



import math
from typing import Optional

import numpy as np
import torch
from torch import nn

from .activations import get_activation



def __lowerCAmelCase       (   SCREAMING_SNAKE_CASE_  ,     SCREAMING_SNAKE_CASE_  ,     SCREAMING_SNAKE_CASE_ = False  ,     SCREAMING_SNAKE_CASE_ = 1  ,     SCREAMING_SNAKE_CASE_ = 1  ,     SCREAMING_SNAKE_CASE_ = 1_0000  ,     ):
			assert len(timesteps.shape     ) == 1, "Timesteps should be a 1d-array"

			lowercase__         = embedding_dim // 2
			lowercase__         = -math.log(a__     ) * torch.arange(
			    start=0  ,     end=a__  ,     dtype=torch.floataa  ,     device=timesteps.device     )
			lowercase__         = exponent / (half_dim - downscale_freq_shift)

			lowercase__         = torch.exp(a__     )
			lowercase__         = timesteps[:, None].float() * emb[None, :]

			# scale embeddings
			lowercase__         = scale * emb

			# concat sine and cosine embeddings
			lowercase__         = torch.cat([torch.sin(a__     ), torch.cos(a__     )]  ,     dim=-1     )

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

			# zero pad
			if embedding_dim % 2 == 1:
						lowercase__         = torch.nn.functional.pad(a__  ,     (0, 1, 0, 0)     )
			return emb



def __lowerCAmelCase       (   SCREAMING_SNAKE_CASE_  ,     SCREAMING_SNAKE_CASE_  ,     SCREAMING_SNAKE_CASE_=False  ,     SCREAMING_SNAKE_CASE_=0     ):
			lowercase__         = np.arange(a__  ,     dtype=np.floataa     )
			lowercase__         = np.arange(a__  ,     dtype=np.floataa     )
			lowercase__         = np.meshgrid(a__  ,     a__     )  # here w goes first
			lowercase__         = np.stack(a__  ,     axis=0     )

			lowercase__         = grid.reshape([2, 1, grid_size, grid_size]     )
			lowercase__         = get_ad_sincos_pos_embed_from_grid(a__  ,     a__     )
			if cls_token and extra_tokens > 0:
						lowercase__         = np.concatenate([np.zeros([extra_tokens, embed_dim]     ), pos_embed]  ,     axis=0     )
			return pos_embed



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

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

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



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

			lowercase__         = np.arange(embed_dim // 2  ,     dtype=np.floataa     )
			omega /= embed_dim / 2.0
			lowercase__         = 1.0 / 1_0000**omega  # (D/2,)

			lowercase__         = pos.reshape(-1     )  # (M,)
			lowercase__         = np.einsum("m,d->md"  ,     a__  ,     a__     )  # (M, D/2), outer product

			lowercase__         = np.sin(a__     )  # (M, D/2)
			lowercase__         = np.cos(a__     )  # (M, D/2)

			lowercase__         = np.concatenate([emb_sin, emb_cos]  ,     axis=1     )  # (M, D)
			return emb
class  _snake_case	(    nn.Module):




				def __init__(  self    :  List[str],    __lowercase    :  Optional[Any]=224,    __lowercase    :  List[Any]=224,    __lowercase    :  Any=16,    __lowercase    :  Union[str, Any]=3,    __lowercase    :  Optional[Any]=768,    __lowercase    :  Optional[int]=False,    __lowercase    :  Any=True,    __lowercase    :  str=True,    ):
							super().__init__()

							lowercase__         = (height // patch_size) * (width // patch_size)
							lowercase__         = flatten
							lowercase__         = layer_norm

							lowercase__         = nn.Convad(
							    _a,    _a,    kernel_size=(patch_size, patch_size),    stride=_a,    bias=_a  )
							if layer_norm:
										lowercase__         = nn.LayerNorm(_a,    elementwise_affine=_a,    eps=1e-6  )
							else:
										lowercase__         = None

							lowercase__         = 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    :  List[str],    __lowercase    :  str  ):
							lowercase__         = self.proj(_a  )
							if self.flatten:
										lowercase__         = latent.flatten(2  ).transpose(1,    2  )  # BCHW -> BNC
							if self.layer_norm:
										lowercase__         = self.norm(_a  )
							return latent + self.pos_embed
class  _snake_case	(    nn.Module):




				def __init__(  self    :  Tuple,    __lowercase    :  int,    __lowercase    :  int,    __lowercase    :  str = "silu",    __lowercase    :  int = None,    __lowercase    :  Optional[str] = None,    __lowercase    :  Union[str, Any]=None,    ):
							super().__init__()

							lowercase__         = nn.Linear(_a,    _a  )

							if cond_proj_dim is not None:
										lowercase__         = nn.Linear(_a,    _a,    bias=_a  )
							else:
										lowercase__         = None

							lowercase__         = get_activation(_a  )

							if out_dim is not None:
										lowercase__         = out_dim
							else:
										lowercase__         = time_embed_dim
							lowercase__         = nn.Linear(_a,    _a  )

							if post_act_fn is None:
										lowercase__         = None
							else:
										lowercase__         = get_activation(_a  )




				def 							A__					(  self    :  Any,    __lowercase    :  str,    __lowercase    :  str=None  ):





							if condition is not None:
										lowercase__         = sample + self.cond_proj(_a  )
							lowercase__         = self.linear_a(_a  )

							if self.act is not None:
										lowercase__         = self.act(_a  )

							lowercase__         = self.linear_a(_a  )

							if self.post_act is not None:
										lowercase__         = self.post_act(_a  )
							return sample
class  _snake_case	(    nn.Module):




				def __init__(  self    :  Optional[Any],    __lowercase    :  int,    __lowercase    :  bool,    __lowercase    :  float  ):
							super().__init__()
							lowercase__         = num_channels
							lowercase__         = flip_sin_to_cos
							lowercase__         = downscale_freq_shift




				def 							A__					(  self    :  List[Any],    __lowercase    :  Optional[int]  ):
							lowercase__         = 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  _snake_case	(    nn.Module):




				def __init__(  self    :  List[Any],    __lowercase    :  int = 256,    __lowercase    :  float = 1.0,    __lowercase    :  Any=True,    __lowercase    :  Any=True,    __lowercase    :  Optional[Any]=False  ):
							super().__init__()
							lowercase__         = nn.Parameter(torch.randn(_a  ) * scale,    requires_grad=_a  )
							lowercase__         = log
							lowercase__         = flip_sin_to_cos

							if set_W_to_weight:
										# to delete later
										lowercase__         = nn.Parameter(torch.randn(_a  ) * scale,    requires_grad=_a  )

										lowercase__         = self.W




				def 							A__					(  self    :  List[Any],    __lowercase    :  int  ):





							if self.log:
										lowercase__         = torch.log(_a  )

							lowercase__         = x[:, None] * self.weight[None, :] * 2 * np.pi

							if self.flip_sin_to_cos:
										lowercase__         = torch.cat([torch.cos(_a  ), torch.sin(_a  )],    dim=-1  )
							else:
										lowercase__         = torch.cat([torch.sin(_a  ), torch.cos(_a  )],    dim=-1  )
							return out
class  _snake_case	(    nn.Module):




				def __init__(  self    :  Dict,    __lowercase    :  int,    __lowercase    :  int,    __lowercase    :  int,    __lowercase    :  int,    ):
							super().__init__()

							lowercase__         = height
							lowercase__         = width
							lowercase__         = num_embed
							lowercase__         = embed_dim

							lowercase__         = nn.Embedding(self.num_embed,    _a  )
							lowercase__         = nn.Embedding(self.height,    _a  )
							lowercase__         = nn.Embedding(self.width,    _a  )




				def 							A__					(  self    :  List[Any],    __lowercase    :  Dict  ):
							lowercase__         = self.emb(_a  )

							lowercase__         = 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__         = height_emb.unsqueeze(2  )

							lowercase__         = 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__         = width_emb.unsqueeze(1  )

							lowercase__         = height_emb + width_emb

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

							lowercase__         = emb + pos_emb[:, : emb.shape[1], :]

							return emb
class  _snake_case	(    nn.Module):




				def __init__(  self    :  Dict,    __lowercase    :  List[Any],    __lowercase    :  Union[str, Any],    __lowercase    :  int  ):
							super().__init__()
							lowercase__         = dropout_prob > 0
							lowercase__         = nn.Embedding(num_classes + use_cfg_embedding,    _a  )
							lowercase__         = num_classes
							lowercase__         = dropout_prob




				def 							A__					(  self    :  Any,    __lowercase    :  Optional[int],    __lowercase    :  Union[str, Any]=None  ):





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




				def 							A__					(  self    :  List[Any],    __lowercase    :  torch.LongTensor,    __lowercase    :  Optional[int]=None  ):
							lowercase__         = self.dropout_prob > 0
							if (self.training and use_dropout) or (force_drop_ids is not None):
										lowercase__         = self.token_drop(_a,    _a  )
							lowercase__         = self.embedding_table(_a  )
							return embeddings
class  _snake_case	(    nn.Module):




				def __init__(  self    :  int,    __lowercase    :  int = 1024,    __lowercase    :  int = 768,    __lowercase    :  int = 768,    __lowercase    :  int = 10,    ):
							super().__init__()

							lowercase__         = num_image_text_embeds
							lowercase__         = nn.Linear(_a,    self.num_image_text_embeds * cross_attention_dim  )
							lowercase__         = nn.Linear(_a,    _a  )




				def 							A__					(  self    :  Optional[Any],    __lowercase    :  torch.FloatTensor,    __lowercase    :  torch.FloatTensor  ):
							lowercase__         = text_embeds.shape[0]

							# image
							lowercase__         = self.image_embeds(_a  )
							lowercase__         = image_text_embeds.reshape(_a,    self.num_image_text_embeds,    -1  )

							# text
							lowercase__         = self.text_proj(_a  )

							return torch.cat([image_text_embeds, text_embeds],    dim=1  )
class  _snake_case	(    nn.Module):




				def __init__(  self    :  Any,    __lowercase    :  int = 768,    __lowercase    :  int = 768,    __lowercase    :  int = 32,    ):
							super().__init__()

							lowercase__         = num_image_text_embeds
							lowercase__         = nn.Linear(_a,    self.num_image_text_embeds * cross_attention_dim  )
							lowercase__         = nn.LayerNorm(_a  )




				def 							A__					(  self    :  Union[str, Any],    __lowercase    :  torch.FloatTensor  ):
							lowercase__         = image_embeds.shape[0]

							# image
							lowercase__         = self.image_embeds(_a  )
							lowercase__         = image_embeds.reshape(_a,    self.num_image_text_embeds,    -1  )
							lowercase__         = self.norm(_a  )
							return image_embeds
class  _snake_case	(    nn.Module):




				def __init__(  self    :  Union[str, Any],    __lowercase    :  Any,    __lowercase    :  List[str],    __lowercase    :  int=0.1  ):
							super().__init__()

							lowercase__         = Timesteps(num_channels=256,    flip_sin_to_cos=_a,    downscale_freq_shift=1  )
							lowercase__         = TimestepEmbedding(in_channels=256,    time_embed_dim=_a  )
							lowercase__         = LabelEmbedding(_a,    _a,    _a  )




				def 							A__					(  self    :  List[str],    __lowercase    :  Any,    __lowercase    :  List[str],    __lowercase    :  Optional[Any]=None  ):
							lowercase__         = self.time_proj(_a  )
							lowercase__         = self.timestep_embedder(timesteps_proj.to(dtype=_a  )  )  # (N, D)

							lowercase__         = self.class_embedder(_a  )  # (N, D)

							lowercase__         = timesteps_emb + class_labels  # (N, D)

							return conditioning
class  _snake_case	(    nn.Module):




				def __init__(  self    :  str,    __lowercase    :  int,    __lowercase    :  int,    __lowercase    :  int = 64  ):
							super().__init__()
							lowercase__         = nn.LayerNorm(_a  )
							lowercase__         = AttentionPooling(_a,    _a  )
							lowercase__         = nn.Linear(_a,    _a  )
							lowercase__         = nn.LayerNorm(_a  )




				def 							A__					(  self    :  Tuple,    __lowercase    :  str  ):
							lowercase__         = self.norma(_a  )
							lowercase__         = self.pool(_a  )
							lowercase__         = self.proj(_a  )
							lowercase__         = self.norma(_a  )
							return hidden_states
class  _snake_case	(    nn.Module):




				def __init__(  self    :  Any,    __lowercase    :  int = 768,    __lowercase    :  int = 768,    __lowercase    :  int = 1536  ):
							super().__init__()
							lowercase__         = nn.Linear(_a,    _a  )
							lowercase__         = nn.LayerNorm(_a  )
							lowercase__         = nn.Linear(_a,    _a  )




				def 							A__					(  self    :  Union[str, Any],    __lowercase    :  torch.FloatTensor,    __lowercase    :  torch.FloatTensor  ):
							lowercase__         = self.text_proj(_a  )
							lowercase__         = self.text_norm(_a  )

							# image
							lowercase__         = self.image_proj(_a  )

							return time_image_embeds + time_text_embeds
class  _snake_case	(    nn.Module):




				def __init__(  self    :  str,    __lowercase    :  int = 768,    __lowercase    :  int = 1536  ):
							super().__init__()
							lowercase__         = nn.Linear(_a,    _a  )
							lowercase__         = nn.LayerNorm(_a  )




				def 							A__					(  self    :  Optional[Any],    __lowercase    :  torch.FloatTensor  ):
							lowercase__         = self.image_proj(_a  )
							lowercase__         = self.image_norm(_a  )
							return time_image_embeds
class  _snake_case	(    nn.Module):




				def __init__(  self    :  Optional[Any],    __lowercase    :  int = 768,    __lowercase    :  int = 1536  ):
							super().__init__()
							lowercase__         = nn.Linear(_a,    _a  )
							lowercase__         = nn.LayerNorm(_a  )
							lowercase__         = 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    :  str,    __lowercase    :  torch.FloatTensor,    __lowercase    :  torch.FloatTensor  ):
							lowercase__         = self.image_proj(_a  )
							lowercase__         = self.image_norm(_a  )
							lowercase__         = self.input_hint_block(_a  )
							return time_image_embeds, hint
class  _snake_case	(    nn.Module):




				def __init__(  self    :  Optional[Any],    __lowercase    :  Union[str, Any],    __lowercase    :  Optional[Any],    __lowercase    :  Dict=None  ):
							super().__init__()
							lowercase__         = dtype
							lowercase__         = nn.Parameter(torch.randn(1,    _a  ) / embed_dim**0.5  )
							lowercase__         = nn.Linear(_a,    _a,    dtype=self.dtype  )
							lowercase__         = nn.Linear(_a,    _a,    dtype=self.dtype  )
							lowercase__         = nn.Linear(_a,    _a,    dtype=self.dtype  )
							lowercase__         = num_heads
							lowercase__         = embed_dim // self.num_heads




				def 							A__					(  self    :  int,    __lowercase    :  str  ):
							lowercase__     ,				lowercase__     ,				lowercase__         = x.size()

							def shape(__lowercase    :  Tuple  ):
										# (bs, length, width) --> (bs, length, n_heads, dim_per_head)
										lowercase__         = 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)
										lowercase__         = x.transpose(1,    2  )
										# (bs, n_heads, length, dim_per_head) --> (bs*n_heads, length, dim_per_head)
										lowercase__         = 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__         = x.transpose(1,    2  )
										return x

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

							# (bs*n_heads, class_token_length, dim_per_head)
							lowercase__         = shape(self.q_proj(_a  )  )
							# (bs*n_heads, length+class_token_length, dim_per_head)
							lowercase__         = shape(self.k_proj(_a  )  )
							lowercase__         = shape(self.v_proj(_a  )  )

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

							# (bs*n_heads, dim_per_head, class_token_length)
							lowercase__         = torch.einsum("bts,bcs->bct",    _a,    _a  )

							# (bs, length+1, width)
							lowercase__         = a.reshape(_a,    -1,    1  ).transpose(1,    2  )

							return a[:, 0, :]  # cls_token








import math as m







def   lowerCamelCase(      a__		,a__		,a__=0.001):
				return (f(a + h) - f(a - h)) / (2 * h)







def   lowerCamelCase(      a__		,a__=0		,a__=100		,a__=0.0001		,a__=1e-6		,a__=False):
				_SCREAMING_SNAKE_CASE	     =xa  # set the initial guess
				_SCREAMING_SNAKE_CASE	     =[a]
				_SCREAMING_SNAKE_CASE	     =abs(f(a__))
				_SCREAMING_SNAKE_CASE	     =lambda a__: calc_derivative(a__		,a__		,h=a__)  # noqa: E731  Derivative of f(x)
				for _ in range(a__):
								if fa(a__) == 0:
												raise ValueError('''No converging solution found''')
								_SCREAMING_SNAKE_CASE	     =a - f(a__) / fa(a__)  # Calculate the next estimate
								if logsteps:
												steps.append(a__)
								if error < maxerror:
												break
				else:
								raise ValueError('''Iteration limit reached, no converging solution found''')
				if logsteps:
								# If logstep is true, then log intermediate steps
								return a, error, steps
				return a, error


if __name__ == "__main__":
							from matplotlib import pyplot as plt

							snake_case_  :	Tuple							  =							lambda x: m.tanh(x) ** 2 - m.exp(3 * x)  # noqa: E731
							snake_case_  , snake_case_  , snake_case_  :	str							  =							newton_raphson(
							    f, xa=10, maxiter=10_00, step=1e-6, logsteps=True
							)
							plt.plot([abs(f(x)) for x in steps])
							plt.xlabel('''step''')
							plt.ylabel('''error''')
							plt.show()
							print(f"""solution = {{{solution:f}}}, error = {{{error:f}}}""")