





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 defaultdict

from graphs.minimum_spanning_tree_prims import prisms_algorithm as mst





def   lowerCamelCase__       (       )     ->	List[str]:



					'''simple docstring'''




					_snake_case							,       _snake_case													=			9, 14  # noqa: F841
					_snake_case													=			[
					    [0, 1, 4],
					    [0, 7, 8],
					    [1, 2, 8],
					    [7, 8, 7],
					    [7, 6, 1],
					    [2, 8, 2],
					    [8, 6, 6],
					    [2, 3, 7],
					    [2, 5, 4],
					    [6, 5, 2],
					    [3, 5, 14],
					    [3, 4, 9],
					    [5, 4, 10],
					    [1, 7, 11],
					]

					_snake_case													=			defaultdict(UpperCamelCase__  )
					for nodea, nodea, cost in edges:
										adjancency[nodea].append([nodea, cost]  )
										adjancency[nodea].append([nodea, cost]  )

					_snake_case													=			mst(UpperCamelCase__  )

					_snake_case													=			[
					    [7, 6, 1],
					    [2, 8, 2],
					    [6, 5, 2],
					    [0, 1, 4],
					    [2, 5, 4],
					    [2, 3, 7],
					    [0, 7, 8],
					    [3, 4, 9],
					]

					for answer in expected:
										_snake_case													=			tuple(answer[:2]  )
										_snake_case													=			tuple(edge[::-1]  )
										assert edge in result or reverse in result



