

'''simple docstring'''





from typing import Any

import numpy as np






def  UpperCamelCase_(							_snake_case     :						np.ndarray			):




			"""simple docstring"""






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

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

			# Get eigenvalues and eignevectors for a symmetric matrix.
			__a   ,					__a						   =np.linalg.eigh(_snake_case			)

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






def  UpperCamelCase_(							_snake_case     :						int			):




			"""simple docstring"""






			__a						   =np.random.randn(_snake_case ,  _snake_case			)
			__a						   =np.dot(_snake_case ,  random_matrix.T			)
			assert _is_matrix_spd(_snake_case			)
			return spd_matrix






def  UpperCamelCase_(							_snake_case     :						np.ndarray ,  _snake_case     :						np.ndarray ,  _snake_case     :						int = 1000 ,  _snake_case     :						float = 1e-8 ,  ):




			"""simple docstring"""






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

			# Initialize solution guess, residual, search direction.
			__a						   =np.zeros((np.shape(_snake_case			)[0], 1)			)
			__a						   =np.copy(_snake_case			)
			__a						   =np.copy(_snake_case			)

			# Set initial errors in solution guess and residual.
			__a						   =1e9
			__a						   =1e9
			__a						   =1e9

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

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

						# The main algorithm.

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

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

						# Update variables.
						__a						   =np.copy(_snake_case			)
						__a						   =np.copy(_snake_case			)
						__a						   =np.copy(_snake_case			)

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

			return x






def  UpperCamelCase_(							):




			"""simple docstring"""






			__a						   =3
			__a						   =_create_spd_matrix(_snake_case			)
			__a						   =np.random.randn(_snake_case ,  1			)
			__a						   =np.dot(_snake_case ,  _snake_case			)

			# Numpy solution.
			__a						   =np.linalg.solve(_snake_case ,  _snake_case			)

			# Our implementation.
			__a						   =conjugate_gradient(_snake_case ,  _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()









from typing import Optional

from ..utils.logging import get_logger
from .audio_classificiation import AudioClassification
from .automatic_speech_recognition import AutomaticSpeechRecognition
from .base import TaskTemplate
from .image_classification import ImageClassification
from .language_modeling import LanguageModeling
from .question_answering import QuestionAnsweringExtractive
from .summarization import Summarization
from .text_classification import TextClassification


_lowerCAmelCase      :    List[Any]						       =    [
    "AutomaticSpeechRecognition",
    "AudioClassification",
    "ImageClassification",
    "LanguageModeling",
    "QuestionAnsweringExtractive",
    "Summarization",
    "TaskTemplate",
    "TextClassification",
]

_lowerCAmelCase      :    List[str]						       =    get_logger(__name__)


_lowerCAmelCase      :    Tuple						       =    {
    AutomaticSpeechRecognition.task: AutomaticSpeechRecognition,
    AudioClassification.task: AudioClassification,
    ImageClassification.task: ImageClassification,
    LanguageModeling.task: LanguageModeling,
    QuestionAnsweringExtractive.task: QuestionAnsweringExtractive,
    Summarization.task: Summarization,
    TextClassification.task: TextClassification,
}






def  UpperCamelCase_(							_snake_case     :						dict			):




			"""simple docstring"""






			__a						   =task_template_dict.get('task'			)
			if task_name is None:
						logger.warning(F'Couldn\'t find template for task \'{task_name}\'. Available templates: {list(_snake_case			)}'			)
						return None
			__a						   =NAMEaTEMPLATE.get(_snake_case			)
			return template.from_dict(_snake_case			)






