"""simple docstring"""






import logging

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

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



def   a_						(					lowerCamelCase       ):
				return input_array.reshape((input_array.size, 1)       )



def   a_						(					lowerCamelCase					,			lowerCamelCase					,			lowerCamelCase       ):
				UpperCAmelCase__             =							np.nan
				for i in range(lowerCamelCase       ):
								UpperCAmelCase__             =							features[:, labels == i]
								UpperCAmelCase__             =							data.mean(1       )
								# Centralize the data of class i
								UpperCAmelCase__             =							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)
												UpperCAmelCase__             =							np.dot(lowerCamelCase					,			centered_data.T       )

				return covariance_sum / features.shape[1]



def   a_						(					lowerCamelCase					,			lowerCamelCase					,			lowerCamelCase       ):
				UpperCAmelCase__             =							features.mean(1       )
				UpperCAmelCase__             =							np.nan
				for i in range(lowerCamelCase       ):
								UpperCAmelCase__             =							features[:, labels == i]
								UpperCAmelCase__             =							data.shape[1]
								UpperCAmelCase__             =							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)
												UpperCAmelCase__             =							device_data * np.dot(
												    column_reshape(lowerCamelCase       ) - column_reshape(lowerCamelCase       )					,			(column_reshape(lowerCamelCase       ) - column_reshape(lowerCamelCase       )).T					,			)

				return covariance_sum / features.shape[1]



def   a_						(					lowerCamelCase					,			lowerCamelCase       ):

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

				# Check if features have been already loaded
				if features.any:
								UpperCAmelCase__      ,	UpperCAmelCase__             =							eigh(
								    covariance_between_classes(lowerCamelCase					,			lowerCamelCase					,			lowerCamelCase       )					,			covariance_within_classes(lowerCamelCase					,			lowerCamelCase					,			lowerCamelCase       )					,			)
								UpperCAmelCase__             =							eigenvectors[:, ::-1][:, :dimensions]
								UpperCAmelCase__      ,	UpperCAmelCase__      ,	UpperCAmelCase__             =							np.linalg.svd(lowerCamelCase       )
								UpperCAmelCase__             =							svd_matrix[:, 0:dimensions]
								UpperCAmelCase__             =							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   a_						(					):
				# Create dummy dataset with 2 classes and 3 features
				UpperCAmelCase__             =							np.array([[1, 2, 3, 4, 5], [2, 3, 4, 5, 6], [3, 4, 5, 6, 7]]       )
				UpperCAmelCase__             =							np.array([0, 0, 0, 1, 1]       )
				UpperCAmelCase__             =							2
				UpperCAmelCase__             =							2

				# Assert that the function raises an AssertionError if dimensions > classes
				with pytest.raises(lowerCamelCase       ) as error_info:
								UpperCAmelCase__             =							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   a_						(					):
				UpperCAmelCase__             =							np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]]       )
				UpperCAmelCase__             =							2
				UpperCAmelCase__             =							np.array([[6.92820323, 8.66025404, 10.39230485], [3.0, 3.0, 3.0]]       )

				with pytest.raises(lowerCamelCase       ) as error_info:
								UpperCAmelCase__             =							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()







def 			_a (      SCREAMING_SNAKE_CASE     ):


		"""simple docstring"""




		return credit_card_number.startswith(('''34''', '''35''', '''37''', '''4''', '''5''', '''6''')     )
def 			_a (      SCREAMING_SNAKE_CASE     ):


		"""simple docstring"""




		lowercase__            =      credit_card_number
		lowercase__            =      0
		lowercase__            =      len(SCREAMING_SNAKE_CASE     ) - 2
		for i in range(SCREAMING_SNAKE_CASE						,				-1						,				-2     ):
				#  double the value of every second digit
				lowercase__            =      int(cc_number[i]     )
				digit *= 2
				# If doubling of a number results in a two digit number
				# i.e greater than 9(e.g., 6 × 2 = 12),
				# then add the digits of the product (e.g., 12: 1 + 2 = 3, 15: 1 + 5 = 6),
				# to get a single digit number.
				if digit > 9:
						digit %= 10
						digit += 1
				lowercase__            =      cc_number[:i] + str(SCREAMING_SNAKE_CASE     ) + cc_number[i + 1 :]
				total += digit

		# Sum up the remaining digits
		for i in range(len(SCREAMING_SNAKE_CASE     ) - 1						,				-1						,				-2     ):
				total += int(cc_number[i]     )

		return total % 10 == 0
def 			_a (      SCREAMING_SNAKE_CASE     ):


		"""simple docstring"""




		lowercase__            =      f'{credit_card_number} is an invalid credit card number because'
		if not credit_card_number.isdigit():
				print(f'{error_message} it has nonnumerical characters.'     )
				return False

		if not 13 <= len(SCREAMING_SNAKE_CASE     ) <= 16:
				print(f'{error_message} of its length.'     )
				return False

		if not validate_initial_digits(SCREAMING_SNAKE_CASE     ):
				print(f'{error_message} of its first two digits.'     )
				return False

		if not luhn_validation(SCREAMING_SNAKE_CASE     ):
				print(f'{error_message} it fails the Luhn check.'     )
				return False

		print(f'{credit_card_number} is a valid credit card number.'     )
		return True


if __name__ == "__main__":
			import doctest

			doctest.testmod()
			validate_credit_card_number('4111111111111111')
			validate_credit_card_number('32323')


