
'''simple docstring'''
from typing import Any

import numpy as np







def 						A_(			A		:						np.ndarray):
							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.
							UpperCamelCase       ,     UpperCamelCase					       =			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 						A_(			A		:						int):
							UpperCamelCase					       =			np.random.randn(A						,			A)
							UpperCamelCase					       =			np.dot(A						,			random_matrix.T)
							assert _is_matrix_spd(A)
							return spd_matrix







def 						A_(			A		:						np.ndarray						,			A		:						np.ndarray						,			A		:						int = 1000						,			A		:						float = 1E-8						,			):
							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.
							UpperCamelCase					       =			np.zeros((np.shape(A)[0], 1))
							UpperCamelCase					       =			np.copy(A)
							UpperCamelCase					       =			np.copy(A)

							# Set initial errors in solution guess and residual.
							UpperCamelCase					       =			1E9
							UpperCamelCase					       =			1E9
							UpperCamelCase					       =			1E9

							# Set iteration counter to threshold number of iterations.
							UpperCamelCase					       =			0

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

														# The main algorithm.

														# Update search direction magnitude.
														UpperCamelCase					       =			np.dot(ra.T						,			A) / np.dot(pa.T						,			A)
														# Update solution guess.
														UpperCamelCase					       =			xa + alpha * pa
														# Calculate new residual.
														UpperCamelCase					       =			ra - alpha * w
														# Calculate new Krylov subspace scale.
														UpperCamelCase					       =			np.dot(r.T						,			A) / np.dot(ra.T						,			A)
														# Calculate new A conjuage search direction.
														UpperCamelCase					       =			r + beta * pa

														# Calculate errors.
														UpperCamelCase					       =			np.linalg.norm(r - ra)
														UpperCamelCase					       =			np.linalg.norm(x - xa)
														UpperCamelCase					       =			np.maximum(A						,			A)

														# Update variables.
														UpperCamelCase					       =			np.copy(A)
														UpperCamelCase					       =			np.copy(A)
														UpperCamelCase					       =			np.copy(A)

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

							return x







def 						A_(			):
							UpperCamelCase					       =			3
							UpperCamelCase					       =			_create_spd_matrix(A)
							UpperCamelCase					       =			np.random.randn(A						,			1)
							UpperCamelCase					       =			np.dot(A						,			A)

							# Numpy solution.
							UpperCamelCase					       =			np.linalg.solve(A						,			A)

							# Our implementation.
							UpperCamelCase					       =			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()






'''simple docstring'''
import copy

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


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

lowerCAmelCase :  List[Any]      =      {
    'facebook/musicgen-small': 'https://huggingface.co/facebook/musicgen-small/resolve/main/config.json',
    # See all Musicgen models at https://huggingface.co/models?filter=musicgen
}


class        SCREAMING_SNAKE_CASE__	(			snake_case_):
				lowerCAmelCase_			       =				"""musicgen_decoder"""
				lowerCAmelCase_			       =				["""past_key_values"""]







				def __init__(    self		,							A_=2048		,							A_=2048		,							A_=24		,							A_=4096		,							A_=16		,							A_=0.0		,							A_=True		,							A_="gelu"		,							A_=1024		,							A_=0.1		,							A_=0.0		,							A_=0.0		,							A_=0.02		,							A_=False		,							A_=4		,							A_=2048		,							A_=2048		,							A_=None		,							A_=False		,							**A_		,							)->						Any:







											'''simple docstring'''






											UpperCamelCase					       =			vocab_size
											UpperCamelCase					       =			max_position_embeddings
											UpperCamelCase					       =			hidden_size
											UpperCamelCase					       =			ffn_dim
											UpperCamelCase					       =			num_hidden_layers
											UpperCamelCase					       =			num_attention_heads
											UpperCamelCase					       =			dropout
											UpperCamelCase					       =			attention_dropout
											UpperCamelCase					       =			activation_dropout
											UpperCamelCase					       =			activation_function
											UpperCamelCase					       =			initializer_factor
											UpperCamelCase					       =			layerdrop
											UpperCamelCase					       =			use_cache
											UpperCamelCase					       =			scale_embedding  # scale factor will be sqrt(d_model) if True
											UpperCamelCase					       =			num_codebooks
											super().__init__(
											    pad_token_id=A_		,							bos_token_id=A_		,							eos_token_id=A_		,							tie_word_embeddings=A_		,							**A_		,							)


class        SCREAMING_SNAKE_CASE__	(			snake_case_):
				lowerCAmelCase_			       =				"""musicgen"""
				lowerCAmelCase_			       =				True







				def __init__(    self		,							**A_			)->						Union[str, Any]:







											'''simple docstring'''






											super().__init__(**A_			)
											if "text_encoder" not in kwargs or "audio_encoder" not in kwargs or "decoder" not in kwargs:
																		raise ValueError('Config has to be initialized with text_encoder, audio_encoder and decoder config'			)

											UpperCamelCase					       =			kwargs.pop('text_encoder'			)
											UpperCamelCase					       =			text_encoder_config.pop('model_type'			)

											UpperCamelCase					       =			kwargs.pop('audio_encoder'			)
											UpperCamelCase					       =			audio_encoder_config.pop('model_type'			)

											UpperCamelCase					       =			kwargs.pop('decoder'			)

											UpperCamelCase					       =			AutoConfig.for_model(A_		,							**A_			)
											UpperCamelCase					       =			AutoConfig.for_model(A_		,							**A_			)
											UpperCamelCase					       =			MusicgenDecoderConfig(**A_			)
											UpperCamelCase					       =			True







				@classmethod
				def 		UpperCAmelCase_  (    cls		,							A_		,							A_		,							A_		,							**A_		,							)->						Tuple:







											'''simple docstring'''






											return cls(
											    text_encoder=text_encoder_config.to_dict()		,							audio_encoder=audio_encoder_config.to_dict()		,							decoder=decoder_config.to_dict()		,							**A_		,							)







				def 		UpperCAmelCase_  (    self			)->						Optional[Any]:







											'''simple docstring'''






											UpperCamelCase					       =			copy.deepcopy(self.__dict__			)
											UpperCamelCase					       =			self.text_encoder.to_dict()
											UpperCamelCase					       =			self.audio_encoder.to_dict()
											UpperCamelCase					       =			self.decoder.to_dict()
											UpperCamelCase					       =			self.__class__.model_type
											return output




