'''simple docstring'''

import logging

import numpy as np
import pytest
from scipy.linalg import eigh

logging.basicConfig(level=logging.INFO, format="""%(message)s""")
def       __UpperCamelCase	(       UpperCAmelCase					):
 return input_array.reshape((input_array.size, 1)					)
def       __UpperCamelCase	(       UpperCAmelCase		,					UpperCAmelCase		,					UpperCAmelCase					):
 lowercase__    :   Any						= np.nan
 for i in range(UpperCAmelCase					):
  lowercase__    :   List[Any]						= features[:, labels == i]
  lowercase__    :   Dict						= data.mean(1					)
  # Centralize the data of class i
  lowercase__    :   Any						= data - column_reshape(UpperCAmelCase					)
  if i > 0:
   # If covariance_sum is not None
   covariance_sum += np.dot(UpperCAmelCase		,					centered_data.T					)
  else:
   # If covariance_sum is np.nan (i.e. first loop)
   lowercase__    :   List[Any]						= np.dot(UpperCAmelCase		,					centered_data.T					)

 return covariance_sum / features.shape[1]
def       __UpperCamelCase	(       UpperCAmelCase		,					UpperCAmelCase		,					UpperCAmelCase					):
 lowercase__    :   Tuple						= features.mean(1					)
 lowercase__    :   int						= np.nan
 for i in range(UpperCAmelCase					):
  lowercase__    :   str						= features[:, labels == i]
  lowercase__    :   Any						= data.shape[1]
  lowercase__    :   Any						= data.mean(1					)
  if i > 0:
   # If covariance_sum is not None
   covariance_sum += device_data * np.dot(
       column_reshape(UpperCAmelCase					) - column_reshape(UpperCAmelCase					)		,					(column_reshape(UpperCAmelCase					) - column_reshape(UpperCAmelCase					)).T		,					)
  else:
   # If covariance_sum is np.nan (i.e. first loop)
   lowercase__    :   int						= device_data * np.dot(
       column_reshape(UpperCAmelCase					) - column_reshape(UpperCAmelCase					)		,					(column_reshape(UpperCAmelCase					) - column_reshape(UpperCAmelCase					)).T		,					)

 return covariance_sum / features.shape[1]
def       __UpperCamelCase	(       UpperCAmelCase		,					UpperCAmelCase					):

 # Check if the features have been loaded
 if features.any():
  lowercase__    :   str						= features.mean(1					)
  # Center the dataset
  lowercase__    :   Optional[Any]						= features - np.reshape(UpperCAmelCase		,					(data_mean.size, 1)					)
  lowercase__    :   str						= np.dot(UpperCAmelCase		,					centered_data.T					) / features.shape[1]
  lowercase__			,							lowercase__    :   Dict						= np.linalg.eigh(UpperCAmelCase					)
  # Take all the columns in the reverse order (-1), and then takes only the first
  lowercase__    :   Any						= eigenvectors[:, ::-1][:, 0:dimensions]
  # Project the database on the new space
  lowercase__    :   Tuple						= np.dot(filtered_eigenvectors.T		,					UpperCAmelCase					)
  logging.info('''Principal Component Analysis computed'''					)

  return projected_data
 else:
  logging.basicConfig(level=logging.ERROR		,					format='''%(message)s'''		,					force=UpperCAmelCase					)
  logging.error('''Dataset empty'''					)
  raise AssertionError
def       __UpperCamelCase	(       UpperCAmelCase		,					UpperCAmelCase		,					UpperCAmelCase		,					UpperCAmelCase					):
 assert classes > dimensions

 # Check if features have been already loaded
 if features.any:
  lowercase__			,							lowercase__    :   Tuple						= eigh(
      covariance_between_classes(UpperCAmelCase		,					UpperCAmelCase		,					UpperCAmelCase					)		,					covariance_within_classes(UpperCAmelCase		,					UpperCAmelCase		,					UpperCAmelCase					)		,					)
  lowercase__    :   List[Any]						= eigenvectors[:, ::-1][:, :dimensions]
  lowercase__			,							lowercase__			,							lowercase__    :   List[str]						= np.linalg.svd(UpperCAmelCase					)
  lowercase__    :   List[str]						= svd_matrix[:, 0:dimensions]
  lowercase__    :   Optional[int]						= np.dot(filtered_svd_matrix.T		,					UpperCAmelCase					)
  logging.info('''Linear Discriminant Analysis computed'''					)

  return projected_data
 else:
  logging.basicConfig(level=logging.ERROR		,					format='''%(message)s'''		,					force=UpperCAmelCase					)
  logging.error('''Dataset empty'''					)
  raise AssertionError
def       __UpperCamelCase	(       ):
 # Create dummy dataset with 2 classes and 3 features
 lowercase__    :   Optional[int]						= np.array([[1, 2, 3, 4, 5], [2, 3, 4, 5, 6], [3, 4, 5, 6, 7]]					)
 lowercase__    :   List[Any]						= np.array([0, 0, 0, 1, 1]					)
 lowercase__    :   Dict						= 2
 lowercase__    :   Optional[int]						= 2

 # Assert that the function raises an AssertionError if dimensions > classes
 with pytest.raises(UpperCAmelCase					) as error_info:
  lowercase__    :   List[str]						= linear_discriminant_analysis(
      UpperCAmelCase		,					UpperCAmelCase		,					UpperCAmelCase		,					UpperCAmelCase					)
  if isinstance(UpperCAmelCase		,					np.ndarray					):
   raise AssertionError(
       '''Did not raise AssertionError for dimensions > classes'''					)
  assert error_info.type is AssertionError
def       __UpperCamelCase	(       ):
 lowercase__    :   Any						= np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]]					)
 lowercase__    :   List[Any]						= 2
 lowercase__    :   Optional[int]						= np.array([[6.9_2_8_2_0_3_2_3, 8.6_6_0_2_5_4_0_4, 1_0.3_9_2_3_0_4_8_5], [3.0, 3.0, 3.0]]					)

 with pytest.raises(UpperCAmelCase					) as error_info:
  lowercase__    :   Union[str, Any]						= principal_component_analysis(UpperCAmelCase		,					UpperCAmelCase					)
  if not np.allclose(UpperCAmelCase		,					UpperCAmelCase					):
   raise AssertionError
  assert error_info.type is AssertionError


if __name__ == "__main__":
  import doctest

  doctest.testmod()


'''simple docstring'''

def       __UpperCamelCase	(       UpperCAmelCase					):

 def merge(UpperCAmelCase		,					UpperCAmelCase					) -> list:

  def _merge():
   while left and right:
    yield (left if left[0] <= right[0] else right).pop(0					)
   yield from left
   yield from right

  return list(_merge()					)

 if len(UpperCAmelCase					) <= 1:
  return collection
 lowercase__    :   int						= len(UpperCAmelCase					) // 2
 return merge(merge_sort(collection[:mid]					)		,					merge_sort(collection[mid:]					)					)


if __name__ == "__main__":
  import doctest

  doctest.testmod()
  __a:			str	       =       input("""Enter numbers separated by a comma:\n""").strip()
  __a:			Optional[int]	       =       [int(item) for item in user_input.split(""",""")]
  print(*merge_sort(unsorted), sep=""",""")

