"""simple docstring"""

import logging

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

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







def 							SCREAMING_SNAKE_CASE__      (		SCREAMING_SNAKE_CASE__ :  np.ndarray			):



					"""simple docstring"""





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







def 							SCREAMING_SNAKE_CASE__      (		SCREAMING_SNAKE_CASE__ :  np.ndarray				,    SCREAMING_SNAKE_CASE__ :  np.ndarray				,    SCREAMING_SNAKE_CASE__ :  int			):



					"""simple docstring"""





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

					return covariance_sum / features.shape[1]







def 							SCREAMING_SNAKE_CASE__      (		SCREAMING_SNAKE_CASE__ :  np.ndarray				,    SCREAMING_SNAKE_CASE__ :  np.ndarray				,    SCREAMING_SNAKE_CASE__ :  int			):



					"""simple docstring"""





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

					return covariance_sum / features.shape[1]







def 							SCREAMING_SNAKE_CASE__      (		SCREAMING_SNAKE_CASE__ :  np.ndarray				,    SCREAMING_SNAKE_CASE__ :  int			):



					"""simple docstring"""





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

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







def 							SCREAMING_SNAKE_CASE__      (		SCREAMING_SNAKE_CASE__ :  np.ndarray				,    SCREAMING_SNAKE_CASE__ :  np.ndarray				,    SCREAMING_SNAKE_CASE__ :  int				,    SCREAMING_SNAKE_CASE__ :  int			):



					"""simple docstring"""





					assert classes > dimensions

					# Check if features have been already loaded
					if features.any:
										snake_case_					:		Union[str, Any] 					=					eigh(
										    covariance_between_classes(SCREAMING_SNAKE_CASE__				,    SCREAMING_SNAKE_CASE__				,    SCREAMING_SNAKE_CASE__			)				,    covariance_within_classes(SCREAMING_SNAKE_CASE__				,    SCREAMING_SNAKE_CASE__				,    SCREAMING_SNAKE_CASE__			)				,    )
										snake_case_					:		Tuple 					=					eigenvectors[:, ::-1][:, :dimensions]
										snake_case_					:		int 					=					np.linalg.svd(SCREAMING_SNAKE_CASE__			)
										snake_case_					:		Any 					=					svd_matrix[:, 0:dimensions]
										snake_case_					:		Dict 					=					np.dot(filtered_svd_matrix.T				,    SCREAMING_SNAKE_CASE__			)
										logging.info("""Linear Discriminant Analysis computed"""			)

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







def 							SCREAMING_SNAKE_CASE__      (		):



					"""simple docstring"""





					snake_case_					:		int 					=					np.array([[1, 2, 3, 4, 5], [2, 3, 4, 5, 6], [3, 4, 5, 6, 7]]			)
					snake_case_					:		Any 					=					np.array([0, 0, 0, 1, 1]			)
					snake_case_					:		Dict 					=					2
					snake_case_					:		Dict 					=					2

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







def 							SCREAMING_SNAKE_CASE__      (		):



					"""simple docstring"""





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

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


if __name__ == "__main__":
			import doctest

			doctest.testmod()









"""simple docstring"""

from random import randint
from tempfile import TemporaryFile

import numpy as np







def 							SCREAMING_SNAKE_CASE__      (		SCREAMING_SNAKE_CASE__ :  List[Any]				,    SCREAMING_SNAKE_CASE__ :  Dict				,    SCREAMING_SNAKE_CASE__ :  Optional[int]			):



					"""simple docstring"""





					snake_case_					:		Union[str, Any] 					=					0
					if start < end:
										snake_case_					:		Union[str, Any] 					=					randint(SCREAMING_SNAKE_CASE__				,    SCREAMING_SNAKE_CASE__			)
										snake_case_					:		List[Any] 					=					a[end]
										snake_case_					:		Dict 					=					a[pivot]
										snake_case_					:		Any 					=					temp

										snake_case_					,			snake_case_					:		Dict 					=					_in_place_partition(SCREAMING_SNAKE_CASE__				,    SCREAMING_SNAKE_CASE__				,    SCREAMING_SNAKE_CASE__			)
										count += _in_place_quick_sort(SCREAMING_SNAKE_CASE__				,    SCREAMING_SNAKE_CASE__				,    p - 1			)
										count += _in_place_quick_sort(SCREAMING_SNAKE_CASE__				,    p + 1				,    SCREAMING_SNAKE_CASE__			)
					return count







def 							SCREAMING_SNAKE_CASE__      (		SCREAMING_SNAKE_CASE__ :  int				,    SCREAMING_SNAKE_CASE__ :  List[Any]				,    SCREAMING_SNAKE_CASE__ :  Dict			):



					"""simple docstring"""





					snake_case_					:		Tuple 					=					0
					snake_case_					:		List[Any] 					=					randint(SCREAMING_SNAKE_CASE__				,    SCREAMING_SNAKE_CASE__			)
					snake_case_					:		Dict 					=					a[end]
					snake_case_					:		List[Any] 					=					a[pivot]
					snake_case_					:		Optional[Any] 					=					temp
					snake_case_					:		List[str] 					=					start - 1
					for index in range(SCREAMING_SNAKE_CASE__				,    SCREAMING_SNAKE_CASE__			):
										count += 1
										if a[index] < a[end]:  # check if current val is less than pivot value
															snake_case_					:		Any 					=					new_pivot_index + 1
															snake_case_					:		Tuple 					=					a[new_pivot_index]
															snake_case_					:		Optional[int] 					=					a[index]
															snake_case_					:		Tuple 					=					temp

					snake_case_					:		Union[str, Any] 					=					a[new_pivot_index + 1]
					snake_case_					:		Union[str, Any] 					=					a[end]
					snake_case_					:		Union[str, Any] 					=					temp
					return new_pivot_index + 1, count


a_			   =					TemporaryFile()
a_			   =					100  # 1000 elements are to be sorted


a_   ,    a_			   =					0, 1  # mean and standard deviation
a_			   =					np.random.normal(mu, sigma, p)
np.save(outfile, X)
print('''The array is''')
print(X)


outfile.seek(0)  # using the same array
a_			   =					np.load(outfile)
a_			   =					len(M) - 1
a_			   =					_in_place_quick_sort(M, 0, r)

print(
    '''No of Comparisons for 100 elements selected from a standard normal distribution'''
    '''is :'''
)


print(z)




