'''simple docstring'''





from __future__ import annotations

import string
from itertools import cycle, product
from pathlib import Path

SCREAMING_SNAKE_CASE_:     str  =(
    string.ascii_letters + string.digits + string.punctuation + string.whitespace
)
SCREAMING_SNAKE_CASE_:     list[int]  =[ord(letter) for letter in string.ascii_lowercase]
SCREAMING_SNAKE_CASE_:     set[int]  ={ord(char) for char in VALID_CHARS}

SCREAMING_SNAKE_CASE_:     list[str]  =["the", "be", "to", "of", "and", "in", "that", "have"]





def 	lowerCAmelCase_				(					snake_case_       : list[int]					,    snake_case_       : tuple[int, ...]			)    ->      str | None:


     '''simple docstring'''




     UpperCAmelCase_           =   ""
     UpperCAmelCase_           =   42
     UpperCAmelCase_           =   42
     UpperCAmelCase_           =   42

     for keychar, cipherchar in zip(cycle(snake_case_			)					,    snake_case_			):
          UpperCAmelCase_           =   cipherchar ^ keychar
          if decodedchar not in VALID_INTS:
               return None
          decoded += chr(snake_case_			)

     return decoded





def 	lowerCAmelCase_				(					snake_case_       : list[int]			)    ->      list[str]:


     '''simple docstring'''




     UpperCAmelCase_           =   []
     for key in product(snake_case_					,    repeat=3			):
          UpperCAmelCase_           =   try_key(snake_case_					,    snake_case_			)
          if encoded is not None:
               possibles.append(snake_case_			)
     return possibles





def 	lowerCAmelCase_				(					snake_case_       : list[str]					,    snake_case_       : str			)    ->      list[str]:


     '''simple docstring'''




     return [possible for possible in possibles if common_word in possible.lower()]





def 	lowerCAmelCase_				(					snake_case_       : str = "p059_cipher.txt"			)    ->      int:


     '''simple docstring'''




     UpperCAmelCase_           =   42
     UpperCAmelCase_           =   42
     UpperCAmelCase_           =   42
     UpperCAmelCase_           =   42
     UpperCAmelCase_           =   Path(snake_case_			).parent.joinpath(snake_case_			).read_text(encoding="utf-8"			)

     UpperCAmelCase_           =   [int(snake_case_			) for number in data.strip().split(","			)]

     UpperCAmelCase_           =   filter_valid_chars(snake_case_			)
     for common_word in COMMON_WORDS:
          UpperCAmelCase_           =   filter_common_word(snake_case_					,    snake_case_			)
          if len(snake_case_			) == 1:
               break

     UpperCAmelCase_           =   possibles[0]
     return sum(ord(snake_case_			) for char in decoded_text			)


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





'''simple docstring'''

import logging

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

logging.basicConfig(level=logging.INFO, format="""%(message)s""")
def 			__UpperCamelCase       (   UpperCAmelCase     ):
 return input_array.reshape((input_array.size, 1)     )
def 			__UpperCamelCase       (   UpperCAmelCase		,     UpperCAmelCase		,     UpperCAmelCase     ):
 lowercase__				:    Dict  =					np.nan
 for i in range(UpperCAmelCase     ):
  lowercase__				:    Optional[Any]  =					features[:, labels == i]
  lowercase__				:    Optional[Any]  =					data.mean(1     )
  # Centralize the data of class i
  lowercase__				:    Dict  =					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)
   lowercase__				:    List[str]  =					np.dot(UpperCAmelCase		,     centered_data.T     )

 return covariance_sum / features.shape[1]
def 			__UpperCamelCase       (   UpperCAmelCase		,     UpperCAmelCase		,     UpperCAmelCase     ):
 lowercase__				:    Tuple  =					features.mean(1     )
 lowercase__				:    Dict  =					np.nan
 for i in range(UpperCAmelCase     ):
  lowercase__				:    List[str]  =					features[:, labels == i]
  lowercase__				:    int  =					data.shape[1]
  lowercase__				:    Optional[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)
   lowercase__				:    Optional[int]  =					device_data * np.dot(
       column_reshape(UpperCAmelCase     ) - column_reshape(UpperCAmelCase     )		,     (column_reshape(UpperCAmelCase     ) - column_reshape(UpperCAmelCase     )).T		,     )

 return covariance_sum / features.shape[1]
def 			__UpperCamelCase       (   UpperCAmelCase		,     UpperCAmelCase     ):

 # Check if the features have been loaded
 if features.any():
  lowercase__				:    Optional[Any]  =					features.mean(1     )
  # Center the dataset
  lowercase__				:    List[str]  =					features - np.reshape(UpperCAmelCase		,     (data_mean.size, 1)     )
  lowercase__				:    Optional[Any]  =					np.dot(UpperCAmelCase		,     centered_data.T     ) / features.shape[1]
  lowercase__ ,							lowercase__				:    Tuple  =					np.linalg.eigh(UpperCAmelCase     )
  # Take all the columns in the reverse order (-1), and then takes only the first
  lowercase__				:    str  =					eigenvectors[:, ::-1][:, 0:dimensions]
  # Project the database on the new space
  lowercase__				:    Tuple  =					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 			__UpperCamelCase       (   UpperCAmelCase		,     UpperCAmelCase		,     UpperCAmelCase		,     UpperCAmelCase     ):
 assert classes > dimensions

 # Check if features have been already loaded
 if features.any:
  lowercase__ ,							lowercase__				:    Any  =					eigh(
      covariance_between_classes(UpperCAmelCase		,     UpperCAmelCase		,     UpperCAmelCase     )		,     covariance_within_classes(UpperCAmelCase		,     UpperCAmelCase		,     UpperCAmelCase     )		,     )
  lowercase__				:    Optional[int]  =					eigenvectors[:, ::-1][:, :dimensions]
  lowercase__ ,							lowercase__ ,							lowercase__				:    Optional[int]  =					np.linalg.svd(UpperCAmelCase     )
  lowercase__				:    List[str]  =					svd_matrix[:, 0:dimensions]
  lowercase__				:    str  =					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 			__UpperCamelCase       (   ):
 # Create dummy dataset with 2 classes and 3 features
 lowercase__				:    List[str]  =					np.array([[1, 2, 3, 4, 5], [2, 3, 4, 5, 6], [3, 4, 5, 6, 7]]     )
 lowercase__				:    Optional[Any]  =					np.array([0, 0, 0, 1, 1]     )
 lowercase__				:    str  =					2
 lowercase__				:    Dict  =					2

 # Assert that the function raises an AssertionError if dimensions > classes
 with pytest.raises(UpperCAmelCase     ) as error_info:
  lowercase__				:    int  =					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 			__UpperCamelCase       (   ):
 lowercase__				:    Optional[int]  =					np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]]     )
 lowercase__				:    int  =					2
 lowercase__				:    Any  =					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(UpperCAmelCase     ) as error_info:
  lowercase__				:    Dict  =					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()

