

import numpy as np

import datasets


lowerCAmelCase__      		=			'''\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'''

lowerCAmelCase__      		=			'''\\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'''

lowerCAmelCase__      		=			'''\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   ):




  """simple docstring"""




  def       SCREAMING_SNAKE_CASE   (   self     :  str    ):
   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       SCREAMING_SNAKE_CASE   (   self     :  List[Any]      ,lowercase__     :  Optional[int]      ,lowercase__     :  Optional[Any]    ):
   __lowercase													=				np.array(lowercase__    )
   __lowercase													=				np.array(lowercase__    )

   # 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(lowercase__    )
   __lowercase													=				np.cov(reference_distribution.T    )
   try:
    __lowercase													=				np.linalg.inv(lowercase__    )
   except np.linalg.LinAlgError:
    __lowercase													=				np.linalg.pinv(lowercase__    )
   __lowercase													=				np.dot(lowercase__      ,lowercase__    )
   __lowercase													=				np.dot(lowercase__      ,X_minus_mu.T    ).diagonal()

   return {"mahalanobis": mahal_dist}




'''simple docstring'''






from __future__ import annotations

import matplotlib.pyplot as plt  # type: ignore
import numpy

# initial triangle of Koch snowflake
lowerCAmelCase__      		=			numpy.array([0, 0])
lowerCAmelCase__      		=			numpy.array([0.5, 0.8_660_254])
lowerCAmelCase__      		=			numpy.array([1, 0])
lowerCAmelCase__      		=			[VECTOR_1, VECTOR_2, VECTOR_3, VECTOR_1]


def 	_A  (					A__  ,       A__   ):






 """simple docstring"""



 __lowercase													=				initial_vectors
 for _ in range(A__   ):
  __lowercase													=				iteration_step(A__   )
 return vectors


def 	_A  (					A__   ):






 """simple docstring"""



 __lowercase													=				[]
 for i, start_vector in enumerate(vectors[:-1]   ):
  __lowercase													=				vectors[i + 1]
  new_vectors.append(A__   )
  __lowercase													=				end_vector - start_vector
  new_vectors.append(start_vector + difference_vector / 3   )
  new_vectors.append(
      start_vector + difference_vector / 3 + rotate(difference_vector / 3  ,       60   )   )
  new_vectors.append(start_vector + difference_vector * 2 / 3   )
 new_vectors.append(vectors[-1]   )
 return new_vectors


def 	_A  (					A__  ,       A__   ):






 """simple docstring"""



 __lowercase													=				numpy.radians(A__   )
 __lowercase						,			__lowercase													=				numpy.cos(A__   ), numpy.sin(A__   )
 __lowercase													=				numpy.array(((c, -s), (s, c))   )
 return numpy.dot(A__  ,       A__   )


def 	_A  (					A__   ):






 """simple docstring"""



 __lowercase													=				plt.gca()
 axes.set_aspect('''equal'''   )

 # matplotlib.pyplot.plot takes a list of all x-coordinates and a list of all
 # y-coordinates as inputs, which are constructed from the vector-list using
 # zip()
 __lowercase						,			__lowercase													=				zip(*A__   )
 plt.plot(A__  ,       A__   )
 plt.show()


if __name__ == "__main__":
 import doctest

 doctest.testmod()

 lowerCAmelCase__      		=			iterate(INITIAL_VECTORS, 5)
 plot(processed_vectors)

