


import inspect
from typing import List, Optional, Tuple, Union

import numpy as np
import PIL
import torch
import torch.utils.checkpoint

from ...models import UNetaDModel, VQModel
from ...schedulers import (
    DDIMScheduler,
    DPMSolverMultistepScheduler,
    EulerAncestralDiscreteScheduler,
    EulerDiscreteScheduler,
    LMSDiscreteScheduler,
    PNDMScheduler,
)
from ...utils import PIL_INTERPOLATION, randn_tensor
from ..pipeline_utils import DiffusionPipeline, ImagePipelineOutput


def   _SCREAMING_SNAKE_CASE	( SCREAMING_SNAKE_CASE       ):
  A_     ,       A_      :				Any		     =					image.size
  A_     ,       A_      :				Tuple		     =					(x - x % 32 for x in (w, h))  # resize to integer multiple of 32
  A_      :				Union[str, Any]		     =					image.resize((w, h) ,			resample=PIL_INTERPOLATION['''lanczos''']       )
  A_      :				Any		     =					np.array(SCREAMING_SNAKE_CASE       ).astype(np.floataa       ) / 2_5_5.0
  A_      :				List[Any]		     =					image[None].transpose(0 ,			3 ,			1 ,			2       )
  A_      :				Dict		     =					torch.from_numpy(SCREAMING_SNAKE_CASE       )
  return 2.0 * image - 1.0







class   _lowerCamelCase (					UpperCamelCase			):




       """simple docstring"""



       def __init__(      self				,       _SCREAMING_SNAKE_CASE				,       _SCREAMING_SNAKE_CASE				,       _SCREAMING_SNAKE_CASE				,       )->List[Any]:




         '''simple docstring'''





         super().__init__()
         self.register_modules(vqvae=_SCREAMING_SNAKE_CASE				,       unet=_SCREAMING_SNAKE_CASE				,       scheduler=_SCREAMING_SNAKE_CASE		)







       @torch.no_grad()
       def __call__(      self				,       _SCREAMING_SNAKE_CASE = None				,       _SCREAMING_SNAKE_CASE = 1				,       _SCREAMING_SNAKE_CASE = 100				,       _SCREAMING_SNAKE_CASE = 0.0				,       _SCREAMING_SNAKE_CASE = None				,       _SCREAMING_SNAKE_CASE = "pil"				,       _SCREAMING_SNAKE_CASE = True				,       )->Union[Tuple, ImagePipelineOutput]:




         '''simple docstring'''





         if isinstance(_SCREAMING_SNAKE_CASE				,       PIL.Image.Image		):
           A_      :				int		     =					1
         elif isinstance(_SCREAMING_SNAKE_CASE				,       torch.Tensor		):
           A_      :				Optional[int]		     =					image.shape[0]
         else:
           raise ValueError(F'''`image` has to be of type `PIL.Image.Image` or `torch.Tensor` but is {type(_SCREAMING_SNAKE_CASE		)}'''		)

         if isinstance(_SCREAMING_SNAKE_CASE				,       PIL.Image.Image		):
           A_      :				Tuple		     =					preprocess(_SCREAMING_SNAKE_CASE		)

         A_     ,       A_      :				Any		     =					image.shape[-2:]

         # in_channels should be 6: 3 for latents, 3 for low resolution image
         A_      :				str		     =					(batch_size, self.unet.config.in_channels // 2, height, width)
         A_      :				Dict		     =					next(self.unet.parameters()		).dtype

         A_      :				Union[str, Any]		     =					randn_tensor(_SCREAMING_SNAKE_CASE				,       generator=_SCREAMING_SNAKE_CASE				,       device=self.device				,       dtype=_SCREAMING_SNAKE_CASE		)

         A_      :				str		     =					image.to(device=self.device				,       dtype=_SCREAMING_SNAKE_CASE		)

         # set timesteps and move to the correct device
         self.scheduler.set_timesteps(_SCREAMING_SNAKE_CASE				,       device=self.device		)
         A_      :				List[str]		     =					self.scheduler.timesteps

         # scale the initial noise by the standard deviation required by the scheduler
         A_      :				Optional[int]		     =					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]
         A_      :				Tuple		     =					'''eta''' in set(inspect.signature(self.scheduler.step		).parameters.keys()		)
         A_      :				List[Any]		     =					{}
         if accepts_eta:
           A_      :				Optional[Any]		     =					eta

         for t in self.progress_bar(_SCREAMING_SNAKE_CASE		):
           # concat latents and low resolution image in the channel dimension.
           A_      :				Optional[Any]		     =					torch.cat([latents, image]				,       dim=1		)
           A_      :				List[str]		     =					self.scheduler.scale_model_input(_SCREAMING_SNAKE_CASE				,       _SCREAMING_SNAKE_CASE		)
           # predict the noise residual
           A_      :				Optional[Any]		     =					self.unet(_SCREAMING_SNAKE_CASE				,       _SCREAMING_SNAKE_CASE		).sample
           # compute the previous noisy sample x_t -> x_t-1
           A_      :				str		     =					self.scheduler.step(_SCREAMING_SNAKE_CASE				,       _SCREAMING_SNAKE_CASE				,       _SCREAMING_SNAKE_CASE				,       **_SCREAMING_SNAKE_CASE		).prev_sample

         # decode the image latents with the VQVAE
         A_      :				Tuple		     =					self.vqvae.decode(_SCREAMING_SNAKE_CASE		).sample
         A_      :				Optional[int]		     =					torch.clamp(_SCREAMING_SNAKE_CASE				,       -1.0				,       1.0		)
         A_      :				Dict		     =					image / 2 + 0.5
         A_      :				Dict		     =					image.cpu().permute(0				,       2				,       3				,       1		).numpy()

         if output_type == "pil":
           A_      :				Optional[int]		     =					self.numpy_to_pil(_SCREAMING_SNAKE_CASE		)

         if not return_dict:
           return (image,)

         return ImagePipelineOutput(images=_SCREAMING_SNAKE_CASE		)








def   _SCREAMING_SNAKE_CASE	( SCREAMING_SNAKE_CASE       ):
  A_      :				List[Any]		     =					current_set.copy()
  for row_index, row in enumerate(SCREAMING_SNAKE_CASE       ):
    A_      :				List[str]		     =					row[0]
    for column_index, column in enumerate(SCREAMING_SNAKE_CASE       ):
      if magnitude == 0:
        A_      :				Union[str, Any]		     =					column
        continue
      A_      :				Dict		     =					column / magnitude
    # Subtract to cancel term
  A_      :				Union[str, Any]		     =					current_set[0]
  A_      :				Tuple		     =					[first_row]
  A_      :				int		     =					current_set[1::]
  for row in current_set:
    A_      :				Tuple		     =					[]
    # If first term is 0, it is already in form we want, so we preserve it
    if row[0] == 0:
      final_set.append(SCREAMING_SNAKE_CASE       )
      continue
    for column_index in range(len(SCREAMING_SNAKE_CASE       )       ):
      temp_row.append(first_row[column_index] - row[column_index]       )
    final_set.append(SCREAMING_SNAKE_CASE       )
  # Create next recursion iteration set
  if len(final_set[0]       ) != 3:
    A_      :				Optional[Any]		     =					final_set[0]
    A_      :				Any		     =					[]
    A_      :				str		     =					[]
    for row in final_set[1::]:
      current_first_column.append(row[0]       )
      next_iteration.append(row[1::]       )
    A_      :				Optional[Any]		     =					simplify(SCREAMING_SNAKE_CASE       )
    for i in range(len(SCREAMING_SNAKE_CASE       )       ):
      resultant[i].insert(0 ,			current_first_column[i]       )
    resultant.insert(0 ,			SCREAMING_SNAKE_CASE       )
    A_      :				List[Any]		     =					resultant
  return final_set


def   _SCREAMING_SNAKE_CASE	( SCREAMING_SNAKE_CASE       ):
  if len(SCREAMING_SNAKE_CASE       ) == 0:
    raise IndexError('''solve_simultaneous() requires n lists of length n+1'''       )
  A_      :				str		     =					len(SCREAMING_SNAKE_CASE       ) + 1
  if any(len(SCREAMING_SNAKE_CASE       ) != _length for item in equations       ):
    raise IndexError('''solve_simultaneous() requires n lists of length n+1'''       )
  for row in equations:
    if any(not isinstance(SCREAMING_SNAKE_CASE ,			(int, float)       ) for column in row       ):
      raise ValueError('''solve_simultaneous() requires lists of integers'''       )
  if len(SCREAMING_SNAKE_CASE       ) == 1:
    return [equations[0][-1] / equations[0][0]]
  A_      :				Dict		     =					equations.copy()
  if any(0 in row for row in data_set       ):
    A_      :				Tuple		     =					data_set.copy()
    A_      :				Optional[Any]		     =					[]
    for row_index, row in enumerate(SCREAMING_SNAKE_CASE       ):
      if 0 not in row:
        A_      :				str		     =					data_set.pop(SCREAMING_SNAKE_CASE       )
        break
    if not full_row:
      raise ValueError('''solve_simultaneous() requires at least 1 full equation'''       )
    data_set.insert(0 ,			SCREAMING_SNAKE_CASE       )
  A_      :				int		     =					data_set.copy()
  A_      :				Dict		     =					simplify(SCREAMING_SNAKE_CASE       )
  A_      :				Dict		     =					simplified[::-1]
  A_      :				list		     =					[]
  for row in simplified:
    A_      :				Union[str, Any]		     =					row[-1]
    if not solutions:
      if row[-2] == 0:
        solutions.append(0       )
        continue
      solutions.append(current_solution / row[-2]       )
      continue
    A_      :				Optional[Any]		     =					row.copy()[: len(SCREAMING_SNAKE_CASE       ) - 1 :]
    while temp_row[0] == 0:
      temp_row.pop(0       )
    if len(SCREAMING_SNAKE_CASE       ) == 0:
      solutions.append(0       )
      continue
    A_      :				int		     =					temp_row[1::]
    A_      :				int		     =					temp_row[::-1]
    for column_index, column in enumerate(SCREAMING_SNAKE_CASE       ):
      current_solution -= column * solutions[column_index]
    solutions.append(SCREAMING_SNAKE_CASE       )
  A_      :				Union[str, Any]		     =					[]
  for item in solutions:
    final.append(float(round(SCREAMING_SNAKE_CASE ,			5       )       )       )
  return final[::-1]


if __name__ == "__main__":
     import doctest

     doctest.testmod()
     UpperCamelCase								=	[
         [2, 1, 1, 1, 1, 4],
         [1, 2, 1, 1, 1, 5],
         [1, 1, 2, 1, 1, 6],
         [1, 1, 1, 2, 1, 7],
         [1, 1, 1, 1, 2, 8],
     ]
     print(solve_simultaneous(eq))
     print(solve_simultaneous([[4, 2]]))




