




'''simple docstring'''





import logging

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

logging.basicConfig(level=logging.INFO, format='''%(message)s''')





def       __a      (  _UpperCamelCase:       Any       )		->					np.ndarray:

     """simple docstring"""




     return input_array.reshape((input_array.size, 1)       )





def       __a      (  _UpperCamelCase:       str   ,		_UpperCamelCase:       List[Any]   ,		_UpperCamelCase:       List[str]       )		->					np.ndarray:

     """simple docstring"""




     _snake_case				= np.nan
     for i in range(__lowerCAmelCase       ):
          _snake_case				= features[:, labels == i]
          _snake_case				= data.mean(1       )
          # Centralize the data of class i
          _snake_case				= data - column_reshape(__lowerCAmelCase       )
          if i > 0:
               # If covariance_sum is not None
               covariance_sum += np.dot(__lowerCAmelCase   ,		centered_data.T       )
          else:
               # If covariance_sum is np.nan (i.e. first loop)
               _snake_case				= np.dot(__lowerCAmelCase   ,		centered_data.T       )

     return covariance_sum / features.shape[1]





def       __a      (  _UpperCamelCase:       int   ,		_UpperCamelCase:       List[str]   ,		_UpperCamelCase:       Optional[Any]       )		->					np.ndarray:

     """simple docstring"""




     _snake_case				= features.mean(1       )
     _snake_case				= np.nan
     for i in range(__lowerCAmelCase       ):
          _snake_case				= features[:, labels == i]
          _snake_case				= data.shape[1]
          _snake_case				= data.mean(1       )
          if i > 0:
               # If covariance_sum is not None
               covariance_sum += device_data * np.dot(
                   column_reshape(__lowerCAmelCase       ) - column_reshape(__lowerCAmelCase       )   ,		(column_reshape(__lowerCAmelCase       ) - column_reshape(__lowerCAmelCase       )).T   ,		)
          else:
               # If covariance_sum is np.nan (i.e. first loop)
               _snake_case				= device_data * np.dot(
                   column_reshape(__lowerCAmelCase       ) - column_reshape(__lowerCAmelCase       )   ,		(column_reshape(__lowerCAmelCase       ) - column_reshape(__lowerCAmelCase       )).T   ,		)

     return covariance_sum / features.shape[1]





def       __a      (  _UpperCamelCase:       Optional[int]   ,		_UpperCamelCase:       Tuple       )		->					np.ndarray:

     """simple docstring"""




     if features.any():
          _snake_case				= features.mean(1       )
          # Center the dataset
          _snake_case				= features - np.reshape(__lowerCAmelCase   ,		(data_mean.size, 1)       )
          _snake_case				= np.dot(__lowerCAmelCase   ,		centered_data.T       ) / features.shape[1]
          _snake_case				= np.linalg.eigh(__lowerCAmelCase       )
          # Take all the columns in the reverse order (-1), and then takes only the first
          _snake_case				= eigenvectors[:, ::-1][:, 0:dimensions]
          # Project the database on the new space
          _snake_case				= np.dot(filtered_eigenvectors.T   ,		__lowerCAmelCase       )
          logging.info("Principal Component Analysis computed"       )

          return projected_data
     else:
          logging.basicConfig(level=logging.ERROR   ,		format="%(message)s"   ,		force=__lowerCAmelCase       )
          logging.error("Dataset empty"       )
          raise AssertionError





def       __a      (  _UpperCamelCase:       List[Any]   ,		_UpperCamelCase:       Optional[Any]   ,		_UpperCamelCase:       Union[str, Any]   ,		_UpperCamelCase:       int       )		->					np.ndarray:

     """simple docstring"""




     assert classes > dimensions

     # Check if features have been already loaded
     if features.any:
          _snake_case				= eigh(
              covariance_between_classes(__lowerCAmelCase   ,		__lowerCAmelCase   ,		__lowerCAmelCase       )   ,		covariance_within_classes(__lowerCAmelCase   ,		__lowerCAmelCase   ,		__lowerCAmelCase       )   ,		)
          _snake_case				= eigenvectors[:, ::-1][:, :dimensions]
          _snake_case				= np.linalg.svd(__lowerCAmelCase       )
          _snake_case				= svd_matrix[:, 0:dimensions]
          _snake_case				= np.dot(filtered_svd_matrix.T   ,		__lowerCAmelCase       )
          logging.info("Linear Discriminant Analysis computed"       )

          return projected_data
     else:
          logging.basicConfig(level=logging.ERROR   ,		format="%(message)s"   ,		force=__lowerCAmelCase       )
          logging.error("Dataset empty"       )
          raise AssertionError





def       __a      (  )		->					None:

     """simple docstring"""




     _snake_case				= np.array([[1, 2, 3, 4, 5], [2, 3, 4, 5, 6], [3, 4, 5, 6, 7]]       )
     _snake_case				= np.array([0, 0, 0, 1, 1]       )
     _snake_case				= 2
     _snake_case				= 2

     # Assert that the function raises an AssertionError if dimensions > classes
     with pytest.raises(__lowerCAmelCase       ) as error_info:
          _snake_case				= linear_discriminant_analysis(
              __lowerCAmelCase   ,		__lowerCAmelCase   ,		__lowerCAmelCase   ,		__lowerCAmelCase       )
          if isinstance(__lowerCAmelCase   ,		np.ndarray       ):
               raise AssertionError(
                   "Did not raise AssertionError for dimensions > classes"       )
          assert error_info.type is AssertionError





def       __a      (  )		->					None:

     """simple docstring"""




     _snake_case				= np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]]       )
     _snake_case				= 2
     _snake_case				= np.array([[6.92820323, 8.66025404, 10.39230485], [3.0, 3.0, 3.0]]       )

     with pytest.raises(__lowerCAmelCase       ) as error_info:
          _snake_case				= principal_component_analysis(__lowerCAmelCase   ,		__lowerCAmelCase       )
          if not np.allclose(__lowerCAmelCase   ,		__lowerCAmelCase       ):
               raise AssertionError
          assert error_info.type is AssertionError


if __name__ == "__main__":
   import doctest

   doctest.testmod()







def        __a			(   __lowerCAmelCase   )     ->     List[str]:
					stooge(__lowerCAmelCase      ,	0      ,	len(__lowerCAmelCase   ) - 1   )
					return arr

def        __a			(   __lowerCAmelCase      ,	__lowerCAmelCase      ,	__lowerCAmelCase   )     ->     int:
					if i >= h:
										return

					# If first element is smaller than the last then swap them
					if arr[i] > arr[h]:
										SCREAMING_SNAKE_CASE					,  SCREAMING_SNAKE_CASE							:     Any						=				arr[h], arr[i]

					# If there are more than 2 elements in the array
					if h - i + 1 > 2:
										SCREAMING_SNAKE_CASE							:     Union[str, Any]						=				(int)((h - i + 1) / 3   )

										# Recursively sort first 2/3 elements
										stooge(__lowerCAmelCase      ,	__lowerCAmelCase      ,	(h - t)   )

										# Recursively sort last 2/3 elements
										stooge(__lowerCAmelCase      ,	i + t      ,	(__lowerCAmelCase)   )

										# Recursively sort first 2/3 elements
										stooge(__lowerCAmelCase      ,	__lowerCAmelCase      ,	(h - t)   )


if __name__ == "__main__":
			_lowerCamelCase    :		List[str]		      =    input("""Enter numbers separated by a comma:\n""").strip()
			_lowerCamelCase    :		List[Any]		      =    [int(item) for item in user_input.split(""",""")]
			print(stooge_sort(unsorted))