






import logging

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

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







def 	__magic_name__( _A					):
						'''simple docstring'''





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







def 	__magic_name__( _A						,      _A						,      _A					):
						'''simple docstring'''





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

						return covariance_sum / features.shape[1]







def 	__magic_name__( _A						,      _A						,      _A					):
						'''simple docstring'''





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

						return covariance_sum / features.shape[1]







def 	__magic_name__( _A						,      _A					):
						'''simple docstring'''





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

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







def 	__magic_name__( _A						,      _A						,      _A						,      _A					):
						'''simple docstring'''





						assert classes > dimensions

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

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







def 	__magic_name__( ):
						'''simple docstring'''





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

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







def 	__magic_name__( ):
						'''simple docstring'''





						UpperCamelCase__         = np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]]					)
						UpperCamelCase__         = 2
						UpperCamelCase__         = np.array([[6.9_2_8_2_0_3_2_3, 8.6_6_0_2_5_4_0_4, 10.3923_0485], [3.0, 3.0, 3.0]]					)

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


if __name__ == "__main__":
					import doctest

					doctest.testmod()








'''simple docstring'''


from __future__ import annotations

from typing import Any
class    _SCREAMING_SNAKE_CASE							:


			'''simple docstring'''





			def __init__(   self							:						Union[str, Any] ,      lowercase							:						int			)							->    None:

									'''simple docstring'''







									UpperCamelCase__         = num_of_nodes
									UpperCamelCase__         = []
									UpperCamelCase__         = {}






			def 				A      (   self							:						Optional[Any] ,      lowercase							:						int ,      lowercase							:						int ,      lowercase							:						int			)							->    None:

									'''simple docstring'''







									self.m_edges.append([u_node, v_node, weight]			)






			def 				A      (   self							:						str ,      lowercase							:						int			)							->    int:

									'''simple docstring'''







									if self.m_component[u_node] == u_node:
															return u_node
									return self.find_component(self.m_component[u_node]			)






			def 				A      (   self							:						Union[str, Any] ,      lowercase							:						int			)							->    None:

									'''simple docstring'''







									if self.m_component[u_node] != u_node:
															for k in self.m_component:
																					UpperCamelCase__         = self.find_component(lowercase			)






			def 				A      (   self							:						Tuple ,      lowercase							:						list[int] ,      lowercase							:						int ,      lowercase							:						int			)							->    None:

									'''simple docstring'''







									if component_size[u_node] <= component_size[v_node]:
															UpperCamelCase__         = v_node
															component_size[v_node] += component_size[u_node]
															self.set_component(lowercase			)

									elif component_size[u_node] >= component_size[v_node]:
															UpperCamelCase__         = self.find_component(lowercase			)
															component_size[u_node] += component_size[v_node]
															self.set_component(lowercase			)







			def 				A      (   self							:						int			)							->    None:

									'''simple docstring'''







									UpperCamelCase__         = []
									UpperCamelCase__         = 0

									UpperCamelCase__         = [-1] * self.m_num_of_nodes

									# A list of components (initialized to all of the nodes)
									for node in range(self.m_num_of_nodes			):
															self.m_component.update({node: node}			)
															component_size.append(1			)

									UpperCamelCase__         = self.m_num_of_nodes

									while num_of_components > 1:
															for edge in self.m_edges:
																					UpperCamelCase__    ,   UpperCamelCase__    ,   UpperCamelCase__         = edge

																					UpperCamelCase__         = self.m_component[u]
																					UpperCamelCase__         = self.m_component[v]

																					if u_component != v_component:

																											for component in (u_component, v_component):
																																	if (
																																	    minimum_weight_edge[component] == -1
																																	    or minimum_weight_edge[component][2] > w
																																	):
																																							UpperCamelCase__         = [u, v, w]

															for edge in minimum_weight_edge:
																					if isinstance(lowercase ,      lowercase			):
																											UpperCamelCase__    ,   UpperCamelCase__    ,   UpperCamelCase__         = edge

																											UpperCamelCase__         = self.m_component[u]
																											UpperCamelCase__         = self.m_component[v]

																											if u_component != v_component:
																																	mst_weight += w
																																	self.union(lowercase ,      lowercase ,      lowercase			)
																																	print(f"Added edge [{u} - {v}]\nAdded weight: {w}\n"			)
																																	num_of_components -= 1

															UpperCamelCase__         = [-1] * self.m_num_of_nodes
									print(f"The total weight of the minimal spanning tree is: {mst_weight}"			)







def 	__magic_name__( ):
						'''simple docstring'''







if __name__ == "__main__":
					import doctest

					doctest.testmod()
