




from typing import Any

import numpy as np






def    snake_case   (				A     )				->				bool:




	'''simple docstring'''


	assert np.shape(A     )[0] == np.shape(A     )[1]

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

	# Get eigenvalues and eignevectors for a symmetric matrix.
	lowerCamelCase_  ,     lowerCamelCase_				:						Tuple				  =				np.linalg.eigh(A     )

	# Check sign of all eigenvalues.
	# np.all returns a value of type np.bool_
	return bool(np.all(eigen_values > 0     )     )






def    snake_case   (				A     )				->				Any:




	'''simple docstring'''


	lowerCamelCase_				:						Optional[int]				  =				np.random.randn(A		,  A     )
	lowerCamelCase_				:						List[Any]				  =				np.dot(A		,  random_matrix.T     )
	assert _is_matrix_spd(A     )
	return spd_matrix






def    snake_case   (				A		,  A		,  A = 1000		,  A = 1e-8		,  )				->				Any:




	'''simple docstring'''


	assert np.shape(A     )[0] == np.shape(A     )[1]
	assert np.shape(A     )[0] == np.shape(A     )[0]
	assert _is_matrix_spd(A     )

	# Initialize solution guess, residual, search direction.
	lowerCamelCase_				:						List[str]				  =				np.zeros((np.shape(A     )[0], 1)     )
	lowerCamelCase_				:						int				  =				np.copy(A     )
	lowerCamelCase_				:						Optional[int]				  =				np.copy(A     )

	# Set initial errors in solution guess and residual.
	lowerCamelCase_				:						Dict				  =				1e9
	lowerCamelCase_				:						int				  =				1e9
	lowerCamelCase_				:						Dict				  =				1e9

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

	while error > tol:
		# Save this value so we only calculate the matrix-vector product once.
		lowerCamelCase_				:						List[Any]				  =				np.dot(A		,  A     )

		# The main algorithm.

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

		# Calculate errors.
		lowerCamelCase_				:						Union[str, Any]				  =				np.linalg.norm(r - ra     )
		lowerCamelCase_				:						List[Any]				  =				np.linalg.norm(x - xa     )
		lowerCamelCase_				:						str				  =				np.maximum(A		,  A     )

		# Update variables.
		lowerCamelCase_				:						Union[str, Any]				  =				np.copy(A     )
		lowerCamelCase_				:						Any				  =				np.copy(A     )
		lowerCamelCase_				:						int				  =				np.copy(A     )

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

	return x






def    snake_case   (				)				->				None:




	'''simple docstring'''


	lowerCamelCase_				:						int				  =				3
	lowerCamelCase_				:						List[str]				  =				_create_spd_matrix(A     )
	lowerCamelCase_				:						List[str]				  =				np.random.randn(A		,  1     )
	lowerCamelCase_				:						str				  =				np.dot(A		,  A     )

	# Numpy solution.
	lowerCamelCase_				:						Dict				  =				np.linalg.solve(A		,  A     )

	# Our implementation.
	lowerCamelCase_				:						Tuple				  =				conjugate_gradient(A		,  A     )

	# 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()





import copy

from ...configuration_utils import PretrainedConfig
from ...utils import logging
from ..auto.configuration_auto import AutoConfig


UpperCAmelCase :				Union[str, Any]							=logging.get_logger(__name__)


class    _lowercase (a_   ):
				'''simple docstring'''







				lowercase__     =    """speech-encoder-decoder"""
				lowercase__     =    True

				def __init__(			self  ,			**snake_case__     ):

									'''simple docstring'''


									super().__init__(**snake_case__     )
									if "encoder" not in kwargs or "decoder" not in kwargs:
														raise ValueError(
														    F"""A configuraton of type {self.model_type} cannot be instantiated because not both `encoder` and"""
														    F""" `decoder` sub-configurations are passed, but only {kwargs}"""     )

									UpperCamelCase_			= kwargs.pop("encoder"     )
									UpperCamelCase_			= encoder_config.pop("model_type"     )
									UpperCamelCase_			= kwargs.pop("decoder"     )
									UpperCamelCase_			= decoder_config.pop("model_type"     )

									UpperCamelCase_			= AutoConfig.for_model(snake_case__  ,			**snake_case__     )
									UpperCamelCase_			= AutoConfig.for_model(snake_case__  ,			**snake_case__     )
									UpperCamelCase_			= True

				@classmethod
				def    _lowerCamelCase       (			cls  ,			snake_case__  ,			snake_case__  ,			**snake_case__     ):

									'''simple docstring'''


									logger.info("Setting `config.is_decoder=True` and `config.add_cross_attention=True` for decoder_config"     )
									UpperCamelCase_			= True
									UpperCamelCase_			= True

									return cls(encoder=encoder_config.to_dict()  ,			decoder=decoder_config.to_dict()  ,			**snake_case__     )

				def    _lowerCamelCase       (			self     ):

									'''simple docstring'''


									UpperCamelCase_			= copy.deepcopy(self.__dict__     )
									UpperCamelCase_			= self.encoder.to_dict()
									UpperCamelCase_			= self.decoder.to_dict()
									UpperCamelCase_			= self.__class__.model_type
									return output
