



import datasets

from .evaluate import (
    apply_no_ans_threshold,
    find_all_best_thresh,
    get_raw_scores,
    make_eval_dict,
    make_qid_to_has_ans,
    merge_eval,
)


_lowercase				:					str     					="""\
@inproceedings{Rajpurkar2016SQuAD10,
  title={SQuAD: 100, 000+ Questions for Machine Comprehension of Text},
  author={Pranav Rajpurkar and Jian Zhang and Konstantin Lopyrev and Percy Liang},
  booktitle={EMNLP},
  year={2016}
}
"""

_lowercase				:					Tuple     					="""
This metric wrap the official scoring script for version 2 of the Stanford Question
Answering Dataset (SQuAD).

Stanford Question Answering Dataset (SQuAD) is a reading comprehension dataset, consisting of questions posed by
crowdworkers on a set of Wikipedia articles, where the answer to every question is a segment of text, or span,
from the corresponding reading passage, or the question might be unanswerable.

SQuAD2.0 combines the 100,000 questions in SQuAD1.1 with over 50,000 unanswerable questions
written adversarially by crowdworkers to look similar to answerable ones.
To do well on SQuAD2.0, systems must not only answer questions when possible, but also
determine when no answer is supported by the paragraph and abstain from answering.
"""

_lowercase				:					Optional[Any]     					="""
Computes SQuAD v2 scores (F1 and EM).
Args:
    predictions: List of triple for question-answers to score with the following elements:
        - the question-answer 'id' field as given in the references (see below)
        - the text of the answer
        - the probability that the question has no answer
    references: List of question-answers dictionaries with the following key-values:
            - 'id': id of the question-answer pair (see above),
            - 'answers': a list of Dict {'text': text of the answer as a string}
    no_answer_threshold: float
        Probability threshold to decide that a question has no answer.
Returns:
    'exact': Exact match (the normalized answer exactly match the gold answer)
    'f1': The F-score of predicted tokens versus the gold answer
    'total': Number of score considered
    'HasAns_exact': Exact match (the normalized answer exactly match the gold answer)
    'HasAns_f1': The F-score of predicted tokens versus the gold answer
    'HasAns_total': Number of score considered
    'NoAns_exact': Exact match (the normalized answer exactly match the gold answer)
    'NoAns_f1': The F-score of predicted tokens versus the gold answer
    'NoAns_total': Number of score considered
    'best_exact': Best exact match (with varying threshold)
    'best_exact_thresh': No-answer probability threshold associated to the best exact match
    'best_f1': Best F1 (with varying threshold)
    'best_f1_thresh': No-answer probability threshold associated to the best F1
Examples:

    >>> predictions = [{'prediction_text': '1976', 'id': '56e10a3be3433e1400422b22', 'no_answer_probability': 0.}]
    >>> references = [{'answers': {'answer_start': [97], 'text': ['1976']}, 'id': '56e10a3be3433e1400422b22'}]
    >>> squad_v2_metric = datasets.load_metric(\"squad_v2\")
    >>> results = squad_v2_metric.compute(predictions=predictions, references=references)
    >>> print(results)
    {'exact': 100.0, 'f1': 100.0, 'total': 1, 'HasAns_exact': 100.0, 'HasAns_f1': 100.0, 'HasAns_total': 1, 'best_exact': 100.0, 'best_exact_thresh': 0.0, 'best_f1': 100.0, 'best_f1_thresh': 0.0}
"""
@datasets.utils.file_utils.add_start_docstrings(_DESCRIPTION ,_KWARGS_DESCRIPTION			)
class lowerCAmelCase_       (   datasets.Metric			):







	'''simple docstring'''




	def 				_A			(	self       ):



				'''simple docstring'''


				return datasets.MetricInfo(
				    description=_DESCRIPTION   ,       citation=_CITATION   ,       inputs_description=_KWARGS_DESCRIPTION   ,       features=datasets.Features(
				        {
				            """predictions""": {
				                """id""": datasets.Value("""string"""       ),
				                """prediction_text""": datasets.Value("""string"""       ),
				                """no_answer_probability""": datasets.Value("""float32"""       ),
				            },
				            """references""": {
				                """id""": datasets.Value("""string"""       ),
				                """answers""": datasets.features.Sequence(
				                    {"""text""": datasets.Value("""string"""       ), """answer_start""": datasets.Value("""int32"""       )}       ),
				            },
				        }       )   ,       codebase_urls=["""https://rajpurkar.github.io/SQuAD-explorer/"""]   ,       reference_urls=["""https://rajpurkar.github.io/SQuAD-explorer/"""]   ,       )







	def 				_A			(	self   ,       lowerCamelCase   ,       lowerCamelCase   ,       lowerCamelCase=1.0       ):



				'''simple docstring'''


				a__					=  {p["""id"""]: p["""no_answer_probability"""] for p in predictions}
				a__					=  [{"""paragraphs""": [{"""qas""": references}]}]
				a__					=  {p["""id"""]: p["""prediction_text"""] for p in predictions}

				a__					=  make_qid_to_has_ans(lowerCamelCase       )  # maps qid to True/False
				a__					=  [k for k, v in qid_to_has_ans.items() if v]
				a__					=  [k for k, v in qid_to_has_ans.items() if not v]

				a__				,       a__					=  get_raw_scores(lowerCamelCase   ,       lowerCamelCase       )
				a__					=  apply_no_ans_threshold(lowerCamelCase   ,       lowerCamelCase   ,       lowerCamelCase   ,       lowerCamelCase       )
				a__					=  apply_no_ans_threshold(lowerCamelCase   ,       lowerCamelCase   ,       lowerCamelCase   ,       lowerCamelCase       )
				a__					=  make_eval_dict(lowerCamelCase   ,       lowerCamelCase       )

				if has_ans_qids:
							a__					=  make_eval_dict(lowerCamelCase   ,       lowerCamelCase   ,       qid_list=lowerCamelCase       )
							merge_eval(lowerCamelCase   ,       lowerCamelCase   ,       """HasAns"""       )
				if no_ans_qids:
							a__					=  make_eval_dict(lowerCamelCase   ,       lowerCamelCase   ,       qid_list=lowerCamelCase       )
							merge_eval(lowerCamelCase   ,       lowerCamelCase   ,       """NoAns"""       )
				find_all_best_thresh(lowerCamelCase   ,       lowerCamelCase   ,       lowerCamelCase   ,       lowerCamelCase   ,       lowerCamelCase   ,       lowerCamelCase       )
				return dict(lowerCamelCase       )






from typing import Any

import numpy as np




def    UpperCAmelCase					(  lowercase__						:					np.ndarray	):



			'''simple docstring'''





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

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

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

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




def    UpperCAmelCase					(  lowercase__						:					int	):



			'''simple docstring'''





			a__					=  np.random.randn(lowercase__				,					lowercase__	)
			a__					=  np.dot(lowercase__				,					random_matrix.T	)
			assert _is_matrix_spd(lowercase__	)
			return spd_matrix




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



			'''simple docstring'''





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

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

			# 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(lowercase__				,					lowercase__	)

						# The main algorithm.

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

						# Update variables.
						a__					=  np.copy(lowercase__	)
						a__					=  np.copy(lowercase__	)
						a__					=  np.copy(lowercase__	)

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

			return x




def    UpperCAmelCase					(  ):



			'''simple docstring'''





			a__					=  3
			a__					=  _create_spd_matrix(lowercase__	)
			a__					=  np.random.randn(lowercase__				,					1	)
			a__					=  np.dot(lowercase__				,					lowercase__	)

			# Numpy solution.
			a__					=  np.linalg.solve(lowercase__				,					lowercase__	)

			# Our implementation.
			a__					=  conjugate_gradient(lowercase__				,					lowercase__	)

			# 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()

