
"""simple docstring"""

from __future__ import annotations






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

      UpperCamelCase      :							List[str]          =					float(input("Enter the last number (n term) of the Geometric Series"))
      UpperCamelCase      :							Optional[int]          =					float(input("Enter the starting term (a) of the Geometric Series"))
      UpperCamelCase      :							List[Any]          =					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))











"""simple docstring"""
import inspect
from typing import List, Optional, Union

import torch
from torch import nn
from torch.nn import functional as F
from torchvision import transforms
from transformers import CLIPImageProcessor, CLIPModel, CLIPTextModel, CLIPTokenizer

from diffusers import (
    AutoencoderKL,
    DDIMScheduler,
    DiffusionPipeline,
    DPMSolverMultistepScheduler,
    LMSDiscreteScheduler,
    PNDMScheduler,
    UNetaDConditionModel,
)
from diffusers.pipelines.stable_diffusion.pipeline_stable_diffusion import StableDiffusionPipelineOutput



class 						a_ (      nn.Module					):







      '''simple docstring'''

      def __init__(self,	lowerCamelCase_,	lowerCamelCase_=1.0   ):

       '''simple docstring'''



       super().__init__()

       lowerCamelCase__	:     Union[str, Any]								=		cut_size
       lowerCamelCase__	:     Optional[int]								=		cut_power





      def      a__				(self,	lowerCamelCase_,	lowerCamelCase_   ):

       '''simple docstring'''



       lowerCamelCase__							,	lowerCamelCase__	:     Union[str, Any]								=		pixel_values.shape[2:4]
       lowerCamelCase__	:     str								=		min(lowerCamelCase_,	lowerCamelCase_   )
       lowerCamelCase__	:     List[Any]								=		min(lowerCamelCase_,	lowerCamelCase_,	self.cut_size   )
       lowerCamelCase__	:     int								=		[]
       for _ in range(lowerCamelCase_   ):
        lowerCamelCase__	:     int								=		int(torch.rand([]   ) ** self.cut_power * (max_size - min_size) + min_size   )
        lowerCamelCase__	:     List[str]								=		torch.randint(0,	sideX - size + 1,	()   )
        lowerCamelCase__	:     Union[str, Any]								=		torch.randint(0,	sideY - size + 1,	()   )
        lowerCamelCase__	:     Tuple								=		pixel_values[:, :, offsety : offsety + size, offsetx : offsetx + size]
        cutouts.append(F.adaptive_avg_poolad(lowerCamelCase_,	self.cut_size   )   )
       return torch.cat(lowerCamelCase_   )






def 			lowerCamelCase_    (		_lowerCamelCase     ,  _lowerCamelCase							):
 lowerCamelCase__	:     List[str]								=		F.normalize(_lowerCamelCase     ,  dim=-1							)
 lowerCamelCase__	:     Optional[int]								=		F.normalize(_lowerCamelCase     ,  dim=-1							)
 return (x - y).norm(dim=-1							).div(2							).arcsin().pow(2							).mul(2							)






def 			lowerCamelCase_    (		_lowerCamelCase     ,  _lowerCamelCase							):
 for param in model.parameters():
  lowerCamelCase__	:     Dict								=		value





class 						a_ (      snake_case_					):







      '''simple docstring'''

      def __init__(self,	lowerCamelCase_,	lowerCamelCase_,	lowerCamelCase_,	lowerCamelCase_,	lowerCamelCase_,	lowerCamelCase_,	lowerCamelCase_,	):

       '''simple docstring'''



       super().__init__()
       self.register_modules(
           vae=lowerCamelCase_,	text_encoder=lowerCamelCase_,	clip_model=lowerCamelCase_,	tokenizer=lowerCamelCase_,	unet=lowerCamelCase_,	scheduler=lowerCamelCase_,	feature_extractor=lowerCamelCase_,	)

       lowerCamelCase__	:     Union[str, Any]								=		transforms.Normalize(mean=feature_extractor.image_mean,	std=feature_extractor.image_std   )
       lowerCamelCase__	:     Dict								=		(
           feature_extractor.size
           if isinstance(feature_extractor.size,	lowerCamelCase_   )
           else feature_extractor.size['shortest_edge']
       )
       lowerCamelCase__	:     Any								=		MakeCutouts(self.cut_out_size   )

       set_requires_grad(self.text_encoder,	lowerCamelCase_   )
       set_requires_grad(self.clip_model,	lowerCamelCase_   )




      def      a__				(self,	lowerCamelCase_ = "auto"   ):

       '''simple docstring'''



       if slice_size == "auto":
        # half the attention head size is usually a good trade-off between
        # speed and memory
        lowerCamelCase__	:     Tuple								=		self.unet.config.attention_head_dim // 2
       self.unet.set_attention_slice(lowerCamelCase_   )




      def      a__				(self   ):

       '''simple docstring'''



       self.enable_attention_slicing(lowerCamelCase_   )




      def      a__				(self   ):

       '''simple docstring'''



       set_requires_grad(self.vae,	lowerCamelCase_   )




      def      a__				(self   ):

       '''simple docstring'''



       set_requires_grad(self.vae,	lowerCamelCase_   )




      def      a__				(self   ):

       '''simple docstring'''



       set_requires_grad(self.unet,	lowerCamelCase_   )




      def      a__				(self   ):

       '''simple docstring'''



       set_requires_grad(self.unet,	lowerCamelCase_   )




      @torch.enable_grad()
      def      a__				(self,	lowerCamelCase_,	lowerCamelCase_,	lowerCamelCase_,	lowerCamelCase_,	lowerCamelCase_,	lowerCamelCase_,	lowerCamelCase_,	lowerCamelCase_,	lowerCamelCase_=True,	):

       '''simple docstring'''



       lowerCamelCase__	:     Any								=		latents.detach().requires_grad_()

       lowerCamelCase__	:     int								=		self.scheduler.scale_model_input(lowerCamelCase_,	lowerCamelCase_   )

       # predict the noise residual
       lowerCamelCase__	:     Tuple								=		self.unet(lowerCamelCase_,	lowerCamelCase_,	encoder_hidden_states=lowerCamelCase_   ).sample

       if isinstance(self.scheduler,	(PNDMScheduler, DDIMScheduler, DPMSolverMultistepScheduler)   ):
        lowerCamelCase__	:     int								=		self.scheduler.alphas_cumprod[timestep]
        lowerCamelCase__	:     Union[str, Any]								=		1 - alpha_prod_t
        # compute predicted original sample from predicted noise also called
        # "predicted x_0" of formula (12) from https://arxiv.org/pdf/2010.02502.pdf
        lowerCamelCase__	:     int								=		(latents - beta_prod_t ** 0.5 * noise_pred) / alpha_prod_t ** 0.5

        lowerCamelCase__	:     Optional[int]								=		torch.sqrt(lowerCamelCase_   )
        lowerCamelCase__	:     Optional[Any]								=		pred_original_sample * (fac) + latents * (1 - fac)
       elif isinstance(self.scheduler,	lowerCamelCase_   ):
        lowerCamelCase__	:     Optional[Any]								=		self.scheduler.sigmas[index]
        lowerCamelCase__	:     List[Any]								=		latents - sigma * noise_pred
       else:
        raise ValueError(f'''scheduler type {type(self.scheduler   )} not supported'''   )

       lowerCamelCase__	:     Tuple								=		1 / self.vae.config.scaling_factor * sample
       lowerCamelCase__	:     List[str]								=		self.vae.decode(lowerCamelCase_   ).sample
       lowerCamelCase__	:     Union[str, Any]								=		(image / 2 + 0.5).clamp(0,	1   )

       if use_cutouts:
        lowerCamelCase__	:     int								=		self.make_cutouts(lowerCamelCase_,	lowerCamelCase_   )
       else:
        lowerCamelCase__	:     Dict								=		transforms.Resize(self.cut_out_size   )(lowerCamelCase_   )
       lowerCamelCase__	:     Union[str, Any]								=		self.normalize(lowerCamelCase_   ).to(latents.dtype   )

       lowerCamelCase__	:     str								=		self.clip_model.get_image_features(lowerCamelCase_   )
       lowerCamelCase__	:     List[Any]								=		image_embeddings_clip / image_embeddings_clip.norm(p=2,	dim=-1,	keepdim=lowerCamelCase_   )

       if use_cutouts:
        lowerCamelCase__	:     List[Any]								=		spherical_dist_loss(lowerCamelCase_,	lowerCamelCase_   )
        lowerCamelCase__	:     Dict								=		dists.view([num_cutouts, sample.shape[0], -1]   )
        lowerCamelCase__	:     List[Any]								=		dists.sum(2   ).mean(0   ).sum() * clip_guidance_scale
       else:
        lowerCamelCase__	:     str								=		spherical_dist_loss(lowerCamelCase_,	lowerCamelCase_   ).mean() * clip_guidance_scale

       lowerCamelCase__	:     Dict								=		-torch.autograd.grad(lowerCamelCase_,	lowerCamelCase_   )[0]

       if isinstance(self.scheduler,	lowerCamelCase_   ):
        lowerCamelCase__	:     Any								=		latents.detach() + grads * (sigma**2)
        lowerCamelCase__	:     Any								=		noise_pred_original
       else:
        lowerCamelCase__	:     Optional[int]								=		noise_pred_original - torch.sqrt(lowerCamelCase_   ) * grads
       return noise_pred, latents





      @torch.no_grad()
      def __call__(self,	lowerCamelCase_,	lowerCamelCase_ = 5_1_2,	lowerCamelCase_ = 5_1_2,	lowerCamelCase_ = 5_0,	lowerCamelCase_ = 7.5,	lowerCamelCase_ = 1,	lowerCamelCase_ = 0.0,	lowerCamelCase_ = 1_0_0,	lowerCamelCase_ = None,	lowerCamelCase_ = 4,	lowerCamelCase_ = True,	lowerCamelCase_ = None,	lowerCamelCase_ = None,	lowerCamelCase_ = "pil",	lowerCamelCase_ = True,	):

       '''simple docstring'''



       if isinstance(lowerCamelCase_,	lowerCamelCase_   ):
        lowerCamelCase__	:     Any								=		1
       elif isinstance(lowerCamelCase_,	lowerCamelCase_   ):
        lowerCamelCase__	:     Optional[int]								=		len(lowerCamelCase_   )
       else:
        raise ValueError(f'''`prompt` has to be of type `str` or `list` but is {type(lowerCamelCase_   )}'''   )

       if height % 8 != 0 or width % 8 != 0:
        raise ValueError(f'''`height` and `width` have to be divisible by 8 but are {height} and {width}.'''   )

       # get prompt text embeddings
       lowerCamelCase__	:     List[Any]								=		self.tokenizer(
           lowerCamelCase_,	padding='max_length',	max_length=self.tokenizer.model_max_length,	truncation=lowerCamelCase_,	return_tensors='pt',	)
       lowerCamelCase__	:     Optional[int]								=		self.text_encoder(text_input.input_ids.to(self.device   )   )[0]
       # duplicate text embeddings for each generation per prompt
       lowerCamelCase__	:     Optional[Any]								=		text_embeddings.repeat_interleave(lowerCamelCase_,	dim=0   )

       if clip_guidance_scale > 0:
        if clip_prompt is not None:
         lowerCamelCase__	:     str								=		self.tokenizer(
             lowerCamelCase_,	padding='max_length',	max_length=self.tokenizer.model_max_length,	truncation=lowerCamelCase_,	return_tensors='pt',	).input_ids.to(self.device   )
        else:
         lowerCamelCase__	:     List[Any]								=		text_input.input_ids.to(self.device   )
        lowerCamelCase__	:     Any								=		self.clip_model.get_text_features(lowerCamelCase_   )
        lowerCamelCase__	:     List[Any]								=		text_embeddings_clip / text_embeddings_clip.norm(p=2,	dim=-1,	keepdim=lowerCamelCase_   )
        # duplicate text embeddings clip for each generation per prompt
        lowerCamelCase__	:     Union[str, Any]								=		text_embeddings_clip.repeat_interleave(lowerCamelCase_,	dim=0   )

       # here `guidance_scale` is defined analog to the guidance weight `w` of equation (2)
       # of the Imagen paper: https://arxiv.org/pdf/2205.11487.pdf . `guidance_scale = 1`
       # corresponds to doing no classifier free guidance.
       lowerCamelCase__	:     Optional[Any]								=		guidance_scale > 1.0
       # get unconditional embeddings for classifier free guidance
       if do_classifier_free_guidance:
        lowerCamelCase__	:     str								=		text_input.input_ids.shape[-1]
        lowerCamelCase__	:     Union[str, Any]								=		self.tokenizer([''],	padding='max_length',	max_length=lowerCamelCase_,	return_tensors='pt'   )
        lowerCamelCase__	:     Optional[int]								=		self.text_encoder(uncond_input.input_ids.to(self.device   )   )[0]
        # duplicate unconditional embeddings for each generation per prompt
        lowerCamelCase__	:     Union[str, Any]								=		uncond_embeddings.repeat_interleave(lowerCamelCase_,	dim=0   )

        # For classifier free guidance, we need to do two forward passes.
        # Here we concatenate the unconditional and text embeddings into a single batch
        # to avoid doing two forward passes
        lowerCamelCase__	:     Optional[Any]								=		torch.cat([uncond_embeddings, text_embeddings]   )

       # get the initial random noise unless the user supplied it

       # Unlike in other pipelines, latents need to be generated in the target device
       # for 1-to-1 results reproducibility with the CompVis implementation.
       # However this currently doesn't work in `mps`.
       lowerCamelCase__	:     str								=		(batch_size * num_images_per_prompt, self.unet.config.in_channels, height // 8, width // 8)
       lowerCamelCase__	:     Any								=		text_embeddings.dtype
       if latents is None:
        if self.device.type == "mps":
         # randn does not work reproducibly on mps
         lowerCamelCase__	:     Optional[Any]								=		torch.randn(lowerCamelCase_,	generator=lowerCamelCase_,	device='cpu',	dtype=lowerCamelCase_   ).to(
             self.device   )
        else:
         lowerCamelCase__	:     Optional[Any]								=		torch.randn(lowerCamelCase_,	generator=lowerCamelCase_,	device=self.device,	dtype=lowerCamelCase_   )
       else:
        if latents.shape != latents_shape:
         raise ValueError(f'''Unexpected latents shape, got {latents.shape}, expected {latents_shape}'''   )
        lowerCamelCase__	:     Dict								=		latents.to(self.device   )

       # set timesteps
       lowerCamelCase__	:     int								=		'offset' in set(inspect.signature(self.scheduler.set_timesteps   ).parameters.keys()   )
       lowerCamelCase__	:     int								=		{}
       if accepts_offset:
        lowerCamelCase__	:     Optional[int]								=		1

       self.scheduler.set_timesteps(lowerCamelCase_,	**lowerCamelCase_   )

       # Some schedulers like PNDM have timesteps as arrays
       # It's more optimized to move all timesteps to correct device beforehand
       lowerCamelCase__	:     int								=		self.scheduler.timesteps.to(self.device   )

       # scale the initial noise by the standard deviation required by the scheduler
       lowerCamelCase__	:     Tuple								=		latents * self.scheduler.init_noise_sigma

       # prepare extra kwargs for the scheduler step, since not all schedulers have the same signature
       # eta (η) is only used with the DDIMScheduler, it will be ignored for other schedulers.
       # eta corresponds to η in DDIM paper: https://arxiv.org/abs/2010.02502
       # and should be between [0, 1]
       lowerCamelCase__	:     Optional[Any]								=		'eta' in set(inspect.signature(self.scheduler.step   ).parameters.keys()   )
       lowerCamelCase__	:     Any								=		{}
       if accepts_eta:
        lowerCamelCase__	:     Any								=		eta

       # check if the scheduler accepts generator
       lowerCamelCase__	:     Tuple								=		'generator' in set(inspect.signature(self.scheduler.step   ).parameters.keys()   )
       if accepts_generator:
        lowerCamelCase__	:     Union[str, Any]								=		generator

       for i, t in enumerate(self.progress_bar(lowerCamelCase_   )   ):
        # expand the latents if we are doing classifier free guidance
        lowerCamelCase__	:     Any								=		torch.cat([latents] * 2   ) if do_classifier_free_guidance else latents
        lowerCamelCase__	:     List[Any]								=		self.scheduler.scale_model_input(lowerCamelCase_,	lowerCamelCase_   )

        # predict the noise residual
        lowerCamelCase__	:     Tuple								=		self.unet(lowerCamelCase_,	lowerCamelCase_,	encoder_hidden_states=lowerCamelCase_   ).sample

        # perform classifier free guidance
        if do_classifier_free_guidance:
         lowerCamelCase__							,	lowerCamelCase__	:     int								=		noise_pred.chunk(2   )
         lowerCamelCase__	:     Any								=		noise_pred_uncond + guidance_scale * (noise_pred_text - noise_pred_uncond)

        # perform clip guidance
        if clip_guidance_scale > 0:
         lowerCamelCase__	:     Optional[Any]								=		(
             text_embeddings.chunk(2   )[1] if do_classifier_free_guidance else text_embeddings
         )
         lowerCamelCase__							,	lowerCamelCase__	:     Union[str, Any]								=		self.cond_fn(
             lowerCamelCase_,	lowerCamelCase_,	lowerCamelCase_,	lowerCamelCase_,	lowerCamelCase_,	lowerCamelCase_,	lowerCamelCase_,	lowerCamelCase_,	lowerCamelCase_,	)

        # compute the previous noisy sample x_t -> x_t-1
        lowerCamelCase__	:     Any								=		self.scheduler.step(lowerCamelCase_,	lowerCamelCase_,	lowerCamelCase_,	**lowerCamelCase_   ).prev_sample

       # scale and decode the image latents with vae
       lowerCamelCase__	:     Dict								=		1 / self.vae.config.scaling_factor * latents
       lowerCamelCase__	:     List[Any]								=		self.vae.decode(lowerCamelCase_   ).sample

       lowerCamelCase__	:     List[Any]								=		(image / 2 + 0.5).clamp(0,	1   )
       lowerCamelCase__	:     Any								=		image.cpu().permute(0,	2,	3,	1   ).numpy()

       if output_type == "pil":
        lowerCamelCase__	:     List[str]								=		self.numpy_to_pil(lowerCamelCase_   )

       if not return_dict:
        return (image, None)

       return StableDiffusionPipelineOutput(images=lowerCamelCase_,	nsfw_content_detected=lowerCamelCase_   )

