


'''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_     (       A__   :  np.ndarray   ):
  '''simple docstring'''





  return input_array.reshape((input_array.size, 1)   )







def 							UpperCamelCase_     (       A__   :  np.ndarray				,       A__   :  np.ndarray				,       A__   :  int   ):
  '''simple docstring'''





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

  return covariance_sum / features.shape[1]







def 							UpperCamelCase_     (       A__   :  np.ndarray				,       A__   :  np.ndarray				,       A__   :  int   ):
  '''simple docstring'''





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

  return covariance_sum / features.shape[1]







def 							UpperCamelCase_     (       A__   :  np.ndarray				,       A__   :  int   ):
  '''simple docstring'''





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

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







def 							UpperCamelCase_     (       A__   :  np.ndarray				,       A__   :  np.ndarray				,       A__   :  int				,       A__   :  int   ):
  '''simple docstring'''





  assert classes > dimensions

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

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







def 							UpperCamelCase_     (       ):
  '''simple docstring'''





  lowerCAmelCase_     : List[str]     =  np.array([[1, 2, 3, 4, 5], [2, 3, 4, 5, 6], [3, 4, 5, 6, 7]]   )
  lowerCAmelCase_     : Optional[Any]     =  np.array([0, 0, 0, 1, 1]   )
  lowerCAmelCase_     : Dict     =  2
  lowerCAmelCase_     : Tuple     =  2

  # Assert that the function raises an AssertionError if dimensions > classes
  with pytest.raises(A__   ) as error_info:
    lowerCAmelCase_     : Tuple     =  linear_discriminant_analysis(
        A__				,       A__				,       A__				,       A__   )
    if isinstance(A__				,       np.ndarray   ):
      raise AssertionError(
          """Did not raise AssertionError for dimensions > classes"""   )
    assert error_info.type is AssertionError







def 							UpperCamelCase_     (       ):
  '''simple docstring'''





  lowerCAmelCase_     : List[Any]     =  np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]]   )
  lowerCAmelCase_     : Optional[Any]     =  2
  lowerCAmelCase_     : List[str]     =  np.array([[6.92820323, 8.66025404, 10.39230485], [3.0, 3.0, 3.0]]   )

  with pytest.raises(A__   ) as error_info:
    lowerCAmelCase_     : Optional[int]     =  principal_component_analysis(A__				,       A__   )
    if not np.allclose(A__				,       A__   ):
      raise AssertionError
    assert error_info.type is AssertionError


if __name__ == "__main__":
  import doctest

  doctest.testmod()







'''simple docstring'''






from collections.abc import Iterator, MutableMapping
from dataclasses import dataclass
from typing import Generic, TypeVar

__A   :    Union[str, Any]											= TypeVar("KEY")
__A   :    Union[str, Any]											= TypeVar("VAL")






@dataclass(frozen=_SCREAMING_SNAKE_CASE      ,slots=_SCREAMING_SNAKE_CASE)
class   __snake_case			(  Generic[KEY, VAL]):







    """simple docstring"""



    lowercase  					=   42
    lowercase  					=   42







class   __snake_case			(  _Item):







    """simple docstring"""



    def __init__(  self       :    int						)  ->    None:
      super().__init__(lowerCamelCase       ,		lowerCamelCase						)





    def __bool__(  self       :    Tuple						)  ->    bool:
      return False







__A   :    Any											= _DeletedItem()






class   __snake_case			(  MutableMapping[KEY, VAL]):







    """simple docstring"""



    def __init__(  self       :    Optional[int]       ,		lowerCamelCase       :    int = 8       ,		lowerCamelCase       :    float = 0.75						)  ->    None:
      lowerCAmelCase_     : str     =  initial_block_size
      lowerCAmelCase_     : list[_Item | None]     =  [None] * initial_block_size
      assert 0.0 < capacity_factor < 1.0
      lowerCAmelCase_     : Optional[Any]     =  capacity_factor
      lowerCAmelCase_     : List[Any]     =  0

    def __lowercase  (  self       :    List[Any]       ,		lowerCamelCase       :    KEY						)  ->    int:
      return hash(lowerCamelCase						) % len(self._buckets						)

    def __lowercase  (  self       :    Optional[Any]       ,		lowerCamelCase       :    int						)  ->    int:
      return (ind + 1) % len(self._buckets						)

    def __lowercase  (  self       :    Union[str, Any]       ,		lowerCamelCase       :    int       ,		lowerCamelCase       :    KEY       ,		lowerCamelCase       :    VAL						)  ->    bool:
      lowerCAmelCase_     : Union[str, Any]     =  self._buckets[ind]
      if not stored:
        lowerCAmelCase_     : List[Any]     =  _Item(lowerCamelCase       ,		lowerCamelCase						)
        self._len += 1
        return True
      elif stored.key == key:
        lowerCAmelCase_     : List[str]     =  _Item(lowerCamelCase       ,		lowerCamelCase						)
        return True
      else:
        return False

    def __lowercase  (  self       :    Optional[Any]						)  ->    bool:
      lowerCAmelCase_     : str     =  len(self._buckets						) * self._capacity_factor
      return len(self						) >= int(lowerCamelCase						)

    def __lowercase  (  self       :    Dict						)  ->    bool:
      if len(self._buckets						) <= self._initial_block_size:
        return False
      lowerCAmelCase_     : Optional[int]     =  len(self._buckets						) * self._capacity_factor / 2
      return len(self						) < limit

    def __lowercase  (  self       :    Tuple       ,		lowerCamelCase       :    int						)  ->    None:
      lowerCAmelCase_     : Union[str, Any]     =  self._buckets
      lowerCAmelCase_     : str     =  [None] * new_size
      lowerCAmelCase_     : str     =  0
      for item in old_buckets:
        if item:
          self._add_item(item.key       ,		item.val						)

    def __lowercase  (  self       :    Tuple						)  ->    None:
      self._resize(len(self._buckets						) * 2						)

    def __lowercase  (  self       :    Union[str, Any]						)  ->    None:
      self._resize(len(self._buckets						) // 2						)

    def __lowercase  (  self       :    Optional[int]       ,		lowerCamelCase       :    KEY						)  ->    Iterator[int]:
      lowerCAmelCase_     : int     =  self._get_bucket_index(lowerCamelCase						)
      for _ in range(len(self._buckets						)						):
        yield ind
        lowerCAmelCase_     : Dict     =  self._get_next_ind(lowerCamelCase						)

    def __lowercase  (  self       :    Tuple       ,		lowerCamelCase       :    KEY       ,		lowerCamelCase       :    VAL						)  ->    None:
      for ind in self._iterate_buckets(lowerCamelCase						):
        if self._try_set(lowerCamelCase       ,		lowerCamelCase       ,		lowerCamelCase						):
          break

    def __setitem__(  self       :    Tuple       ,		lowerCamelCase       :    KEY       ,		lowerCamelCase       :    VAL						)  ->    None:
      if self._is_full():
        self._size_up()

      self._add_item(lowerCamelCase       ,		lowerCamelCase						)

    def __delitem__(  self       :    Optional[int]       ,		lowerCamelCase       :    KEY						)  ->    None:
      for ind in self._iterate_buckets(lowerCamelCase						):
        lowerCAmelCase_     : int     =  self._buckets[ind]
        if item is None:
          raise KeyError(lowerCamelCase						)
        if item is _deleted:
          continue
        if item.key == key:
          lowerCAmelCase_     : List[Any]     =  _deleted
          self._len -= 1
          break
      if self._is_sparse():
        self._size_down()

    def __getitem__(  self       :    Any       ,		lowerCamelCase       :    KEY						)  ->    VAL:
      for ind in self._iterate_buckets(lowerCamelCase						):
        lowerCAmelCase_     : Dict     =  self._buckets[ind]
        if item is None:
          break
        if item is _deleted:
          continue
        if item.key == key:
          return item.val
      raise KeyError(lowerCamelCase						)

    def __len__(  self       :    Any						)  ->    int:
      return self._len

    def __iter__(  self       :    Optional[Any]						)  ->    Iterator[KEY]:
      yield from (item.key for item in self._buckets if item)





    def __repr__(  self       :    List[Any]						)  ->    str:
      lowerCAmelCase_     : int     =  """ ,""".join(
          F'{item.key}: {item.val}' for item in self._buckets if item						)
      return F'HashMap({val_string})'



