

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





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

		return covariance_sum / features.shape[1]





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

		return covariance_sum / features.shape[1]





def    A_  ( snake_case      ,       snake_case ):

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

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





def    A_  ( snake_case      ,       snake_case      ,       snake_case      ,       snake_case ):
		assert classes > dimensions

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

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





def    A_  ( ):
		# Create dummy dataset with 2 classes and 3 features
		SCREAMING_SNAKE_CASE:Union[str, Any]						      =					np.array([[1, 2, 3, 4, 5], [2, 3, 4, 5, 6], [3, 4, 5, 6, 7]] )
		SCREAMING_SNAKE_CASE:List[str]						      =					np.array([0, 0, 0, 1, 1] )
		SCREAMING_SNAKE_CASE:Optional[int]						      =					2
		SCREAMING_SNAKE_CASE:List[Any]						      =					2

		# Assert that the function raises an AssertionError if dimensions > classes
		with pytest.raises(snake_case ) as error_info:
				SCREAMING_SNAKE_CASE:Union[str, Any]						      =					linear_discriminant_analysis(
				    snake_case      ,       snake_case      ,       snake_case      ,       snake_case )
				if isinstance(snake_case      ,       np.ndarray ):
						raise AssertionError(
						    "Did not raise AssertionError for dimensions > classes" )
				assert error_info.type is AssertionError





def    A_  ( ):
		SCREAMING_SNAKE_CASE:Union[str, Any]						      =					np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]] )
		SCREAMING_SNAKE_CASE:Any						      =					2
		SCREAMING_SNAKE_CASE:Dict						      =					np.array([[6.9282_0323, 8.6602_5404, 10.3923_0485], [3.0, 3.0, 3.0]] )

		with pytest.raises(snake_case ) as error_info:
				SCREAMING_SNAKE_CASE:int						      =					principal_component_analysis(snake_case      ,       snake_case )
				if not np.allclose(snake_case      ,       snake_case ):
						raise AssertionError
				assert error_info.type is AssertionError


if __name__ == "__main__":
				import doctest

				doctest.testmod()









'''simple docstring'''

import random





def    A_  ( snake_case      ,       snake_case      ,       snake_case = False ):
  SCREAMING_SNAKE_CASE:dict						      =					{i: [] for i in range(snake_case )}

  # if probability is greater or equal than 1, then generate a complete graph
  if probability >= 1:
    return complete_graph(snake_case )
  # if probability is lower or equal than 0, then return a graph without edges
  if probability <= 0:
    return graph

  # for each couple of nodes, add an edge from u to v
  # if the number randomly generated is greater than probability probability
  for i in range(snake_case ):
    for j in range(i + 1      ,       snake_case ):
      if random.random() < probability:
        graph[i].append(snake_case )
        if not directed:
          # if the graph is undirected, add an edge in from j to i, either
          graph[j].append(snake_case )
  return graph





def    A_  ( snake_case ):
  return {
      i: [j for j in range(snake_case ) if i != j] for i in range(snake_case )
  }


if __name__ == "__main__":
    import doctest

    doctest.testmod()






