

import logging

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

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

def        lowerCamelCase__       (    _a):
	return input_array.reshape((input_array.size, 1))

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

	return covariance_sum / features.shape[1]

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

	return covariance_sum / features.shape[1]

def        lowerCamelCase__       (    _a							,	_a):

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

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

def        lowerCamelCase__       (    _a							,	_a							,	_a							,	_a):
	assert classes > dimensions

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

		return projected_data
	else:
		logging.basicConfig(level=logging.ERROR							,	format="%(message)s"							,	force=_a)
		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[Any]    =				np.array([0, 0, 0, 1, 1])
	SCREAMING_SNAKE_CASE      :					List[str]    =				2
	SCREAMING_SNAKE_CASE      :					List[Any]    =				2

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

def        lowerCamelCase__       (    ):
	SCREAMING_SNAKE_CASE      :					Dict    =				np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]])
	SCREAMING_SNAKE_CASE      :					str    =				2
	SCREAMING_SNAKE_CASE      :					List[str]    =				np.array([[6.9282_0323, 8.6602_5404, 10.3923_0485], [3.0, 3.0, 3.0]])

	with pytest.raises(_a) as error_info:
		SCREAMING_SNAKE_CASE      :					Union[str, Any]    =				principal_component_analysis(_a							,	_a)
		if not np.allclose(_a							,	_a):
			raise AssertionError
		assert error_info.type is AssertionError


if __name__ == "__main__":
			import doctest

			doctest.testmod()





def 			lowerCamelCase_		(       UpperCamelCase__				:      int      )     ->       bool:





				"""simple docstring"""


				return number & 1 == 0


if __name__ == "__main__":
					import doctest

					doctest.testmod()


