





import logging

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

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



def 	_a						(   UpperCAmelCase					)    ->    np.ndarray:







   """simple docstring"""
   return input_array.reshape((input_array.size, 1)					)



def 	_a						(   UpperCAmelCase      ,  UpperCAmelCase      ,  UpperCAmelCase					)    ->    np.ndarray:







   """simple docstring"""
   lowerCamelCase__       :						Tuple        =							np.nan
   for i in range(UpperCAmelCase					):
      lowerCamelCase__       :						str        =							features[:, labels == i]
      lowerCamelCase__       :						Dict        =							data.mean(1					)
      # Centralize the data of class i
      lowerCamelCase__       :						Tuple        =							data - column_reshape(UpperCAmelCase					)
      if i > 0:
         # If covariance_sum is not None
         covariance_sum += np.dot(UpperCAmelCase      ,  centered_data.T					)
      else:
         # If covariance_sum is np.nan (i.e. first loop)
         lowerCamelCase__       :						Any        =							np.dot(UpperCAmelCase      ,  centered_data.T					)

   return covariance_sum / features.shape[1]



def 	_a						(   UpperCAmelCase      ,  UpperCAmelCase      ,  UpperCAmelCase					)    ->    np.ndarray:







   """simple docstring"""
   lowerCamelCase__       :						Optional[Any]        =							features.mean(1					)
   lowerCamelCase__       :						Optional[int]        =							np.nan
   for i in range(UpperCAmelCase					):
      lowerCamelCase__       :						Optional[Any]        =							features[:, labels == i]
      lowerCamelCase__       :						List[Any]        =							data.shape[1]
      lowerCamelCase__       :						int        =							data.mean(1					)
      if i > 0:
         # If covariance_sum is not None
         covariance_sum += device_data * np.dot(
             column_reshape(UpperCAmelCase					) - column_reshape(UpperCAmelCase					)      ,  (column_reshape(UpperCAmelCase					) - column_reshape(UpperCAmelCase					)).T      ,  )
      else:
         # If covariance_sum is np.nan (i.e. first loop)
         lowerCamelCase__       :						Union[str, Any]        =							device_data * np.dot(
             column_reshape(UpperCAmelCase					) - column_reshape(UpperCAmelCase					)      ,  (column_reshape(UpperCAmelCase					) - column_reshape(UpperCAmelCase					)).T      ,  )

   return covariance_sum / features.shape[1]



def 	_a						(   UpperCAmelCase      ,  UpperCAmelCase					)    ->    np.ndarray:







   """simple docstring"""

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

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



def 	_a						(   UpperCAmelCase      ,  UpperCAmelCase      ,  UpperCAmelCase      ,  UpperCAmelCase					)    ->    np.ndarray:







   """simple docstring"""
   assert classes > dimensions

   # Check if features have been already loaded
   if features.any:
      lowerCamelCase__       ,							lowerCamelCase__       :						List[Any]        =							eigh(
          covariance_between_classes(UpperCAmelCase      ,  UpperCAmelCase      ,  UpperCAmelCase					)      ,  covariance_within_classes(UpperCAmelCase      ,  UpperCAmelCase      ,  UpperCAmelCase					)      ,  )
      lowerCamelCase__       :						List[Any]        =							eigenvectors[:, ::-1][:, :dimensions]
      lowerCamelCase__       ,							lowerCamelCase__       ,							lowerCamelCase__       :						Optional[int]        =							np.linalg.svd(UpperCAmelCase					)
      lowerCamelCase__       :						str        =							svd_matrix[:, 0:dimensions]
      lowerCamelCase__       :						Dict        =							np.dot(filtered_svd_matrix.T      ,  UpperCAmelCase					)
      logging.info('''Linear Discriminant Analysis computed'''					)

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



def 	_a						(   )    ->    None:







   """simple docstring"""
   # Create dummy dataset with 2 classes and 3 features
   lowerCamelCase__       :						Union[str, Any]        =							np.array([[1, 2, 3, 4, 5], [2, 3, 4, 5, 6], [3, 4, 5, 6, 7]]					)
   lowerCamelCase__       :						Optional[Any]        =							np.array([0, 0, 0, 1, 1]					)
   lowerCamelCase__       :						List[str]        =							2
   lowerCamelCase__       :						str        =							2

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



def 	_a						(   )    ->    None:







   """simple docstring"""
   lowerCamelCase__       :						Optional[Any]        =							np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]]					)
   lowerCamelCase__       :						Tuple        =							2
   lowerCamelCase__       :						Union[str, Any]        =							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(UpperCAmelCase					) as error_info:
      lowerCamelCase__       :						Any        =							principal_component_analysis(UpperCAmelCase      ,  UpperCAmelCase					)
      if not np.allclose(UpperCAmelCase      ,  UpperCAmelCase					):
         raise AssertionError
      assert error_info.type is AssertionError


if __name__ == "__main__":
       import doctest

       doctest.testmod()










import inspect
import warnings
from typing import Any, Dict, Optional, Union

from packaging import version



def 	_a						(   *UpperCAmelCase      ,  UpperCAmelCase = None      ,  UpperCAmelCase=True      ,  UpperCAmelCase=2					)    ->    str:







   """simple docstring"""
   from .. import __version__

   lowerCamelCase__       :						Optional[Any]        =							take_from
   lowerCamelCase__       :						Any        =							()
   if not isinstance(args[0]      ,  UpperCAmelCase					):
      lowerCamelCase__       :						Optional[int]        =							(args,)

   for attribute, version_name, message in args:
      if version.parse(version.parse(UpperCAmelCase					).base_version					) >= version.parse(UpperCAmelCase					):
         raise ValueError(
             f"The deprecation tuple {(attribute, version_name, message)} should be removed since diffusers'"
             f" version {__version__} is >= {version_name}"					)

      lowerCamelCase__       :						List[Any]        =							None
      if isinstance(UpperCAmelCase      ,  UpperCAmelCase					) and attribute in deprecated_kwargs:
         values += (deprecated_kwargs.pop(UpperCAmelCase					),)
         lowerCamelCase__       :						Tuple        =							f"The `{attribute}` argument is deprecated and will be removed in version {version_name}."
      elif hasattr(UpperCAmelCase      ,  UpperCAmelCase					):
         values += (getattr(UpperCAmelCase      ,  UpperCAmelCase					),)
         lowerCamelCase__       :						Union[str, Any]        =							f"The `{attribute}` attribute is deprecated and will be removed in version {version_name}."
      elif deprecated_kwargs is None:
         lowerCamelCase__       :						int        =							f"`{attribute}` is deprecated and will be removed in version {version_name}."

      if warning is not None:
         lowerCamelCase__       :						int        =							warning + ''' ''' if standard_warn else ''''''
         warnings.warn(warning + message      ,  UpperCAmelCase      ,  stacklevel=UpperCAmelCase					)

   if isinstance(UpperCAmelCase      ,  UpperCAmelCase					) and len(UpperCAmelCase					) > 0:
      lowerCamelCase__       :						Tuple        =							inspect.getouterframes(inspect.currentframe()					)[1]
      lowerCamelCase__       :						Optional[Any]        =							call_frame.filename
      lowerCamelCase__       :						List[Any]        =							call_frame.lineno
      lowerCamelCase__       :						Optional[Any]        =							call_frame.function
      lowerCamelCase__       ,							lowerCamelCase__       :						Union[str, Any]        =							next(iter(deprecated_kwargs.items()					)					)
      raise TypeError(f"{function} in {filename} line {line_number-1} got an unexpected keyword argument `{key}`"					)

   if len(UpperCAmelCase					) == 0:
      return
   elif len(UpperCAmelCase					) == 1:
      return values[0]
   return values



