
from typing import List, Optional, Tuple, Union

import torch

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







class 	A__				(	__magic_name__      ):






				def __init__(		self   : Any       ,	a   : Any       ,	a   : Optional[int]  ):






							'''simple docstring'''







							super().__init__()
							self.register_modules(unet=a       ,	scheduler=a  )






				@torch.no_grad()
				def __call__(		self   : Optional[Any]       ,	a   : int = 1       ,	a   : Optional[Union[torch.Generator, List[torch.Generator]]] = None       ,	a   : int = 1_000       ,	a   : Optional[str] = "pil"       ,	a   : bool = True       ,	):






							'''simple docstring'''







							if isinstance(self.unet.config.sample_size       ,	a  ):
										lowerCAmelCase__ : Union[str, Any]   =						(
										    batch_size,
										    self.unet.config.in_channels,
										    self.unet.config.sample_size,
										    self.unet.config.sample_size,
										)
							else:
										lowerCAmelCase__ : str   =						(batch_size, self.unet.config.in_channels, *self.unet.config.sample_size)

							if self.device.type == "mps":
										# randn does not work reproducibly on mps
										lowerCAmelCase__ : Optional[int]   =						randn_tensor(a       ,	generator=a  )
										lowerCAmelCase__ : Optional[int]   =						image.to(self.device  )
							else:
										lowerCAmelCase__ : Dict   =						randn_tensor(a       ,	generator=a       ,	device=self.device  )

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

							for t in self.progress_bar(self.scheduler.timesteps  ):
										# 1. predict noise model_output
										lowerCAmelCase__ : Tuple   =						self.unet(a       ,	a  ).sample

										# 2. compute previous image: x_t -> x_t-1
										lowerCAmelCase__ : Optional[Any]   =						self.scheduler.step(a       ,	a       ,	a       ,	generator=a  ).prev_sample

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

							if not return_dict:
										return (image,)

							return ImagePipelineOutput(images=a  )

from typing import Any

import numpy as np
def 					lowerCAmelCase__     (    SCREAMING_SNAKE_CASE_	)							->						bool:
			assert np.shape(SCREAMING_SNAKE_CASE_	)[0] == np.shape(SCREAMING_SNAKE_CASE_	)[1]

			# If matrix not symmetric, exit right away.
			if np.allclose(SCREAMING_SNAKE_CASE_			,				matrix.T	) is False:
						return False

			# Get eigenvalues and eignevectors for a symmetric matrix.
			lowerCAmelCase__ ,							lowerCAmelCase__ : Optional[int]   =						np.linalg.eigh(SCREAMING_SNAKE_CASE_	)

			# Check sign of all eigenvalues.
			# np.all returns a value of type np.bool_
			return bool(np.all(eigen_values > 0	)	)
def 					lowerCAmelCase__     (    SCREAMING_SNAKE_CASE_	)							->						Any:
			lowerCAmelCase__ : List[Any]   =						np.random.randn(SCREAMING_SNAKE_CASE_			,				SCREAMING_SNAKE_CASE_	)
			lowerCAmelCase__ : Any   =						np.dot(SCREAMING_SNAKE_CASE_			,				random_matrix.T	)
			assert _is_matrix_spd(SCREAMING_SNAKE_CASE_	)
			return spd_matrix
def 					lowerCAmelCase__     (    SCREAMING_SNAKE_CASE_			,				SCREAMING_SNAKE_CASE_			,				SCREAMING_SNAKE_CASE_ = 1_000			,				SCREAMING_SNAKE_CASE_ = 1e-8			,				)							->						Any:
			assert np.shape(SCREAMING_SNAKE_CASE_	)[0] == np.shape(SCREAMING_SNAKE_CASE_	)[1]
			assert np.shape(SCREAMING_SNAKE_CASE_	)[0] == np.shape(SCREAMING_SNAKE_CASE_	)[0]
			assert _is_matrix_spd(SCREAMING_SNAKE_CASE_	)

			# Initialize solution guess, residual, search direction.
			lowerCAmelCase__ : Optional[Any]   =						np.zeros((np.shape(SCREAMING_SNAKE_CASE_	)[0], 1)	)
			lowerCAmelCase__ : str   =						np.copy(SCREAMING_SNAKE_CASE_	)
			lowerCAmelCase__ : Dict   =						np.copy(SCREAMING_SNAKE_CASE_	)

			# Set initial errors in solution guess and residual.
			lowerCAmelCase__ : Union[str, Any]   =						1e9
			lowerCAmelCase__ : int   =						1e9
			lowerCAmelCase__ : Union[str, Any]   =						1e9

			# Set iteration counter to threshold number of iterations.
			lowerCAmelCase__ : List[str]   =						0

			while error > tol:
						# Save this value so we only calculate the matrix-vector product once.
						lowerCAmelCase__ : int   =						np.dot(SCREAMING_SNAKE_CASE_			,				SCREAMING_SNAKE_CASE_	)

						# The main algorithm.

						# Update search direction magnitude.
						lowerCAmelCase__ : List[str]   =						np.dot(ra.T			,				SCREAMING_SNAKE_CASE_	) / np.dot(pa.T			,				SCREAMING_SNAKE_CASE_	)
						# Update solution guess.
						lowerCAmelCase__ : Dict   =						xa + alpha * pa
						# Calculate new residual.
						lowerCAmelCase__ : Tuple   =						ra - alpha * w
						# Calculate new Krylov subspace scale.
						lowerCAmelCase__ : str   =						np.dot(r.T			,				SCREAMING_SNAKE_CASE_	) / np.dot(ra.T			,				SCREAMING_SNAKE_CASE_	)
						# Calculate new A conjuage search direction.
						lowerCAmelCase__ : Dict   =						r + beta * pa

						# Calculate errors.
						lowerCAmelCase__ : List[str]   =						np.linalg.norm(r - ra	)
						lowerCAmelCase__ : Tuple   =						np.linalg.norm(x - xa	)
						lowerCAmelCase__ : str   =						np.maximum(SCREAMING_SNAKE_CASE_			,				SCREAMING_SNAKE_CASE_	)

						# Update variables.
						lowerCAmelCase__ : List[Any]   =						np.copy(SCREAMING_SNAKE_CASE_	)
						lowerCAmelCase__ : Dict   =						np.copy(SCREAMING_SNAKE_CASE_	)
						lowerCAmelCase__ : str   =						np.copy(SCREAMING_SNAKE_CASE_	)

						# Update number of iterations.
						iterations += 1
						if iterations > max_iterations:
									break

			return x
def 					lowerCAmelCase__     (    )							->						None:
			lowerCAmelCase__ : Optional[Any]   =						3
			lowerCAmelCase__ : Optional[int]   =						_create_spd_matrix(SCREAMING_SNAKE_CASE_	)
			lowerCAmelCase__ : Tuple   =						np.random.randn(SCREAMING_SNAKE_CASE_			,				1	)
			lowerCAmelCase__ : int   =						np.dot(SCREAMING_SNAKE_CASE_			,				SCREAMING_SNAKE_CASE_	)

			# Numpy solution.
			lowerCAmelCase__ : Optional[Any]   =						np.linalg.solve(SCREAMING_SNAKE_CASE_			,				SCREAMING_SNAKE_CASE_	)

			# Our implementation.
			lowerCAmelCase__ : Optional[int]   =						conjugate_gradient(SCREAMING_SNAKE_CASE_			,				SCREAMING_SNAKE_CASE_	)

			# Ensure both solutions are close to x_true (and therefore one another).
			assert np.linalg.norm(x_numpy - x_true	) <= 1e-6
			assert np.linalg.norm(x_conjugate_gradient - x_true	) <= 1e-6


if __name__ == "__main__":
					import doctest

					doctest.testmod()
					test_conjugate_gradient()