


import logging

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

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







def        _lowerCamelCase(	lowercase__	)						->	np.ndarray:

		'''simple docstring'''







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







def        _lowerCamelCase(	lowercase__   , lowercase__   , lowercase__	)						->	np.ndarray:

		'''simple docstring'''







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

		return covariance_sum / features.shape[1]







def        _lowerCamelCase(	lowercase__   , lowercase__   , lowercase__	)						->	np.ndarray:

		'''simple docstring'''







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

		return covariance_sum / features.shape[1]







def        _lowerCamelCase(	lowercase__   , lowercase__	)						->	np.ndarray:

		'''simple docstring'''







		if features.any():
				__lowercase=			features.mean(1	)
				# Center the dataset
				__lowercase=			features - np.reshape(lowercase__   , (data_mean.size, 1)	)
				__lowercase=			np.dot(lowercase__   , centered_data.T	) / features.shape[1]
				__lowercase,							__lowercase=			np.linalg.eigh(lowercase__	)
				# Take all the columns in the reverse order (-1), and then takes only the first
				__lowercase=			eigenvectors[:, ::-1][:, 0:dimensions]
				# Project the database on the new space
				__lowercase=			np.dot(filtered_eigenvectors.T   , lowercase__	)
				logging.info('Principal Component Analysis computed'	)

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







def        _lowerCamelCase(	lowercase__   , lowercase__   , lowercase__   , lowercase__	)						->	np.ndarray:

		'''simple docstring'''







		assert classes > dimensions

		# Check if features have been already loaded
		if features.any:
				__lowercase,							__lowercase=			eigh(
				    covariance_between_classes(lowercase__   , lowercase__   , lowercase__	)   , covariance_within_classes(lowercase__   , lowercase__   , lowercase__	)   , )
				__lowercase=			eigenvectors[:, ::-1][:, :dimensions]
				__lowercase,							__lowercase,							__lowercase=			np.linalg.svd(lowercase__	)
				__lowercase=			svd_matrix[:, 0:dimensions]
				__lowercase=			np.dot(filtered_svd_matrix.T   , lowercase__	)
				logging.info('Linear Discriminant Analysis computed'	)

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







def        _lowerCamelCase(	)						->	None:

		'''simple docstring'''







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

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







def        _lowerCamelCase(	)						->	None:

		'''simple docstring'''







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

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


if __name__ == "__main__":
	import doctest

	doctest.testmod()










def        _lowerCamelCase(	lowercase__	)						->	int:

		'''simple docstring'''







		if collection == []:
				return []

		# get some information about the collection
		__lowercase=			len(lowercase__	)
		__lowercase=			max(lowercase__	)
		__lowercase=			min(lowercase__	)

		# create the counting array
		__lowercase=			coll_max + 1 - coll_min
		__lowercase=			[0] * counting_arr_length

		# count how much a number appears in the collection
		for number in collection:
				counting_arr[number - coll_min] += 1

		# sum each position with it's predecessors. now, counting_arr[i] tells
		# us how many elements <= i has in the collection
		for i in range(1   , lowercase__	):
				__lowercase=			counting_arr[i] + counting_arr[i - 1]

		# create the output collection
		__lowercase=			[0] * coll_len

		# place the elements in the output, respecting the original order (stable
		# sort) from end to begin, updating counting_arr
		for i in reversed(range(0   , lowercase__	)	):
				__lowercase=			collection[i]
				counting_arr[collection[i] - coll_min] -= 1

		return ordered







def        _lowerCamelCase(	lowercase__	)						->	List[str]:

		'''simple docstring'''







		return "".join([chr(lowercase__	) for i in counting_sort([ord(lowercase__	) for c in string]	)]	)


if __name__ == "__main__":
	# Test string sort
	assert counting_sort_string('''thisisthestring''') == "eghhiiinrsssttt"

	lowerCAmelCase           =		input('''Enter numbers separated by a comma:\n''').strip()
	lowerCAmelCase           =		[int(item) for item in user_input.split(''',''')]
	print(counting_sort(unsorted))






