

"""simple docstring"""



import logging

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

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





def  _snake_case     (    UpperCAmelCase_  :					np.ndarray			):
     return input_array.reshape((input_array.size, 1)			)





def  _snake_case     (    UpperCAmelCase_  :					np.ndarray					,   UpperCAmelCase_  :					np.ndarray					,   UpperCAmelCase_  :					int			):
     A__										=  np.nan
     for i in range(UpperCAmelCase_			):
          A__										=  features[:, labels == i]
          A__										=  data.mean(1			)
          # Centralize the data of class i
          A__										=  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)
               A__										=  np.dot(UpperCAmelCase_					,   centered_data.T			)

     return covariance_sum / features.shape[1]





def  _snake_case     (    UpperCAmelCase_  :					np.ndarray					,   UpperCAmelCase_  :					np.ndarray					,   UpperCAmelCase_  :					int			):
     A__										=  features.mean(1			)
     A__										=  np.nan
     for i in range(UpperCAmelCase_			):
          A__										=  features[:, labels == i]
          A__										=  data.shape[1]
          A__										=  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)
               A__										=  device_data * np.dot(
                   column_reshape(UpperCAmelCase_			) - column_reshape(UpperCAmelCase_			)					,   (column_reshape(UpperCAmelCase_			) - column_reshape(UpperCAmelCase_			)).T					,   )

     return covariance_sum / features.shape[1]





def  _snake_case     (    UpperCAmelCase_  :					np.ndarray					,   UpperCAmelCase_  :					int			):

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

     # Check if features have been already loaded
     if features.any:
          A__			,				A__										=  eigh(
              covariance_between_classes(UpperCAmelCase_					,   UpperCAmelCase_					,   UpperCAmelCase_			)					,   covariance_within_classes(UpperCAmelCase_					,   UpperCAmelCase_					,   UpperCAmelCase_			)					,   )
          A__										=  eigenvectors[:, ::-1][:, :dimensions]
          A__			,				A__			,				A__										=  np.linalg.svd(UpperCAmelCase_			)
          A__										=  svd_matrix[:, 0:dimensions]
          A__										=  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  _snake_case     (    ):
     # Create dummy dataset with 2 classes and 3 features
     A__										=  np.array([[1, 2, 3, 4, 5], [2, 3, 4, 5, 6], [3, 4, 5, 6, 7]]			)
     A__										=  np.array([0, 0, 0, 1, 1]			)
     A__										=  2
     A__										=  2

     # Assert that the function raises an AssertionError if dimensions > classes
     with pytest.raises(UpperCAmelCase_			) as error_info:
          A__										=  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  _snake_case     (    ):
     A__										=  np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]]			)
     A__										=  2
     A__										=  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:
          A__										=  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()









"""simple docstring"""



from itertools import count





def  _snake_case     (    UpperCAmelCase_  :					int = 50			):
     A__										=  [1] * min_block_length

     for n in count(UpperCAmelCase_			):
          fill_count_functions.append(1			)

          for block_length in range(UpperCAmelCase_					,   n + 1			):
               for block_start in range(n - block_length			):
                    fill_count_functions[n] += fill_count_functions[
                        n - block_start - block_length - 1
                    ]

               fill_count_functions[n] += 1

          if fill_count_functions[n] > 100_0000:
               break

     return n


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






