





'''simple docstring'''


import logging

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

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







def    _lowerCamelCase  (__lowerCamelCase  :     np.ndarray     )   ->    np.ndarray:
			return input_array.reshape((input_array.size, 1)     )







def    _lowerCamelCase  (__lowerCamelCase  :     np.ndarray					,  __lowerCamelCase  :     np.ndarray					,  __lowerCamelCase  :     int     )   ->    np.ndarray:
			a__     = np.nan
			for i in range(__lowerCamelCase     ):
						a__     = features[:, labels == i]
						a__     = data.mean(1     )
						# Centralize the data of class i
						a__     = 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)
									a__     = np.dot(__lowerCamelCase					,  centered_data.T     )

			return covariance_sum / features.shape[1]







def    _lowerCamelCase  (__lowerCamelCase  :     np.ndarray					,  __lowerCamelCase  :     np.ndarray					,  __lowerCamelCase  :     int     )   ->    np.ndarray:
			a__     = features.mean(1     )
			a__     = np.nan
			for i in range(__lowerCamelCase     ):
						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(__lowerCamelCase     ) - column_reshape(__lowerCamelCase     )					,  (column_reshape(__lowerCamelCase     ) - column_reshape(__lowerCamelCase     )).T					,  )
						else:
									# If covariance_sum is np.nan (i.e. first loop)
									a__     = device_data * np.dot(
									    column_reshape(__lowerCamelCase     ) - column_reshape(__lowerCamelCase     )					,  (column_reshape(__lowerCamelCase     ) - column_reshape(__lowerCamelCase     )).T					,  )

			return covariance_sum / features.shape[1]







def    _lowerCamelCase  (__lowerCamelCase  :     np.ndarray					,  __lowerCamelCase  :     int     )   ->    np.ndarray:

			# Check if the features have been loaded
			if features.any():
						a__     = features.mean(1     )
						# Center the dataset
						a__     = features - np.reshape(__lowerCamelCase					,  (data_mean.size, 1)     )
						a__     = np.dot(__lowerCamelCase					,  centered_data.T     ) / features.shape[1]
						a__   ,				a__     = np.linalg.eigh(__lowerCamelCase     )
						# 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					,  __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    _lowerCamelCase  (__lowerCamelCase  :     np.ndarray					,  __lowerCamelCase  :     np.ndarray					,  __lowerCamelCase  :     int					,  __lowerCamelCase  :     int     )   ->    np.ndarray:
			assert classes > dimensions

			# Check if features have been already loaded
			if features.any:
						a__   ,				a__     = eigh(
						    covariance_between_classes(__lowerCamelCase					,  __lowerCamelCase					,  __lowerCamelCase     )					,  covariance_within_classes(__lowerCamelCase					,  __lowerCamelCase					,  __lowerCamelCase     )					,  )
						a__     = eigenvectors[:, ::-1][:, :dimensions]
						a__   ,				a__   ,				a__     = np.linalg.svd(__lowerCamelCase     )
						a__     = svd_matrix[:, 0:dimensions]
						a__     = 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    _lowerCamelCase  ()   ->    None:
			# Create dummy dataset with 2 classes and 3 features
			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(__lowerCamelCase     ) as error_info:
						a__     = 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    _lowerCamelCase  ()   ->    None:
			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(__lowerCamelCase     ) as error_info:
						a__     = 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()










'''simple docstring'''


import math







def    _lowerCamelCase  (__lowerCamelCase  :     list					,  __lowerCamelCase  :     int = 0					,  __lowerCamelCase  :     int = 0     )   ->    list:
			a__     = end or len(__lowerCamelCase     )
			for i in range(__lowerCamelCase					,  __lowerCamelCase     ):
						a__     = i
						a__     = array[i]
						while temp_index != start and temp_index_value < array[temp_index - 1]:
									a__     = array[temp_index - 1]
									temp_index -= 1
						a__     = temp_index_value
			return array







def    _lowerCamelCase  (__lowerCamelCase  :     list					,  __lowerCamelCase  :     int					,  __lowerCamelCase  :     int     )   ->    None:  # Max Heap
			a__     = index
			a__     = 2 * index + 1  # Left Node
			a__     = 2 * index + 2  # Right Node

			if left_index < heap_size and array[largest] < array[left_index]:
						a__     = left_index

			if right_index < heap_size and array[largest] < array[right_index]:
						a__     = right_index

			if largest != index:
						a__   ,				a__     = array[largest], array[index]
						heapify(__lowerCamelCase					,  __lowerCamelCase					,  __lowerCamelCase     )







def    _lowerCamelCase  (__lowerCamelCase  :     list     )   ->    list:
			a__     = len(__lowerCamelCase     )

			for i in range(n // 2					,  -1					,  -1     ):
						heapify(__lowerCamelCase					,  __lowerCamelCase					,  __lowerCamelCase     )

			for i in range(n - 1					,  0					,  -1     ):
						a__   ,				a__     = array[0], array[i]
						heapify(__lowerCamelCase					,  0					,  __lowerCamelCase     )

			return array







def    _lowerCamelCase  (__lowerCamelCase  :     list					,  __lowerCamelCase  :     int					,  __lowerCamelCase  :     int					,  __lowerCamelCase  :     int     )   ->    int:
			if (array[first_index] > array[middle_index]) != (
			    array[first_index] > array[last_index]
			):
						return array[first_index]
			elif (array[middle_index] > array[first_index]) != (
			    array[middle_index] > array[last_index]
			):
						return array[middle_index]
			else:
						return array[last_index]







def    _lowerCamelCase  (__lowerCamelCase  :     list					,  __lowerCamelCase  :     int					,  __lowerCamelCase  :     int					,  __lowerCamelCase  :     int     )   ->    int:
			a__     = low
			a__     = high
			while True:
						while array[i] < pivot:
									i += 1
						j -= 1
						while pivot < array[j]:
									j -= 1
						if i >= j:
									return i
						a__   ,				a__     = array[j], array[i]
						i += 1







def    _lowerCamelCase  (__lowerCamelCase  :     list     )   ->    list:
			if len(__lowerCamelCase     ) == 0:
						return array
			a__     = 2 * math.ceil(math.loga(len(__lowerCamelCase     )     )     )
			a__     = 16
			return intro_sort(__lowerCamelCase					,  0					,  len(__lowerCamelCase     )					,  __lowerCamelCase					,  __lowerCamelCase     )







def    _lowerCamelCase  (__lowerCamelCase  :     list					,  __lowerCamelCase  :     int					,  __lowerCamelCase  :     int					,  __lowerCamelCase  :     int					,  __lowerCamelCase  :     int     )   ->    list:
			while end - start > size_threshold:
						if max_depth == 0:
									return heap_sort(__lowerCamelCase     )
						max_depth -= 1
						a__     = median_of_a(__lowerCamelCase					,  __lowerCamelCase					,  start + ((end - start) // 2) + 1					,  end - 1     )
						a__     = partition(__lowerCamelCase					,  __lowerCamelCase					,  __lowerCamelCase					,  __lowerCamelCase     )
						intro_sort(__lowerCamelCase					,  __lowerCamelCase					,  __lowerCamelCase					,  __lowerCamelCase					,  __lowerCamelCase     )
						a__     = p
			return insertion_sort(__lowerCamelCase					,  __lowerCamelCase					,  __lowerCamelCase     )


if __name__ == "__main__":
		import doctest

		doctest.testmod()

		lowerCAmelCase_   :   Optional[int]       =					input("Enter numbers separated by a comma : ").strip()
		lowerCAmelCase_   :   List[str]       =					[float(item) for item in user_input.split(",")]
		print(sort(unsorted))



