




'''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						(					UpperCAmelCase_      ,  UpperCAmelCase_      ,  UpperCAmelCase_ = False      ,  UpperCAmelCase_ = 1      ,  UpperCAmelCase_ = 1      ,  UpperCAmelCase_ = 10_000      ,  ):
    assert len(timesteps.shape	) == 1, "Timesteps should be a 1d-array"

    _a							:       int       					=			embedding_dim // 2
    _a							:       List[str]       					=			-math.log(UpperCAmelCase_	) * torch.arange(
        start=0      ,  end=UpperCAmelCase_      ,  dtype=torch.floataa      ,  device=timesteps.device	)
    _a							:       int       					=			exponent / (half_dim - downscale_freq_shift)

    _a							:       Optional[Any]       					=			torch.exp(UpperCAmelCase_	)
    _a							:       int       					=			timesteps[:, None].float() * emb[None, :]

    # scale embeddings
    _a							:       List[Any]       					=			scale * emb

    # concat sine and cosine embeddings
    _a							:       Optional[int]       					=			torch.cat([torch.sin(UpperCAmelCase_	), torch.cos(UpperCAmelCase_	)]      ,  dim=-1	)

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

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





def UpperCAmelCase						(					UpperCAmelCase_      ,  UpperCAmelCase_      ,  UpperCAmelCase_=False      ,  UpperCAmelCase_=0	):
    _a							:       Optional[Any]       					=			np.arange(UpperCAmelCase_      ,  dtype=np.floataa	)
    _a							:       List[str]       					=			np.arange(UpperCAmelCase_      ,  dtype=np.floataa	)
    _a							:       Tuple       					=			np.meshgrid(UpperCAmelCase_      ,  UpperCAmelCase_	)  # here w goes first
    _a							:       Tuple       					=			np.stack(UpperCAmelCase_      ,  axis=0	)

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





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

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

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





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

    _a							:       Optional[int]       					=			np.arange(embed_dim // 2      ,  dtype=np.floataa	)
    omega /= embed_dim / 2.0
    _a							:       str       					=			1.0 / 10_000**omega  # (D/2,)

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

    _a							:       str       					=			np.sin(UpperCAmelCase_	)  # (M, D/2)
    _a							:       Optional[int]       					=			np.cos(UpperCAmelCase_	)  # (M, D/2)

    _a							:       List[Any]       					=			np.concatenate([emb_sin, emb_cos]      ,  axis=1	)  # (M, D)
    return emb




class     UpperCamelCase					(  nn.Module					):



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







      '''simple docstring'''


      super().__init__()

      _a							:       int       					=			(height // patch_size) * (width // patch_size)
      _a							:       Optional[int]       					=			flatten
      _a							:       Tuple       					=			layer_norm

      _a							:       Any       					=			nn.Convad(
          __lowerCAmelCase		,    __lowerCAmelCase		,    kernel_size=(patch_size, patch_size)		,    stride=__lowerCAmelCase		,    bias=__lowerCAmelCase   )
      if layer_norm:
          _a							:       int       					=			nn.LayerNorm(__lowerCAmelCase		,    elementwise_affine=__lowerCAmelCase		,    eps=1e-6   )
      else:
          _a							:       List[Any]       					=			None

      _a							:       Any       					=			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 						a_       ( self		,    __lowerCAmelCase   ):







      '''simple docstring'''


      _a							:       int       					=			self.proj(__lowerCAmelCase   )
      if self.flatten:
          _a							:       str       					=			latent.flatten(2   ).transpose(1		,    2   )  # BCHW -> BNC
      if self.layer_norm:
          _a							:       Dict       					=			self.norm(__lowerCAmelCase   )
      return latent + self.pos_embed






class     UpperCamelCase					(  nn.Module					):



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







      '''simple docstring'''


      super().__init__()

      _a							:       int       					=			nn.Linear(__lowerCAmelCase		,    __lowerCAmelCase   )

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

      _a							:       Tuple       					=			get_activation(__lowerCAmelCase   )

      if out_dim is not None:
          _a							:       List[Any]       					=			out_dim
      else:
          _a							:       List[str]       					=			time_embed_dim
      _a							:       Optional[int]       					=			nn.Linear(__lowerCAmelCase		,    __lowerCAmelCase   )

      if post_act_fn is None:
          _a							:       Optional[int]       					=			None
      else:
          _a							:       Dict       					=			get_activation(__lowerCAmelCase   )



  def 						a_       ( self		,    __lowerCAmelCase		,    __lowerCAmelCase=None   ):







      '''simple docstring'''


      if condition is not None:
          _a							:       Union[str, Any]       					=			sample + self.cond_proj(__lowerCAmelCase   )
      _a							:       List[Any]       					=			self.linear_a(__lowerCAmelCase   )

      if self.act is not None:
          _a							:       Optional[int]       					=			self.act(__lowerCAmelCase   )

      _a							:       Any       					=			self.linear_a(__lowerCAmelCase   )

      if self.post_act is not None:
          _a							:       Optional[Any]       					=			self.post_act(__lowerCAmelCase   )
      return sample






class     UpperCamelCase					(  nn.Module					):



  def __init__( self		,    __lowerCAmelCase		,    __lowerCAmelCase		,    __lowerCAmelCase   ):







      '''simple docstring'''


      super().__init__()
      _a							:       Optional[int]       					=			num_channels
      _a							:       Any       					=			flip_sin_to_cos
      _a							:       Any       					=			downscale_freq_shift



  def 						a_       ( self		,    __lowerCAmelCase   ):







      '''simple docstring'''


      _a							:       Optional[Any]       					=			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     UpperCamelCase					(  nn.Module					):



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







      '''simple docstring'''


      super().__init__()
      _a							:       str       					=			nn.Parameter(torch.randn(__lowerCAmelCase   ) * scale		,    requires_grad=__lowerCAmelCase   )
      _a							:       Optional[Any]       					=			log
      _a							:       Union[str, Any]       					=			flip_sin_to_cos

      if set_W_to_weight:
          # to delete later
          _a							:       Optional[Any]       					=			nn.Parameter(torch.randn(__lowerCAmelCase   ) * scale		,    requires_grad=__lowerCAmelCase   )

          _a							:       Dict       					=			self.W



  def 						a_       ( self		,    __lowerCAmelCase   ):







      '''simple docstring'''


      if self.log:
          _a							:       Any       					=			torch.log(__lowerCAmelCase   )

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

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






class     UpperCamelCase					(  nn.Module					):



  def __init__( self		,    __lowerCAmelCase		,    __lowerCAmelCase		,    __lowerCAmelCase		,    __lowerCAmelCase		,    ):







      '''simple docstring'''


      super().__init__()

      _a							:       Dict       					=			height
      _a							:       str       					=			width
      _a							:       Optional[int]       					=			num_embed
      _a							:       Dict       					=			embed_dim

      _a							:       Optional[Any]       					=			nn.Embedding(self.num_embed		,    __lowerCAmelCase   )
      _a							:       str       					=			nn.Embedding(self.height		,    __lowerCAmelCase   )
      _a							:       str       					=			nn.Embedding(self.width		,    __lowerCAmelCase   )



  def 						a_       ( self		,    __lowerCAmelCase   ):







      '''simple docstring'''


      _a							:       List[Any]       					=			self.emb(__lowerCAmelCase   )

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

      _a							:       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
      _a							:       int       					=			width_emb.unsqueeze(1   )

      _a							:       Tuple       					=			height_emb + width_emb

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

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

      return emb






class     UpperCamelCase					(  nn.Module					):



  def __init__( self		,    __lowerCAmelCase		,    __lowerCAmelCase		,    __lowerCAmelCase   ):







      '''simple docstring'''


      super().__init__()
      _a							:       str       					=			dropout_prob > 0
      _a							:       Any       					=			nn.Embedding(num_classes + use_cfg_embedding		,    __lowerCAmelCase   )
      _a							:       List[Any]       					=			num_classes
      _a							:       Union[str, Any]       					=			dropout_prob



  def 						a_       ( self		,    __lowerCAmelCase		,    __lowerCAmelCase=None   ):







      '''simple docstring'''


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



  def 						a_       ( self		,    __lowerCAmelCase		,    __lowerCAmelCase=None   ):







      '''simple docstring'''


      _a							:       str       					=			self.dropout_prob > 0
      if (self.training and use_dropout) or (force_drop_ids is not None):
          _a							:       int       					=			self.token_drop(__lowerCAmelCase		,    __lowerCAmelCase   )
      _a							:       List[str]       					=			self.embedding_table(__lowerCAmelCase   )
      return embeddings






class     UpperCamelCase					(  nn.Module					):



  def __init__( self		,    __lowerCAmelCase = 1024		,    __lowerCAmelCase = 768		,    __lowerCAmelCase = 768		,    __lowerCAmelCase = 10		,    ):







      '''simple docstring'''


      super().__init__()

      _a							:       Tuple       					=			num_image_text_embeds
      _a							:       List[str]       					=			nn.Linear(__lowerCAmelCase		,    self.num_image_text_embeds * cross_attention_dim   )
      _a							:       List[str]       					=			nn.Linear(__lowerCAmelCase		,    __lowerCAmelCase   )



  def 						a_       ( self		,    __lowerCAmelCase		,    __lowerCAmelCase   ):







      '''simple docstring'''


      _a							:       List[str]       					=			text_embeds.shape[0]

      # image
      _a							:       str       					=			self.image_embeds(__lowerCAmelCase   )
      _a							:       str       					=			image_text_embeds.reshape(__lowerCAmelCase		,    self.num_image_text_embeds		,    -1   )

      # text
      _a							:       List[Any]       					=			self.text_proj(__lowerCAmelCase   )

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






class     UpperCamelCase					(  nn.Module					):



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







      '''simple docstring'''


      super().__init__()

      _a							:       Any       					=			num_image_text_embeds
      _a							:       List[Any]       					=			nn.Linear(__lowerCAmelCase		,    self.num_image_text_embeds * cross_attention_dim   )
      _a							:       Optional[int]       					=			nn.LayerNorm(__lowerCAmelCase   )



  def 						a_       ( self		,    __lowerCAmelCase   ):







      '''simple docstring'''


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

      # image
      _a							:       Optional[Any]       					=			self.image_embeds(__lowerCAmelCase   )
      _a							:       Tuple       					=			image_embeds.reshape(__lowerCAmelCase		,    self.num_image_text_embeds		,    -1   )
      _a							:       Tuple       					=			self.norm(__lowerCAmelCase   )
      return image_embeds






class     UpperCamelCase					(  nn.Module					):



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







      '''simple docstring'''


      super().__init__()

      _a							:       Any       					=			Timesteps(num_channels=256		,    flip_sin_to_cos=__lowerCAmelCase		,    downscale_freq_shift=1   )
      _a							:       Dict       					=			TimestepEmbedding(in_channels=256		,    time_embed_dim=__lowerCAmelCase   )
      _a							:       Tuple       					=			LabelEmbedding(__lowerCAmelCase		,    __lowerCAmelCase		,    __lowerCAmelCase   )



  def 						a_       ( self		,    __lowerCAmelCase		,    __lowerCAmelCase		,    __lowerCAmelCase=None   ):







      '''simple docstring'''


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

      _a							:       List[str]       					=			self.class_embedder(__lowerCAmelCase   )  # (N, D)

      _a							:       str       					=			timesteps_emb + class_labels  # (N, D)

      return conditioning






class     UpperCamelCase					(  nn.Module					):



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







      '''simple docstring'''


      super().__init__()
      _a							:       Union[str, Any]       					=			nn.LayerNorm(__lowerCAmelCase   )
      _a							:       Optional[Any]       					=			AttentionPooling(__lowerCAmelCase		,    __lowerCAmelCase   )
      _a							:       Dict       					=			nn.Linear(__lowerCAmelCase		,    __lowerCAmelCase   )
      _a							:       Dict       					=			nn.LayerNorm(__lowerCAmelCase   )



  def 						a_       ( self		,    __lowerCAmelCase   ):







      '''simple docstring'''


      _a							:       List[str]       					=			self.norma(__lowerCAmelCase   )
      _a							:       List[str]       					=			self.pool(__lowerCAmelCase   )
      _a							:       List[str]       					=			self.proj(__lowerCAmelCase   )
      _a							:       str       					=			self.norma(__lowerCAmelCase   )
      return hidden_states






class     UpperCamelCase					(  nn.Module					):



  def __init__( self		,    __lowerCAmelCase = 768		,    __lowerCAmelCase = 768		,    __lowerCAmelCase = 1536   ):







      '''simple docstring'''


      super().__init__()
      _a							:       List[str]       					=			nn.Linear(__lowerCAmelCase		,    __lowerCAmelCase   )
      _a							:       Tuple       					=			nn.LayerNorm(__lowerCAmelCase   )
      _a							:       Any       					=			nn.Linear(__lowerCAmelCase		,    __lowerCAmelCase   )



  def 						a_       ( self		,    __lowerCAmelCase		,    __lowerCAmelCase   ):







      '''simple docstring'''


      _a							:       Dict       					=			self.text_proj(__lowerCAmelCase   )
      _a							:       Optional[int]       					=			self.text_norm(__lowerCAmelCase   )

      # image
      _a							:       Optional[Any]       					=			self.image_proj(__lowerCAmelCase   )

      return time_image_embeds + time_text_embeds






class     UpperCamelCase					(  nn.Module					):



  def __init__( self		,    __lowerCAmelCase = 768		,    __lowerCAmelCase = 1536   ):







      '''simple docstring'''


      super().__init__()
      _a							:       Union[str, Any]       					=			nn.Linear(__lowerCAmelCase		,    __lowerCAmelCase   )
      _a							:       Tuple       					=			nn.LayerNorm(__lowerCAmelCase   )



  def 						a_       ( self		,    __lowerCAmelCase   ):







      '''simple docstring'''


      _a							:       int       					=			self.image_proj(__lowerCAmelCase   )
      _a							:       Optional[Any]       					=			self.image_norm(__lowerCAmelCase   )
      return time_image_embeds






class     UpperCamelCase					(  nn.Module					):



  def __init__( self		,    __lowerCAmelCase = 768		,    __lowerCAmelCase = 1536   ):







      '''simple docstring'''


      super().__init__()
      _a							:       Dict       					=			nn.Linear(__lowerCAmelCase		,    __lowerCAmelCase   )
      _a							:       Tuple       					=			nn.LayerNorm(__lowerCAmelCase   )
      _a							:       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 						a_       ( self		,    __lowerCAmelCase		,    __lowerCAmelCase   ):







      '''simple docstring'''


      _a							:       List[str]       					=			self.image_proj(__lowerCAmelCase   )
      _a							:       Any       					=			self.image_norm(__lowerCAmelCase   )
      _a							:       List[str]       					=			self.input_hint_block(__lowerCAmelCase   )
      return time_image_embeds, hint






class     UpperCamelCase					(  nn.Module					):



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







      '''simple docstring'''


      super().__init__()
      _a							:       Union[str, Any]       					=			dtype
      _a							:       List[str]       					=			nn.Parameter(torch.randn(1		,    __lowerCAmelCase   ) / embed_dim**0.5   )
      _a							:       List[str]       					=			nn.Linear(__lowerCAmelCase		,    __lowerCAmelCase		,    dtype=self.dtype   )
      _a							:       List[str]       					=			nn.Linear(__lowerCAmelCase		,    __lowerCAmelCase		,    dtype=self.dtype   )
      _a							:       Tuple       					=			nn.Linear(__lowerCAmelCase		,    __lowerCAmelCase		,    dtype=self.dtype   )
      _a							:       Union[str, Any]       					=			num_heads
      _a							:       str       					=			embed_dim // self.num_heads



  def 						a_       ( self		,    __lowerCAmelCase   ):







      '''simple docstring'''


      _a					,   _a					,   _a							:       Dict       					=			x.size()

      def shape(__lowerCAmelCase   ):
          # (bs, length, width) --> (bs, length, n_heads, dim_per_head)
          _a							:       Any       					=			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)
          _a							:       List[str]       					=			x.transpose(1		,    2   )
          # (bs, n_heads, length, dim_per_head) --> (bs*n_heads, length, dim_per_head)
          _a							:       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)
          _a							:       Dict       					=			x.transpose(1		,    2   )
          return x

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

      # (bs*n_heads, class_token_length, dim_per_head)
      _a							:       int       					=			shape(self.q_proj(__lowerCAmelCase   )   )
      # (bs*n_heads, length+class_token_length, dim_per_head)
      _a							:       Union[str, Any]       					=			shape(self.k_proj(__lowerCAmelCase   )   )
      _a							:       int       					=			shape(self.v_proj(__lowerCAmelCase   )   )

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

      # (bs*n_heads, dim_per_head, class_token_length)
      _a							:       Optional[int]       					=			torch.einsum("""bts,bcs->bct"""		,    __lowerCAmelCase		,    __lowerCAmelCase   )

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

      return a[:, 0, :]  # cls_token








'''simple docstring'''





from math import exp





def UpperCAmelCase						(					UpperCAmelCase_	):
    return 8 * x - 2 * exp(-x	)





def UpperCAmelCase						(					UpperCAmelCase_      ,  UpperCAmelCase_      ,  UpperCAmelCase_	):
    _a							:       Optional[int]       					=			lower_bound
    _a							:       str       					=			upper_bound
    for _ in range(0      ,  UpperCAmelCase_	):
        _a					,   _a							:       List[str]       					=			xa, xa - (f(UpperCAmelCase_	) * (xa - xa)) / (f(UpperCAmelCase_	) - f(UpperCAmelCase_	))
    return xa


if __name__ == "__main__":
  print(F"""Example: {secant_method(1, 3, 2)}""")


