


'''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__(				_SCREAMING_SNAKE_CASE					: np.ndarray ):






			"""simple docstring"""




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






def 						UpperCAmelCase__(				_SCREAMING_SNAKE_CASE					: np.ndarray,_SCREAMING_SNAKE_CASE					: np.ndarray,_SCREAMING_SNAKE_CASE					: int ):






			"""simple docstring"""




			__A=	np.nan
			for i in range(_SCREAMING_SNAKE_CASE ):
						__A=	features[:, labels == i]
						__A=	data.mean(1 )
						# Centralize the data of class i
						__A=	data - column_reshape(_SCREAMING_SNAKE_CASE )
						if i > 0:
									# If covariance_sum is not None
									covariance_sum += np.dot(_SCREAMING_SNAKE_CASE,centered_data.T )
						else:
									# If covariance_sum is np.nan (i.e. first loop)
									__A=	np.dot(_SCREAMING_SNAKE_CASE,centered_data.T )

			return covariance_sum / features.shape[1]






def 						UpperCAmelCase__(				_SCREAMING_SNAKE_CASE					: np.ndarray,_SCREAMING_SNAKE_CASE					: np.ndarray,_SCREAMING_SNAKE_CASE					: int ):






			"""simple docstring"""




			__A=	features.mean(1 )
			__A=	np.nan
			for i in range(_SCREAMING_SNAKE_CASE ):
						__A=	features[:, labels == i]
						__A=	data.shape[1]
						__A=	data.mean(1 )
						if i > 0:
									# If covariance_sum is not None
									covariance_sum += device_data * np.dot(
									    column_reshape(_SCREAMING_SNAKE_CASE ) - column_reshape(_SCREAMING_SNAKE_CASE ),(column_reshape(_SCREAMING_SNAKE_CASE ) - column_reshape(_SCREAMING_SNAKE_CASE )).T,)
						else:
									# If covariance_sum is np.nan (i.e. first loop)
									__A=	device_data * np.dot(
									    column_reshape(_SCREAMING_SNAKE_CASE ) - column_reshape(_SCREAMING_SNAKE_CASE ),(column_reshape(_SCREAMING_SNAKE_CASE ) - column_reshape(_SCREAMING_SNAKE_CASE )).T,)

			return covariance_sum / features.shape[1]






def 						UpperCAmelCase__(				_SCREAMING_SNAKE_CASE					: np.ndarray,_SCREAMING_SNAKE_CASE					: int ):






			"""simple docstring"""




			if features.any():
						__A=	features.mean(1 )
						# Center the dataset
						__A=	features - np.reshape(_SCREAMING_SNAKE_CASE,(data_mean.size, 1) )
						__A=	np.dot(_SCREAMING_SNAKE_CASE,centered_data.T ) / features.shape[1]
						__A,	__A=	np.linalg.eigh(_SCREAMING_SNAKE_CASE )
						# Take all the columns in the reverse order (-1), and then takes only the first
						__A=	eigenvectors[:, ::-1][:, 0:dimensions]
						# Project the database on the new space
						__A=	np.dot(filtered_eigenvectors.T,_SCREAMING_SNAKE_CASE )
						logging.info('Principal Component Analysis computed' )

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






def 						UpperCAmelCase__(				_SCREAMING_SNAKE_CASE					: np.ndarray,_SCREAMING_SNAKE_CASE					: np.ndarray,_SCREAMING_SNAKE_CASE					: int,_SCREAMING_SNAKE_CASE					: int ):






			"""simple docstring"""




			assert classes > dimensions

			# Check if features have been already loaded
			if features.any:
						__A,	__A=	eigh(
						    covariance_between_classes(_SCREAMING_SNAKE_CASE,_SCREAMING_SNAKE_CASE,_SCREAMING_SNAKE_CASE ),covariance_within_classes(_SCREAMING_SNAKE_CASE,_SCREAMING_SNAKE_CASE,_SCREAMING_SNAKE_CASE ),)
						__A=	eigenvectors[:, ::-1][:, :dimensions]
						__A,	__A,	__A=	np.linalg.svd(_SCREAMING_SNAKE_CASE )
						__A=	svd_matrix[:, 0:dimensions]
						__A=	np.dot(filtered_svd_matrix.T,_SCREAMING_SNAKE_CASE )
						logging.info('Linear Discriminant Analysis computed' )

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






def 						UpperCAmelCase__(				):






			"""simple docstring"""




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

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






def 						UpperCAmelCase__(				):






			"""simple docstring"""




			__A=	np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]] )
			__A=	2
			__A=	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(_SCREAMING_SNAKE_CASE ) as error_info:
						__A=	principal_component_analysis(_SCREAMING_SNAKE_CASE,_SCREAMING_SNAKE_CASE )
						if not np.allclose(_SCREAMING_SNAKE_CASE,_SCREAMING_SNAKE_CASE ):
									raise AssertionError
						assert error_info.type is AssertionError


if __name__ == "__main__":
					import doctest

					doctest.testmod()







'''simple docstring'''





# Lint as: python3
import itertools
import os
import re


UpperCAmelCase__  			=				re.compile(r'''([A-Z]+)([A-Z][a-z])''')
UpperCAmelCase__  			=				re.compile(r'''([a-z\d])([A-Z])''')

UpperCAmelCase__  			=				re.compile(r'''(?<!_)_(?!_)''')
UpperCAmelCase__  			=				re.compile(r'''(_{2,})''')

UpperCAmelCase__  			=				r'''^\w+(\.\w+)*$'''

UpperCAmelCase__  			=				r'''<>:/\|?*'''






def 						UpperCAmelCase__(				_SCREAMING_SNAKE_CASE					: Union[str, Any] ):






			"""simple docstring"""




			__A=	_uppercase_uppercase_re.sub(r'\1_\2',_SCREAMING_SNAKE_CASE )
			__A=	_lowercase_uppercase_re.sub(r'\1_\2',_SCREAMING_SNAKE_CASE )
			return name.lower()






def 						UpperCAmelCase__(				_SCREAMING_SNAKE_CASE					: int ):






			"""simple docstring"""




			__A=	_single_underscore_re.split(_SCREAMING_SNAKE_CASE )
			__A=	[_multiple_underscores_re.split(_SCREAMING_SNAKE_CASE ) for n in name]
			return "".join(n.capitalize() for n in itertools.chain.from_iterable(_SCREAMING_SNAKE_CASE ) if n != '' )






def 						UpperCAmelCase__(				_SCREAMING_SNAKE_CASE					: str ):






			"""simple docstring"""




			if os.path.basename(_SCREAMING_SNAKE_CASE ) != name:
						raise ValueError(f"""Should be a dataset name, not a path: {name}""" )
			return camelcase_to_snakecase(_SCREAMING_SNAKE_CASE )






def 						UpperCAmelCase__(				_SCREAMING_SNAKE_CASE					: Union[str, Any],_SCREAMING_SNAKE_CASE					: str ):






			"""simple docstring"""




			if os.path.basename(_SCREAMING_SNAKE_CASE ) != name:
						raise ValueError(f"""Should be a dataset name, not a path: {name}""" )
			if not re.match(_split_re,_SCREAMING_SNAKE_CASE ):
						raise ValueError(f"""Split name should match '{_split_re}'' but got '{split}'.""" )
			return f"""{filename_prefix_for_name(_SCREAMING_SNAKE_CASE )}-{split}"""






def 						UpperCAmelCase__(				_SCREAMING_SNAKE_CASE					: Union[str, Any],_SCREAMING_SNAKE_CASE					: Optional[Any],_SCREAMING_SNAKE_CASE					: Optional[int],_SCREAMING_SNAKE_CASE					: Union[str, Any]=None ):






			"""simple docstring"""




			__A=	filename_prefix_for_split(_SCREAMING_SNAKE_CASE,_SCREAMING_SNAKE_CASE )
			if filetype_suffix:
						prefix += f""".{filetype_suffix}"""
			__A=	os.path.join(_SCREAMING_SNAKE_CASE,_SCREAMING_SNAKE_CASE )
			return f"""{filepath}*"""






def 						UpperCAmelCase__(				_SCREAMING_SNAKE_CASE					: int,_SCREAMING_SNAKE_CASE					: List[str],_SCREAMING_SNAKE_CASE					: int,_SCREAMING_SNAKE_CASE					: List[Any]=None,_SCREAMING_SNAKE_CASE					: List[str]=None ):






			"""simple docstring"""




			__A=	filename_prefix_for_split(_SCREAMING_SNAKE_CASE,_SCREAMING_SNAKE_CASE )
			__A=	os.path.join(_SCREAMING_SNAKE_CASE,_SCREAMING_SNAKE_CASE )

			if shard_lengths:
						__A=	len(_SCREAMING_SNAKE_CASE )
						__A=	[f"""{prefix}-{shard_id:05d}-of-{num_shards:05d}""" for shard_id in range(_SCREAMING_SNAKE_CASE )]
						if filetype_suffix:
									__A=	[filename + f""".{filetype_suffix}""" for filename in filenames]
						return filenames
			else:
						__A=	prefix
						if filetype_suffix:
									filename += f""".{filetype_suffix}"""
						return [filename]



