





from __future__ import annotations

from typing import Any

class 	A_       :
	def __init__(    self							,					_A							,					_A							,					_A = 0		):






				'''simple docstring'''







				UpperCAmelCase		,			UpperCAmelCase   		=				row, column
				UpperCAmelCase   		=				[[default_value for c in range(_A		)] for r in range(_A		)]
	def __str__(    self		):






				'''simple docstring'''







				UpperCAmelCase   		=				F"""Matrix consist of {self.row} rows and {self.column} columns\n"""

				# Make string identifier
				UpperCAmelCase   		=				0
				for row_vector in self.array:
							for obj in row_vector:
										UpperCAmelCase   		=				max(_A							,					len(str(_A		)		)		)
				UpperCAmelCase   		=				F"""%{max_element_length}s"""

				# Make string and return
				def single_line(_A		) -> str:
							nonlocal string_format_identifier
							UpperCAmelCase   		=				'''['''
							line += ", ".join(string_format_identifier % (obj,) for obj in row_vector		)
							line += "]"
							return line

				s += "\n".join(single_line(_A		) for row_vector in self.array		)
				return s
	def __repr__(    self		):






				'''simple docstring'''







				return str(self		)
	def      _lowercase				(    self							,					_A		):






				'''simple docstring'''







				if not (isinstance(_A							,					(list, tuple)		) and len(_A		) == 2):
							return False
				elif not (0 <= loc[0] < self.row and 0 <= loc[1] < self.column):
							return False
				else:
							return True
	def __getitem__(    self							,					_A		):






				'''simple docstring'''







				assert self.validate_indicies(_A		)
				return self.array[loc[0]][loc[1]]
	def __setitem__(    self							,					_A							,					_A		):






				'''simple docstring'''







				assert self.validate_indicies(_A		)
				UpperCAmelCase   		=				value
	def __add__(    self							,					_A		):






				'''simple docstring'''







				assert isinstance(_A							,					_A		)
				assert self.row == another.row and self.column == another.column

				# Add
				UpperCAmelCase   		=				Matrix(self.row							,					self.column		)
				for r in range(self.row		):
							for c in range(self.column		):
										UpperCAmelCase   		=				self[r, c] + another[r, c]
				return result
	def __neg__(    self		):






				'''simple docstring'''







				UpperCAmelCase   		=				Matrix(self.row							,					self.column		)
				for r in range(self.row		):
							for c in range(self.column		):
										UpperCAmelCase   		=				-self[r, c]
				return result
	def __sub__(    self							,					_A		):






				'''simple docstring'''







				return self + (-another)
	def __mul__(    self							,					_A		):






				'''simple docstring'''







				if isinstance(_A							,					(int, float)		):  # Scalar multiplication
							UpperCAmelCase   		=				Matrix(self.row							,					self.column		)
							for r in range(self.row		):
										for c in range(self.column		):
													UpperCAmelCase   		=				self[r, c] * another
							return result
				elif isinstance(_A							,					_A		):  # Matrix multiplication
							assert self.column == another.row
							UpperCAmelCase   		=				Matrix(self.row							,					another.column		)
							for r in range(self.row		):
										for c in range(another.column		):
													for i in range(self.column		):
																result[r, c] += self[r, i] * another[i, c]
							return result
				else:
							UpperCAmelCase   		=				F"""Unsupported type given for another ({type(_A		)})"""
							raise TypeError(_A		)
	def      _lowercase				(    self		):






				'''simple docstring'''







				UpperCAmelCase   		=				Matrix(self.column							,					self.row		)
				for r in range(self.row		):
							for c in range(self.column		):
										UpperCAmelCase   		=				self[r, c]
				return result







	def      _lowercase				(    self							,					_A							,					_A		):






				'''simple docstring'''







				assert isinstance(_A							,					_A		) and isinstance(_A							,					_A		)
				assert self.row == self.column == u.row == v.row  # u, v should be column vector
				assert u.column == v.column == 1  # u, v should be column vector

				# Calculate
				UpperCAmelCase   		=				v.transpose()
				UpperCAmelCase   		=				(v_t * self * u)[0, 0] + 1
				if numerator_factor == 0:
							return None  # It's not invertable
				return self - ((self * u) * (v_t * self) * (1.0 / numerator_factor))


# Testing
if __name__ == "__main__":





				def 						__SCREAMING_SNAKE_CASE  (				)  ->				None:







							'''simple docstring'''

							UpperCAmelCase   		=				Matrix(3			,			3			,			0 )
							for i in range(3 ):
										UpperCAmelCase   		=				1
							print(F"""a^(-1) is {ainv}""" )
							# u, v
							UpperCAmelCase   		=				Matrix(3			,			1			,			0 )
							UpperCAmelCase		,			UpperCAmelCase		,			UpperCAmelCase   		=				1, 2, -3
							UpperCAmelCase   		=				Matrix(3			,			1			,			0 )
							UpperCAmelCase		,			UpperCAmelCase		,			UpperCAmelCase   		=				4, -2, 5
							print(F"""u is {u}""" )
							print(F"""v is {v}""" )
							print(F"""uv^T is {u * v.transpose()}""" )
							# Sherman Morrison
							print(F"""(a + uv^T)^(-1) is {ainv.sherman_morrison(UpperCamelCase__			,			UpperCamelCase__ )}""" )





				def 						__SCREAMING_SNAKE_CASE  (				)  ->				None:







							'''simple docstring'''

							import doctest

							doctest.testmod()






				testa()










from typing import List, Optional, Tuple, Union

import torch

from ...models import UNetaDModel
from ...schedulers import KarrasVeScheduler
from ...utils import randn_tensor
from ..pipeline_utils import DiffusionPipeline, ImagePipelineOutput

class 	A_       (a_			):
	UpperCAmelCase__					=			42
	UpperCAmelCase__					=			42
	def __init__(    self							,					_A							,					_A		):






				'''simple docstring'''







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







	@torch.no_grad()
	def __call__(    self							,					_A = 1							,					_A = 5_0							,					_A = None							,					_A = "pil"							,					_A = True							,					**_A							,					):






				'''simple docstring'''







				UpperCAmelCase   		=				self.unet.config.sample_size
				UpperCAmelCase   		=				(batch_size, 3, img_size, img_size)

				UpperCAmelCase   		=				self.unet

				# sample x_0 ~ N(0, sigma_0^2 * I)
				UpperCAmelCase   		=				randn_tensor(_A							,					generator=_A							,					device=self.device		) * self.scheduler.init_noise_sigma

				self.scheduler.set_timesteps(_A		)

				for t in self.progress_bar(self.scheduler.timesteps		):
							# here sigma_t == t_i from the paper
							UpperCAmelCase   		=				self.scheduler.schedule[t]
							UpperCAmelCase   		=				self.scheduler.schedule[t - 1] if t > 0 else 0

							# 1. Select temporarily increased noise level sigma_hat
							# 2. Add new noise to move from sample_i to sample_hat
							UpperCAmelCase		,			UpperCAmelCase   		=				self.scheduler.add_noise_to_input(_A							,					_A							,					generator=_A		)

							# 3. Predict the noise residual given the noise magnitude `sigma_hat`
							# The model inputs and output are adjusted by following eq. (213) in [1].
							UpperCAmelCase   		=				(sigma_hat / 2) * model((sample_hat + 1) / 2							,					sigma_hat / 2		).sample

							# 4. Evaluate dx/dt at sigma_hat
							# 5. Take Euler step from sigma to sigma_prev
							UpperCAmelCase   		=				self.scheduler.step(_A							,					_A							,					_A							,					_A		)

							if sigma_prev != 0:
										# 6. Apply 2nd order correction
										# The model inputs and output are adjusted by following eq. (213) in [1].
										UpperCAmelCase   		=				(sigma_prev / 2) * model((step_output.prev_sample + 1) / 2							,					sigma_prev / 2		).sample
										UpperCAmelCase   		=				self.scheduler.step_correct(
										    _A							,					_A							,					_A							,					_A							,					step_output.prev_sample							,					step_output['''derivative''']							,					)
							UpperCAmelCase   		=				step_output.prev_sample

				UpperCAmelCase   		=				(sample / 2 + 0.5).clamp(0							,					1		)
				UpperCAmelCase   		=				sample.cpu().permute(0							,					2							,					3							,					1		).numpy()
				if output_type == "pil":
							UpperCAmelCase   		=				self.numpy_to_pil(_A		)

				if not return_dict:
							return (image,)

				return ImagePipelineOutput(images=_A		)



