






from dataclasses import dataclass
from typing import Optional, Tuple, Union

import numpy as np
import torch

from ..configuration_utils import ConfigMixin, register_to_config
from ..utils import BaseOutput, randn_tensor
from .scheduling_utils import SchedulerMixin




@dataclass
class 					UpperCamelCase_ (     snake_case_							):



	'''simple docstring'''




	lowerCAmelCase						=					42
	lowerCAmelCase						=					42
	lowerCAmelCase						=					None






class 					UpperCamelCase_ (     snake_case_			,   snake_case_							):



	'''simple docstring'''




	lowerCAmelCase						=					2




	@register_to_config
	def __init__(			self			,     a = 0.02			,     a = 1_00			,     a = 1.007			,     a = 80			,     a = 0.05			,     a = 50			,     )			->       List[Any]:
								# standard deviation of the initial noise distribution
								snake_case_           =				sigma_max

								# setable values
								snake_case_           =				None
								snake_case_           =				None
								snake_case_           =				None  # sigma(t_i)




	def 				_UpperCamelCase     (			self			,     a			,     a = None   )			->       torch.FloatTensor:
								return sample




	def 				_UpperCamelCase     (			self			,     a			,     a = None   )			->       Optional[int]:
								snake_case_           =				num_inference_steps
								snake_case_           =				np.arange(0			,     self.num_inference_steps   )[::-1].copy()
								snake_case_           =				torch.from_numpy(a   ).to(a   )
								snake_case_           =				[
								    (
								        self.config.sigma_max**2
								        * (self.config.sigma_min**2 / self.config.sigma_max**2) ** (i / (num_inference_steps - 1))
								    )
								    for i in self.timesteps
								]
								snake_case_           =				torch.tensor(a			,     dtype=torch.floataa			,     device=a   )




	def 				_UpperCamelCase     (			self			,     a			,     a			,     a = None   )			->       Tuple[torch.FloatTensor, float]:
								if self.config.s_min <= sigma <= self.config.s_max:
															snake_case_           =				min(self.config.s_churn / self.num_inference_steps			,     2**0.5 - 1   )
								else:
															snake_case_           =				0

								# sample eps ~ N(0, S_noise^2 * I)
								snake_case_           =				self.config.s_noise * randn_tensor(sample.shape			,     generator=a   ).to(sample.device   )
								snake_case_           =				sigma + gamma * sigma
								snake_case_           =				sample + ((sigma_hat**2 - sigma**2) ** 0.5 * eps)

								return sample_hat, sigma_hat




	def 				_UpperCamelCase     (			self			,     a			,     a			,     a			,     a			,     a = True			,     )			->       Union[KarrasVeOutput, Tuple]:
								snake_case_           =				sample_hat + sigma_hat * model_output
								snake_case_           =				(sample_hat - pred_original_sample) / sigma_hat
								snake_case_           =				sample_hat + (sigma_prev - sigma_hat) * derivative

								if not return_dict:
															return (sample_prev, derivative)

								return KarrasVeOutput(
								    prev_sample=a			,     derivative=a			,     pred_original_sample=a   )




	def 				_UpperCamelCase     (			self			,     a			,     a			,     a			,     a			,     a			,     a			,     a = True			,     )			->       Union[KarrasVeOutput, Tuple]:
								snake_case_           =				sample_prev + sigma_prev * model_output
								snake_case_           =				(sample_prev - pred_original_sample) / sigma_prev
								snake_case_           =				sample_hat + (sigma_prev - sigma_hat) * (0.5 * derivative + 0.5 * derivative_corr)

								if not return_dict:
															return (sample_prev, derivative)

								return KarrasVeOutput(
								    prev_sample=a			,     derivative=a			,     pred_original_sample=a   )






	def 				_UpperCamelCase     (			self			,     a			,     a			,     a   )			->       Dict:
								raise NotImplementedError()













import unittest

import numpy as np





def 		__UpperCAmelCase     (	a_				,	a_				,	a_				,	a_ = None				,	):
							snake_case_           =				np.shape(a_)
							snake_case_           =				np.shape(a_)
							snake_case_           =				np.shape(a_)

							if shape_a[0] != shape_b[0]:
														snake_case_           =				(
														    'Expected the same number of rows for A and B. '
														    f'''Instead found A of size {shape_a} and B of size {shape_b}'''
														)
														raise ValueError(a_)

							if shape_b[1] != shape_c[1]:
														snake_case_           =				(
														    'Expected the same number of columns for B and C. '
														    f'''Instead found B of size {shape_b} and C of size {shape_c}'''
														)
														raise ValueError(a_)

							snake_case_           =				pseudo_inv
							if a_inv is None:
														try:
																					snake_case_           =				np.linalg.inv(a_)
														except np.linalg.LinAlgError:
																					raise ValueError(
																					    'Input matrix A is not invertible. Cannot compute Schur complement.')

							return mat_c - mat_b.T @ a_inv @ mat_b




class 					UpperCamelCase_ (     unittest.TestCase							):



	'''simple docstring'''




	def 				_UpperCamelCase     (			self   )			->       None:
								snake_case_           =				np.array([[1, 2, 1], [2, 1, 2], [3, 2, 4]]   )
								snake_case_           =				np.array([[0, 3], [3, 0], [2, 3]]   )
								snake_case_           =				np.array([[2, 1], [6, 3]]   )

								snake_case_           =				schur_complement(a			,     a			,     a   )

								snake_case_           =				np.block([[a, b], [b.T, c]]   )

								snake_case_           =				np.linalg.det(a   )
								snake_case_           =				np.linalg.det(a   )
								snake_case_           =				np.linalg.det(a   )

								self.assertAlmostEqual(a			,     det_a * det_s   )




	def 				_UpperCamelCase     (			self   )			->       None:
								snake_case_           =				np.array([[1, 2, 1], [2, 1, 2], [3, 2, 4]]   )
								snake_case_           =				np.array([[0, 3], [3, 0], [2, 3]]   )
								snake_case_           =				np.array([[2, 1], [6, 3]]   )

								with self.assertRaises(a   ):
															schur_complement(a			,     a			,     a   )






	def 				_UpperCamelCase     (			self   )			->       None:
								snake_case_           =				np.array([[1, 2, 1], [2, 1, 2], [3, 2, 4]]   )
								snake_case_           =				np.array([[0, 3], [3, 0], [2, 3]]   )
								snake_case_           =				np.array([[2, 1, 3], [6, 3, 5]]   )

								with self.assertRaises(a   ):
															schur_complement(a			,     a			,     a   )


if __name__ == "__main__":
	import doctest

	doctest.testmod()
	unittest.main()





