

import logging

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

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





def    __lowerCamelCase      (					UpperCamelCase__ ):







							'''simple docstring'''






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





def    __lowerCamelCase      (					UpperCamelCase__  ,				UpperCamelCase__  ,				UpperCamelCase__ ):







							'''simple docstring'''






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

							return covariance_sum / features.shape[1]





def    __lowerCamelCase      (					UpperCamelCase__  ,				UpperCamelCase__  ,				UpperCamelCase__ ):







							'''simple docstring'''






							snake_case_     							=       features.mean(1 )
							snake_case_     							=       np.nan
							for i in range(_SCREAMING_SNAKE_CASE ):
														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(_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_     							=       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    __lowerCamelCase      (					UpperCamelCase__  ,				UpperCamelCase__ ):







							'''simple docstring'''






							if features.any():
														snake_case_     							=       features.mean(1 )
														# Center the dataset
														snake_case_     							=       features - np.reshape(_SCREAMING_SNAKE_CASE  ,				(data_mean.size, 1) )
														snake_case_     							=       np.dot(_SCREAMING_SNAKE_CASE  ,				centered_data.T ) / features.shape[1]
														snake_case_							,       snake_case_     							=       np.linalg.eigh(_SCREAMING_SNAKE_CASE )
														# 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  ,				_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    __lowerCamelCase      (					UpperCamelCase__  ,				UpperCamelCase__  ,				UpperCamelCase__  ,				UpperCamelCase__ ):







							'''simple docstring'''






							assert classes > dimensions

							# Check if features have been already loaded
							if features.any:
														snake_case_							,       snake_case_     							=       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_     							=       eigenvectors[:, ::-1][:, :dimensions]
														snake_case_							,       snake_case_							,       snake_case_     							=       np.linalg.svd(_SCREAMING_SNAKE_CASE )
														snake_case_     							=       svd_matrix[:, 0:dimensions]
														snake_case_     							=       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    __lowerCamelCase      (					):







							'''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(_SCREAMING_SNAKE_CASE ) as error_info:
														snake_case_     							=       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    __lowerCamelCase      (					):







							'''simple docstring'''






							snake_case_     							=       np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]] )
							snake_case_     							=       2
							snake_case_     							=       np.array([[6.92_82_03_23, 8.66_02_54_04, 10.39_23_04_85], [3.0, 3.0, 3.0]] )

							with pytest.raises(_SCREAMING_SNAKE_CASE ) as error_info:
														snake_case_     							=       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'''





class 						a__					:





			'''simple docstring'''

			def __init__(  self							:			Tuple			,    lowerCAmelCase_							:			Optional[Any]			,    lowerCAmelCase_							:			Dict	)      ->		List[str]:
						__A=	name
						__A=	val
			def __str__(  self							:			int	)      ->		List[Any]:
						return F"""{self.__class__.__name__}({self.name}, {self.val})"""

			def __lt__(  self							:			Optional[Any]			,    lowerCAmelCase_							:			str	)      ->		List[Any]:
						return self.val < other.val


class 						a__					:





			'''simple docstring'''

			def __init__(  self							:			Tuple			,    lowerCAmelCase_							:			int	)      ->		Any:
						__A=	{}
						__A=	{}
						__A=	self.build_heap(lowerCAmelCase_	)
			def __getitem__(  self							:			int			,    lowerCAmelCase_							:			Dict	)      ->		Tuple:
						return self.get_value(lowerCAmelCase_	)
			def 					lowerCAmelCase     (  self							:			Tuple			,    lowerCAmelCase_							:			List[str]	)      ->		List[str]:
						return (idx - 1) // 2
			def 					lowerCAmelCase     (  self							:			Union[str, Any]			,    lowerCAmelCase_							:			Union[str, Any]	)      ->		List[str]:
						return idx * 2 + 1
			def 					lowerCAmelCase     (  self							:			Optional[Any]			,    lowerCAmelCase_							:			Union[str, Any]	)      ->		Any:
						return idx * 2 + 2
			def 					lowerCAmelCase     (  self							:			str			,    lowerCAmelCase_							:			Union[str, Any]	)      ->		Dict:
						return self.heap_dict[key]
			def 					lowerCAmelCase     (  self							:			List[Any]			,    lowerCAmelCase_							:			List[Any]	)      ->		Tuple:
						__A=	len(lowerCAmelCase_	) - 1
						__A=	self.get_parent_idx(lowerCAmelCase_	)

						for idx, i in enumerate(lowerCAmelCase_	):
									__A=	idx
									__A=	i.val

						for i in range(lowerCAmelCase_			,    -1			,    -1	):
									self.sift_down(lowerCAmelCase_			,    lowerCAmelCase_	)
						return array
			def 					lowerCAmelCase     (  self							:			int			,    lowerCAmelCase_							:			List[Any]			,    lowerCAmelCase_							:			Tuple	)      ->		Dict:
						while True:
									__A=	self.get_left_child_idx(lowerCAmelCase_	)  # noqa: E741
									__A=	self.get_right_child_idx(lowerCAmelCase_	)

									__A=	idx
									if l < len(lowerCAmelCase_	) and array[l] < array[idx]:
												__A=	l
									if r < len(lowerCAmelCase_	) and array[r] < array[smallest]:
												__A=	r

									if smallest != idx:
												__A,	__A=	array[smallest], array[idx]
												(
												    (
												    __A
												),	(
												    __A
												),	
												)=	(
												    self.idx_of_element[array[smallest]],
												    self.idx_of_element[array[idx]],
												)
												__A=	smallest
									else:
												break
			def 					lowerCAmelCase     (  self							:			Dict			,    lowerCAmelCase_							:			Dict	)      ->		str:
						__A=	self.get_parent_idx(lowerCAmelCase_	)
						while p >= 0 and self.heap[p] > self.heap[idx]:
									__A,	__A=	self.heap[idx], self.heap[p]
									__A,	__A=	(
									    self.idx_of_element[self.heap[idx]],
									    self.idx_of_element[self.heap[p]],
									)
									__A=	p
									__A=	self.get_parent_idx(lowerCAmelCase_	)
			def 					lowerCAmelCase     (  self							:			Optional[Any]	)      ->		Tuple:
						return self.heap[0]
			def 					lowerCAmelCase     (  self							:			List[Any]	)      ->		int:
						__A,	__A=	self.heap[-1], self.heap[0]
						__A,	__A=	(
						    self.idx_of_element[self.heap[-1]],
						    self.idx_of_element[self.heap[0]],
						)

						__A=	self.heap.pop()
						del self.idx_of_element[x]
						self.sift_down(0			,    self.heap	)
						return x
			def 					lowerCAmelCase     (  self							:			Optional[int]			,    lowerCAmelCase_							:			Union[str, Any]	)      ->		Optional[int]:
						self.heap.append(lowerCAmelCase_	)
						__A=	len(self.heap	) - 1
						__A=	node.val
						self.sift_up(len(self.heap	) - 1	)
			def 					lowerCAmelCase     (  self							:			Optional[Any]	)      ->		Tuple:
						return len(self.heap	) == 0

			def 					lowerCAmelCase     (  self							:			Optional[int]			,    lowerCAmelCase_							:			List[Any]			,    lowerCAmelCase_							:			List[Any]	)      ->		Optional[Any]:
						assert (
						    self.heap[self.idx_of_element[node]].val > new_value
						), "newValue must be less that current value"
						__A=	new_value
						__A=	new_value
						self.sift_up(self.idx_of_element[node]	)


UpperCAmelCase__  			=				Node('''R''', -1)
UpperCAmelCase__  			=				Node('''B''', 6)
UpperCAmelCase__  			=				Node('''A''', 3)
UpperCAmelCase__  			=				Node('''X''', 1)
UpperCAmelCase__  			=				Node('''E''', 4)

# Use one of these two ways to generate Min-Heap

# Generating Min-Heap from array
UpperCAmelCase__  			=				MinHeap([r, b, a, x, e])

# Generating Min-Heap by Insert method
# myMinHeap.insert(a)
# myMinHeap.insert(b)
# myMinHeap.insert(x)
# myMinHeap.insert(r)
# myMinHeap.insert(e)

# Before
print('''Min Heap - before decrease key''')
for i in my_min_heap.heap:
					print(i)

print('''Min Heap - After decrease key of node [B -> -17]''')
my_min_heap.decrease_key(b, -1_7)

# After
for i in my_min_heap.heap:
					print(i)

if __name__ == "__main__":
					import doctest

					doctest.testmod()



