
"""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						(						lowercase		):







    """simple docstring"""
    return input_array.reshape((input_array.size, 1)		)
def _A						(						lowercase	,   lowercase	,   lowercase		):







    """simple docstring"""
    a					=np.nan
    for i in range(a__		):
        a					=features[:, labels == i]
        a					=data.mean(1		)
        # Centralize the data of class i
        a					=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)
            a					=np.dot(a__	,   centered_data.T		)

    return covariance_sum / features.shape[1]
def _A						(						lowercase	,   lowercase	,   lowercase		):







    """simple docstring"""
    a					=features.mean(1		)
    a					=np.nan
    for i in range(a__		):
        a					=features[:, labels == i]
        a					=data.shape[1]
        a					=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)
            a					=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						(						lowercase	,   lowercase		):







    """simple docstring"""





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







    """simple docstring"""
    assert classes > dimensions

    # Check if features have been already loaded
    if features.any:
        a		,				a					=eigh(
            covariance_between_classes(a__	,   a__	,   a__		)	,   covariance_within_classes(a__	,   a__	,   a__		)	,   )
        a					=eigenvectors[:, ::-1][:, :dimensions]
        a		,				a		,				a					=np.linalg.svd(a__		)
        a					=svd_matrix[:, 0:dimensions]
        a					=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						(						):







    """simple docstring"""
    a					=np.array([[1, 2, 3, 4, 5], [2, 3, 4, 5, 6], [3, 4, 5, 6, 7]]		)
    a					=np.array([0, 0, 0, 1, 1]		)
    a					=2
    a					=2

    # Assert that the function raises an AssertionError if dimensions > classes
    with pytest.raises(a__		) as error_info:
        a					=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						(						):







    """simple docstring"""
    a					=np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]]		)
    a					=2
    a					=np.array([[6.92820323, 8.66025404, 10.39230485], [3.0, 3.0, 3.0]]		)

    with pytest.raises(a__		) as error_info:
        a					=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 __future__ import annotations

from typing import Generic, TypeVar

lowerCamelCase_       :       List[Any]      						=  TypeVar("""T""")






class 				__A    (	Generic[T]      ):






 """simple docstring"""




 def __init__(		self			,   __A						) ->					None:
     a					=data
     a					=self
     a					=0






class 				__A    (	Generic[T]      ):






 """simple docstring"""




 def __init__(		self						) ->					None:
     # map from node name to the node object
     a					={}


 def 				SCREAMING_SNAKE_CASE							(		self			,   __A						) ->					None:
     # create a new set with x as its member
     a					=DisjointSetTreeNode(__A						)


 def 				SCREAMING_SNAKE_CASE							(		self			,   __A						) ->					DisjointSetTreeNode[T]:
     # find the set x belongs to (with path-compression)
     a					=self.map[data]
     if elem_ref != elem_ref.parent:
         a					=self.find_set(elem_ref.parent.data						)
     return elem_ref.parent


 def 				SCREAMING_SNAKE_CASE							(		self			,   __A			,   __A						) ->					None:
     # helper function for union operation
     if nodea.rank > nodea.rank:
         a					=nodea
     else:
         a					=nodea
         if nodea.rank == nodea.rank:
             nodea.rank += 1





 def 				SCREAMING_SNAKE_CASE							(		self			,   __A			,   __A						) ->					None:
     # merge 2 disjoint sets
     self.link(self.find_set(__A						)			,   self.find_set(__A						)						)






class 				__A    (	Generic[T]      ):






 """simple docstring"""




 def __init__(		self						) ->					None:
     # connections: map from the node to the neighbouring nodes (with weights)
     a					={}


 def 				SCREAMING_SNAKE_CASE							(		self			,   __A						) ->					None:
     # add a node ONLY if its not present in the graph
     if node not in self.connections:
         a					={}


 def 				SCREAMING_SNAKE_CASE							(		self			,   __A			,   __A			,   __A						) ->					None:
     # add an edge with the given weight
     self.add_node(__A						)
     self.add_node(__A						)
     a					=weight
     a					=weight





 def 				SCREAMING_SNAKE_CASE							(		self						) ->					GraphUndirectedWeighted[T]:
     a					=[]
     a					=set()
     for start in self.connections:
         for end in self.connections[start]:
             if (start, end) not in seen:
                 seen.add((end, start)						)
                 edges.append((start, end, self.connections[start][end])						)
     edges.sort(key=lambda __A						: x[2]						)

     # creating the disjoint set
     a					=DisjointSetTree[T]()
     for node in self.connections:
         disjoint_set.make_set(__A						)

     # MST generation
     a					=0
     a					=0
     a					=GraphUndirectedWeighted[T]()
     while num_edges < len(self.connections						) - 1:
         a		,				a		,				a					=edges[index]
         index += 1
         a					=disjoint_set.find_set(__A						)
         a					=disjoint_set.find_set(__A						)
         if parent_u != parent_v:
             num_edges += 1
             graph.add_edge(__A			,   __A			,   __A						)
             disjoint_set.union(__A			,   __A						)
     return graph