





'''simple docstring'''






import logging

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

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


def 					_a   (__SCREAMING_SNAKE_CASE   ):


  """simple docstring"""

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


def 					_a   (__SCREAMING_SNAKE_CASE  ,      __SCREAMING_SNAKE_CASE  ,      __SCREAMING_SNAKE_CASE   ):


  """simple docstring"""

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

  return covariance_sum / features.shape[1]


def 					_a   (__SCREAMING_SNAKE_CASE  ,      __SCREAMING_SNAKE_CASE  ,      __SCREAMING_SNAKE_CASE   ):


  """simple docstring"""

  _UpperCamelCase       			=features.mean(1   )
  _UpperCamelCase       			=np.nan
  for i in range(__SCREAMING_SNAKE_CASE   ):
    _UpperCamelCase       			=features[:, labels == i]
    _UpperCamelCase       			=data.shape[1]
    _UpperCamelCase       			=data.mean(1   )
    if i > 0:
      # If covariance_sum is not None
      covariance_sum += device_data * np.dot(
          column_reshape(__SCREAMING_SNAKE_CASE   ) - column_reshape(__SCREAMING_SNAKE_CASE   )  ,      (column_reshape(__SCREAMING_SNAKE_CASE   ) - column_reshape(__SCREAMING_SNAKE_CASE   )).T  ,      )
    else:
      # If covariance_sum is np.nan (i.e. first loop)
      _UpperCamelCase       			=device_data * np.dot(
          column_reshape(__SCREAMING_SNAKE_CASE   ) - column_reshape(__SCREAMING_SNAKE_CASE   )  ,      (column_reshape(__SCREAMING_SNAKE_CASE   ) - column_reshape(__SCREAMING_SNAKE_CASE   )).T  ,      )

  return covariance_sum / features.shape[1]


def 					_a   (__SCREAMING_SNAKE_CASE  ,      __SCREAMING_SNAKE_CASE   ):


  """simple docstring"""

  if features.any():
    _UpperCamelCase       			=features.mean(1   )
    # Center the dataset
    _UpperCamelCase       			=features - np.reshape(__SCREAMING_SNAKE_CASE  ,      (data_mean.size, 1)   )
    _UpperCamelCase       			=np.dot(__SCREAMING_SNAKE_CASE  ,      centered_data.T   ) / features.shape[1]
    _UpperCamelCase			,     _UpperCamelCase       			=np.linalg.eigh(__SCREAMING_SNAKE_CASE   )
    # Take all the columns in the reverse order (-1), and then takes only the first
    _UpperCamelCase       			=eigenvectors[:, ::-1][:, 0:dimensions]
    # Project the database on the new space
    _UpperCamelCase       			=np.dot(filtered_eigenvectors.T  ,      __SCREAMING_SNAKE_CASE   )
    logging.info('''Principal Component Analysis computed'''   )

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


def 					_a   (__SCREAMING_SNAKE_CASE  ,      __SCREAMING_SNAKE_CASE  ,      __SCREAMING_SNAKE_CASE  ,      __SCREAMING_SNAKE_CASE   ):


  """simple docstring"""

  assert classes > dimensions

  # Check if features have been already loaded
  if features.any:
    _UpperCamelCase			,     _UpperCamelCase       			=eigh(
        covariance_between_classes(__SCREAMING_SNAKE_CASE  ,      __SCREAMING_SNAKE_CASE  ,      __SCREAMING_SNAKE_CASE   )  ,      covariance_within_classes(__SCREAMING_SNAKE_CASE  ,      __SCREAMING_SNAKE_CASE  ,      __SCREAMING_SNAKE_CASE   )  ,      )
    _UpperCamelCase       			=eigenvectors[:, ::-1][:, :dimensions]
    _UpperCamelCase			,     _UpperCamelCase			,     _UpperCamelCase       			=np.linalg.svd(__SCREAMING_SNAKE_CASE   )
    _UpperCamelCase       			=svd_matrix[:, 0:dimensions]
    _UpperCamelCase       			=np.dot(filtered_svd_matrix.T  ,      __SCREAMING_SNAKE_CASE   )
    logging.info('''Linear Discriminant Analysis computed'''   )

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


def 					_a   ():


  """simple docstring"""

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

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


def 					_a   ():


  """simple docstring"""

  _UpperCamelCase       			=np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]]   )
  _UpperCamelCase       			=2
  _UpperCamelCase       			=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(__SCREAMING_SNAKE_CASE   ) as error_info:
    _UpperCamelCase       			=principal_component_analysis(__SCREAMING_SNAKE_CASE  ,      __SCREAMING_SNAKE_CASE   )
    if not np.allclose(__SCREAMING_SNAKE_CASE  ,      __SCREAMING_SNAKE_CASE   ):
      raise AssertionError
    assert error_info.type is AssertionError


if __name__ == "__main__":
      import doctest

      doctest.testmod()













'''simple docstring'''






from __future__ import annotations

import sys
from collections import deque
from typing import Generic, TypeVar

__lowerCamelCase						: Optional[int]		=   TypeVar('T')







class 		UpperCAmelCase   (				Generic[T]):


  """simple docstring"""







  lowerCAmelCase_					=				42  # Cache store of keys
  lowerCAmelCase_					=				42  # References of the keys in cache
  lowerCAmelCase_					=				10  # Maximum capacity of cache


  def __init__(				self    :					Union[str, Any]							,	UpperCamelCase__    :					int  )     ->						None:
    _UpperCamelCase       			=deque()
    _UpperCamelCase       			=set()
    if not n:
      _UpperCamelCase       			=sys.maxsize
    elif n < 0:
      raise ValueError('''n should be an integer greater than 0.'''  )
    else:
      _UpperCamelCase       			=n


  def   UpperCamelCase__      (				self    :					List[str]							,	UpperCamelCase__    :					T  )     ->						None:
    if x not in self.key_reference:
      if len(self.dq_store  ) == LRUCache._MAX_CAPACITY:
        _UpperCamelCase       			=self.dq_store.pop()
        self.key_reference.remove(UpperCamelCase__  )
    else:
      self.dq_store.remove(UpperCamelCase__  )

    self.dq_store.appendleft(UpperCamelCase__  )
    self.key_reference.add(UpperCamelCase__  )


  def   UpperCamelCase__      (				self    :					Union[str, Any]  )     ->						None:
    for k in self.dq_store:
      print(UpperCamelCase__  )




  def __repr__(				self    :					str  )     ->						str:
    return F'''LRUCache({self._MAX_CAPACITY}) => {list(self.dq_store  )}'''


if __name__ == "__main__":
      import doctest

      doctest.testmod()

      __lowerCamelCase						: LRUCache[str | int]		=   LRUCache(4)
      lru_cache.refer('A')
      lru_cache.refer(2)
      lru_cache.refer(3)
      lru_cache.refer('A')
      lru_cache.refer(4)
      lru_cache.refer(5)
      lru_cache.display()

      print(lru_cache)
      assert str(lru_cache) == "LRUCache(4) => [5, 4, 'A', 3]"






