




import math
from typing import Optional

import numpy as np
import torch
from torch import nn

from .activations import get_activation






def    snake_case   (				A		,  A		,  A = False		,  A = 1		,  A = 1		,  A = 10000		,  )				->				List[Any]:




	'''simple docstring'''


	assert len(timesteps.shape     ) == 1, "Timesteps should be a 1d-array"

	lowerCamelCase_				:						List[Any]				  =				embedding_dim // 2
	lowerCamelCase_				:						Dict				  =				-math.log(A     ) * torch.arange(
	    start=0		,  end=A		,  dtype=torch.floataa		,  device=timesteps.device     )
	lowerCamelCase_				:						Dict				  =				exponent / (half_dim - downscale_freq_shift)

	lowerCamelCase_				:						Any				  =				torch.exp(A     )
	lowerCamelCase_				:						int				  =				timesteps[:, None].float() * emb[None, :]

	# scale embeddings
	lowerCamelCase_				:						Dict				  =				scale * emb

	# concat sine and cosine embeddings
	lowerCamelCase_				:						Any				  =				torch.cat([torch.sin(A     ), torch.cos(A     )]		,  dim=-1     )

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

	# zero pad
	if embedding_dim % 2 == 1:
		lowerCamelCase_				:						Optional[Any]				  =				torch.nn.functional.pad(A		,  (0, 1, 0, 0)     )
	return emb






def    snake_case   (				A		,  A		,  A=False		,  A=0     )				->				List[str]:




	'''simple docstring'''


	lowerCamelCase_				:						Optional[int]				  =				np.arange(A		,  dtype=np.floataa     )
	lowerCamelCase_				:						Dict				  =				np.arange(A		,  dtype=np.floataa     )
	lowerCamelCase_				:						Union[str, Any]				  =				np.meshgrid(A		,  A     )  # here w goes first
	lowerCamelCase_				:						List[Any]				  =				np.stack(A		,  axis=0     )

	lowerCamelCase_				:						Union[str, Any]				  =				grid.reshape([2, 1, grid_size, grid_size]     )
	lowerCamelCase_				:						Any				  =				get_ad_sincos_pos_embed_from_grid(A		,  A     )
	if cls_token and extra_tokens > 0:
		lowerCamelCase_				:						List[Any]				  =				np.concatenate([np.zeros([extra_tokens, embed_dim]     ), pos_embed]		,  axis=0     )
	return pos_embed






def    snake_case   (				A		,  A     )				->				Tuple:




	'''simple docstring'''


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

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

	lowerCamelCase_				:						Tuple				  =				np.concatenate([emb_h, emb_w]		,  axis=1     )  # (H*W, D)
	return emb






def    snake_case   (				A		,  A     )				->				List[Any]:




	'''simple docstring'''


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

	lowerCamelCase_				:						Union[str, Any]				  =				np.arange(embed_dim // 2		,  dtype=np.floataa     )
	omega /= embed_dim / 2.0
	lowerCamelCase_				:						int				  =				1.0 / 10000**omega  # (D/2,)

	lowerCamelCase_				:						List[str]				  =				pos.reshape(-1     )  # (M,)
	lowerCamelCase_				:						List[Any]				  =				np.einsum('m,d->md'		,  A		,  A     )  # (M, D/2), outer product

	lowerCamelCase_				:						Union[str, Any]				  =				np.sin(A     )  # (M, D/2)
	lowerCamelCase_				:						List[Any]				  =				np.cos(A     )  # (M, D/2)

	lowerCamelCase_				:						int				  =				np.concatenate([emb_sin, emb_cos]		,  axis=1     )  # (M, D)
	return emb


class 							__SCREAMING_SNAKE_CASE				(						nn.Module    ):

					def __init__(							self					,			__lowercase=224					,			__lowercase=224					,			__lowercase=16					,			__lowercase=3					,			__lowercase=768					,			__lowercase=False					,			__lowercase=True					,			__lowercase=True					,			):







						'''simple docstring'''




						super().__init__()

						lowerCamelCase_				:						Any				  =				(height // patch_size) * (width // patch_size)
						lowerCamelCase_				:						Dict				  =				flatten
						lowerCamelCase_				:						Union[str, Any]				  =				layer_norm

						lowerCamelCase_				:						List[Any]				  =				nn.Convad(
						    __lowercase					,			__lowercase					,			kernel_size=(patch_size, patch_size)					,			stride=__lowercase					,			bias=__lowercase   )
						if layer_norm:
							lowerCamelCase_				:						str				  =				nn.LayerNorm(__lowercase					,			elementwise_affine=__lowercase					,			eps=1E-6   )
						else:
							lowerCamelCase_				:						int				  =				None

						lowerCamelCase_				:						Optional[Any]				  =				get_ad_sincos_pos_embed(__lowercase					,			int(num_patches**0.5   )   )
						self.register_buffer('pos_embed'					,			torch.from_numpy(__lowercase   ).float().unsqueeze(0   )					,			persistent=__lowercase   )





					def       lowercase_				(							self					,			__lowercase   ):







						'''simple docstring'''




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


class 							__SCREAMING_SNAKE_CASE				(						nn.Module    ):

					def __init__(							self					,			__lowercase					,			__lowercase					,			__lowercase = "silu"					,			__lowercase = None					,			__lowercase = None					,			__lowercase=None					,			):







						'''simple docstring'''




						super().__init__()

						lowerCamelCase_				:						List[str]				  =				nn.Linear(__lowercase					,			__lowercase   )

						if cond_proj_dim is not None:
							lowerCamelCase_				:						Optional[Any]				  =				nn.Linear(__lowercase					,			__lowercase					,			bias=__lowercase   )
						else:
							lowerCamelCase_				:						Union[str, Any]				  =				None

						lowerCamelCase_				:						Optional[int]				  =				get_activation(__lowercase   )

						if out_dim is not None:
							lowerCamelCase_				:						int				  =				out_dim
						else:
							lowerCamelCase_				:						int				  =				time_embed_dim
						lowerCamelCase_				:						int				  =				nn.Linear(__lowercase					,			__lowercase   )

						if post_act_fn is None:
							lowerCamelCase_				:						int				  =				None
						else:
							lowerCamelCase_				:						int				  =				get_activation(__lowercase   )





					def       lowercase_				(							self					,			__lowercase					,			__lowercase=None   ):







						'''simple docstring'''




						if condition is not None:
							lowerCamelCase_				:						int				  =				sample + self.cond_proj(__lowercase   )
						lowerCamelCase_				:						str				  =				self.linear_a(__lowercase   )

						if self.act is not None:
							lowerCamelCase_				:						Tuple				  =				self.act(__lowercase   )

						lowerCamelCase_				:						Any				  =				self.linear_a(__lowercase   )

						if self.post_act is not None:
							lowerCamelCase_				:						Union[str, Any]				  =				self.post_act(__lowercase   )
						return sample


class 							__SCREAMING_SNAKE_CASE				(						nn.Module    ):

					def __init__(							self					,			__lowercase					,			__lowercase					,			__lowercase   ):







						'''simple docstring'''




						super().__init__()
						lowerCamelCase_				:						int				  =				num_channels
						lowerCamelCase_				:						List[str]				  =				flip_sin_to_cos
						lowerCamelCase_				:						int				  =				downscale_freq_shift





					def       lowercase_				(							self					,			__lowercase   ):







						'''simple docstring'''




						lowerCamelCase_				:						Union[str, Any]				  =				get_timestep_embedding(
						    __lowercase					,			self.num_channels					,			flip_sin_to_cos=self.flip_sin_to_cos					,			downscale_freq_shift=self.downscale_freq_shift					,			)
						return t_emb


class 							__SCREAMING_SNAKE_CASE				(						nn.Module    ):

					def __init__(							self					,			__lowercase = 256					,			__lowercase = 1.0					,			__lowercase=True					,			__lowercase=True					,			__lowercase=False   ):







						'''simple docstring'''




						super().__init__()
						lowerCamelCase_				:						Tuple				  =				nn.Parameter(torch.randn(__lowercase   ) * scale					,			requires_grad=__lowercase   )
						lowerCamelCase_				:						int				  =				log
						lowerCamelCase_				:						List[Any]				  =				flip_sin_to_cos

						if set_W_to_weight:
							# to delete later
							lowerCamelCase_				:						List[str]				  =				nn.Parameter(torch.randn(__lowercase   ) * scale					,			requires_grad=__lowercase   )

							lowerCamelCase_				:						Tuple				  =				self.W





					def       lowercase_				(							self					,			__lowercase   ):







						'''simple docstring'''




						if self.log:
							lowerCamelCase_				:						Optional[Any]				  =				torch.log(__lowercase   )

						lowerCamelCase_				:						List[Any]				  =				x[:, None] * self.weight[None, :] * 2 * np.pi

						if self.flip_sin_to_cos:
							lowerCamelCase_				:						List[Any]				  =				torch.cat([torch.cos(__lowercase   ), torch.sin(__lowercase   )]					,			dim=-1   )
						else:
							lowerCamelCase_				:						Any				  =				torch.cat([torch.sin(__lowercase   ), torch.cos(__lowercase   )]					,			dim=-1   )
						return out


class 							__SCREAMING_SNAKE_CASE				(						nn.Module    ):

					def __init__(							self					,			__lowercase					,			__lowercase					,			__lowercase					,			__lowercase					,			):







						'''simple docstring'''




						super().__init__()

						lowerCamelCase_				:						Optional[Any]				  =				height
						lowerCamelCase_				:						Union[str, Any]				  =				width
						lowerCamelCase_				:						Optional[int]				  =				num_embed
						lowerCamelCase_				:						List[str]				  =				embed_dim

						lowerCamelCase_				:						Any				  =				nn.Embedding(self.num_embed					,			__lowercase   )
						lowerCamelCase_				:						int				  =				nn.Embedding(self.height					,			__lowercase   )
						lowerCamelCase_				:						int				  =				nn.Embedding(self.width					,			__lowercase   )





					def       lowercase_				(							self					,			__lowercase   ):







						'''simple docstring'''




						lowerCamelCase_				:						List[str]				  =				self.emb(__lowercase   )

						lowerCamelCase_				:						Dict				  =				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
						lowerCamelCase_				:						List[Any]				  =				height_emb.unsqueeze(2   )

						lowerCamelCase_				:						List[str]				  =				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
						lowerCamelCase_				:						Optional[Any]				  =				width_emb.unsqueeze(1   )

						lowerCamelCase_				:						List[str]				  =				height_emb + width_emb

						# 1 x H x W x D -> 1 x L xD
						lowerCamelCase_				:						Any				  =				pos_emb.view(1					,			self.height * self.width					,			-1   )

						lowerCamelCase_				:						Any				  =				emb + pos_emb[:, : emb.shape[1], :]

						return emb


class 							__SCREAMING_SNAKE_CASE				(						nn.Module    ):

					def __init__(							self					,			__lowercase					,			__lowercase					,			__lowercase   ):







						'''simple docstring'''




						super().__init__()
						lowerCamelCase_				:						List[Any]				  =				dropout_prob > 0
						lowerCamelCase_				:						Dict				  =				nn.Embedding(num_classes + use_cfg_embedding					,			__lowercase   )
						lowerCamelCase_				:						Any				  =				num_classes
						lowerCamelCase_				:						Optional[int]				  =				dropout_prob

					def       lowercase_				(							self					,			__lowercase					,			__lowercase=None   ):







						'''simple docstring'''




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





					def       lowercase_				(							self					,			__lowercase					,			__lowercase=None   ):







						'''simple docstring'''




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


class 							__SCREAMING_SNAKE_CASE				(						nn.Module    ):

					def __init__(							self					,			__lowercase = 1_024					,			__lowercase = 768					,			__lowercase = 768					,			__lowercase = 10					,			):







						'''simple docstring'''




						super().__init__()

						lowerCamelCase_				:						Dict				  =				num_image_text_embeds
						lowerCamelCase_				:						List[Any]				  =				nn.Linear(__lowercase					,			self.num_image_text_embeds * cross_attention_dim   )
						lowerCamelCase_				:						Dict				  =				nn.Linear(__lowercase					,			__lowercase   )





					def       lowercase_				(							self					,			__lowercase					,			__lowercase   ):







						'''simple docstring'''




						lowerCamelCase_				:						Optional[int]				  =				text_embeds.shape[0]

						# image
						lowerCamelCase_				:						List[str]				  =				self.image_embeds(__lowercase   )
						lowerCamelCase_				:						Optional[Any]				  =				image_text_embeds.reshape(__lowercase					,			self.num_image_text_embeds					,			-1   )

						# text
						lowerCamelCase_				:						List[str]				  =				self.text_proj(__lowercase   )

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


class 							__SCREAMING_SNAKE_CASE				(						nn.Module    ):

					def __init__(							self					,			__lowercase = 768					,			__lowercase = 768					,			__lowercase = 32					,			):







						'''simple docstring'''




						super().__init__()

						lowerCamelCase_				:						List[str]				  =				num_image_text_embeds
						lowerCamelCase_				:						Union[str, Any]				  =				nn.Linear(__lowercase					,			self.num_image_text_embeds * cross_attention_dim   )
						lowerCamelCase_				:						Tuple				  =				nn.LayerNorm(__lowercase   )





					def       lowercase_				(							self					,			__lowercase   ):







						'''simple docstring'''




						lowerCamelCase_				:						Union[str, Any]				  =				image_embeds.shape[0]

						# image
						lowerCamelCase_				:						List[Any]				  =				self.image_embeds(__lowercase   )
						lowerCamelCase_				:						Union[str, Any]				  =				image_embeds.reshape(__lowercase					,			self.num_image_text_embeds					,			-1   )
						lowerCamelCase_				:						Union[str, Any]				  =				self.norm(__lowercase   )
						return image_embeds


class 							__SCREAMING_SNAKE_CASE				(						nn.Module    ):

					def __init__(							self					,			__lowercase					,			__lowercase					,			__lowercase=0.1   ):







						'''simple docstring'''




						super().__init__()

						lowerCamelCase_				:						str				  =				Timesteps(num_channels=256					,			flip_sin_to_cos=__lowercase					,			downscale_freq_shift=1   )
						lowerCamelCase_				:						List[str]				  =				TimestepEmbedding(in_channels=256					,			time_embed_dim=__lowercase   )
						lowerCamelCase_				:						List[Any]				  =				LabelEmbedding(__lowercase					,			__lowercase					,			__lowercase   )





					def       lowercase_				(							self					,			__lowercase					,			__lowercase					,			__lowercase=None   ):







						'''simple docstring'''




						lowerCamelCase_				:						List[Any]				  =				self.time_proj(__lowercase   )
						lowerCamelCase_				:						str				  =				self.timestep_embedder(timesteps_proj.to(dtype=__lowercase   )   )  # (N, D)

						lowerCamelCase_				:						Tuple				  =				self.class_embedder(__lowercase   )  # (N, D)

						lowerCamelCase_				:						List[str]				  =				timesteps_emb + class_labels  # (N, D)

						return conditioning


class 							__SCREAMING_SNAKE_CASE				(						nn.Module    ):

					def __init__(							self					,			__lowercase					,			__lowercase					,			__lowercase = 64   ):







						'''simple docstring'''




						super().__init__()
						lowerCamelCase_				:						Optional[int]				  =				nn.LayerNorm(__lowercase   )
						lowerCamelCase_				:						List[Any]				  =				AttentionPooling(__lowercase					,			__lowercase   )
						lowerCamelCase_				:						Dict				  =				nn.Linear(__lowercase					,			__lowercase   )
						lowerCamelCase_				:						List[Any]				  =				nn.LayerNorm(__lowercase   )





					def       lowercase_				(							self					,			__lowercase   ):







						'''simple docstring'''




						lowerCamelCase_				:						List[str]				  =				self.norma(__lowercase   )
						lowerCamelCase_				:						Optional[int]				  =				self.pool(__lowercase   )
						lowerCamelCase_				:						Tuple				  =				self.proj(__lowercase   )
						lowerCamelCase_				:						Any				  =				self.norma(__lowercase   )
						return hidden_states


class 							__SCREAMING_SNAKE_CASE				(						nn.Module    ):

					def __init__(							self					,			__lowercase = 768					,			__lowercase = 768					,			__lowercase = 1_536   ):







						'''simple docstring'''




						super().__init__()
						lowerCamelCase_				:						Optional[int]				  =				nn.Linear(__lowercase					,			__lowercase   )
						lowerCamelCase_				:						Any				  =				nn.LayerNorm(__lowercase   )
						lowerCamelCase_				:						List[Any]				  =				nn.Linear(__lowercase					,			__lowercase   )





					def       lowercase_				(							self					,			__lowercase					,			__lowercase   ):







						'''simple docstring'''




						lowerCamelCase_				:						Tuple				  =				self.text_proj(__lowercase   )
						lowerCamelCase_				:						Dict				  =				self.text_norm(__lowercase   )

						# image
						lowerCamelCase_				:						Tuple				  =				self.image_proj(__lowercase   )

						return time_image_embeds + time_text_embeds


class 							__SCREAMING_SNAKE_CASE				(						nn.Module    ):

					def __init__(							self					,			__lowercase = 768					,			__lowercase = 1_536   ):







						'''simple docstring'''




						super().__init__()
						lowerCamelCase_				:						Any				  =				nn.Linear(__lowercase					,			__lowercase   )
						lowerCamelCase_				:						Union[str, Any]				  =				nn.LayerNorm(__lowercase   )





					def       lowercase_				(							self					,			__lowercase   ):







						'''simple docstring'''




						lowerCamelCase_				:						Any				  =				self.image_proj(__lowercase   )
						lowerCamelCase_				:						Optional[int]				  =				self.image_norm(__lowercase   )
						return time_image_embeds


class 							__SCREAMING_SNAKE_CASE				(						nn.Module    ):

					def __init__(							self					,			__lowercase = 768					,			__lowercase = 1_536   ):







						'''simple docstring'''




						super().__init__()
						lowerCamelCase_				:						str				  =				nn.Linear(__lowercase					,			__lowercase   )
						lowerCamelCase_				:						Any				  =				nn.LayerNorm(__lowercase   )
						lowerCamelCase_				:						str				  =				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					,			__lowercase					,			__lowercase   ):







						'''simple docstring'''




						lowerCamelCase_				:						Any				  =				self.image_proj(__lowercase   )
						lowerCamelCase_				:						Optional[int]				  =				self.image_norm(__lowercase   )
						lowerCamelCase_				:						List[str]				  =				self.input_hint_block(__lowercase   )
						return time_image_embeds, hint


class 							__SCREAMING_SNAKE_CASE				(						nn.Module    ):

					def __init__(							self					,			__lowercase					,			__lowercase					,			__lowercase=None   ):







						'''simple docstring'''




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





					def       lowercase_				(							self					,			__lowercase   ):







						'''simple docstring'''




						lowerCamelCase_  ,     lowerCamelCase_  ,     lowerCamelCase_				:						Optional[int]				  =				x.size()

						def shape(__lowercase   ):
							# (bs, length, width) --> (bs, length, n_heads, dim_per_head)
							lowerCamelCase_				:						int				  =				x.view(__lowercase					,			-1					,			self.num_heads					,			self.dim_per_head   )
							# (bs, length, n_heads, dim_per_head) --> (bs, n_heads, length, dim_per_head)
							lowerCamelCase_				:						List[Any]				  =				x.transpose(1					,			2   )
							# (bs, n_heads, length, dim_per_head) --> (bs*n_heads, length, dim_per_head)
							lowerCamelCase_				:						Optional[int]				  =				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)
							lowerCamelCase_				:						List[str]				  =				x.transpose(1					,			2   )
							return x

						lowerCamelCase_				:						List[str]				  =				x.mean(dim=1					,			keepdim=__lowercase   ) + self.positional_embedding.to(x.dtype   )
						lowerCamelCase_				:						List[Any]				  =				torch.cat([class_token, x]					,			dim=1   )  # (bs, length+1, width)

						# (bs*n_heads, class_token_length, dim_per_head)
						lowerCamelCase_				:						str				  =				shape(self.q_proj(__lowercase   )   )
						# (bs*n_heads, length+class_token_length, dim_per_head)
						lowerCamelCase_				:						Dict				  =				shape(self.k_proj(__lowercase   )   )
						lowerCamelCase_				:						List[Any]				  =				shape(self.v_proj(__lowercase   )   )

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

						# (bs*n_heads, dim_per_head, class_token_length)
						lowerCamelCase_				:						str				  =				torch.einsum('bts,bcs->bct'					,			__lowercase					,			__lowercase   )

						# (bs, length+1, width)
						lowerCamelCase_				:						Optional[int]				  =				a.reshape(__lowercase					,			-1					,			1   ).transpose(1					,			2   )

						return a[:, 0, :]  # cls_token








from __future__ import annotations


def __A       ( __lowerCAmelCase					,						__lowerCAmelCase					,						__lowerCAmelCase					,						)->    list[float | int]:





						"""simple docstring"""



						if not all((nth_term, start_term_a, common_ratio_r)      ):
												return []
						_UpperCAmelCase							   =     []
						_UpperCAmelCase							   =     1
						_UpperCAmelCase							   =     common_ratio_r
						for _ in range(int(__lowerCAmelCase      )      ):
												if not series:
																		series.append(__lowerCAmelCase      )
												else:
																		power += 1
																		series.append(float(start_term_a * multiple      )      )
																		_UpperCAmelCase							   =     pow(float(__lowerCAmelCase      )					,						__lowerCAmelCase      )
						return series


if __name__ == "__main__":
		import doctest

		doctest.testmod()

		_a       =    float(input('''Enter the last number (n term) of the Geometric Series'''))
		_a       =    float(input('''Enter the starting term (a) of the Geometric Series'''))
		_a       =    float(
		    input('''Enter the common ratio between two terms (r) of the Geometric Series''')
		)
		print('''Formula of Geometric Series => a + ar + ar^2 ... +ar^n''')
		print(geometric_series(nth_term, start_term_a, common_ratio_r))
