

'''simple docstring'''

import logging

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

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





def    A_  ( snake_case ):
  return input_array.reshape((input_array.size, 1) )





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

  return covariance_sum / features.shape[1]





def    A_  ( snake_case      ,       snake_case      ,       snake_case ):
  SCREAMING_SNAKE_CASE:Union[str, Any]						      =					features.mean(1 )
  SCREAMING_SNAKE_CASE:str						      =					np.nan
  for i in range(snake_case ):
    SCREAMING_SNAKE_CASE:Dict						      =					features[:, labels == i]
    SCREAMING_SNAKE_CASE:Tuple						      =					data.shape[1]
    SCREAMING_SNAKE_CASE:Union[str, Any]						      =					data.mean(1 )
    if i > 0:
      # If covariance_sum is not None
      covariance_sum += device_data * np.dot(
          column_reshape(snake_case ) - column_reshape(snake_case )      ,       (column_reshape(snake_case ) - column_reshape(snake_case )).T      ,       )
    else:
      # If covariance_sum is np.nan (i.e. first loop)
      SCREAMING_SNAKE_CASE:Any						      =					device_data * np.dot(
          column_reshape(snake_case ) - column_reshape(snake_case )      ,       (column_reshape(snake_case ) - column_reshape(snake_case )).T      ,       )

  return covariance_sum / features.shape[1]





def    A_  ( snake_case      ,       snake_case ):

  # Check if the features have been loaded
  if features.any():
    SCREAMING_SNAKE_CASE:Dict						      =					features.mean(1 )
    # Center the dataset
    SCREAMING_SNAKE_CASE:Tuple						      =					features - np.reshape(snake_case      ,       (data_mean.size, 1) )
    SCREAMING_SNAKE_CASE:Dict						      =					np.dot(snake_case      ,       centered_data.T ) / features.shape[1]
    SCREAMING_SNAKE_CASE      ,    SCREAMING_SNAKE_CASE:List[Any]						      =					np.linalg.eigh(snake_case )
    # Take all the columns in the reverse order (-1), and then takes only the first
    SCREAMING_SNAKE_CASE:Any						      =					eigenvectors[:, ::-1][:, 0:dimensions]
    # Project the database on the new space
    SCREAMING_SNAKE_CASE:str						      =					np.dot(filtered_eigenvectors.T      ,       snake_case )
    logging.info("Principal Component Analysis computed" )

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





def    A_  ( snake_case      ,       snake_case      ,       snake_case      ,       snake_case ):
  assert classes > dimensions

  # Check if features have been already loaded
  if features.any:
    SCREAMING_SNAKE_CASE      ,    SCREAMING_SNAKE_CASE:List[str]						      =					eigh(
        covariance_between_classes(snake_case      ,       snake_case      ,       snake_case )      ,       covariance_within_classes(snake_case      ,       snake_case      ,       snake_case )      ,       )
    SCREAMING_SNAKE_CASE:Optional[int]						      =					eigenvectors[:, ::-1][:, :dimensions]
    SCREAMING_SNAKE_CASE      ,    SCREAMING_SNAKE_CASE      ,    SCREAMING_SNAKE_CASE:Optional[int]						      =					np.linalg.svd(snake_case )
    SCREAMING_SNAKE_CASE:Optional[Any]						      =					svd_matrix[:, 0:dimensions]
    SCREAMING_SNAKE_CASE:int						      =					np.dot(filtered_svd_matrix.T      ,       snake_case )
    logging.info("Linear Discriminant Analysis computed" )

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





def    A_  ( ):
  # Create dummy dataset with 2 classes and 3 features
  SCREAMING_SNAKE_CASE:Union[str, Any]						      =					np.array([[1, 2, 3, 4, 5], [2, 3, 4, 5, 6], [3, 4, 5, 6, 7]] )
  SCREAMING_SNAKE_CASE:List[str]						      =					np.array([0, 0, 0, 1, 1] )
  SCREAMING_SNAKE_CASE:Optional[int]						      =					2
  SCREAMING_SNAKE_CASE:List[Any]						      =					2

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





def    A_  ( ):
  SCREAMING_SNAKE_CASE:Union[str, Any]						      =					np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]] )
  SCREAMING_SNAKE_CASE:Any						      =					2
  SCREAMING_SNAKE_CASE:Dict						      =					np.array([[6.9282_0323, 8.6602_5404, 10.3923_0485], [3.0, 3.0, 3.0]] )

  with pytest.raises(snake_case ) as error_info:
    SCREAMING_SNAKE_CASE:int						      =					principal_component_analysis(snake_case      ,       snake_case )
    if not np.allclose(snake_case      ,       snake_case ):
      raise AssertionError
    assert error_info.type is AssertionError


if __name__ == "__main__":
    import doctest

    doctest.testmod()









'''simple docstring'''

def    A_  ( snake_case = 100 ):
  SCREAMING_SNAKE_CASE:Dict						      =					0
  SCREAMING_SNAKE_CASE:Optional[int]						      =					0
  for i in range(1      ,       n + 1 ):
    sum_of_squares += i**2
    sum_of_ints += i
  return sum_of_ints**2 - sum_of_squares


if __name__ == "__main__":
    print(f'''{solution() = }''')






