





'''simple docstring'''


import math
from typing import Optional

import numpy as np
import torch
from torch import nn

from .activations import get_activation
def 							UpperCAmelCase_						(		__lowerCamelCase      :      torch.Tensor			,__lowerCamelCase      :      int			,__lowerCamelCase      :      bool = False			,__lowerCamelCase      :      float = 1			,__lowerCamelCase      :      float = 1			,__lowerCamelCase      :      int = 1_00_00			,):
   assert len(timesteps.shape				) == 1, "Timesteps should be a 1d-array"

   lowercase_    :Optional[int]					    =				embedding_dim // 2
   lowercase_    :Tuple					    =				-math.log(__lowerCamelCase				) * torch.arange(
       start=0			,end=__lowerCamelCase			,dtype=torch.floataa			,device=timesteps.device				)
   lowercase_    :Any					    =				exponent / (half_dim - downscale_freq_shift)

   lowercase_    :List[Any]					    =				torch.exp(__lowerCamelCase				)
   lowercase_    :Union[str, Any]					    =				timesteps[:, None].float() * emb[None, :]

   # scale embeddings
   lowercase_    :Tuple					    =				scale * emb

   # concat sine and cosine embeddings
   lowercase_    :Dict					    =				torch.cat([torch.sin(__lowerCamelCase				), torch.cos(__lowerCamelCase				)]			,dim=-1				)

   # flip sine and cosine embeddings
   if flip_sin_to_cos:
      lowercase_    :Optional[int]					    =				torch.cat([emb[:, half_dim:], emb[:, :half_dim]]			,dim=-1				)

   # zero pad
   if embedding_dim % 2 == 1:
      lowercase_    :Tuple					    =				torch.nn.functional.pad(__lowerCamelCase			,(0, 1, 0, 0)				)
   return emb
def 							UpperCAmelCase_						(		__lowerCamelCase      :      Dict			,__lowerCamelCase      :      Union[str, Any]			,__lowerCamelCase      :      List[Any]=False			,__lowerCamelCase      :      str=0				):
   lowercase_    :List[Any]					    =				np.arange(__lowerCamelCase			,dtype=np.floataa				)
   lowercase_    :str					    =				np.arange(__lowerCamelCase			,dtype=np.floataa				)
   lowercase_    :List[Any]					    =				np.meshgrid(__lowerCamelCase			,__lowerCamelCase				)  # here w goes first
   lowercase_    :Union[str, Any]					    =				np.stack(__lowerCamelCase			,axis=0				)

   lowercase_    :List[Any]					    =				grid.reshape([2, 1, grid_size, grid_size]				)
   lowercase_    :Optional[Any]					    =				get_ad_sincos_pos_embed_from_grid(__lowerCamelCase			,__lowerCamelCase				)
   if cls_token and extra_tokens > 0:
      lowercase_    :Tuple					    =				np.concatenate([np.zeros([extra_tokens, embed_dim]				), pos_embed]			,axis=0				)
   return pos_embed
def 							UpperCAmelCase_						(		__lowerCamelCase      :      Optional[int]			,__lowerCamelCase      :      Tuple				):



   if embed_dim % 2 != 0:
      raise ValueError("embed_dim must be divisible by 2"				)

   # use half of dimensions to encode grid_h
   lowercase_    :Any					    =				get_ad_sincos_pos_embed_from_grid(embed_dim // 2			,grid[0]				)  # (H*W, D/2)
   lowercase_    :Any					    =				get_ad_sincos_pos_embed_from_grid(embed_dim // 2			,grid[1]				)  # (H*W, D/2)

   lowercase_    :str					    =				np.concatenate([emb_h, emb_w]			,axis=1				)  # (H*W, D)
   return emb
def 							UpperCAmelCase_						(		__lowerCamelCase      :      List[Any]			,__lowerCamelCase      :      Optional[Any]				):



   if embed_dim % 2 != 0:
      raise ValueError("embed_dim must be divisible by 2"				)

   lowercase_    :List[Any]					    =				np.arange(embed_dim // 2			,dtype=np.floataa				)
   omega /= embed_dim / 2.0
   lowercase_    :Union[str, Any]					    =				1.0 / 1_00_00**omega  # (D/2,)

   lowercase_    :str					    =				pos.reshape(-1				)  # (M,)
   lowercase_    :Optional[Any]					    =				np.einsum("m,d->md"			,__lowerCamelCase			,__lowerCamelCase				)  # (M, D/2), outer product

   lowercase_    :List[str]					    =				np.sin(__lowerCamelCase				)  # (M, D/2)
   lowercase_    :Dict					    =				np.cos(__lowerCamelCase				)  # (M, D/2)

   lowercase_    :Union[str, Any]					    =				np.concatenate([emb_sin, emb_cos]			,axis=1				)  # (M, D)
   return emb
class    a_     (       nn.Module							):





     def __init__(				self	:      int			,   lowercase	:      Tuple=224			,   lowercase	:      Optional[int]=224			,   lowercase	:      List[Any]=16			,   lowercase	:      Optional[int]=3			,   lowercase	:      str=768			,   lowercase	:      Optional[int]=False			,   lowercase	:      Any=True			,   lowercase	:      Dict=True			,   ):





        """simple docstring"""




        super().__init__()

        lowercase_    :List[Any]					    =				(height // patch_size) * (width // patch_size)
        lowercase_    :int					    =				flatten
        lowercase_    :Dict					    =				layer_norm

        lowercase_    :Tuple					    =				nn.Convad(
            lowerCAmelCase__			,   lowerCAmelCase__			,   kernel_size=(patch_size, patch_size)			,   stride=lowerCAmelCase__			,   bias=lowerCAmelCase__		)
        if layer_norm:
           lowercase_    :Dict					    =				nn.LayerNorm(lowerCAmelCase__			,   elementwise_affine=lowerCAmelCase__			,   eps=1e-6		)
        else:
           lowercase_    :Union[str, Any]					    =				None

        lowercase_    :Optional[int]					    =				get_ad_sincos_pos_embed(lowerCAmelCase__			,   int(num_patches**0.5		)		)
        self.register_buffer("pos_embed"			,   torch.from_numpy(lowerCAmelCase__		).float().unsqueeze(0		)			,   persistent=lowerCAmelCase__		)







     def 							lowercase__   (				self	:      int			,   lowercase	:      int		):





        """simple docstring"""




        lowercase_    :List[str]					    =				self.proj(lowerCAmelCase__		)
        if self.flatten:
           lowercase_    :int					    =				latent.flatten(2		).transpose(1			,   2		)  # BCHW -> BNC
        if self.layer_norm:
           lowercase_    :Tuple					    =				self.norm(lowerCAmelCase__		)
        return latent + self.pos_embed







class    a_     (       nn.Module							):





     def __init__(				self	:      Optional[int]			,   lowercase	:      List[Any]			,   lowercase	:      Optional[int]			,   lowercase	:      List[Any] = "silu"			,   lowercase	:      List[str] = None			,   lowercase	:      List[Any] = None			,   lowercase	:      Union[str, Any]=None			,   ):





        """simple docstring"""




        super().__init__()

        lowercase_    :Any					    =				nn.Linear(lowerCAmelCase__			,   lowerCAmelCase__		)

        if cond_proj_dim is not None:
           lowercase_    :Optional[Any]					    =				nn.Linear(lowerCAmelCase__			,   lowerCAmelCase__			,   bias=lowerCAmelCase__		)
        else:
           lowercase_    :List[Any]					    =				None

        lowercase_    :Optional[int]					    =				get_activation(lowerCAmelCase__		)

        if out_dim is not None:
           lowercase_    :Union[str, Any]					    =				out_dim
        else:
           lowercase_    :int					    =				time_embed_dim
        lowercase_    :Union[str, Any]					    =				nn.Linear(lowerCAmelCase__			,   lowerCAmelCase__		)

        if post_act_fn is None:
           lowercase_    :int					    =				None
        else:
           lowercase_    :Any					    =				get_activation(lowerCAmelCase__		)







     def 							lowercase__   (				self	:      Optional[Any]			,   lowercase	:      Optional[int]			,   lowercase	:      Optional[Any]=None		):





        """simple docstring"""




        if condition is not None:
           lowercase_    :Dict					    =				sample + self.cond_proj(lowerCAmelCase__		)
        lowercase_    :Any					    =				self.linear_a(lowerCAmelCase__		)

        if self.act is not None:
           lowercase_    :Dict					    =				self.act(lowerCAmelCase__		)

        lowercase_    :str					    =				self.linear_a(lowerCAmelCase__		)

        if self.post_act is not None:
           lowercase_    :Optional[int]					    =				self.post_act(lowerCAmelCase__		)
        return sample







class    a_     (       nn.Module							):





     def __init__(				self	:      Optional[Any]			,   lowercase	:      str			,   lowercase	:      str			,   lowercase	:      List[Any]		):





        """simple docstring"""




        super().__init__()
        lowercase_    :str					    =				num_channels
        lowercase_    :Optional[int]					    =				flip_sin_to_cos
        lowercase_    :int					    =				downscale_freq_shift







     def 							lowercase__   (				self	:      Optional[Any]			,   lowercase	:      Optional[Any]		):





        """simple docstring"""




        lowercase_    :Dict					    =				get_timestep_embedding(
            lowerCAmelCase__			,   self.num_channels			,   flip_sin_to_cos=self.flip_sin_to_cos			,   downscale_freq_shift=self.downscale_freq_shift			,   )
        return t_emb







class    a_     (       nn.Module							):





     def __init__(				self	:      Optional[int]			,   lowercase	:      int = 256			,   lowercase	:      List[str] = 1.0			,   lowercase	:      List[str]=True			,   lowercase	:      Optional[Any]=True			,   lowercase	:      int=False		):





        """simple docstring"""




        super().__init__()
        lowercase_    :str					    =				nn.Parameter(torch.randn(lowerCAmelCase__		) * scale			,   requires_grad=lowerCAmelCase__		)
        lowercase_    :Optional[Any]					    =				log
        lowercase_    :List[Any]					    =				flip_sin_to_cos

        if set_W_to_weight:
           # to delete later
           lowercase_    :Optional[int]					    =				nn.Parameter(torch.randn(lowerCAmelCase__		) * scale			,   requires_grad=lowerCAmelCase__		)

           lowercase_    :int					    =				self.W







     def 							lowercase__   (				self	:      str			,   lowercase	:      List[str]		):





        """simple docstring"""




        if self.log:
           lowercase_    :List[Any]					    =				torch.log(lowerCAmelCase__		)

        lowercase_    :Union[str, Any]					    =				x[:, None] * self.weight[None, :] * 2 * np.pi

        if self.flip_sin_to_cos:
           lowercase_    :List[str]					    =				torch.cat([torch.cos(lowerCAmelCase__		), torch.sin(lowerCAmelCase__		)]			,   dim=-1		)
        else:
           lowercase_    :Optional[int]					    =				torch.cat([torch.sin(lowerCAmelCase__		), torch.cos(lowerCAmelCase__		)]			,   dim=-1		)
        return out







class    a_     (       nn.Module							):





     def __init__(				self	:      Tuple			,   lowercase	:      List[Any]			,   lowercase	:      Any			,   lowercase	:      List[str]			,   lowercase	:      List[Any]			,   ):





        """simple docstring"""




        super().__init__()

        lowercase_    :Optional[Any]					    =				height
        lowercase_    :Tuple					    =				width
        lowercase_    :Dict					    =				num_embed
        lowercase_    :int					    =				embed_dim

        lowercase_    :Optional[Any]					    =				nn.Embedding(self.num_embed			,   lowerCAmelCase__		)
        lowercase_    :Union[str, Any]					    =				nn.Embedding(self.height			,   lowerCAmelCase__		)
        lowercase_    :List[Any]					    =				nn.Embedding(self.width			,   lowerCAmelCase__		)







     def 							lowercase__   (				self	:      int			,   lowercase	:      List[str]		):





        """simple docstring"""




        lowercase_    :Any					    =				self.emb(lowerCAmelCase__		)

        lowercase_    :List[Any]					    =				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
        lowercase_    :List[str]					    =				height_emb.unsqueeze(2		)

        lowercase_    :Optional[int]					    =				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
        lowercase_    :Union[str, Any]					    =				width_emb.unsqueeze(1		)

        lowercase_    :Tuple					    =				height_emb + width_emb

        # 1 x H x W x D -> 1 x L xD
        lowercase_    :Optional[int]					    =				pos_emb.view(1			,   self.height * self.width			,   -1		)

        lowercase_    :int					    =				emb + pos_emb[:, : emb.shape[1], :]

        return emb







class    a_     (       nn.Module							):





     def __init__(				self	:      List[Any]			,   lowercase	:      Optional[Any]			,   lowercase	:      Any			,   lowercase	:      List[Any]		):





        """simple docstring"""




        super().__init__()
        lowercase_    :Any					    =				dropout_prob > 0
        lowercase_    :Tuple					    =				nn.Embedding(num_classes + use_cfg_embedding			,   lowerCAmelCase__		)
        lowercase_    :Union[str, Any]					    =				num_classes
        lowercase_    :Optional[int]					    =				dropout_prob





     def 							lowercase__   (				self	:      Tuple			,   lowercase	:      str			,   lowercase	:      Optional[Any]=None		):





        """simple docstring"""




        if force_drop_ids is None:
           lowercase_    :Any					    =				torch.rand(labels.shape[0]			,   device=labels.device		) < self.dropout_prob
        else:
           lowercase_    :Dict					    =				torch.tensor(force_drop_ids == 1		)
        lowercase_    :Any					    =				torch.where(lowerCAmelCase__			,   self.num_classes			,   lowerCAmelCase__		)
        return labels







     def 							lowercase__   (				self	:      str			,   lowercase	:      List[Any]			,   lowercase	:      Optional[Any]=None		):





        """simple docstring"""




        lowercase_    :Optional[Any]					    =				self.dropout_prob > 0
        if (self.training and use_dropout) or (force_drop_ids is not None):
           lowercase_    :Any					    =				self.token_drop(lowerCAmelCase__			,   lowerCAmelCase__		)
        lowercase_    :Dict					    =				self.embedding_table(lowerCAmelCase__		)
        return embeddings







class    a_     (       nn.Module							):





     def __init__(				self	:      Optional[int]			,   lowercase	:      Tuple = 1_024			,   lowercase	:      int = 768			,   lowercase	:      Optional[Any] = 768			,   lowercase	:      Optional[int] = 10			,   ):





        """simple docstring"""




        super().__init__()

        lowercase_    :List[Any]					    =				num_image_text_embeds
        lowercase_    :Union[str, Any]					    =				nn.Linear(lowerCAmelCase__			,   self.num_image_text_embeds * cross_attention_dim		)
        lowercase_    :Any					    =				nn.Linear(lowerCAmelCase__			,   lowerCAmelCase__		)







     def 							lowercase__   (				self	:      Tuple			,   lowercase	:      Tuple			,   lowercase	:      Union[str, Any]		):





        """simple docstring"""




        lowercase_    :Union[str, Any]					    =				text_embeds.shape[0]

        # image
        lowercase_    :Dict					    =				self.image_embeds(lowerCAmelCase__		)
        lowercase_    :Optional[Any]					    =				image_text_embeds.reshape(lowerCAmelCase__			,   self.num_image_text_embeds			,   -1		)

        # text
        lowercase_    :List[Any]					    =				self.text_proj(lowerCAmelCase__		)

        return torch.cat([image_text_embeds, text_embeds]			,   dim=1		)







class    a_     (       nn.Module							):





     def __init__(				self	:      List[Any]			,   lowercase	:      Tuple = 768			,   lowercase	:      List[Any] = 768			,   lowercase	:      List[str] = 32			,   ):





        """simple docstring"""




        super().__init__()

        lowercase_    :List[Any]					    =				num_image_text_embeds
        lowercase_    :Any					    =				nn.Linear(lowerCAmelCase__			,   self.num_image_text_embeds * cross_attention_dim		)
        lowercase_    :str					    =				nn.LayerNorm(lowerCAmelCase__		)







     def 							lowercase__   (				self	:      List[Any]			,   lowercase	:      Tuple		):





        """simple docstring"""




        lowercase_    :List[str]					    =				image_embeds.shape[0]

        # image
        lowercase_    :Tuple					    =				self.image_embeds(lowerCAmelCase__		)
        lowercase_    :Optional[int]					    =				image_embeds.reshape(lowerCAmelCase__			,   self.num_image_text_embeds			,   -1		)
        lowercase_    :Optional[int]					    =				self.norm(lowerCAmelCase__		)
        return image_embeds







class    a_     (       nn.Module							):





     def __init__(				self	:      Union[str, Any]			,   lowercase	:      Optional[Any]			,   lowercase	:      List[str]			,   lowercase	:      Union[str, Any]=0.1		):





        """simple docstring"""




        super().__init__()

        lowercase_    :List[Any]					    =				Timesteps(num_channels=256			,   flip_sin_to_cos=lowerCAmelCase__			,   downscale_freq_shift=1		)
        lowercase_    :int					    =				TimestepEmbedding(in_channels=256			,   time_embed_dim=lowerCAmelCase__		)
        lowercase_    :List[Any]					    =				LabelEmbedding(lowerCAmelCase__			,   lowerCAmelCase__			,   lowerCAmelCase__		)







     def 							lowercase__   (				self	:      Any			,   lowercase	:      List[str]			,   lowercase	:      Optional[int]			,   lowercase	:      Dict=None		):





        """simple docstring"""




        lowercase_    :Tuple					    =				self.time_proj(lowerCAmelCase__		)
        lowercase_    :Union[str, Any]					    =				self.timestep_embedder(timesteps_proj.to(dtype=lowerCAmelCase__		)		)  # (N, D)

        lowercase_    :List[Any]					    =				self.class_embedder(lowerCAmelCase__		)  # (N, D)

        lowercase_    :int					    =				timesteps_emb + class_labels  # (N, D)

        return conditioning







class    a_     (       nn.Module							):





     def __init__(				self	:      int			,   lowercase	:      Optional[int]			,   lowercase	:      str			,   lowercase	:      Optional[Any] = 64		):





        """simple docstring"""




        super().__init__()
        lowercase_    :int					    =				nn.LayerNorm(lowerCAmelCase__		)
        lowercase_    :Tuple					    =				AttentionPooling(lowerCAmelCase__			,   lowerCAmelCase__		)
        lowercase_    :Optional[Any]					    =				nn.Linear(lowerCAmelCase__			,   lowerCAmelCase__		)
        lowercase_    :Any					    =				nn.LayerNorm(lowerCAmelCase__		)







     def 							lowercase__   (				self	:      Tuple			,   lowercase	:      Union[str, Any]		):





        """simple docstring"""




        lowercase_    :Any					    =				self.norma(lowerCAmelCase__		)
        lowercase_    :int					    =				self.pool(lowerCAmelCase__		)
        lowercase_    :Optional[Any]					    =				self.proj(lowerCAmelCase__		)
        lowercase_    :Optional[int]					    =				self.norma(lowerCAmelCase__		)
        return hidden_states







class    a_     (       nn.Module							):





     def __init__(				self	:      List[str]			,   lowercase	:      int = 768			,   lowercase	:      List[Any] = 768			,   lowercase	:      int = 1_536		):





        """simple docstring"""




        super().__init__()
        lowercase_    :Dict					    =				nn.Linear(lowerCAmelCase__			,   lowerCAmelCase__		)
        lowercase_    :Union[str, Any]					    =				nn.LayerNorm(lowerCAmelCase__		)
        lowercase_    :str					    =				nn.Linear(lowerCAmelCase__			,   lowerCAmelCase__		)







     def 							lowercase__   (				self	:      Union[str, Any]			,   lowercase	:      List[str]			,   lowercase	:      Any		):





        """simple docstring"""




        lowercase_    :Any					    =				self.text_proj(lowerCAmelCase__		)
        lowercase_    :Optional[int]					    =				self.text_norm(lowerCAmelCase__		)

        # image
        lowercase_    :Any					    =				self.image_proj(lowerCAmelCase__		)

        return time_image_embeds + time_text_embeds







class    a_     (       nn.Module							):





     def __init__(				self	:      Optional[int]			,   lowercase	:      List[Any] = 768			,   lowercase	:      Tuple = 1_536		):





        """simple docstring"""




        super().__init__()
        lowercase_    :str					    =				nn.Linear(lowerCAmelCase__			,   lowerCAmelCase__		)
        lowercase_    :Tuple					    =				nn.LayerNorm(lowerCAmelCase__		)







     def 							lowercase__   (				self	:      Optional[int]			,   lowercase	:      int		):





        """simple docstring"""




        lowercase_    :Union[str, Any]					    =				self.image_proj(lowerCAmelCase__		)
        lowercase_    :Dict					    =				self.image_norm(lowerCAmelCase__		)
        return time_image_embeds







class    a_     (       nn.Module							):





     def __init__(				self	:      Optional[int]			,   lowercase	:      int = 768			,   lowercase	:      Dict = 1_536		):





        """simple docstring"""




        super().__init__()
        lowercase_    :Union[str, Any]					    =				nn.Linear(lowerCAmelCase__			,   lowerCAmelCase__		)
        lowercase_    :Union[str, Any]					    =				nn.LayerNorm(lowerCAmelCase__		)
        lowercase_    :int					    =				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 							lowercase__   (				self	:      Optional[Any]			,   lowercase	:      Optional[int]			,   lowercase	:      List[str]		):





        """simple docstring"""




        lowercase_    :int					    =				self.image_proj(lowerCAmelCase__		)
        lowercase_    :Optional[int]					    =				self.image_norm(lowerCAmelCase__		)
        lowercase_    :List[Any]					    =				self.input_hint_block(lowerCAmelCase__		)
        return time_image_embeds, hint







class    a_     (       nn.Module							):





     def __init__(				self	:      Union[str, Any]			,   lowercase	:      int			,   lowercase	:      Any			,   lowercase	:      List[str]=None		):





        """simple docstring"""




        super().__init__()
        lowercase_    :Dict					    =				dtype
        lowercase_    :Dict					    =				nn.Parameter(torch.randn(1			,   lowerCAmelCase__		) / embed_dim**0.5		)
        lowercase_    :Union[str, Any]					    =				nn.Linear(lowerCAmelCase__			,   lowerCAmelCase__			,   dtype=self.dtype		)
        lowercase_    :Tuple					    =				nn.Linear(lowerCAmelCase__			,   lowerCAmelCase__			,   dtype=self.dtype		)
        lowercase_    :Union[str, Any]					    =				nn.Linear(lowerCAmelCase__			,   lowerCAmelCase__			,   dtype=self.dtype		)
        lowercase_    :str					    =				num_heads
        lowercase_    :Optional[Any]					    =				embed_dim // self.num_heads







     def 							lowercase__   (				self	:      Any			,   lowercase	:      List[str]		):





        """simple docstring"""




        lowercase_    :Optional[Any]					    =				x.size()

        def shape(lowercase	:      str		):
           # (bs, length, width) --> (bs, length, n_heads, dim_per_head)
           lowercase_    :Dict					    =				x.view(lowerCAmelCase__			,   -1			,   self.num_heads			,   self.dim_per_head		)
           # (bs, length, n_heads, dim_per_head) --> (bs, n_heads, length, dim_per_head)
           lowercase_    :Union[str, Any]					    =				x.transpose(1			,   2		)
           # (bs, n_heads, length, dim_per_head) --> (bs*n_heads, length, dim_per_head)
           lowercase_    :Any					    =				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)
           lowercase_    :Union[str, Any]					    =				x.transpose(1			,   2		)
           return x

        lowercase_    :int					    =				x.mean(dim=1			,   keepdim=lowerCAmelCase__		) + self.positional_embedding.to(x.dtype		)
        lowercase_    :int					    =				torch.cat([class_token, x]			,   dim=1		)  # (bs, length+1, width)

        # (bs*n_heads, class_token_length, dim_per_head)
        lowercase_    :int					    =				shape(self.q_proj(lowerCAmelCase__		)		)
        # (bs*n_heads, length+class_token_length, dim_per_head)
        lowercase_    :Optional[Any]					    =				shape(self.k_proj(lowerCAmelCase__		)		)
        lowercase_    :Optional[int]					    =				shape(self.v_proj(lowerCAmelCase__		)		)

        # (bs*n_heads, class_token_length, length+class_token_length):
        lowercase_    :str					    =				1 / math.sqrt(math.sqrt(self.dim_per_head		)		)
        lowercase_    :int					    =				torch.einsum("bct,bcs->bts"			,   q * scale			,   k * scale		)  # More stable with f16 than dividing afterwards
        lowercase_    :List[str]					    =				torch.softmax(weight.float()			,   dim=-1		).type(weight.dtype		)

        # (bs*n_heads, dim_per_head, class_token_length)
        lowercase_    :Union[str, Any]					    =				torch.einsum("bts,bcs->bct"			,   lowerCAmelCase__			,   lowerCAmelCase__		)

        # (bs, length+1, width)
        lowercase_    :str					    =				a.reshape(lowerCAmelCase__			,   -1			,   1		).transpose(1			,   2		)

        return a[:, 0, :]  # cls_token









'''simple docstring'''


class    a_     :





     def __init__(				self	:      str			,   lowercase	:      List[Any]		):





        """simple docstring"""




        lowercase_    :List[str]					    =				val
        # Number of nodes in left subtree
        lowercase_    :Optional[int]					    =				0
        lowercase_    :List[str]					    =				None
        lowercase_    :List[Any]					    =				None
        lowercase_    :Optional[Any]					    =				None







     def 							lowercase__   (				self	:      Union[str, Any]			,   lowercase	:      Dict		):





        """simple docstring"""




        assert self.left_tree_size == other.left_tree_size, "Unequal Sizes of Blocks"

        if self.val < other.val:
           lowercase_    :List[Any]					    =				self.right
           lowercase_    :str					    =				None
           if self.right:
              lowercase_    :Optional[int]					    =				other
           lowercase_    :Optional[Any]					    =				other
           lowercase_    :str					    =				self.left_tree_size * 2 + 1
           return self
        else:
           lowercase_    :Any					    =				other.right
           lowercase_    :Any					    =				None
           if other.right:
              lowercase_    :List[Any]					    =				self
           lowercase_    :Union[str, Any]					    =				self
           lowercase_    :Optional[int]					    =				other.left_tree_size * 2 + 1
           return other







class    a_     :





     def __init__(				self	:      Optional[Any]			,   lowercase	:      Any=None			,   lowercase	:      Optional[Any]=None			,   lowercase	:      int=0		):





        """simple docstring"""




        lowercase_    :Optional[int]					    =				heap_size
        lowercase_    :List[str]					    =				bottom_root
        lowercase_    :Dict					    =				min_node





     def 							lowercase__   (				self	:      List[str]			,   lowercase	:      List[Any]		):





        """simple docstring"""




        if other.size == 0:
           return None
        if self.size == 0:
           lowercase_    :Dict					    =				other.size
           lowercase_    :int					    =				other.bottom_root
           lowercase_    :Tuple					    =				other.min_node
           return None
        # Update size
        lowercase_    :Optional[int]					    =				self.size + other.size

        # Update min.node
        if self.min_node.val > other.min_node.val:
           lowercase_    :int					    =				other.min_node
        # Merge

        # Order roots by left_subtree_size
        lowercase_    :Any					    =				[]
        lowercase_    ,							lowercase_    :List[str]					    =				self.bottom_root, other.bottom_root
        while i or j:
           if i and ((not j) or i.left_tree_size < j.left_tree_size):
              combined_roots_list.append((i, True)		)
              lowercase_    :str					    =				i.parent
           else:
              combined_roots_list.append((j, False)		)
              lowercase_    :Dict					    =				j.parent
        # Insert links between them
        for i in range(len(lowercase		) - 1		):
           if combined_roots_list[i][1] != combined_roots_list[i + 1][1]:
              lowercase_    :Dict					    =				combined_roots_list[i + 1][0]
              lowercase_    :str					    =				combined_roots_list[i][0]
        # Consecutively merge roots with same left_tree_size
        lowercase_    :int					    =				combined_roots_list[0][0]
        while i.parent:
           if (
               (i.left_tree_size == i.parent.left_tree_size) and (not i.parent.parent)
           ) or (
               i.left_tree_size == i.parent.left_tree_size
               and i.left_tree_size != i.parent.parent.left_tree_size
           ):
              # Neighbouring Nodes
              lowercase_    :List[Any]					    =				i.left
              lowercase_    :Any					    =				i.parent.parent

              # Merging trees
              lowercase_    :Any					    =				i.merge_trees(i.parent		)

              # Updating links
              lowercase_    :List[Any]					    =				previous_node
              lowercase_    :int					    =				next_node
              if previous_node:
                 lowercase_    :int					    =				i
              if next_node:
                 lowercase_    :str					    =				i
           else:
              lowercase_    :str					    =				i.parent
        # Updating self.bottom_root
        while i.left:
           lowercase_    :List[str]					    =				i.left
        lowercase_    :List[str]					    =				i

        # Update other
        lowercase_    :Any					    =				self.size
        lowercase_    :Optional[Any]					    =				self.bottom_root
        lowercase_    :int					    =				self.min_node

        # Return the merged heap
        return self





     def 							lowercase__   (				self	:      int			,   lowercase	:      List[Any]		):





        """simple docstring"""




        if self.size == 0:
           lowercase_    :Dict					    =				Node(lowercase		)
           lowercase_    :Optional[Any]					    =				1
           lowercase_    :Optional[Any]					    =				self.bottom_root
        else:
           # Create new node
           lowercase_    :Union[str, Any]					    =				Node(lowercase		)

           # Update size
           self.size += 1

           # update min_node
           if val < self.min_node.val:
              lowercase_    :Union[str, Any]					    =				new_node
           # Put new_node as a bottom_root in heap
           lowercase_    :int					    =				new_node
           lowercase_    :List[str]					    =				self.bottom_root
           lowercase_    :Any					    =				new_node

           # Consecutively merge roots with same left_tree_size
           while (
               self.bottom_root.parent
               and self.bottom_root.left_tree_size
               == self.bottom_root.parent.left_tree_size
           ):
              # Next node
              lowercase_    :int					    =				self.bottom_root.parent.parent

              # Merge
              lowercase_    :Union[str, Any]					    =				self.bottom_root.merge_trees(self.bottom_root.parent		)

              # Update Links
              lowercase_    :Optional[Any]					    =				next_node
              lowercase_    :Any					    =				None
              if next_node:
                 lowercase_    :Union[str, Any]					    =				self.bottom_root





     def 							lowercase__   (				self	:      str		):





        """simple docstring"""




        return self.min_node.val





     def 							lowercase__   (				self	:      Optional[int]		):





        """simple docstring"""




        return self.size == 0





     def 							lowercase__   (				self	:      str		):





        """simple docstring"""




        lowercase_    :str					    =				self.min_node.val

        # Last element in heap corner case
        if self.size == 1:
           # Update size
           lowercase_    :Dict					    =				0

           # Update bottom root
           lowercase_    :int					    =				None

           # Update min_node
           lowercase_    :Tuple					    =				None

           return min_value
        # No right subtree corner case
        # The structure of the tree implies that this should be the bottom root
        # and there is at least one other root
        if self.min_node.right is None:
           # Update size
           self.size -= 1

           # Update bottom root
           lowercase_    :Optional[Any]					    =				self.bottom_root.parent
           lowercase_    :Tuple					    =				None

           # Update min_node
           lowercase_    :Dict					    =				self.bottom_root
           lowercase_    :List[str]					    =				self.bottom_root.parent
           while i:
              if i.val < self.min_node.val:
                 lowercase_    :Union[str, Any]					    =				i
              lowercase_    :Dict					    =				i.parent
           return min_value
        # General case
        # Find the BinomialHeap of the right subtree of min_node
        lowercase_    :List[str]					    =				self.min_node.right
        lowercase_    :Dict					    =				None
        lowercase_    :str					    =				bottom_of_new
        lowercase_    :Optional[int]					    =				1

        # Size, min_node and bottom_root
        while bottom_of_new.left:
           lowercase_    :List[Any]					    =				size_of_new * 2 + 1
           lowercase_    :Union[str, Any]					    =				bottom_of_new.left
           if bottom_of_new.val < min_of_new.val:
              lowercase_    :Optional[int]					    =				bottom_of_new
        # Corner case of single root on top left path
        if (not self.min_node.left) and (not self.min_node.parent):
           lowercase_    :Optional[int]					    =				size_of_new
           lowercase_    :Union[str, Any]					    =				bottom_of_new
           lowercase_    :Dict					    =				min_of_new
           # print("Single root, multiple nodes case")
           return min_value
        # Remaining cases
        # Construct heap of right subtree
        lowercase_    :Tuple					    =				BinomialHeap(
            bottom_root=lowercase			,   min_node=lowercase			,   heap_size=lowercase		)

        # Update size
        lowercase_    :Dict					    =				self.size - 1 - size_of_new

        # Neighbour nodes
        lowercase_    :Optional[Any]					    =				self.min_node.left
        lowercase_    :str					    =				self.min_node.parent

        # Initialize new bottom_root and min_node
        lowercase_    :int					    =				previous_node or next_node
        lowercase_    :Any					    =				next_node

        # Update links of previous_node and search below for new min_node and
        # bottom_root
        if previous_node:
           lowercase_    :int					    =				next_node

           # Update bottom_root and search for min_node below
           lowercase_    :str					    =				previous_node
           lowercase_    :List[Any]					    =				previous_node
           while self.bottom_root.left:
              lowercase_    :List[str]					    =				self.bottom_root.left
              if self.bottom_root.val < self.min_node.val:
                 lowercase_    :List[Any]					    =				self.bottom_root
        if next_node:
           lowercase_    :List[Any]					    =				previous_node

           # Search for new min_node above min_node
           lowercase_    :Dict					    =				next_node
           while i:
              if i.val < self.min_node.val:
                 lowercase_    :Optional[Any]					    =				i
              lowercase_    :str					    =				i.parent
        # Merge heaps
        self.merge_heaps(lowercase		)

        return min_value





     def 							lowercase__   (				self	:      Dict		):





        """simple docstring"""




        lowercase_    :Optional[Any]					    =				self.bottom_root
        while top_root.parent:
           lowercase_    :int					    =				top_root.parent
        # preorder
        lowercase_    :List[str]					    =				[]
        self.__traversal(lowercase			,   lowercase		)
        return heap_pre_order





     def 							lowercase__   (				self	:      Union[str, Any]			,   lowercase	:      List[Any]			,   lowercase	:      List[str]			,   lowercase	:      Dict=0		):





        """simple docstring"""




        if curr_node:
           preorder.append((curr_node.val, level)		)
           self.__traversal(curr_node.left			,   lowercase			,   level + 1		)
           self.__traversal(curr_node.right			,   lowercase			,   level + 1		)
        else:
           preorder.append(("#", level)		)







     def __str__(				self	:      Optional[int]		):





        """simple docstring"""




        if self.is_empty():
           return ""
        lowercase_    :int					    =				self.pre_order()

        return "\n".join(("-" * level + str(lowercase		)) for value, level in preorder_heap		)


# Unit Tests
if __name__ == "__main__":
 import doctest

 doctest.testmod()


