
from __future__ import annotations

import numpy as np
from numpy import floataa
from numpy.typing import NDArray




def 	A_ (							snake_case							:   NDArray[floataa] ,      snake_case							:   NDArray[floataa] ,      snake_case							:   list[int] ,      snake_case							:   int ,      )      ->    list[float]:



						'''simple docstring'''

						__UpperCamelCase  ,							__UpperCamelCase       =			coefficient_matrix.shape
						__UpperCamelCase  ,							__UpperCamelCase       =			constant_matrix.shape

						if rowsa != colsa:
												__UpperCamelCase       =			f"Coefficient matrix dimensions must be nxn but received {rowsa}x{colsa}"
												raise ValueError(snake_case )

						if colsa != 1:
												__UpperCamelCase       =			f"Constant matrix must be nx1 but received {rowsa}x{colsa}"
												raise ValueError(snake_case )

						if rowsa != rowsa:
												__UpperCamelCase       =			(
												    '''Coefficient and constant matrices dimensions must be nxn and nx1 but '''
												    f"received {rowsa}x{colsa} and {rowsa}x{colsa}"
												)
												raise ValueError(snake_case )

						if len(snake_case ) != rowsa:
												__UpperCamelCase       =			(
												    '''Number of initial values must be equal to number of rows in coefficient '''
												    f"matrix but received {len(snake_case )} and {rowsa}"
												)
												raise ValueError(snake_case )

						if iterations <= 0:
												raise ValueError('''Iterations must be at least 1''' )

						__UpperCamelCase       =			np.concatenate(
						    (coefficient_matrix, constant_matrix) ,      axis=1 )

						__UpperCamelCase  ,							__UpperCamelCase       =			table.shape

						strictly_diagonally_dominant(snake_case )

						# Iterates the whole matrix for given number of times
						for _ in range(snake_case ):
												__UpperCamelCase       =			[]
												for row in range(snake_case ):
																		__UpperCamelCase       =			0
																		for col in range(snake_case ):
																								if col == row:
																														__UpperCamelCase       =			table[row][col]
																								elif col == cols - 1:
																														__UpperCamelCase       =			table[row][col]
																								else:
																														temp += (-1) * table[row][col] * init_val[col]
																		__UpperCamelCase       =			(temp + val) / denom
																		new_val.append(snake_case )
												__UpperCamelCase       =			new_val

						return [float(snake_case ) for i in new_val]




def 	A_ (							snake_case							:   NDArray[floataa] )      ->    bool:



						'''simple docstring'''

						__UpperCamelCase  ,							__UpperCamelCase       =			table.shape

						__UpperCamelCase       =			True

						for i in range(0 ,      snake_case ):
												__UpperCamelCase       =			0
												for j in range(0 ,      cols - 1 ):
																		if i == j:
																								continue
																		else:
																								total += table[i][j]

												if table[i][i] <= total:
																		raise ValueError('''Coefficient matrix is not strictly diagonally dominant''' )

						return is_diagonally_dominant


# Test Cases
if __name__ == "__main__":
				import doctest

				doctest.testmod()






from typing import List, Optional, Tuple, Union

import torch

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






class        SCREAMING_SNAKE_CASE__    (							SCREAMING_SNAKE_CASE_    ):

							"""simple docstring"""






							def __init__(  self     ,	SCREAMING_SNAKE_CASE_     ,	SCREAMING_SNAKE_CASE_			)->   str:





													'''simple docstring'''






													super().__init__()

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

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



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





													'''simple docstring'''






													if isinstance(self.unet.config.sample_size     ,	SCREAMING_SNAKE_CASE_			):
																			__UpperCamelCase       =			(
																			    batch_size,
																			    self.unet.config.in_channels,
																			    self.unet.config.sample_size,
																			    self.unet.config.sample_size,
																			)
													else:
																			__UpperCamelCase       =			(batch_size, self.unet.config.in_channels, *self.unet.config.sample_size)

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

													__UpperCamelCase       =			randn_tensor(SCREAMING_SNAKE_CASE_     ,	generator=SCREAMING_SNAKE_CASE_     ,	device=self.device     ,	dtype=self.unet.dtype			)

													# set step values
													self.scheduler.set_timesteps(SCREAMING_SNAKE_CASE_			)

													for t in self.progress_bar(self.scheduler.timesteps			):
																			# 1. predict noise model_output
																			__UpperCamelCase       =			self.unet(SCREAMING_SNAKE_CASE_     ,	SCREAMING_SNAKE_CASE_			).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
																			__UpperCamelCase       =			self.scheduler.step(
																			    SCREAMING_SNAKE_CASE_     ,	SCREAMING_SNAKE_CASE_     ,	SCREAMING_SNAKE_CASE_     ,	eta=SCREAMING_SNAKE_CASE_     ,	use_clipped_model_output=SCREAMING_SNAKE_CASE_     ,	generator=SCREAMING_SNAKE_CASE_			).prev_sample

													__UpperCamelCase       =			(image / 2 + 0.5).clamp(0     ,	1			)
													__UpperCamelCase       =			image.cpu().permute(0     ,	2     ,	3     ,	1			).numpy()
													if output_type == "pil":
																			__UpperCamelCase       =			self.numpy_to_pil(SCREAMING_SNAKE_CASE_			)

													if not return_dict:
																			return (image,)

													return ImagePipelineOutput(images=SCREAMING_SNAKE_CASE_			)




