
"""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						(    snake_case				:np.ndarray		)				->     Optional[int]:
 return input_array.reshape((input_array.size, 1)		)






def 							A						(    snake_case				:np.ndarray    , snake_case				:np.ndarray    , snake_case				:int		)				->     str:
 __UpperCamelCase      =	np.nan
 for i in range(_a		):
  __UpperCamelCase      =	features[:, labels == i]
  __UpperCamelCase      =	data.mean(1		)
  # Centralize the data of class i
  __UpperCamelCase      =	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)
   __UpperCamelCase      =	np.dot(_a    , centered_data.T		)

 return covariance_sum / features.shape[1]






def 							A						(    snake_case				:np.ndarray    , snake_case				:np.ndarray    , snake_case				:int		)				->     Optional[int]:
 __UpperCamelCase      =	features.mean(1		)
 __UpperCamelCase      =	np.nan
 for i in range(_a		):
  __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(_a		) - column_reshape(_a		)    , (column_reshape(_a		) - column_reshape(_a		)).T    , )
  else:
   # If covariance_sum is np.nan (i.e. first loop)
   __UpperCamelCase      =	device_data * np.dot(
       column_reshape(_a		) - column_reshape(_a		)    , (column_reshape(_a		) - column_reshape(_a		)).T    , )

 return covariance_sum / features.shape[1]






def 							A						(    snake_case				:np.ndarray    , snake_case				:int		)				->     int:






 if features.any():
  __UpperCamelCase      =	features.mean(1		)
  # Center the dataset
  __UpperCamelCase      =	features - np.reshape(_a    , (data_mean.size, 1)		)
  __UpperCamelCase      =	np.dot(_a    , centered_data.T		) / features.shape[1]
  __UpperCamelCase  ,     __UpperCamelCase      =	np.linalg.eigh(_a		)
  # 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    , _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 							A						(    snake_case				:np.ndarray    , snake_case				:np.ndarray    , snake_case				:int    , snake_case				:int		)				->     Optional[int]:
 assert classes > dimensions

 # Check if features have been already loaded
 if features.any:
  __UpperCamelCase  ,     __UpperCamelCase      =	eigh(
      covariance_between_classes(_a    , _a    , _a		)    , covariance_within_classes(_a    , _a    , _a		)    , )
  __UpperCamelCase      =	eigenvectors[:, ::-1][:, :dimensions]
  __UpperCamelCase  ,     __UpperCamelCase  ,     __UpperCamelCase      =	np.linalg.svd(_a		)
  __UpperCamelCase      =	svd_matrix[:, 0:dimensions]
  __UpperCamelCase      =	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 							A						(    )				->     Tuple:
 __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(_a		) as error_info:
  __UpperCamelCase      =	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 							A						(    )				->     Optional[Any]:
 __UpperCamelCase      =	np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]]		)
 __UpperCamelCase      =	2
 __UpperCamelCase      =	np.array([[6.92_820_323, 8.66_025_404, 10.39_230_485], [3.0, 3.0, 3.0]]		)

 with pytest.raises(_a		) as error_info:
  __UpperCamelCase      =	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"""

UpperCamelCase     :    Union[str, Any]       =			[
    [0, 1_6, 1_3, 0, 0, 0],
    [0, 0, 1_0, 1_2, 0, 0],
    [0, 4, 0, 0, 1_4, 0],
    [0, 0, 9, 0, 0, 2_0],
    [0, 0, 0, 7, 0, 4],
    [0, 0, 0, 0, 0, 0],
]






def 							A						(    snake_case				:Dict    , snake_case				:Tuple    , snake_case				:str    , snake_case				:Optional[int]		)				->     Union[str, Any]:
 # Return True if there is node that has not iterated.
 __UpperCamelCase      =	[False] * len(snake_case		)
 __UpperCamelCase      =	[s]
 __UpperCamelCase      =	True

 while queue:
  __UpperCamelCase      =	queue.pop(0		)
  for ind in range(len(graph[u]		)		):
   if visited[ind] is False and graph[u][ind] > 0:
    queue.append(snake_case		)
    __UpperCamelCase      =	True
    __UpperCamelCase      =	u

 return visited[t]






def 							A						(    snake_case				:int    , snake_case				:Any    , snake_case				:Union[str, Any]		)				->     Optional[int]:
 __UpperCamelCase      =	[-1] * (len(snake_case		))
 __UpperCamelCase      =	0
 __UpperCamelCase      =	[]
 __UpperCamelCase      =	[i[:] for i in graph]  # Record original cut, copy.
 while bfs(snake_case    , snake_case    , snake_case    , snake_case		):
  __UpperCamelCase      =	float('Inf'		)
  __UpperCamelCase      =	sink

  while s != source:
   # Find the minimum value in select path
   __UpperCamelCase      =	min(snake_case    , graph[parent[s]][s]		)
   __UpperCamelCase      =	parent[s]

  max_flow += path_flow
  __UpperCamelCase      =	sink

  while v != source:
   __UpperCamelCase      =	parent[v]
   graph[u][v] -= path_flow
   graph[v][u] += path_flow
   __UpperCamelCase      =	parent[v]

 for i in range(len(snake_case		)		):
  for j in range(len(graph[0]		)		):
   if graph[i][j] == 0 and temp[i][j] > 0:
    res.append((i, j)		)

 return res


if __name__ == "__main__":
      print(mincut(test_graph, source=0, sink=5))



