




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()







'''simple docstring'''






import argparse
import json
import re
import string
import sys
from collections import Counter





def      lowercase  (  lowerCAmelCase :						int):



				"""simple docstring"""


				def remove_articles(lowerCAmelCase :						List[Any]):
								return re.sub(R'''\b(a|an|the)\b'''   , ''' '''   , lowerCAmelCase)

				def white_space_fix(lowerCAmelCase :						Tuple):
								return " ".join(text.split())

				def remove_punc(lowerCAmelCase :						str):
								_A :				List[Any]				=  set(string.punctuation)
								return "".join(ch for ch in text if ch not in exclude)

				def lower(lowerCAmelCase :						Any):
								return text.lower()

				return white_space_fix(remove_articles(remove_punc(lower(lowerCAmelCase))))





def      lowercase  (  lowerCAmelCase :						int   , lowerCAmelCase :						Dict):



				"""simple docstring"""


				_A :				str				=  normalize_answer(lowerCAmelCase).split()
				_A :				Dict				=  normalize_answer(lowerCAmelCase).split()
				_A :				str				=  Counter(lowerCAmelCase) & Counter(lowerCAmelCase)
				_A :				List[Any]				=  sum(common.values())
				if num_same == 0:
								return 0
				_A :				Tuple				=  1.0 * num_same / len(lowerCAmelCase)
				_A :				List[Any]				=  1.0 * num_same / len(lowerCAmelCase)
				_A :				int				=  (2 * precision * recall) / (precision + recall)
				return fa





def      lowercase  (  lowerCAmelCase :						Any   , lowerCAmelCase :						str):



				"""simple docstring"""


				return normalize_answer(lowerCAmelCase) == normalize_answer(lowerCAmelCase)





def      lowercase  (  lowerCAmelCase :						Optional[Any]   , lowerCAmelCase :						Optional[int]   , lowerCAmelCase :						Optional[int]):



				"""simple docstring"""


				_A :				Optional[int]				=  []
				for ground_truth in ground_truths:
								_A :				Union[str, Any]				=  metric_fn(lowerCAmelCase   , lowerCAmelCase)
								scores_for_ground_truths.append(lowerCAmelCase)
				return max(lowerCAmelCase)





def      lowercase  (  lowerCAmelCase :						int   , lowerCAmelCase :						str):



				"""simple docstring"""


				_A :				Union[str, Any]				=  0
				_A :				List[Any]				=  []
				for passage in dataset:
								for qa in passage["qas"]:
												total += 1
												if qa["id"] not in predictions:
																_A :				str				=  f"""Unanswered question {qa['id']} will receive score 0."""
																print(lowerCAmelCase   , file=sys.stderr)
																continue

												_A :				Optional[int]				=  [x['''text'''] for x in qa['''answers''']]
												_A :				Union[str, Any]				=  predictions[qa['''id''']]

												_A :				Optional[Any]				=  metric_max_over_ground_truths(lowerCAmelCase   , lowerCAmelCase   , lowerCAmelCase)
												if int(_exact_match) == 1:
																correct_ids.append(qa['''id'''])
												exact_match += _exact_match

												fa += metric_max_over_ground_truths(lowerCAmelCase   , lowerCAmelCase   , lowerCAmelCase)

				_A :				Dict				=  exact_match / total
				_A :				Dict				=  fa / total

				return {"exact_match": exact_match, "f1": fa}, correct_ids


if __name__ == "__main__":
	__UpperCamelCase      :   List[str]								=     '''1.0'''
	__UpperCamelCase      :   Union[str, Any]								=     argparse.ArgumentParser('''Official evaluation script for ReCoRD v1.0.''')
	parser.add_argument('''data_file''', help='''The dataset file in JSON format.''')
	parser.add_argument('''pred_file''', help='''The model prediction file in JSON format.''')
	parser.add_argument('''--output_correct_ids''', action='''store_true''', help='''Output the correctly answered query IDs.''')
	__UpperCamelCase      :   Optional[int]								=     parser.parse_args()

	with open(args.data_file) as data_file:
		__UpperCamelCase      :   Optional[int]								=     json.load(data_file)
		if dataset_json["version"] != expected_version:
			print(
			    f'Evaluation expects v-{expected_version}, but got dataset with v-{dataset_json["version"]}',
			    file=sys.stderr,
			)
		__UpperCamelCase      :   Optional[Any]								=     dataset_json['''data''']

	with open(args.pred_file) as pred_file:
		__UpperCamelCase      :   int								=     json.load(pred_file)

	__UpperCamelCase							,  __UpperCamelCase      :   List[str]								=     evaluate(dataset, predictions)

	if args.output_correct_ids:
		print(f'Output {len(correct_ids)} correctly answered question IDs.')
		with open('''correct_ids.json''', '''w''') as f:
			json.dump(correct_ids, f)
