


"""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__			(lowerCAmelCase_  ):




					'''simple docstring'''


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




def   UpperCAmelCase__			(lowerCAmelCase_    ,		lowerCAmelCase_    ,		lowerCAmelCase_  ):




					'''simple docstring'''


					__SCREAMING_SNAKE_CASE		  =							np.nan
					for i in range(__lowerCAmelCase  ):
										__SCREAMING_SNAKE_CASE		  =							features[:, labels == i]
										__SCREAMING_SNAKE_CASE		  =							data.mean(1  )
										# Centralize the data of class i
										__SCREAMING_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)
															__SCREAMING_SNAKE_CASE		  =							np.dot(__lowerCAmelCase    ,		centered_data.T  )

					return covariance_sum / features.shape[1]




def   UpperCAmelCase__			(lowerCAmelCase_    ,		lowerCAmelCase_    ,		lowerCAmelCase_  ):




					'''simple docstring'''


					__SCREAMING_SNAKE_CASE		  =							features.mean(1  )
					__SCREAMING_SNAKE_CASE		  =							np.nan
					for i in range(__lowerCAmelCase  ):
										__SCREAMING_SNAKE_CASE		  =							features[:, labels == i]
										__SCREAMING_SNAKE_CASE		  =							data.shape[1]
										__SCREAMING_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)
															__SCREAMING_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   UpperCAmelCase__			(lowerCAmelCase_    ,		lowerCAmelCase_  ):




					'''simple docstring'''


					if features.any():
										__SCREAMING_SNAKE_CASE		  =							features.mean(1  )
										# Center the dataset
										__SCREAMING_SNAKE_CASE		  =							features - np.reshape(__lowerCAmelCase    ,		(data_mean.size, 1)  )
										__SCREAMING_SNAKE_CASE		  =							np.dot(__lowerCAmelCase    ,		centered_data.T  ) / features.shape[1]
										__SCREAMING_SNAKE_CASE  ,    __SCREAMING_SNAKE_CASE		  =							np.linalg.eigh(__lowerCAmelCase  )
										# Take all the columns in the reverse order (-1), and then takes only the first
										__SCREAMING_SNAKE_CASE		  =							eigenvectors[:, ::-1][:, 0:dimensions]
										# Project the database on the new space
										__SCREAMING_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   UpperCAmelCase__			(lowerCAmelCase_    ,		lowerCAmelCase_    ,		lowerCAmelCase_    ,		lowerCAmelCase_  ):




					'''simple docstring'''


					assert classes > dimensions

					# Check if features have been already loaded
					if features.any:
										__SCREAMING_SNAKE_CASE  ,    __SCREAMING_SNAKE_CASE		  =							eigh(
										    covariance_between_classes(__lowerCAmelCase    ,		__lowerCAmelCase    ,		__lowerCAmelCase  )    ,		covariance_within_classes(__lowerCAmelCase    ,		__lowerCAmelCase    ,		__lowerCAmelCase  )    ,		)
										__SCREAMING_SNAKE_CASE		  =							eigenvectors[:, ::-1][:, :dimensions]
										__SCREAMING_SNAKE_CASE  ,    __SCREAMING_SNAKE_CASE  ,    __SCREAMING_SNAKE_CASE		  =							np.linalg.svd(__lowerCAmelCase  )
										__SCREAMING_SNAKE_CASE		  =							svd_matrix[:, 0:dimensions]
										__SCREAMING_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   UpperCAmelCase__			():




					'''simple docstring'''


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

					# Assert that the function raises an AssertionError if dimensions > classes
					with pytest.raises(__lowerCAmelCase  ) as error_info:
										__SCREAMING_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   UpperCAmelCase__			():




					'''simple docstring'''


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

					with pytest.raises(__lowerCAmelCase  ) as error_info:
										__SCREAMING_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()







'''simple docstring'''




def 	__lowerCamelCase			(      __lowerCAmelCase       :							int		)		->  int:
   assert isinstance(__lowerCAmelCase      ,    __lowerCAmelCase		), F'''The input value of [n={number}] is not an integer'''

   if number == 1:
      return 2
   elif number < 1:
      snake_case 						=   F'''The input value of [n={number}] has to be > 0'''
      raise ValueError(__lowerCAmelCase		)
   else:
      snake_case 						=   sylvester(number - 1		)
      snake_case 						=   num - 1
      snake_case 						=   num
      return lower * upper + 1


if __name__ == "__main__":
 print(F"""The 8th number in Sylvester's sequence: {sylvester(8)}""")

