






'''simple docstring'''


import logging

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

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







def 	__magic_name__( _A					):
						'''simple docstring'''





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







def 	__magic_name__( _A						,      _A						,      _A					):
						'''simple docstring'''





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

						return covariance_sum / features.shape[1]







def 	__magic_name__( _A						,      _A						,      _A					):
						'''simple docstring'''





						UpperCamelCase__         = features.mean(1					)
						UpperCamelCase__         = np.nan
						for i in range(_A					):
												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(_A					) - column_reshape(_A					)						,      (column_reshape(_A					) - column_reshape(_A					)).T						,      )
												else:
																		# If covariance_sum is np.nan (i.e. first loop)
																		UpperCamelCase__         = device_data * np.dot(
																		    column_reshape(_A					) - column_reshape(_A					)						,      (column_reshape(_A					) - column_reshape(_A					)).T						,      )

						return covariance_sum / features.shape[1]







def 	__magic_name__( _A						,      _A					):
						'''simple docstring'''





						if features.any():
												UpperCamelCase__         = features.mean(1					)
												# Center the dataset
												UpperCamelCase__         = features - np.reshape(_A						,      (data_mean.size, 1)					)
												UpperCamelCase__         = np.dot(_A						,      centered_data.T					) / features.shape[1]
												UpperCamelCase__    ,   UpperCamelCase__         = np.linalg.eigh(_A					)
												# 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						,      _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 	__magic_name__( _A						,      _A						,      _A						,      _A					):
						'''simple docstring'''





						assert classes > dimensions

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





						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(_A					) as error_info:
												UpperCamelCase__         = 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 	__magic_name__( ):
						'''simple docstring'''





						UpperCamelCase__         = np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]]					)
						UpperCamelCase__         = 2
						UpperCamelCase__         = np.array([[6.9_2_8_2_0_3_2_3, 8.6_6_0_2_5_4_0_4, 1_0.3_9_2_3_0_4_8_5], [3.0, 3.0, 3.0]]					)

						with pytest.raises(_A					) as error_info:
												UpperCamelCase__         = 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()








'''simple docstring'''


# We ignore warnings about stepping the scheduler since we step it ourselves during gradient accumulation

import warnings

from .state import AcceleratorState, GradientState


warnings.filterwarnings('''ignore''', category=UserWarning, module='''torch.optim.lr_scheduler''')
class    _SCREAMING_SNAKE_CASE							:


			'''simple docstring'''





			def __init__(   self							:						Optional[int] ,      lowercase							:						Optional[int] ,      lowercase							:						Optional[Any] ,      lowercase							:						bool = True ,      lowercase							:						bool = False			)							->    Optional[int]:

									'''simple docstring'''







									UpperCamelCase__         = scheduler
									UpperCamelCase__         = optimizers if isinstance(lowercase ,      (list, tuple)			) else [optimizers]
									UpperCamelCase__         = split_batches
									UpperCamelCase__         = step_with_optimizer
									UpperCamelCase__         = GradientState()






			def 				A      (   self							:						int ,      *lowercase							:						int ,      **lowercase							:						str			)							->    str:

									'''simple docstring'''







									if not self.step_with_optimizer:
															# No link between scheduler and optimizer -> just step
															self.scheduler.step(*lowercase ,      **lowercase			)
															return

									# Otherwise, first make sure the optimizer was stepped.
									if not self.gradient_state.sync_gradients:
															if self.gradient_state.adjust_scheduler:
																					self.scheduler._step_count += 1
															return

									for opt in self.optimizers:
															if opt.step_was_skipped:
																					return
									if self.split_batches:
															# Split batches -> the training dataloader batch size is not changed so one step per training step
															self.scheduler.step(*lowercase ,      **lowercase			)
									else:
															# Otherwise the training dataloader batch size was multiplied by `num_processes`, so we need to do
															# num_processes steps per training step
															UpperCamelCase__         = AcceleratorState().num_processes
															for _ in range(lowercase			):
																					# Special case when using OneCycle and `drop_last` was not used
																					if hasattr(self.scheduler ,      """total_steps"""			):
																											if self.scheduler._step_count <= self.scheduler.total_steps:
																																	self.scheduler.step(*lowercase ,      **lowercase			)
																					else:
																											self.scheduler.step(*lowercase ,      **lowercase			)






			def 				A      (   self							:						List[str]			)							->    Optional[Any]:

									'''simple docstring'''







									return self.scheduler.get_last_lr()






			def 				A      (   self							:						Any			)							->    int:

									'''simple docstring'''







									return self.scheduler.state_dict()






			def 				A      (   self							:						Any ,      lowercase							:						int			)							->    Optional[int]:

									'''simple docstring'''







									self.scheduler.load_state_dict(lowercase			)






			def 				A      (   self							:						str			)							->    int:

									'''simple docstring'''







									return self.scheduler.get_lr()







			def 				A      (   self							:						Union[str, Any] ,      *lowercase							:						List[Any] ,      **lowercase							:						str			)							->    str:

									'''simple docstring'''







									return self.scheduler.print_lr(*lowercase ,      **lowercase			)
