class  UpperCamelCase				:

     '''simple docstring'''

     def __init__(					self				,				A_ = ""				,				A_ = False						) ->				None:






           """simple docstring"""
           # Mapping from the first character of the prefix of the node
           _lowerCamelCase			    =				{}

           # A node will be a leaf if the tree contains its word
           _lowerCamelCase			    =				is_leaf

           _lowerCamelCase			    =				prefix



     def 		UpperCamelCase_						(					self				,				A_						) ->				tuple[str, str, str]:






           """simple docstring"""
           _lowerCamelCase			    =				0
           for q, w in zip(self.prefix				,				A_						):
                 if q != w:
                       break

                 x += 1

           return self.prefix[:x], self.prefix[x:], word[x:]



     def 		UpperCamelCase_						(					self				,				A_						) ->				None:






           """simple docstring"""
           for word in words:
                 self.insert(A_						)



     def 		UpperCamelCase_						(					self				,				A_						) ->				None:






           """simple docstring"""
           # Case 1: If the word is the prefix of the node
           # Solution: We set the current node as leaf
           if self.prefix == word:
                 _lowerCamelCase			    =				True

           # Case 2: The node has no edges that have a prefix to the word
           # Solution: We create an edge from the current node to a new one
           # containing the word
           elif word[0] not in self.nodes:
                 _lowerCamelCase			    =				RadixNode(prefix=A_				,				is_leaf=A_						)

           else:
                 _lowerCamelCase			    =				self.nodes[word[0]]
                 _lowerCamelCase    ,					_lowerCamelCase    ,					_lowerCamelCase			    =				incoming_node.match(
                     A_						)

                 # Case 3: The node prefix is equal to the matching
                 # Solution: We insert remaining word on the next node
                 if remaining_prefix == "":
                       self.nodes[matching_string[0]].insert(A_						)

                 # Case 4: The word is greater equal to the matching
                 # Solution: Create a node in between both nodes, change
                 # prefixes and add the new node for the remaining word
                 else:
                       _lowerCamelCase			    =				remaining_prefix

                       _lowerCamelCase			    =				self.nodes[matching_string[0]]
                       _lowerCamelCase			    =				RadixNode(A_				,				A_						)
                       _lowerCamelCase			    =				aux_node

                       if remaining_word == "":
                             _lowerCamelCase			    =				True
                       else:
                             self.nodes[matching_string[0]].insert(A_						)



     def 		UpperCamelCase_						(					self				,				A_						) ->				bool:






           """simple docstring"""
           _lowerCamelCase			    =				self.nodes.get(word[0]				,				A_						)
           if not incoming_node:
                 return False
           else:
                 _lowerCamelCase    ,					_lowerCamelCase    ,					_lowerCamelCase			    =				incoming_node.match(
                     A_						)
                 # If there is remaining prefix, the word can't be on the tree
                 if remaining_prefix != "":
                       return False
                 # This applies when the word and the prefix are equal
                 elif remaining_word == "":
                       return incoming_node.is_leaf
                 # We have word remaining so we check the next node
                 else:
                       return incoming_node.find(A_						)



     def 		UpperCamelCase_						(					self				,				A_						) ->				bool:






           """simple docstring"""
           _lowerCamelCase			    =				self.nodes.get(word[0]				,				A_						)
           if not incoming_node:
                 return False
           else:
                 _lowerCamelCase    ,					_lowerCamelCase    ,					_lowerCamelCase			    =				incoming_node.match(
                     A_						)
                 # If there is remaining prefix, the word can't be on the tree
                 if remaining_prefix != "":
                       return False
                 # We have word remaining so we check the next node
                 elif remaining_word != "":
                       return incoming_node.delete(A_						)
                 else:
                       # If it is not a leaf, we don't have to delete
                       if not incoming_node.is_leaf:
                             return False
                       else:
                             # We delete the nodes if no edges go from it
                             if len(incoming_node.nodes						) == 0:
                                   del self.nodes[word[0]]
                                   # We merge the current node with its only child
                                   if len(self.nodes						) == 1 and not self.is_leaf:
                                         _lowerCamelCase			    =				list(self.nodes.values()						)[0]
                                         _lowerCamelCase			    =				merging_node.is_leaf
                                         self.prefix += merging_node.prefix
                                         _lowerCamelCase			    =				merging_node.nodes
                    # If there is more than 1 edge, we just mark it as non-leaf
                             elif len(incoming_node.nodes						) > 1:
                                   _lowerCamelCase			    =				False
                             # If there is 1 edge, we merge it with its child
                             else:
                                   _lowerCamelCase			    =				list(incoming_node.nodes.values()						)[0]
                                   _lowerCamelCase			    =				merging_node.is_leaf
                                   incoming_node.prefix += merging_node.prefix
                                   _lowerCamelCase			    =				merging_node.nodes

                             return True





     def 		UpperCamelCase_						(					self				,				A_ = 0						) ->				None:






           """simple docstring"""
           if self.prefix != "":
                 print('''-''' * height				,				self.prefix				,				'''  (leaf)''' if self.is_leaf else ''''''						)

           for value in self.nodes.values():
                 value.print_tree(height + 1						)





def       __magic_name__(  )						->    bool:



      '''simple docstring'''

      _lowerCamelCase			    =				'''banana bananas bandana band apple all beast'''.split()
      _lowerCamelCase			    =				RadixNode()
      root.insert_many(__UpperCAmelCase		)

      assert all(root.find(__UpperCAmelCase		) for word in words		)
      assert not root.find('''bandanas'''		)
      assert not root.find('''apps'''		)
      root.delete('''all'''		)
      assert not root.find('''all'''		)
      root.delete('''banana'''		)
      assert not root.find('''banana'''		)
      assert root.find('''bananas'''		)

      return True
def       __magic_name__(  )						->    None:



      '''simple docstring'''

      assert test_trie()
def       __magic_name__(  )						->    None:



      '''simple docstring'''

      _lowerCamelCase			    =				RadixNode()
      _lowerCamelCase			    =				'''banana bananas bandanas bandana band apple all beast'''.split()
      root.insert_many(__UpperCAmelCase		)

      print('''Words:''' ,						__UpperCAmelCase		)
      print('''Tree:'''		)
      root.print_tree()


if __name__ == "__main__":
     main()
import logging

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

logging.basicConfig(level=logging.INFO, format='%(message)s')
def       __magic_name__(  __UpperCAmelCase		)						->    np.ndarray:



      '''simple docstring'''

      return input_array.reshape((input_array.size, 1)		)
def       __magic_name__(  __UpperCAmelCase ,						__UpperCAmelCase ,						__UpperCAmelCase		)						->    np.ndarray:



      '''simple docstring'''

      _lowerCamelCase			    =				np.nan
      for i in range(__UpperCAmelCase		):
            _lowerCamelCase			    =				features[:, labels == i]
            _lowerCamelCase			    =				data.mean(1		)
            # Centralize the data of class i
            _lowerCamelCase			    =				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			    =				np.dot(__UpperCAmelCase ,						centered_data.T		)

      return covariance_sum / features.shape[1]
def       __magic_name__(  __UpperCAmelCase ,						__UpperCAmelCase ,						__UpperCAmelCase		)						->    np.ndarray:



      '''simple docstring'''

      _lowerCamelCase			    =				features.mean(1		)
      _lowerCamelCase			    =				np.nan
      for i in range(__UpperCAmelCase		):
            _lowerCamelCase			    =				features[:, labels == i]
            _lowerCamelCase			    =				data.shape[1]
            _lowerCamelCase			    =				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			    =				device_data * np.dot(
                      column_reshape(__UpperCAmelCase		) - column_reshape(__UpperCAmelCase		) ,						(column_reshape(__UpperCAmelCase		) - column_reshape(__UpperCAmelCase		)).T ,						)

      return covariance_sum / features.shape[1]
def       __magic_name__(  __UpperCAmelCase ,						__UpperCAmelCase		)						->    np.ndarray:



      '''simple docstring'''

      if features.any():
            _lowerCamelCase			    =				features.mean(1		)
            # Center the dataset
            _lowerCamelCase			    =				features - np.reshape(__UpperCAmelCase ,						(data_mean.size, 1)		)
            _lowerCamelCase			    =				np.dot(__UpperCAmelCase ,						centered_data.T		) / features.shape[1]
            _lowerCamelCase    ,					_lowerCamelCase			    =				np.linalg.eigh(__UpperCAmelCase		)
            # Take all the columns in the reverse order (-1), and then takes only the first
            _lowerCamelCase			    =				eigenvectors[:, ::-1][:, 0:dimensions]
            # Project the database on the new space
            _lowerCamelCase			    =				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       __magic_name__(  __UpperCAmelCase ,						__UpperCAmelCase ,						__UpperCAmelCase ,						__UpperCAmelCase		)						->    np.ndarray:



      '''simple docstring'''

      assert classes > dimensions

      # Check if features have been already loaded
      if features.any:
            _lowerCamelCase    ,					_lowerCamelCase			    =				eigh(
                covariance_between_classes(__UpperCAmelCase ,						__UpperCAmelCase ,						__UpperCAmelCase		) ,						covariance_within_classes(__UpperCAmelCase ,						__UpperCAmelCase ,						__UpperCAmelCase		) ,						)
            _lowerCamelCase			    =				eigenvectors[:, ::-1][:, :dimensions]
            _lowerCamelCase    ,					_lowerCamelCase    ,					_lowerCamelCase			    =				np.linalg.svd(__UpperCAmelCase		)
            _lowerCamelCase			    =				svd_matrix[:, 0:dimensions]
            _lowerCamelCase			    =				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       __magic_name__(  )						->    None:



      '''simple docstring'''

      _lowerCamelCase			    =				np.array([[1, 2, 3, 4, 5], [2, 3, 4, 5, 6], [3, 4, 5, 6, 7]]		)
      _lowerCamelCase			    =				np.array([0, 0, 0, 1, 1]		)
      _lowerCamelCase			    =				2
      _lowerCamelCase			    =				2

      # Assert that the function raises an AssertionError if dimensions > classes
      with pytest.raises(__UpperCAmelCase		) as error_info:
            _lowerCamelCase			    =				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       __magic_name__(  )						->    None:



      '''simple docstring'''

      _lowerCamelCase			    =				np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]]		)
      _lowerCamelCase			    =				2
      _lowerCamelCase			    =				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:
            _lowerCamelCase			    =				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()