





import logging

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

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

def       A__(		__lowerCAmelCase ):
				return input_array.reshape((input_array.size, 1) )

def       A__(		__lowerCAmelCase	,			__lowerCAmelCase	,			__lowerCAmelCase ):
				_snake_case :			Tuple  						=   np.nan
				for i in range(__lowerCAmelCase ):
								_snake_case :			List[Any]  						=   features[:, labels == i]
								_snake_case :			int  						=   data.mean(1 )
								# Centralize the data of class i
								_snake_case :			List[Any]  						=   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)
												_snake_case :			List[str]  						=   np.dot(__lowerCAmelCase	,			centered_data.T )

				return covariance_sum / features.shape[1]

def       A__(		__lowerCAmelCase	,			__lowerCAmelCase	,			__lowerCAmelCase ):
				_snake_case :			str  						=   features.mean(1 )
				_snake_case :			Union[str, Any]  						=   np.nan
				for i in range(__lowerCAmelCase ):
								_snake_case :			str  						=   features[:, labels == i]
								_snake_case :			int  						=   data.shape[1]
								_snake_case :			Optional[Any]  						=   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)
												_snake_case :			List[Any]  						=   device_data * np.dot(
												    column_reshape(__lowerCAmelCase ) - column_reshape(__lowerCAmelCase )	,			(column_reshape(__lowerCAmelCase ) - column_reshape(__lowerCAmelCase )).T	,			)

				return covariance_sum / features.shape[1]

def       A__(		__lowerCAmelCase	,			__lowerCAmelCase ):

				# Check if the features have been loaded
				if features.any():
								_snake_case :			Optional[Any]  						=   features.mean(1 )
								# Center the dataset
								_snake_case :			int  						=   features - np.reshape(__lowerCAmelCase	,			(data_mean.size, 1) )
								_snake_case :			Optional[int]  						=   np.dot(__lowerCAmelCase	,			centered_data.T ) / features.shape[1]
								_snake_case						,			_snake_case :			Any  						=   np.linalg.eigh(__lowerCAmelCase )
								# Take all the columns in the reverse order (-1), and then takes only the first
								_snake_case :			List[Any]  						=   eigenvectors[:, ::-1][:, 0:dimensions]
								# Project the database on the new space
								_snake_case :			List[Any]  						=   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       A__(		__lowerCAmelCase	,			__lowerCAmelCase	,			__lowerCAmelCase	,			__lowerCAmelCase ):
				assert classes > dimensions

				# Check if features have been already loaded
				if features.any:
								_snake_case						,			_snake_case :			Optional[int]  						=   eigh(
								    covariance_between_classes(__lowerCAmelCase	,			__lowerCAmelCase	,			__lowerCAmelCase )	,			covariance_within_classes(__lowerCAmelCase	,			__lowerCAmelCase	,			__lowerCAmelCase )	,			)
								_snake_case :			Optional[int]  						=   eigenvectors[:, ::-1][:, :dimensions]
								_snake_case						,			_snake_case						,			_snake_case :			Union[str, Any]  						=   np.linalg.svd(__lowerCAmelCase )
								_snake_case :			int  						=   svd_matrix[:, 0:dimensions]
								_snake_case :			List[str]  						=   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       A__(		):
				# Create dummy dataset with 2 classes and 3 features
				_snake_case :			str  						=   np.array([[1, 2, 3, 4, 5], [2, 3, 4, 5, 6], [3, 4, 5, 6, 7]] )
				_snake_case :			str  						=   np.array([0, 0, 0, 1, 1] )
				_snake_case :			Union[str, Any]  						=   2
				_snake_case :			List[str]  						=   2

				# Assert that the function raises an AssertionError if dimensions > classes
				with pytest.raises(__lowerCAmelCase ) as error_info:
								_snake_case :			Optional[Any]  						=   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       A__(		):
				_snake_case :			str  						=   np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]] )
				_snake_case :			List[Any]  						=   2
				_snake_case :			Any  						=   np.array([[6.92_820_323, 8.66_025_404, 10.39_230_485], [3.0, 3.0, 3.0]] )

				with pytest.raises(__lowerCAmelCase ) as error_info:
								_snake_case :			Dict  						=   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()













from math import factorial

def       A__(		__lowerCAmelCase	,			__lowerCAmelCase	,			__lowerCAmelCase ):
				if successes > trials:
								raise ValueError('successes must be lower or equal to trials' )
				if trials < 0 or successes < 0:
								raise ValueError('the function is defined for non-negative integers' )
				if not isinstance(__lowerCAmelCase	,			__lowerCAmelCase ) or not isinstance(__lowerCAmelCase	,			__lowerCAmelCase ):
								raise ValueError('the function is defined for non-negative integers' )
				if not 0 < prob < 1:
								raise ValueError('prob has to be in range of 1 - 0' )
				_snake_case :			Optional[int]  						=   (prob**successes) * ((1 - prob) ** (trials - successes))
				# Calculate the binomial coefficient: n! / k!(n-k)!
				_snake_case :			List[Any]  						=   float(factorial(__lowerCAmelCase ) )
				coefficient /= factorial(__lowerCAmelCase ) * factorial(trials - successes )
				return probability * coefficient


if __name__ == "__main__":
		from doctest import testmod

		testmod()
		print('''Probability of 2 successes out of 4 trails''')
		print('''with probability of 0.75 is:''', end=''' ''')
		print(binomial_distribution(2, 4, 0.75))






