
def 	UpperCamelCase   (							lowerCAmelCase__		):
					'''simple docstring'''

					# bit count represents no. of bits in the gray code
					if bit_count < 0:
										raise ValueError('''The given input must be positive'''		)

					# get the generated string sequence
					lowercase						     =						gray_code_sequence_string(lowerCAmelCase__		)
					#
					# convert them to integers
					for i in range(len(lowerCAmelCase__		)		):
										lowercase						     =						int(sequence[i]			,      2		)

					return sequence



def 	UpperCamelCase   (							lowerCAmelCase__		):
					'''simple docstring'''

					# The approach is a recursive one
					# Base case achieved when either n = 0 or n=1
					if bit_count == 0:
										return ["0"]

					if bit_count == 1:
										return ["0", "1"]

					lowercase						     =						1 << bit_count  # defines the length of the sequence
					# 1<< n is equivalent to 2^n

					# recursive answer will generate answer for n-1 bits
					lowercase						     =						gray_code_sequence_string(bit_count - 1		)

					lowercase						     =						[]

					# append 0 to first half of the smaller sequence generated
					for i in range(seq_len // 2		):
										lowercase						     =						'''0''' + smaller_sequence[i]
										sequence.append(lowerCAmelCase__		)

					# append 1 to second half ... start from the end of the list
					for i in reversed(range(seq_len // 2		)		):
										lowercase						     =						'''1''' + smaller_sequence[i]
										sequence.append(lowerCAmelCase__		)

					return sequence


if __name__ == "__main__":
							import doctest

							doctest.testmod()






import numpy as np

import datasets


lowercase__		:Dict			  =   "\nCompute the Mahalanobis Distance\n\nMahalonobis distance is the distance between a point and a distribution.\nAnd not between two distinct points. It is effectively a multivariate equivalent of the Euclidean distance.\nIt was introduced by Prof. P. C. Mahalanobis in 1936\nand has been used in various statistical applications ever since\n[source: https://www.machinelearningplus.com/statistics/mahalanobis-distance/]\n"

lowercase__		:List[Any]			  =   "\\n@article{de2000mahalanobis,\n  title={The mahalanobis distance},\n  author={De Maesschalck, Roy and Jouan-Rimbaud, Delphine and Massart, D{\'e}sir{\'e} L},\n  journal={Chemometrics and intelligent laboratory systems},\n  volume={50},\n  number={1},\n  pages={1--18},\n  year={2000},\n  publisher={Elsevier}\n}\n"

lowercase__		:Dict			  =   "\nArgs:\n    X: List of datapoints to be compared with the `reference_distribution`.\n    reference_distribution: List of datapoints from the reference distribution we want to compare to.\nReturns:\n    mahalanobis: The Mahalonobis distance for each datapoint in `X`.\nExamples:\n\n    >>> mahalanobis_metric = datasets.load_metric(\"mahalanobis\")\n    >>> results = mahalanobis_metric.compute(reference_distribution=[[0, 1], [1, 0]], X=[[0, 1]])\n    >>> print(results)\n    {'mahalanobis': array([0.5])}\n"







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




							def 			A__				(    self):
												return datasets.MetricInfo(
												    description=_DESCRIPTION       ,citation=_CITATION       ,inputs_description=_KWARGS_DESCRIPTION       ,features=datasets.Features(
												        {
												            '''X''': datasets.Sequence(datasets.Value('''float'''       ,id='''sequence''')       ,id='''X'''),
												        })       ,)





							def 			A__				(    self       ,A__       ,A__):
												# convert to numpy arrays
												lowercase						     =						np.array(A__)
												lowercase						     =						np.array(A__)

												# Assert that arrays are 2D
												if len(X.shape) != 2:
																	raise ValueError('''Expected `X` to be a 2D vector''')
												if len(reference_distribution.shape) != 2:
																	raise ValueError('''Expected `reference_distribution` to be a 2D vector''')
												if reference_distribution.shape[0] < 2:
																	raise ValueError(
																	    '''Expected `reference_distribution` to be a 2D vector with more than one element in the first dimension''')

												# Get mahalanobis distance for each prediction
												lowercase						     =						X - np.mean(A__)
												lowercase						     =						np.cov(reference_distribution.T)
												try:
																	lowercase						     =						np.linalg.inv(A__)
												except np.linalg.LinAlgError:
																	lowercase						     =						np.linalg.pinv(A__)
												lowercase						     =						np.dot(A__       ,A__)
												lowercase						     =						np.dot(A__       ,X_minus_mu.T).diagonal()

												return {"mahalanobis": mahal_dist}




