"""simple docstring"""
from __future__ import annotations

import math







def 						__a   (	_SCREAMING_SNAKE_CASE		,     _SCREAMING_SNAKE_CASE   )	->list:
  if len(_SCREAMING_SNAKE_CASE   ) != 2 or len(a[0]   ) != 2 or len(_SCREAMING_SNAKE_CASE   ) != 2 or len(b[0]   ) != 2:
    raise Exception('Matrices are not 2x2'   )
  a__:     List[Any]										=	[
      [a[0][0] * b[0][0] + a[0][1] * b[1][0], a[0][0] * b[0][1] + a[0][1] * b[1][1]],
      [a[1][0] * b[0][0] + a[1][1] * b[1][0], a[1][0] * b[0][1] + a[1][1] * b[1][1]],
  ]
  return new_matrix







def 						__a   (	_SCREAMING_SNAKE_CASE		,     _SCREAMING_SNAKE_CASE   )	->List[str]:
  return [
      [matrix_a[row][col] + matrix_b[row][col] for col in range(len(matrix_a[row]   )   )]
      for row in range(len(_SCREAMING_SNAKE_CASE   )   )
  ]







def 						__a   (	_SCREAMING_SNAKE_CASE		,     _SCREAMING_SNAKE_CASE   )	->str:
  return [
      [matrix_a[row][col] - matrix_b[row][col] for col in range(len(matrix_a[row]   )   )]
      for row in range(len(_SCREAMING_SNAKE_CASE   )   )
  ]







def 						__a   (	_SCREAMING_SNAKE_CASE   )	->tuple[list, list, list, list]:
  if len(_SCREAMING_SNAKE_CASE   ) % 2 != 0 or len(a[0]   ) % 2 != 0:
    raise Exception('Odd matrices are not supported!'   )

  a__:     Tuple										=	len(_SCREAMING_SNAKE_CASE   )
  a__:     int										=	matrix_length // 2

  a__:     int										=	[[a[i][j] for j in range(_SCREAMING_SNAKE_CASE		,     _SCREAMING_SNAKE_CASE   )] for i in range(_SCREAMING_SNAKE_CASE   )]
  a__:     int										=	[
      [a[i][j] for j in range(_SCREAMING_SNAKE_CASE		,     _SCREAMING_SNAKE_CASE   )] for i in range(_SCREAMING_SNAKE_CASE		,     _SCREAMING_SNAKE_CASE   )
  ]

  a__:     Optional[Any]										=	[[a[i][j] for j in range(_SCREAMING_SNAKE_CASE   )] for i in range(_SCREAMING_SNAKE_CASE   )]
  a__:     Dict										=	[[a[i][j] for j in range(_SCREAMING_SNAKE_CASE   )] for i in range(_SCREAMING_SNAKE_CASE		,     _SCREAMING_SNAKE_CASE   )]

  return top_left, top_right, bot_left, bot_right







def 						__a   (	_SCREAMING_SNAKE_CASE   )	->tuple[int, int]:
  return len(_SCREAMING_SNAKE_CASE   ), len(matrix[0]   )







def 						__a   (	_SCREAMING_SNAKE_CASE   )	->None:
  print('\n'.join(str(_SCREAMING_SNAKE_CASE   ) for line in matrix   )   )







def 						__a   (	_SCREAMING_SNAKE_CASE		,     _SCREAMING_SNAKE_CASE   )	->list:
  if matrix_dimensions(_SCREAMING_SNAKE_CASE   ) == (2, 2):
    return default_matrix_multiplication(_SCREAMING_SNAKE_CASE		,     _SCREAMING_SNAKE_CASE   )

  a__							,    a__							,    a__							,    a__:     str										=	split_matrix(_SCREAMING_SNAKE_CASE   )
  a__							,    a__							,    a__							,    a__:     Dict										=	split_matrix(_SCREAMING_SNAKE_CASE   )

  a__:     Optional[Any]										=	actual_strassen(_SCREAMING_SNAKE_CASE		,     matrix_subtraction(_SCREAMING_SNAKE_CASE		,     _SCREAMING_SNAKE_CASE   )   )
  a__:     str										=	actual_strassen(matrix_addition(_SCREAMING_SNAKE_CASE		,     _SCREAMING_SNAKE_CASE   )		,     _SCREAMING_SNAKE_CASE   )
  a__:     int										=	actual_strassen(matrix_addition(_SCREAMING_SNAKE_CASE		,     _SCREAMING_SNAKE_CASE   )		,     _SCREAMING_SNAKE_CASE   )
  a__:     Optional[int]										=	actual_strassen(_SCREAMING_SNAKE_CASE		,     matrix_subtraction(_SCREAMING_SNAKE_CASE		,     _SCREAMING_SNAKE_CASE   )   )
  a__:     List[Any]										=	actual_strassen(matrix_addition(_SCREAMING_SNAKE_CASE		,     _SCREAMING_SNAKE_CASE   )		,     matrix_addition(_SCREAMING_SNAKE_CASE		,     _SCREAMING_SNAKE_CASE   )   )
  a__:     List[str]										=	actual_strassen(matrix_subtraction(_SCREAMING_SNAKE_CASE		,     _SCREAMING_SNAKE_CASE   )		,     matrix_addition(_SCREAMING_SNAKE_CASE		,     _SCREAMING_SNAKE_CASE   )   )
  a__:     Optional[Any]										=	actual_strassen(matrix_subtraction(_SCREAMING_SNAKE_CASE		,     _SCREAMING_SNAKE_CASE   )		,     matrix_addition(_SCREAMING_SNAKE_CASE		,     _SCREAMING_SNAKE_CASE   )   )

  a__:     Optional[Any]										=	matrix_addition(matrix_subtraction(matrix_addition(_SCREAMING_SNAKE_CASE		,     _SCREAMING_SNAKE_CASE   )		,     _SCREAMING_SNAKE_CASE   )		,     _SCREAMING_SNAKE_CASE   )
  a__:     Optional[int]										=	matrix_addition(_SCREAMING_SNAKE_CASE		,     _SCREAMING_SNAKE_CASE   )
  a__:     str										=	matrix_addition(_SCREAMING_SNAKE_CASE		,     _SCREAMING_SNAKE_CASE   )
  a__:     Tuple										=	matrix_subtraction(matrix_subtraction(matrix_addition(_SCREAMING_SNAKE_CASE		,     _SCREAMING_SNAKE_CASE   )		,     _SCREAMING_SNAKE_CASE   )		,     _SCREAMING_SNAKE_CASE   )

  # construct the new matrix from our 4 quadrants
  a__:     Optional[Any]										=	[]
  for i in range(len(_SCREAMING_SNAKE_CASE   )   ):
    new_matrix.append(top_left[i] + top_right[i]   )
  for i in range(len(_SCREAMING_SNAKE_CASE   )   ):
    new_matrix.append(bot_left[i] + bot_right[i]   )
  return new_matrix







def 						__a   (	_SCREAMING_SNAKE_CASE		,     _SCREAMING_SNAKE_CASE   )	->list:
  if matrix_dimensions(_SCREAMING_SNAKE_CASE   )[1] != matrix_dimensions(_SCREAMING_SNAKE_CASE   )[0]:
    a__:     int										=	(
        'Unable to multiply these matrices, please check the dimensions.\n'
        F'Matrix A: {matrixa}\n'
        F'Matrix B: {matrixa}'
    )
    raise Exception(_SCREAMING_SNAKE_CASE   )
  a__:     List[Any]										=	matrix_dimensions(_SCREAMING_SNAKE_CASE   )
  a__:     Union[str, Any]										=	matrix_dimensions(_SCREAMING_SNAKE_CASE   )

  if dimensiona[0] == dimensiona[1] and dimensiona[0] == dimensiona[1]:
    return [matrixa, matrixa]

  a__:     Optional[int]										=	max(*_SCREAMING_SNAKE_CASE		,     *_SCREAMING_SNAKE_CASE   )
  a__:     Optional[Any]										=	int(math.pow(2		,     math.ceil(math.loga(_SCREAMING_SNAKE_CASE   )   )   )   )
  a__:     int										=	matrixa
  a__:     Any										=	matrixa

  # Adding zeros to the matrices so that the arrays dimensions are the same and also
  # power of 2
  for i in range(0		,     _SCREAMING_SNAKE_CASE   ):
    if i < dimensiona[0]:
      for _ in range(dimensiona[1]		,     _SCREAMING_SNAKE_CASE   ):
        new_matrixa[i].append(0   )
    else:
      new_matrixa.append([0] * maxim   )
    if i < dimensiona[0]:
      for _ in range(dimensiona[1]		,     _SCREAMING_SNAKE_CASE   ):
        new_matrixa[i].append(0   )
    else:
      new_matrixa.append([0] * maxim   )

  a__:     Any										=	actual_strassen(_SCREAMING_SNAKE_CASE		,     _SCREAMING_SNAKE_CASE   )

  # Removing the additional zeros
  for i in range(0		,     _SCREAMING_SNAKE_CASE   ):
    if i < dimensiona[0]:
      for _ in range(dimensiona[1]		,     _SCREAMING_SNAKE_CASE   ):
        final_matrix[i].pop()
    else:
      final_matrix.pop()
  return final_matrix


if __name__ == "__main__":
 lowercase__					       =	[
     [2, 3, 4, 5],
     [6, 4, 3, 1],
     [2, 3, 6, 7],
     [3, 1, 2, 4],
     [2, 3, 4, 5],
     [6, 4, 3, 1],
     [2, 3, 6, 7],
     [3, 1, 2, 4],
     [2, 3, 4, 5],
     [6, 2, 3, 1],
 ]
 lowercase__					       =	[[0, 2, 1, 1], [16, 2, 3, 3], [2, 2, 7, 7], [13, 11, 22, 4]]
 print(strassen(matrixa, matrixa))



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

import PIL
import torch
from torchvision import transforms

from diffusers.pipeline_utils import DiffusionPipeline, ImagePipelineOutput
from diffusers.schedulers import DDIMScheduler
from diffusers.utils import randn_tensor


lowercase__					       =	transforms.Compose(
    [
        transforms.Resize((256, 256)),
        transforms.ToTensor(),
        transforms.Normalize([0.5], [0.5]),
    ]
)







def 						__a   (	_SCREAMING_SNAKE_CASE   )	->Any:
  if isinstance(_SCREAMING_SNAKE_CASE		,     torch.Tensor   ):
    return image
  elif isinstance(_SCREAMING_SNAKE_CASE		,     PIL.Image.Image   ):
    a__:     Optional[int]										=	[image]

  a__:     str										=	[trans(img.convert('RGB'   )   ) for img in image]
  a__:     Any										=	torch.stack(_SCREAMING_SNAKE_CASE   )
  return image




class    __snake_case       (     __lowerCAmelCase				):



      def __init__(						self    ,			lowercase    ,			lowercase)	->			Optional[int]:





        '''simple docstring'''





        super().__init__()

        # make sure scheduler can always be converted to DDIM
        a__:     Dict										=	DDIMScheduler.from_config(scheduler.config)

        self.register_modules(unet=lowercase    ,			scheduler=lowercase)



      def   lowerCamelCase_   (						self    ,			lowercase)	->			int:





        '''simple docstring'''





        if strength < 0 or strength > 1:
          raise ValueError(f'The value of strength should in [0.0, 1.0] but is {strength}')



      def   lowerCamelCase_   (						self    ,			lowercase    ,			lowercase    ,			lowercase)	->			Dict:





        '''simple docstring'''





        a__:     int										=	min(int(num_inference_steps * strength)    ,			lowercase)

        a__:     Any										=	max(num_inference_steps - init_timestep    ,			0)
        a__:     Union[str, Any]										=	self.scheduler.timesteps[t_start:]

        return timesteps, num_inference_steps - t_start



      def   lowerCamelCase_   (						self    ,			lowercase    ,			lowercase    ,			lowercase    ,			lowercase    ,			lowercase    ,			lowercase=None)	->			List[Any]:





        '''simple docstring'''





        if not isinstance(lowercase    ,			(torch.Tensor, PIL.Image.Image, list)):
          raise ValueError(
              f'`image` has to be of type `torch.Tensor`, `PIL.Image.Image` or list but is {type(lowercase)}')

        a__:     Tuple										=	image.to(device=lowercase    ,			dtype=lowercase)

        if isinstance(lowercase    ,			lowercase) and len(lowercase) != batch_size:
          raise ValueError(
              f'You have passed a list of generators of length {len(lowercase)}, but requested an effective batch'
              f' size of {batch_size}. Make sure the batch size matches the length of the generators.')

        a__:     List[str]										=	init_latents.shape
        a__:     List[Any]										=	randn_tensor(lowercase    ,			generator=lowercase    ,			device=lowercase    ,			dtype=lowercase)

        # get latents
        print('add noise to latents at timestep'    ,			lowercase)
        a__:     int										=	self.scheduler.add_noise(lowercase    ,			lowercase    ,			lowercase)
        a__:     Dict										=	init_latents

        return latents



      @torch.no_grad()
      def __call__(						self    ,			lowercase = None    ,			lowercase = 0.8    ,			lowercase = 1    ,			lowercase = None    ,			lowercase = 0.0    ,			lowercase = 50    ,			lowercase = None    ,			lowercase = "pil"    ,			lowercase = True    ,			)	->			Union[ImagePipelineOutput, Tuple]:





        '''simple docstring'''





        self.check_inputs(lowercase)

        # 2. Preprocess image
        a__:     Tuple										=	preprocess(lowercase)

        # 3. set timesteps
        self.scheduler.set_timesteps(lowercase    ,			device=self.device)
        a__							,    a__:     Union[str, Any]										=	self.get_timesteps(lowercase    ,			lowercase    ,			self.device)
        a__:     Optional[int]										=	timesteps[:1].repeat(lowercase)

        # 4. Prepare latent variables
        a__:     Union[str, Any]										=	self.prepare_latents(lowercase    ,			lowercase    ,			lowercase    ,			self.unet.dtype    ,			self.device    ,			lowercase)
        a__:     Optional[Any]										=	latents

        # 5. Denoising loop
        for t in self.progress_bar(lowercase):
          # 1. predict noise model_output
          a__:     Dict										=	self.unet(lowercase    ,			lowercase).sample

          # 2. predict previous mean of image x_t-1 and add variance depending on eta
          # eta corresponds to η in paper and should be between [0, 1]
          # do x_t -> x_t-1
          a__:     Optional[Any]										=	self.scheduler.step(
              lowercase    ,			lowercase    ,			lowercase    ,			eta=lowercase    ,			use_clipped_model_output=lowercase    ,			generator=lowercase    ,			).prev_sample

        a__:     Union[str, Any]										=	(image / 2 + 0.5).clamp(0    ,			1)
        a__:     Optional[int]										=	image.cpu().permute(0    ,			2    ,			3    ,			1).numpy()
        if output_type == "pil":
          a__:     Dict										=	self.numpy_to_pil(lowercase)

        if not return_dict:
          return (image, latent_timestep.item())

        return ImagePipelineOutput(images=lowercase)


