






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       )		->    np.ndarray:


				'''simple docstring'''




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





def 	lowerCAmelCase_		(lowercase__						:       np.ndarray     ,					lowercase__						:       np.ndarray     ,					lowercase__						:       int       )		->    np.ndarray:


				'''simple docstring'''




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

				return covariance_sum / features.shape[1]





def 	lowerCAmelCase_		(lowercase__						:       np.ndarray     ,					lowercase__						:       np.ndarray     ,					lowercase__						:       int       )		->    np.ndarray:


				'''simple docstring'''




				lowerCAmelCase__      			=						features.mean(1       )
				lowerCAmelCase__      			=						np.nan
				for i in range(lowercase__       ):
								lowerCAmelCase__      			=						features[:, labels == i]
								lowerCAmelCase__      			=						data.shape[1]
								lowerCAmelCase__      			=						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)
												lowerCAmelCase__      			=						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__						:       np.ndarray     ,					lowercase__						:       int       )		->    np.ndarray:


				'''simple docstring'''




				if features.any():
								lowerCAmelCase__      			=						features.mean(1       )
								# Center the dataset
								lowerCAmelCase__      			=						features - np.reshape(lowercase__     ,					(data_mean.size, 1)       )
								lowerCAmelCase__      			=						np.dot(lowercase__     ,					centered_data.T       ) / features.shape[1]
								lowerCAmelCase__			,		lowerCAmelCase__      			=						np.linalg.eigh(lowercase__       )
								# Take all the columns in the reverse order (-1), and then takes only the first
								lowerCAmelCase__      			=						eigenvectors[:, ::-1][:, 0:dimensions]
								# Project the database on the new space
								lowerCAmelCase__      			=						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__						:       np.ndarray     ,					lowercase__						:       np.ndarray     ,					lowercase__						:       int     ,					lowercase__						:       int       )		->    np.ndarray:


				'''simple docstring'''




				assert classes > dimensions

				# Check if features have been already loaded
				if features.any:
								lowerCAmelCase__			,		lowerCAmelCase__      			=						eigh(
								    covariance_between_classes(lowercase__     ,					lowercase__     ,					lowercase__       )     ,					covariance_within_classes(lowercase__     ,					lowercase__     ,					lowercase__       )     ,					)
								lowerCAmelCase__      			=						eigenvectors[:, ::-1][:, :dimensions]
								lowerCAmelCase__			,		lowerCAmelCase__			,		lowerCAmelCase__      			=						np.linalg.svd(lowercase__       )
								lowerCAmelCase__      			=						svd_matrix[:, 0:dimensions]
								lowerCAmelCase__      			=						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'''




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

				# Assert that the function raises an AssertionError if dimensions > classes
				with pytest.raises(lowercase__       ) as error_info:
								lowerCAmelCase__      			=						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'''




				lowerCAmelCase__      			=						np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]]       )
				lowerCAmelCase__      			=						2
				lowerCAmelCase__      			=						np.array([[6.92820323, 8.66025404, 10.39230485], [3.0, 3.0, 3.0]]       )

				with pytest.raises(lowercase__       ) as error_info:
								lowerCAmelCase__      			=						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()













# Imports
import numpy as np
class  lowerCAmelCase_       :




							def __init__(   self     :   Any ,							SCREAMING_SNAKE_CASE_     :   Dict=None ,							SCREAMING_SNAKE_CASE_     :   Optional[Any]=None ,							SCREAMING_SNAKE_CASE_     :   List[str]=None ,							SCREAMING_SNAKE_CASE_     :   Dict=None ,							SCREAMING_SNAKE_CASE_     :   int=None	):
											self.set_matricies(red=SCREAMING_SNAKE_CASE_ ,							green=SCREAMING_SNAKE_CASE_ ,							blue=SCREAMING_SNAKE_CASE_ ,							red_edge=SCREAMING_SNAKE_CASE_ ,							nir=SCREAMING_SNAKE_CASE_	)




							def 						__snake_case					(   self     :   str ,							SCREAMING_SNAKE_CASE_     :   Union[str, Any]=None ,							SCREAMING_SNAKE_CASE_     :   Optional[int]=None ,							SCREAMING_SNAKE_CASE_     :   Optional[Any]=None ,							SCREAMING_SNAKE_CASE_     :   Optional[Any]=None ,							SCREAMING_SNAKE_CASE_     :   Dict=None	):
											if red is not None:
															lowerCAmelCase__      			=						red
											if green is not None:
															lowerCAmelCase__      			=						green
											if blue is not None:
															lowerCAmelCase__      			=						blue
											if red_edge is not None:
															lowerCAmelCase__      			=						red_edge
											if nir is not None:
															lowerCAmelCase__      			=						nir
											return True




							def 						__snake_case					(   self     :   Union[str, Any] ,							SCREAMING_SNAKE_CASE_     :   Any="" ,							SCREAMING_SNAKE_CASE_     :   str=None ,							SCREAMING_SNAKE_CASE_     :   Optional[Any]=None ,							SCREAMING_SNAKE_CASE_     :   List[str]=None ,							SCREAMING_SNAKE_CASE_     :   Optional[Any]=None ,							SCREAMING_SNAKE_CASE_     :   Optional[Any]=None	):
											self.set_matricies(red=SCREAMING_SNAKE_CASE_ ,							green=SCREAMING_SNAKE_CASE_ ,							blue=SCREAMING_SNAKE_CASE_ ,							red_edge=SCREAMING_SNAKE_CASE_ ,							nir=SCREAMING_SNAKE_CASE_	)
											lowerCAmelCase__      			=						{
											    '''ARVI2''': self.arvaa,
											    '''CCCI''': self.ccci,
											    '''CVI''': self.cvi,
											    '''GLI''': self.gli,
											    '''NDVI''': self.ndvi,
											    '''BNDVI''': self.bndvi,
											    '''redEdgeNDVI''': self.red_edge_ndvi,
											    '''GNDVI''': self.gndvi,
											    '''GBNDVI''': self.gbndvi,
											    '''GRNDVI''': self.grndvi,
											    '''RBNDVI''': self.rbndvi,
											    '''PNDVI''': self.pndvi,
											    '''ATSAVI''': self.atsavi,
											    '''BWDRVI''': self.bwdrvi,
											    '''CIgreen''': self.ci_green,
											    '''CIrededge''': self.ci_rededge,
											    '''CI''': self.ci,
											    '''CTVI''': self.ctvi,
											    '''GDVI''': self.gdvi,
											    '''EVI''': self.evi,
											    '''GEMI''': self.gemi,
											    '''GOSAVI''': self.gosavi,
											    '''GSAVI''': self.gsavi,
											    '''Hue''': self.hue,
											    '''IVI''': self.ivi,
											    '''IPVI''': self.ipvi,
											    '''I''': self.i,
											    '''RVI''': self.rvi,
											    '''MRVI''': self.mrvi,
											    '''MSAVI''': self.m_savi,
											    '''NormG''': self.norm_g,
											    '''NormNIR''': self.norm_nir,
											    '''NormR''': self.norm_r,
											    '''NGRDI''': self.ngrdi,
											    '''RI''': self.ri,
											    '''S''': self.s,
											    '''IF''': self._if,
											    '''DVI''': self.dvi,
											    '''TVI''': self.tvi,
											    '''NDRE''': self.ndre,
											}

											try:
															return funcs[index]()
											except KeyError:
															print('''Index not in the list!'''	)
															return False




							def 						__snake_case					(   self     :   List[str]	):
											return -0.18 + (1.17 * ((self.nir - self.red) / (self.nir + self.red)))




							def 						__snake_case					(   self     :   Optional[int]	):
											return ((self.nir - self.redEdge) / (self.nir + self.redEdge)) / (
											    (self.nir - self.red) / (self.nir + self.red)
											)




							def 						__snake_case					(   self     :   str	):
											return self.nir * (self.red / (self.green**2))




							def 						__snake_case					(   self     :   List[str]	):
											return (2 * self.green - self.red - self.blue) / (
											    2 * self.green + self.red + self.blue
											)




							def 						__snake_case					(   self     :   List[str]	):
											return (self.nir - self.red) / (self.nir + self.red)




							def 						__snake_case					(   self     :   Optional[Any]	):
											return (self.nir - self.blue) / (self.nir + self.blue)




							def 						__snake_case					(   self     :   Optional[Any]	):
											return (self.redEdge - self.red) / (self.redEdge + self.red)




							def 						__snake_case					(   self     :   Tuple	):
											return (self.nir - self.green) / (self.nir + self.green)




							def 						__snake_case					(   self     :   List[Any]	):
											return (self.nir - (self.green + self.blue)) / (
											    self.nir + (self.green + self.blue)
											)




							def 						__snake_case					(   self     :   Optional[int]	):
											return (self.nir - (self.green + self.red)) / (
											    self.nir + (self.green + self.red)
											)




							def 						__snake_case					(   self     :   Optional[Any]	):
											return (self.nir - (self.blue + self.red)) / (self.nir + (self.blue + self.red))




							def 						__snake_case					(   self     :   Optional[int]	):
											return (self.nir - (self.green + self.red + self.blue)) / (
											    self.nir + (self.green + self.red + self.blue)
											)




							def 						__snake_case					(   self     :   Union[str, Any] ,							SCREAMING_SNAKE_CASE_     :   List[Any]=0.08 ,							SCREAMING_SNAKE_CASE_     :   List[str]=1.22 ,							SCREAMING_SNAKE_CASE_     :   Union[str, Any]=0.03	):
											return a * (
											    (self.nir - a * self.red - b)
											    / (a * self.nir + self.red - a * b + x * (1 + a**2))
											)




							def 						__snake_case					(   self     :   Tuple	):
											return (0.1 * self.nir - self.blue) / (0.1 * self.nir + self.blue)




							def 						__snake_case					(   self     :   Dict	):
											return (self.nir / self.green) - 1




							def 						__snake_case					(   self     :   str	):
											return (self.nir / self.redEdge) - 1




							def 						__snake_case					(   self     :   Tuple	):
											return (self.red - self.blue) / self.red




							def 						__snake_case					(   self     :   Any	):
											lowerCAmelCase__      			=						self.ndvi()
											return ((ndvi + 0.5) / (abs(ndvi + 0.5	))) * (abs(ndvi + 0.5	) ** (1 / 2))




							def 						__snake_case					(   self     :   Dict	):
											return self.nir - self.green




							def 						__snake_case					(   self     :   List[Any]	):
											return 2.5 * (
											    (self.nir - self.red) / (self.nir + 6 * self.red - 7.5 * self.blue + 1)
											)




							def 						__snake_case					(   self     :   Tuple	):
											lowerCAmelCase__      			=						(2 * (self.nir**2 - self.red**2) + 1.5 * self.nir + 0.5 * self.red) / (
											    self.nir + self.red + 0.5
											)
											return n * (1 - 0.25 * n) - (self.red - 0.125) / (1 - self.red)




							def 						__snake_case					(   self     :   Optional[Any] ,							SCREAMING_SNAKE_CASE_     :   Dict=0.16	):
											return (self.nir - self.green) / (self.nir + self.green + y)




							def 						__snake_case					(   self     :   Optional[int] ,							SCREAMING_SNAKE_CASE_     :   Any=0.5	):
											return ((self.nir - self.green) / (self.nir + self.green + n)) * (1 + n)




							def 						__snake_case					(   self     :   Any	):
											return np.arctan(
											    ((2 * self.red - self.green - self.blue) / 30.5) * (self.green - self.blue)	)




							def 						__snake_case					(   self     :   List[str] ,							SCREAMING_SNAKE_CASE_     :   List[str]=None ,							SCREAMING_SNAKE_CASE_     :   Union[str, Any]=None	):
											return (self.nir - b) / (a * self.red)




							def 						__snake_case					(   self     :   Union[str, Any]	):
											return (self.nir / ((self.nir + self.red) / 2)) * (self.ndvi() + 1)




							def 						__snake_case					(   self     :   List[str]	):
											return (self.red + self.green + self.blue) / 30.5




							def 						__snake_case					(   self     :   Optional[int]	):
											return self.nir / self.red




							def 						__snake_case					(   self     :   Dict	):
											return (self.rvi() - 1) / (self.rvi() + 1)




							def 						__snake_case					(   self     :   Union[str, Any]	):
											return (
											    (2 * self.nir + 1)
											    - ((2 * self.nir + 1) ** 2 - 8 * (self.nir - self.red)) ** (1 / 2)
											) / 2




							def 						__snake_case					(   self     :   List[Any]	):
											return self.green / (self.nir + self.red + self.green)




							def 						__snake_case					(   self     :   List[str]	):
											return self.nir / (self.nir + self.red + self.green)




							def 						__snake_case					(   self     :   Any	):
											return self.red / (self.nir + self.red + self.green)




							def 						__snake_case					(   self     :   Union[str, Any]	):
											return (self.green - self.red) / (self.green + self.red)




							def 						__snake_case					(   self     :   Dict	):
											return (self.red - self.green) / (self.red + self.green)




							def 						__snake_case					(   self     :   Optional[int]	):
											lowerCAmelCase__      			=						np.max([np.max(self.red	), np.max(self.green	), np.max(self.blue	)]	)
											lowerCAmelCase__      			=						np.min([np.min(self.red	), np.min(self.green	), np.min(self.blue	)]	)
											return (max_value - min_value) / max_value




							def 						__snake_case					(   self     :   str	):
											return (2 * self.red - self.green - self.blue) / (self.green - self.blue)




							def 						__snake_case					(   self     :   Optional[Any]	):
											return self.nir / self.red




							def 						__snake_case					(   self     :   Union[str, Any]	):
											return (self.ndvi() + 0.5) ** (1 / 2)




							def 						__snake_case					(   self     :   List[Any]	):
											return (self.nir - self.redEdge) / (self.nir + self.redEdge)





