
import logging

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

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


def 						UpperCAmelCase			(	a_						)		->	np.ndarray:







				"""simple docstring"""



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


def 						UpperCAmelCase			(	a_		,   a_		,   a_						)		->	np.ndarray:







				"""simple docstring"""



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

				return covariance_sum / features.shape[1]


def 						UpperCAmelCase			(	a_		,   a_		,   a_						)		->	np.ndarray:







				"""simple docstring"""



				__A   			= features.mean(1						)
				__A   			= np.nan
				for i in range(a_						):
								__A   			= features[:, labels == i]
								__A   			= data.shape[1]
								__A   			= 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)
												__A   			= device_data * np.dot(
												    column_reshape(a_						) - column_reshape(a_						)		,   (column_reshape(a_						) - column_reshape(a_						)).T		,   )

				return covariance_sum / features.shape[1]


def 						UpperCAmelCase			(	a_		,   a_						)		->	np.ndarray:







				"""simple docstring"""



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







				"""simple docstring"""



				assert classes > dimensions

				# Check if features have been already loaded
				if features.any:
								__A			,							__A   			= eigh(
								    covariance_between_classes(a_		,   a_		,   a_						)		,   covariance_within_classes(a_		,   a_		,   a_						)		,   )
								__A   			= eigenvectors[:, ::-1][:, :dimensions]
								__A			,							__A			,							__A   			= np.linalg.svd(a_						)
								__A   			= svd_matrix[:, 0:dimensions]
								__A   			= 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 						UpperCAmelCase			(	)		->	None:







				"""simple docstring"""



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

				# Assert that the function raises an AssertionError if dimensions > classes
				with pytest.raises(a_						) as error_info:
								__A   			= 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 						UpperCAmelCase			(	)		->	None:







				"""simple docstring"""



				__A   			= np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]]						)
				__A   			= 2
				__A   			= np.array([[6.92_820_323, 8.66_025_404, 10.39_230_485], [3.0, 3.0, 3.0]]						)

				with pytest.raises(a_						) as error_info:
								__A   			= 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 collections import Counter
from random import random






class  lowerCAmelCase__   :






					def __init__(   self		):


											"""simple docstring"""





											lowercase_	:     int													=       {}






					def 	_snake_case    (   self				,							__SCREAMING_SNAKE_CASE		):


											"""simple docstring"""





											lowercase_	:     Dict													=       {}






					def 	_snake_case    (   self				,							__SCREAMING_SNAKE_CASE				,							__SCREAMING_SNAKE_CASE				,							__SCREAMING_SNAKE_CASE		):


											"""simple docstring"""





											if nodea not in self.connections:
																	self.add_node(__SCREAMING_SNAKE_CASE		)
											if nodea not in self.connections:
																	self.add_node(__SCREAMING_SNAKE_CASE		)
											lowercase_	:     Optional[Any]													=       probability






					def 	_snake_case    (   self		):


											"""simple docstring"""





											return list(self.connections		)






					def 	_snake_case    (   self				,							__SCREAMING_SNAKE_CASE		):


											"""simple docstring"""





											lowercase_	:     Any													=       0
											lowercase_	:     Tuple													=       random()

											for dest in self.connections[node]:
																	current_probability += self.connections[node][dest]
																	if current_probability > random_value:
																							return dest
											return ""







def 					snake_case_		(				__SCREAMING_SNAKE_CASE					: str      ,      __SCREAMING_SNAKE_CASE					: list[tuple[str, str, float]]      ,      __SCREAMING_SNAKE_CASE					: int							):



						"""simple docstring"""





						lowercase_	:     List[Any]													=       MarkovChainGraphUndirectedUnweighted()

						for nodea, nodea, probability in transitions:
												graph.add_transition_probability(__SCREAMING_SNAKE_CASE      ,      __SCREAMING_SNAKE_CASE      ,      __SCREAMING_SNAKE_CASE							)

						lowercase_	:     str													=       Counter(graph.get_nodes()							)
						lowercase_	:     Any													=       start

						for _ in range(__SCREAMING_SNAKE_CASE							):
												lowercase_	:     int													=       graph.transition(__SCREAMING_SNAKE_CASE							)
												visited[node] += 1

						return visited


if __name__ == "__main__":
							import doctest

							doctest.testmod()



