


'''simple docstring'''



import logging

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

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







def     _UpperCamelCase      (		UpperCamelCase__					):
			return input_array.reshape((input_array.size, 1)					)







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

			return covariance_sum / features.shape[1]







def     _UpperCamelCase      (		UpperCamelCase__ ,      UpperCamelCase__ ,      UpperCamelCase__					):
			UpperCAmelCase__  :					int        =     features.mean(1					)
			UpperCAmelCase__  :					Optional[int]        =     np.nan
			for i in range(UpperCamelCase__					):
						UpperCAmelCase__  :					Optional[int]        =     features[:, labels == i]
						UpperCAmelCase__  :					Any        =     data.shape[1]
						UpperCAmelCase__  :					List[str]        =     data.mean(1					)
						if i > 0:
									# If covariance_sum is not None
									covariance_sum += device_data * np.dot(
									    column_reshape(UpperCamelCase__					) - column_reshape(UpperCamelCase__					) ,      (column_reshape(UpperCamelCase__					) - column_reshape(UpperCamelCase__					)).T ,      )
						else:
									# If covariance_sum is np.nan (i.e. first loop)
									UpperCAmelCase__  :					int        =     device_data * np.dot(
									    column_reshape(UpperCamelCase__					) - column_reshape(UpperCamelCase__					) ,      (column_reshape(UpperCamelCase__					) - column_reshape(UpperCamelCase__					)).T ,      )

			return covariance_sum / features.shape[1]







def     _UpperCamelCase      (		UpperCamelCase__ ,      UpperCamelCase__					):

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

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







def     _UpperCamelCase      (		UpperCamelCase__ ,      UpperCamelCase__ ,      UpperCamelCase__ ,      UpperCamelCase__					):
			assert classes > dimensions

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

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







def     _UpperCamelCase      (		):
			# Create dummy dataset with 2 classes and 3 features
			UpperCAmelCase__  :					Union[str, Any]        =     np.array([[1, 2, 3, 4, 5], [2, 3, 4, 5, 6], [3, 4, 5, 6, 7]]					)
			UpperCAmelCase__  :					str        =     np.array([0, 0, 0, 1, 1]					)
			UpperCAmelCase__  :					int        =     2
			UpperCAmelCase__  :					Optional[int]        =     2

			# Assert that the function raises an AssertionError if dimensions > classes
			with pytest.raises(UpperCamelCase__					) as error_info:
						UpperCAmelCase__  :					Optional[Any]        =     linear_discriminant_analysis(
						    UpperCamelCase__ ,      UpperCamelCase__ ,      UpperCamelCase__ ,      UpperCamelCase__					)
						if isinstance(UpperCamelCase__ ,      np.ndarray					):
									raise AssertionError(
									    """Did not raise AssertionError for dimensions > classes"""					)
						assert error_info.type is AssertionError







def     _UpperCamelCase      (		):
			UpperCAmelCase__  :					List[str]        =     np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]]					)
			UpperCAmelCase__  :					Optional[Any]        =     2
			UpperCAmelCase__  :					Optional[Any]        =     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(UpperCamelCase__					) as error_info:
						UpperCAmelCase__  :					Union[str, Any]        =     principal_component_analysis(UpperCamelCase__ ,      UpperCamelCase__					)
						if not np.allclose(UpperCamelCase__ ,      UpperCamelCase__					):
									raise AssertionError
						assert error_info.type is AssertionError


if __name__ == "__main__":
		import doctest

		doctest.testmod()



'''simple docstring'''



def     _UpperCamelCase      (		UpperCamelCase__ ,      UpperCamelCase__ ,      UpperCamelCase__ ,      UpperCamelCase__					):
			if height >= 1:
						move_tower(height - 1 ,      UpperCamelCase__ ,      UpperCamelCase__ ,      UpperCamelCase__					)
						move_disk(UpperCamelCase__ ,      UpperCamelCase__					)
						move_tower(height - 1 ,      UpperCamelCase__ ,      UpperCamelCase__ ,      UpperCamelCase__					)







def     _UpperCamelCase      (		UpperCamelCase__ ,      UpperCamelCase__					):
			print("""moving disk from""" ,      UpperCamelCase__ ,      """to""" ,      UpperCamelCase__					)







def     _UpperCamelCase      (		):
			UpperCAmelCase__  :					List[str]        =     int(input("""Height of hanoi: """					).strip()					)
			move_tower(UpperCamelCase__ ,      """A""" ,      """B""" ,      """C"""					)


if __name__ == "__main__":
		main()