





import logging

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

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





def  __magic_name__  (				lowercase				)				-> int:

							"""simple docstring"""



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





def  __magic_name__  (				lowercase				,       lowercase				,       lowercase				)				-> int:

							"""simple docstring"""



							lowercase_	:   Tuple  				=     np.nan
							for i in range(__a				):
														lowercase_	:   Optional[int]  				=     features[:, labels == i]
														lowercase_	:   str  				=     data.mean(1				)
														# Centralize the data of class i
														lowercase_	:   List[Any]  				=     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)
																					lowercase_	:   Tuple  				=     np.dot(__a				,       centered_data.T				)

							return covariance_sum / features.shape[1]





def  __magic_name__  (				lowercase				,       lowercase				,       lowercase				)				-> Any:

							"""simple docstring"""



							lowercase_	:   Dict  				=     features.mean(1				)
							lowercase_	:   Dict  				=     np.nan
							for i in range(__a				):
														lowercase_	:   List[Any]  				=     features[:, labels == i]
														lowercase_	:   Any  				=     data.shape[1]
														lowercase_	:   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)
																					lowercase_	:   str  				=     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__  (				lowercase				,       lowercase				)				-> Union[str, Any]:

							"""simple docstring"""



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

							"""simple docstring"""



							assert classes > dimensions

							# Check if features have been already loaded
							if features.any:
														lowercase_				,		lowercase_	:   List[str]  				=     eigh(
														    covariance_between_classes(__a				,       __a				,       __a				)				,       covariance_within_classes(__a				,       __a				,       __a				)				,       )
														lowercase_	:   Dict  				=     eigenvectors[:, ::-1][:, :dimensions]
														lowercase_				,		lowercase_				,		lowercase_	:   Tuple  				=     np.linalg.svd(__a				)
														lowercase_	:   Optional[Any]  				=     svd_matrix[:, 0:dimensions]
														lowercase_	:   Optional[int]  				=     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__  (				)				-> int:

							"""simple docstring"""



							lowercase_	:   Union[str, Any]  				=     np.array([[1, 2, 3, 4, 5], [2, 3, 4, 5, 6], [3, 4, 5, 6, 7]]				)
							lowercase_	:   Any  				=     np.array([0, 0, 0, 1, 1]				)
							lowercase_	:   Any  				=     2
							lowercase_	:   List[Any]  				=     2

							# Assert that the function raises an AssertionError if dimensions > classes
							with pytest.raises(__a				) as error_info:
														lowercase_	:   Optional[Any]  				=     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__  (				)				-> Optional[int]:

							"""simple docstring"""



							lowercase_	:   Dict  				=     np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]]				)
							lowercase_	:   List[str]  				=     2
							lowercase_	:   Any  				=     np.array([[6.92_820_323, 8.66_025_404, 10.39230485], [3.0, 3.0, 3.0]]				)

							with pytest.raises(__a				) as error_info:
														lowercase_	:   Optional[int]  				=     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"""




from ..utils import (
    OptionalDependencyNotAvailable,
    is_flax_available,
    is_scipy_available,
    is_torch_available,
    is_torchsde_available,
)


try:
						if not is_torch_available():
												raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
						from ..utils.dummy_pt_objects import *  # noqa F403
else:
						from .scheduling_consistency_models import CMStochasticIterativeScheduler
						from .scheduling_ddim import DDIMScheduler
						from .scheduling_ddim_inverse import DDIMInverseScheduler
						from .scheduling_ddim_parallel import DDIMParallelScheduler
						from .scheduling_ddpm import DDPMScheduler
						from .scheduling_ddpm_parallel import DDPMParallelScheduler
						from .scheduling_deis_multistep import DEISMultistepScheduler
						from .scheduling_dpmsolver_multistep import DPMSolverMultistepScheduler
						from .scheduling_dpmsolver_multistep_inverse import DPMSolverMultistepInverseScheduler
						from .scheduling_dpmsolver_singlestep import DPMSolverSinglestepScheduler
						from .scheduling_euler_ancestral_discrete import EulerAncestralDiscreteScheduler
						from .scheduling_euler_discrete import EulerDiscreteScheduler
						from .scheduling_heun_discrete import HeunDiscreteScheduler
						from .scheduling_ipndm import IPNDMScheduler
						from .scheduling_k_dpm_2_ancestral_discrete import KDPMaAncestralDiscreteScheduler
						from .scheduling_k_dpm_2_discrete import KDPMaDiscreteScheduler
						from .scheduling_karras_ve import KarrasVeScheduler
						from .scheduling_pndm import PNDMScheduler
						from .scheduling_repaint import RePaintScheduler
						from .scheduling_sde_ve import ScoreSdeVeScheduler
						from .scheduling_sde_vp import ScoreSdeVpScheduler
						from .scheduling_unclip import UnCLIPScheduler
						from .scheduling_unipc_multistep import UniPCMultistepScheduler
						from .scheduling_utils import KarrasDiffusionSchedulers, SchedulerMixin
						from .scheduling_vq_diffusion import VQDiffusionScheduler

try:
						if not is_flax_available():
												raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
						from ..utils.dummy_flax_objects import *  # noqa F403
else:
						from .scheduling_ddim_flax import FlaxDDIMScheduler
						from .scheduling_ddpm_flax import FlaxDDPMScheduler
						from .scheduling_dpmsolver_multistep_flax import FlaxDPMSolverMultistepScheduler
						from .scheduling_karras_ve_flax import FlaxKarrasVeScheduler
						from .scheduling_lms_discrete_flax import FlaxLMSDiscreteScheduler
						from .scheduling_pndm_flax import FlaxPNDMScheduler
						from .scheduling_sde_ve_flax import FlaxScoreSdeVeScheduler
						from .scheduling_utils_flax import (
						    FlaxKarrasDiffusionSchedulers,
						    FlaxSchedulerMixin,
						    FlaxSchedulerOutput,
						    broadcast_to_shape_from_left,
						)


try:
						if not (is_torch_available() and is_scipy_available()):
												raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
						from ..utils.dummy_torch_and_scipy_objects import *  # noqa F403
else:
						from .scheduling_lms_discrete import LMSDiscreteScheduler

try:
						if not (is_torch_available() and is_torchsde_available()):
												raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
						from ..utils.dummy_torch_and_torchsde_objects import *  # noqa F403
else:
						from .scheduling_dpmsolver_sde import DPMSolverSDEScheduler