
from sklearn.metrics import mean_absolute_error

import datasets


lowercase__							:							str													=     "\\n@article{scikit-learn,\n title={Scikit-learn: Machine Learning in {P}ython},\n author={Pedregosa, F. and Varoquaux, G. and Gramfort, A. and Michel, V.\n         and Thirion, B. and Grisel, O. and Blondel, M. and Prettenhofer, P.\n         and Weiss, R. and Dubourg, V. and Vanderplas, J. and Passos, A. and\n         Cournapeau, D. and Brucher, M. and Perrot, M. and Duchesnay, E.},\n journal={Journal of Machine Learning Research},\n volume={12},\n pages={2825--2830},\n year={2011}\n}\n"

lowercase__							:							List[Any]													=     "\\nMean Absolute Error (MAE) is the mean of the magnitude of difference between the predicted and actual\nvalues.\n"


lowercase__							:							Dict													=     "\nArgs:\n    predictions: array-like of shape (n_samples,) or (n_samples, n_outputs)\n        Estimated target values.\n    references: array-like of shape (n_samples,) or (n_samples, n_outputs)\n        Ground truth (correct) target values.\n    sample_weight: array-like of shape (n_samples,), default=None\n        Sample weights.\n    multioutput: {\"raw_values\", \"uniform_average\"} or array-like of shape (n_outputs,), default=\"uniform_average\"\n        Defines aggregating of multiple output values. Array-like value defines weights used to average errors.\n\n                 \"raw_values\" : Returns a full set of errors in case of multioutput input.\n\n                 \"uniform_average\" : Errors of all outputs are averaged with uniform weight.\n\nReturns:\n    mae : mean absolute error.\n        If multioutput is \"raw_values\", then mean absolute error is returned for each output separately. If multioutput is \"uniform_average\" or an ndarray of weights, then the weighted average of all output errors is returned.\n        MAE output is non-negative floating point. The best value is 0.0.\nExamples:\n\n    >>> mae_metric = datasets.load_metric(\"mae\")\n    >>> predictions = [2.5, 0.0, 2, 8]\n    >>> references = [3, -0.5, 2, 7]\n    >>> results = mae_metric.compute(predictions=predictions, references=references)\n    >>> print(results)\n    {'mae': 0.5}\n\n    If you're using multi-dimensional lists, then set the config as follows :\n\n    >>> mae_metric = datasets.load_metric(\"mae\", \"multilist\")\n    >>> predictions = [[0.5, 1], [-1, 1], [7, -6]]\n    >>> references = [[0, 2], [-1, 2], [8, -5]]\n    >>> results = mae_metric.compute(predictions=predictions, references=references)\n    >>> print(results)\n    {'mae': 0.75}\n    >>> results = mae_metric.compute(predictions=predictions, references=references, multioutput='raw_values')\n    >>> print(results)\n    {'mae': array([0.5, 1. ])}\n"






@datasets.utils.file_utils.add_start_docstrings(_DESCRIPTION				,						_KWARGS_DESCRIPTION      )
class     SCREAMING_SNAKE_CASE__      (							datasets.Metric      ):

							"""simple docstring"""






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





													'''simple docstring'''






													return datasets.MetricInfo(
													    description=_DESCRIPTION       ,		citation=_CITATION       ,		inputs_description=_KWARGS_DESCRIPTION       ,		features=datasets.Features(self._get_feature_types()     )       ,		reference_urls=[
													        '''https://scikit-learn.org/stable/modules/generated/sklearn.metrics.mean_absolute_error.html'''
													    ]       ,		)



							def       A__						(					self     )->				int:





													'''simple docstring'''






													if self.config_name == "multilist":
																			return {
																			    "predictions": datasets.Sequence(datasets.Value('''float'''     )     ),
																			    "references": datasets.Sequence(datasets.Value('''float'''     )     ),
																			}
													else:
																			return {
																			    "predictions": datasets.Value('''float'''     ),
																			    "references": datasets.Value('''float'''     ),
																			}



							def       A__						(					self       ,		SCREAMING_SNAKE_CASE_       ,		SCREAMING_SNAKE_CASE_       ,		SCREAMING_SNAKE_CASE_=None       ,		SCREAMING_SNAKE_CASE_="uniform_average"     )->				Any:





													'''simple docstring'''






													__UpperCamelCase       					=     mean_absolute_error(SCREAMING_SNAKE_CASE_       ,		SCREAMING_SNAKE_CASE_       ,		sample_weight=SCREAMING_SNAKE_CASE_       ,		multioutput=SCREAMING_SNAKE_CASE_     )

													return {"mae": mae_score}






from typing import Any

import numpy as np




def 		A_	(							snake_case							:				np.ndarray	) ->      bool:



						'''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.
						__UpperCamelCase					,							__UpperCamelCase       					=     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 		A_	(							snake_case							:				int	) ->      Any:



						'''simple docstring'''

						__UpperCamelCase       					=     np.random.randn(snake_case	, snake_case	)
						__UpperCamelCase       					=     np.dot(snake_case	, random_matrix.T	)
						assert _is_matrix_spd(snake_case	)
						return spd_matrix




def 		A_	(							snake_case							:				np.ndarray	, snake_case							:				np.ndarray	, snake_case							:				int = 1000	, snake_case							:				float = 1e-8	, ) ->      Any:



						'''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.
						__UpperCamelCase       					=     np.zeros((np.shape(snake_case	)[0], 1)	)
						__UpperCamelCase       					=     np.copy(snake_case	)
						__UpperCamelCase       					=     np.copy(snake_case	)

						# 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(snake_case	, snake_case	)

												# The main algorithm.

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

												# Update variables.
												__UpperCamelCase       					=     np.copy(snake_case	)
												__UpperCamelCase       					=     np.copy(snake_case	)
												__UpperCamelCase       					=     np.copy(snake_case	)

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

						return x




def 		A_	(							) ->      None:



						'''simple docstring'''

						__UpperCamelCase       					=     3
						__UpperCamelCase       					=     _create_spd_matrix(snake_case	)
						__UpperCamelCase       					=     np.random.randn(snake_case	, 1	)
						__UpperCamelCase       					=     np.dot(snake_case	, snake_case	)

						# Numpy solution.
						__UpperCamelCase       					=     np.linalg.solve(snake_case	, snake_case	)

						# Our implementation.
						__UpperCamelCase       					=     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()




