



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


def 				lowerCAmelCase_   (	_lowerCamelCase:   np.ndarray       ,      _lowerCamelCase:   np.ndarray       ,      _lowerCamelCase:   int					):
		__SCREAMING_SNAKE_CASE       :		Union[str, Any]           =		np.nan
		for i in range(_lowerCamelCase					):
				__SCREAMING_SNAKE_CASE       :		Optional[Any]           =		features[:, labels == i]
				__SCREAMING_SNAKE_CASE       :		Union[str, Any]           =		data.mean(1					)
				# Centralize the data of class i
				__SCREAMING_SNAKE_CASE       :		int           =		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)
						__SCREAMING_SNAKE_CASE       :		List[str]           =		np.dot(_lowerCamelCase       ,      centered_data.T					)

		return covariance_sum / features.shape[1]


def 				lowerCAmelCase_   (	_lowerCamelCase:   np.ndarray       ,      _lowerCamelCase:   np.ndarray       ,      _lowerCamelCase:   int					):
		__SCREAMING_SNAKE_CASE       :		Optional[Any]           =		features.mean(1					)
		__SCREAMING_SNAKE_CASE       :		Optional[Any]           =		np.nan
		for i in range(_lowerCamelCase					):
				__SCREAMING_SNAKE_CASE       :		Optional[int]           =		features[:, labels == i]
				__SCREAMING_SNAKE_CASE       :		int           =		data.shape[1]
				__SCREAMING_SNAKE_CASE       :		Union[str, 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)
						__SCREAMING_SNAKE_CASE       :		List[str]           =		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					):

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

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

		# Assert that the function raises an AssertionError if dimensions > classes
		with pytest.raises(_lowerCamelCase					) as error_info:
				__SCREAMING_SNAKE_CASE       :		List[str]           =		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_   (	):
		__SCREAMING_SNAKE_CASE       :		int           =		np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]]					)
		__SCREAMING_SNAKE_CASE       :		Tuple           =		2
		__SCREAMING_SNAKE_CASE       :		str           =		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(_lowerCamelCase					) as error_info:
				__SCREAMING_SNAKE_CASE       :		int           =		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'''




def 				lowerCAmelCase_   (	_lowerCamelCase:   list					):
		if any(not isinstance(_lowerCamelCase       ,      _lowerCamelCase					) or x < 0 for x in sequence					):
				raise TypeError("""Sequence must be list of non-negative integers"""					)
		for _ in range(len(_lowerCamelCase					)					):
				for i, (rod_upper, rod_lower) in enumerate(zip(_lowerCamelCase       ,      sequence[1:]					)					):
						if rod_upper > rod_lower:
								sequence[i] -= rod_upper - rod_lower
								sequence[i + 1] += rod_upper - rod_lower
		return sequence


if __name__ == "__main__":
						assert bead_sort([5, 4, 3, 2, 1]) == [1, 2, 3, 4, 5]
						assert bead_sort([7, 9, 4, 3, 5]) == [3, 4, 5, 7, 9]