





import logging

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

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





def 						lowerCamelCase__     (     UpperCamelCase__			:       np.ndarray						)			-> np.ndarray:



					'''simple docstring'''




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





def 						lowerCamelCase__     (     UpperCamelCase__			:       np.ndarray       ,    UpperCamelCase__			:       np.ndarray       ,    UpperCamelCase__			:       int						)			-> np.ndarray:



					'''simple docstring'''




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

					return covariance_sum / features.shape[1]





def 						lowerCamelCase__     (     UpperCamelCase__			:       np.ndarray       ,    UpperCamelCase__			:       np.ndarray       ,    UpperCamelCase__			:       int						)			-> np.ndarray:



					'''simple docstring'''




					_snake_case									=				features.mean(1						)
					_snake_case									=				np.nan
					for i in range(UpperCamelCase__						):
										_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(UpperCamelCase__						) - column_reshape(UpperCamelCase__						)       ,    (column_reshape(UpperCamelCase__						) - column_reshape(UpperCamelCase__						)).T       ,    )
										else:
															# If covariance_sum is np.nan (i.e. first loop)
															_snake_case									=				device_data * np.dot(
															    column_reshape(UpperCamelCase__						) - column_reshape(UpperCamelCase__						)       ,    (column_reshape(UpperCamelCase__						) - column_reshape(UpperCamelCase__						)).T       ,    )

					return covariance_sum / features.shape[1]





def 						lowerCamelCase__     (     UpperCamelCase__			:       np.ndarray       ,    UpperCamelCase__			:       int						)			-> np.ndarray:



					'''simple docstring'''




					if features.any():
										_snake_case									=				features.mean(1						)
										# Center the dataset
										_snake_case									=				features - np.reshape(UpperCamelCase__       ,    (data_mean.size, 1)						)
										_snake_case									=				np.dot(UpperCamelCase__       ,    centered_data.T						) / features.shape[1]
										_snake_case							,     _snake_case									=				np.linalg.eigh(UpperCamelCase__						)
										# 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       ,    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 						lowerCamelCase__     (     UpperCamelCase__			:       np.ndarray       ,    UpperCamelCase__			:       np.ndarray       ,    UpperCamelCase__			:       int       ,    UpperCamelCase__			:       int						)			-> np.ndarray:



					'''simple docstring'''




					assert classes > dimensions

					# Check if features have been already loaded
					if features.any:
										_snake_case							,     _snake_case									=				eigh(
										    covariance_between_classes(UpperCamelCase__       ,    UpperCamelCase__       ,    UpperCamelCase__						)       ,    covariance_within_classes(UpperCamelCase__       ,    UpperCamelCase__       ,    UpperCamelCase__						)       ,    )
										_snake_case									=				eigenvectors[:, ::-1][:, :dimensions]
										_snake_case							,     _snake_case							,     _snake_case									=				np.linalg.svd(UpperCamelCase__						)
										_snake_case									=				svd_matrix[:, 0:dimensions]
										_snake_case									=				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 						lowerCamelCase__     (     )			-> 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(UpperCamelCase__						) as error_info:
										_snake_case									=				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 						lowerCamelCase__     (     )			-> None:



					'''simple docstring'''




					_snake_case									=				np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]]						)
					_snake_case									=				2
					_snake_case									=				np.array([[6.9282_0323, 8.6602_5404, 10.3923_0485], [3.0, 3.0, 3.0]]						)

					with pytest.raises(UpperCamelCase__						) as error_info:
										_snake_case									=				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()










from collections import deque

from .hash_table import HashTable
class 			UpperCamelCase_		(  _lowerCamelCase					):




					def __init__(		self				,						*lowerCAmelCase_				,						**lowerCAmelCase_  )		->							Any:
										super().__init__(*lowerCAmelCase_				,						**lowerCAmelCase_  )




					def 	lowerCAmelCase			(		self				,						lowerCAmelCase_				,						lowerCAmelCase_  )		->							Optional[int]:
										_snake_case									=				deque([]  ) if self.values[key] is None else self.values[key]
										self.values[key].appendleft(lowerCAmelCase_  )
										_snake_case									=				self.values[key]




					def 	lowerCAmelCase			(		self  )		->							Optional[int]:
										return (
										    sum(self.charge_factor - len(lowerCAmelCase_  ) for slot in self.values  )
										    / self.size_table
										    * self.charge_factor
										)






					def 	lowerCAmelCase			(		self				,						lowerCAmelCase_				,						lowerCAmelCase_=None  )		->							str:
										if not (
										    len(self.values[key]  ) == self.charge_factor and self.values.count(lowerCAmelCase_  ) == 0
										):
															return key
										return super()._collision_resolution(lowerCAmelCase_				,						lowerCAmelCase_  )



