

import logging

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

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



def 					lowerCAmelCase__							(	SCREAMING_SNAKE_CASE_:							np.ndarray      )			->      np.ndarray:




				'''simple docstring'''





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



def 					lowerCAmelCase__							(	SCREAMING_SNAKE_CASE_:							np.ndarray	,       SCREAMING_SNAKE_CASE_:							np.ndarray	,       SCREAMING_SNAKE_CASE_:							int      )			->      np.ndarray:




				'''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 					lowerCAmelCase__							(	SCREAMING_SNAKE_CASE_:							np.ndarray	,       SCREAMING_SNAKE_CASE_:							np.ndarray	,       SCREAMING_SNAKE_CASE_:							int      )			->      np.ndarray:




				'''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 					lowerCAmelCase__							(	SCREAMING_SNAKE_CASE_:							np.ndarray	,       SCREAMING_SNAKE_CASE_:							int      )			->      np.ndarray:




				'''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 					lowerCAmelCase__							(	SCREAMING_SNAKE_CASE_:							np.ndarray	,       SCREAMING_SNAKE_CASE_:							np.ndarray	,       SCREAMING_SNAKE_CASE_:							int	,       SCREAMING_SNAKE_CASE_:							int      )			->      np.ndarray:




				'''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 					lowerCAmelCase__							(	)			->      None:




				'''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 					lowerCAmelCase__							(	)			->      None:




				'''simple docstring'''





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




from ..utils import is_flax_available, is_torch_available


if is_torch_available():
	from .autoencoder_kl import AutoencoderKL
	from .controlnet import ControlNetModel
	from .dual_transformer_ad import DualTransformeraDModel
	from .modeling_utils import ModelMixin
	from .prior_transformer import PriorTransformer
	from .ta_film_transformer import TaFilmDecoder
	from .transformer_ad import TransformeraDModel
	from .unet_ad import UNetaDModel
	from .unet_ad import UNetaDModel
	from .unet_ad_condition import UNetaDConditionModel
	from .unet_ad_condition import UNetaDConditionModel
	from .vq_model import VQModel

if is_flax_available():
	from .controlnet_flax import FlaxControlNetModel
	from .unet_ad_condition_flax import FlaxUNetaDConditionModel
	from .vae_flax import FlaxAutoencoderKL

