
"""simple docstring"""
import logging

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

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





def    _lowerCAmelCase    (     lowerCamelCase__							:							np.ndarray				)  ->    np.ndarray:
  return input_array.reshape((input_array.size, 1)				)





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

  return covariance_sum / features.shape[1]





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

  return covariance_sum / features.shape[1]





def    _lowerCAmelCase    (     lowerCamelCase__							:							np.ndarray,						lowerCamelCase__							:							int				)  ->    np.ndarray:

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

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





def    _lowerCAmelCase    (     lowerCamelCase__							:							np.ndarray,						lowerCamelCase__							:							np.ndarray,						lowerCamelCase__							:							int,						lowerCamelCase__							:							int				)  ->    np.ndarray:
  assert classes > dimensions

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

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





def    _lowerCAmelCase    (     )  ->    None:
  # Create dummy dataset with 2 classes and 3 features
  _SCREAMING_SNAKE_CASE   :				Any							    = np.array([[1, 2, 3, 4, 5], [2, 3, 4, 5, 6], [3, 4, 5, 6, 7]]				)
  _SCREAMING_SNAKE_CASE   :				Optional[int]							    = np.array([0, 0, 0, 1, 1]				)
  _SCREAMING_SNAKE_CASE   :				Tuple							    = 2
  _SCREAMING_SNAKE_CASE   :				Tuple							    = 2

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





def    _lowerCAmelCase    (     )  ->    None:
  _SCREAMING_SNAKE_CASE   :				List[str]							    = np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]]				)
  _SCREAMING_SNAKE_CASE   :				str							    = 2
  _SCREAMING_SNAKE_CASE   :				Dict							    = np.array([[6.92820323, 8.66025404, 10.39230485], [3.0, 3.0, 3.0]]				)

  with pytest.raises(lowerCamelCase__				) as error_info:
    _SCREAMING_SNAKE_CASE   :				List[Any]							    = principal_component_analysis(lowerCamelCase__,						lowerCamelCase__				)
    if not np.allclose(lowerCamelCase__,						lowerCamelCase__				):
      raise AssertionError
    assert error_info.type is AssertionError


if __name__ == "__main__":
      import doctest

      doctest.testmod()





"""simple docstring"""
from __future__ import annotations

lowercase_       :						List[str]     					=	'''#'''
class 			UpperCamelCase      :
     def __init__(     self				):




       """simple docstring"""


       _SCREAMING_SNAKE_CASE   :				dict							    = {}
     def 				__SCREAMING_SNAKE_CASE							(     self  ,     snake_case__				):




       """simple docstring"""


       _SCREAMING_SNAKE_CASE   :				str							    = self._trie
       for char in text:
         if char not in trie:
           _SCREAMING_SNAKE_CASE   :				List[str]							    = {}
         _SCREAMING_SNAKE_CASE   :				List[str]							    = trie[char]
       _SCREAMING_SNAKE_CASE   :				Optional[Any]							    = True
     def 				__SCREAMING_SNAKE_CASE							(     self  ,     snake_case__				):




       """simple docstring"""


       _SCREAMING_SNAKE_CASE   :				Optional[Any]							    = self._trie
       for char in prefix:
         if char in trie:
           _SCREAMING_SNAKE_CASE   :				str							    = trie[char]
         else:
           return []
       return self._elements(snake_case__				)




     def 				__SCREAMING_SNAKE_CASE							(     self  ,     snake_case__				):




       """simple docstring"""


       _SCREAMING_SNAKE_CASE   :				str							    = []
       for c, v in d.items():
         _SCREAMING_SNAKE_CASE   :				int							    = [" "] if c == END else [(c + s) for s in self._elements(snake_case__				)]
         result.extend(snake_case__				)
       return tuple(snake_case__				)
lowercase_       :						Union[str, Any]     					=	Trie()
lowercase_       :						Optional[Any]     					=	('''depart''', '''detergent''', '''daring''', '''dog''', '''deer''', '''deal''')
for word in words:
      trie.insert_word(word)





def    _lowerCAmelCase    (     lowerCamelCase__							:							str				)  ->    tuple:
  _SCREAMING_SNAKE_CASE   :				Dict							    = trie.find_word(lowerCamelCase__				)
  return tuple(string + word for word in suffixes				)





def    _lowerCAmelCase    (     )  ->    None:
  print(autocomplete_using_trie("de"				)				)


if __name__ == "__main__":
      import doctest

      doctest.testmod()
      main()



