N, D)
  
  													__SCREAMING_SNAKE_CASE								=      timesteps_emb + class_labels  # (N, D)
  
  													return conditioning
  
  
  
  
  
  
  
  class      UpperCAmelCase_						(     nn.Module ):
  
  						'''simple docstring'''
  
  
  
  
  						def __init__(					self   ,							_A   ,							_A   ,							_A = 64	):
  
  
  
  
  
  
  
  													'''simple docstring'''
  
  													super().__init__()
  													__SCREAMING_SNAKE_CASE								=      nn.LayerNorm(_A	)
  													__SCREAMING_SNAKE_CASE								=      AttentionPooling(_A   ,							_A	)
  													__SCREAMING_SNAKE_CASE								=      nn.Linear(_A   ,							_A	)
  													__SCREAMING_SNAKE_CASE								=      nn.LayerNorm(_A	)
  
  
  
  
  
  
  						def  _A			(					self   ,							_A	):
  
  
  
  
  
  
  
  													'''simple docstring'''
  
  													__SCREAMING_SNAKE_CASE								=      self.norma(_A	)
  													__SCREAMING_SNAKE_CASE								=      self.pool(_A	)
  													__SCREAMING_SNAKE_CASE								=      self.proj(_A	)
  													__SCREAMING_SNAKE_CASE								=      self.norma(_A	)
  													return hidden_states
  
  
  
  
  
  
  
  class      UpperCAmelCase_						(     nn.Module ):
  
  						'''simple docstring'''
  
  
  
  
  						def __init__(					self   ,							_A = 768   ,							_A = 768   ,							_A = 1_536	):
  
  
  
  
  
  
  
  													'''simple docstring'''
  
  													super().__init__()
  													__SCREAMING_SNAKE_CASE								=      nn.Linear(_A   ,							_A	)
  													__SCREAMING_SNAKE_CASE								=      nn.LayerNorm(_A	)
  													__SCREAMING_SNAKE_CASE								=      nn.Linear(_A   ,							_A	)
  
  
  
  
  
  
  						def  _A			(					self   ,							_A   ,							_A	):
  
  
  
  
  
  
  
  													'''simple docstring'''
  
  													__SCREAMING_SNAKE_CASE								=      self.text_proj(_A	)
  													__SCREAMING_SNAKE_CASE								=      self.text_norm(_A	)
  
  													# image
  													__SCREAMING_SNAKE_CASE								=      self.image_proj(_A	)
  
  													return time_image_embeds + time_text_embeds
  
  
  
  
  
  
  
  class      UpperCAmelCase_						(     nn.Module ):
  
  						'''simple docstring'''
  
  
  
  
  						def __init__(					self   ,							_A = 768   ,							_A = 1_536	):
  
  
  
  
  
  
  
  													'''simple docstring'''
  
  													super().__init__()
  													__SCREAMING_SNAKE_CASE								=      nn.Linear(_A   ,							_A	)
  													__SCREAMING_SNAKE_CASE								=      nn.LayerNorm(_A	)
  
  
  
  
  
  
  						def  _A			(					self   ,							_A	):
  
  
  
  
  
  
  
  													'''simple docstring'''
  
  													__SCREAMING_SNAKE_CASE								=      self.image_proj(_A	)
  													__SCREAMING_SNAKE_CASE								=      self.image_norm(_A	)
  													return time_image_embeds
  
  
  
  
  
  
  
  class      UpperCAmelCase_						(     nn.Module ):
  
  						'''simple docstring'''
  
  
  
  
  						def __init__(					self   ,							_A = 768   ,							_A = 1_536	):
  
  
  
  
  
  
  
  													'''simple docstring'''
  
  													super().__init__()
  													__SCREAMING_SNAKE_CASE								=      nn.Linear(_A   ,							_A	)
  													__SCREAMING_SNAKE_CASE								=      nn.LayerNorm(_A	)
  													__SCREAMING_SNAKE_CASE								=      nn.Sequential(
  													    nn.Convad(3   ,							16   ,							3   ,							padding=1	)   ,							nn.SiLU()   ,							nn.Convad(16   ,							16   ,							3   ,							padding=1	)   ,							nn.SiLU()   ,							nn.Convad(16   ,							32   ,							3   ,							padding=1   ,							stride=2	)   ,							nn.SiLU()   ,							nn.Convad(32   ,							32   ,							3   ,							padding=1	)   ,							nn.SiLU()   ,							nn.Convad(32   ,							96   ,							3   ,							padding=1   ,							stride=2	)   ,							nn.SiLU()   ,							nn.Convad(96   ,							96   ,							3   ,							padding=1	)   ,							nn.SiLU()   ,							nn.Convad(96   ,							256   ,							3   ,							padding=1   ,							stride=2	)   ,							nn.SiLU()   ,							nn.Convad(256   ,							4   ,							3   ,							padding=1	)   ,							)
  
  
  
  
  
  
  						def  _A			(					self   ,							_A   ,							_A	):
  
  
  
  
  
  
  
  													'''simple docstring'''
  
  													__SCREAMING_SNAKE_CASE								=      self.image_proj(_A	)
  													__SCREAMING_SNAKE_CASE								=      self.image_norm(_A	)
  													__SCREAMING_SNAKE_CASE								=      self.input_hint_block(_A	)
  													return time_image_embeds, hint
  
  
  
  
  
  
  
  class      UpperCAmelCase_						(     nn.Module ):
  
  						'''simple docstring'''
  
  
  
  
  						def __init__(					self   ,							_A   ,							_A   ,							_A=None	):
  
  
  
  
  
  
  
  													'''simple docstring'''
  
  													super().__init__()
  													__SCREAMING_SNAKE_CASE								=      dtype
  													__SCREAMING_SNAKE_CASE								=      nn.Parameter(torch.randn(1   ,							_A	) / embed_dim**0.5	)
  													__SCREAMING_SNAKE_CASE								=      nn.Linear(_A   ,							_A   ,							dtype=self.dtype	)
  													__SCREAMING_SNAKE_CASE								=      nn.Linear(_A   ,							_A   ,							dtype=self.dtype	)
  													__SCREAMING_SNAKE_CASE								=      nn.Linear(_A   ,							_A   ,							dtype=self.dtype	)
  													__SCREAMING_SNAKE_CASE								=      num_heads
  													__SCREAMING_SNAKE_CASE								=      embed_dim // self.num_heads
  
  
  
  
  
  
  						def  _A			(					self   ,							_A	):
  
  
  
  
  
  
  
  													'''simple docstring'''
  
  													__SCREAMING_SNAKE_CASE							, __SCREAMING_SNAKE_CASE							, __SCREAMING_SNAKE_CASE								=      x.size()
  
  													def shape(_A	):
  																				# (bs, length, width) --> (bs, length, n_heads, dim_per_head)
  																				__SCREAMING_SNAKE_CASE								=      x.view(_A   ,							-1   ,							self.num_heads   ,							self.dim_per_head	)
  																				# (bs, length, n_heads, dim_per_head) --> (bs, n_heads, length, dim_per_head)
  																				__SCREAMING_SNAKE_CASE								=      x.transpose(1   ,							2	)
  																				# (bs, n_heads, length, dim_per_head) --> (bs*n_heads, length, dim_per_head)
  																				__SCREAMING_SNAKE_CASE								=      x.reshape(bs * self.num_heads   ,							-1   ,							self.dim_per_head	)
  																				# (bs*n_heads, length, dim_per_head) --> (bs*n_heads, dim_per_head, length)
  																				__SCREAMING_SNAKE_CASE								=      x.transpose(1   ,							2	)
  																				return x
  
  													__SCREAMING_SNAKE_CASE								=      x.mean(dim=1   ,							keepdim=_A	) + self.positional_embedding.to(x.dtype	)
  													__SCREAMING_SNAKE_CASE								=      torch.cat([class_token, x]   ,							dim=1	)  # (bs, length+1, width)
  
  													# (bs*n_heads, class_token_length, dim_per_head)
  													__SCREAMING_SNAKE_CASE								=      shape(self.q_proj(_A	)	)
  													# (bs*n_heads, length+class_token_length, dim_per_head)
  													__SCREAMING_SNAKE_CASE								=      shape(self.k_proj(_A	)	)
  													__SCREAMING_SNAKE_CASE								=      shape(self.v_proj(_A	)	)
  
  													# (bs*n_heads, class_token_length, length+class_token_length):
  													__SCREAMING_SNAKE_CASE								=      1 / math.sqrt(math.sqrt(self.dim_per_head	)	)
  													__SCREAMING_SNAKE_CASE								=      torch.einsum('bct,bcs->bts'   ,							q * scale   ,							k * scale	)  # More stable with f16 than dividing afterwards
  													__SCREAMING_SNAKE_CASE								=      torch.softmax(weight.float()   ,							dim=-1	).type(weight.dtype	)
  
  													# (bs*n_heads, dim_per_head, class_token_length)
  													__SCREAMING_SNAKE_CASE								=      torch.einsum('bts,bcs->bct'   ,							_A   ,							_A	)
  
  													# (bs, length+1, width)
  													__SCREAMING_SNAKE_CASE								=      a.reshape(_A   ,							-1   ,							1	).transpose(1   ,							2	)
  
  													return a[:, 0, :]  # cls_token
  
  
  
  
  
  
  
style_context: 
  
  
  
  from itertools import combinations, product
  
  
  
  
  
  
  def 			__lowercase     (				a__							,     a__							,     a__							,     a__     )       ->				bool:
  							if xa == ya == 0 or xa == ya == 0:
  														return False
  							__SCREAMING_SNAKE_CASE								=      xa * xa + ya * ya
  							__SCREAMING_SNAKE_CASE								=      xa * xa + ya * ya
  							__SCREAMING_SNAKE_CASE								=      (xa - xa) * (xa - xa) + (ya - ya) * (ya - ya)
  							return (
  							    a_square + b_square == c_square
  							    or a_square + c_square == b_square
  							    or b_square + c_square == a_square
  							)
  
  
  
  
  
  
  def 			__lowercase     (				a__ = 50     )       ->				int:
  							return sum(
  							    1
  							    for pta, pta in combinations(product(range(limit + 1     )							,     repeat=2     )							,     2     )
  							    if is_right(*a__							,     *a__     )     )
  
  
  if __name__ == "__main__":
  			print(F'''{solution() = }''')
  
  
  
  
  
  
  