import unittest

import numpy as np





def 		__lowerCamelCase							(UpperCAmelCase__       :							np.ndarray ,	UpperCAmelCase__       :							np.ndarray ,	UpperCAmelCase__       :							np.ndarray ,	UpperCAmelCase__       :							np.ndarray | None = None ,	) ->    Optional[int]:
					SCREAMING_SNAKE_CASE           =    np.shape(UpperCAmelCase__					)
					SCREAMING_SNAKE_CASE           =    np.shape(UpperCAmelCase__					)
					SCREAMING_SNAKE_CASE           =    np.shape(UpperCAmelCase__					)

					if shape_a[0] != shape_b[0]:
										SCREAMING_SNAKE_CASE           =    (
										    "Expected the same number of rows for A and B. "
										    F"Instead found A of size {shape_a} and B of size {shape_b}"
										)
										raise ValueError(UpperCAmelCase__					)

					if shape_b[1] != shape_c[1]:
										SCREAMING_SNAKE_CASE           =    (
										    "Expected the same number of columns for B and C. "
										    F"Instead found B of size {shape_b} and C of size {shape_c}"
										)
										raise ValueError(UpperCAmelCase__					)

					SCREAMING_SNAKE_CASE           =    pseudo_inv
					if a_inv is None:
										try:
															SCREAMING_SNAKE_CASE           =    np.linalg.inv(UpperCAmelCase__					)
										except np.linalg.LinAlgError:
															raise ValueError(
															    "Input matrix A is not invertible. Cannot compute Schur complement."					)

					return mat_c - mat_b.T @ a_inv @ mat_b


class   lowercase      (       unittest.TestCase       ):




							def 		__snake_case(  self				:   Tuple )   ->			None:



												'''simple docstring'''

												SCREAMING_SNAKE_CASE           =    np.array([[1, 2, 1], [2, 1, 2], [3, 2, 4]] )
												SCREAMING_SNAKE_CASE           =    np.array([[0, 3], [3, 0], [2, 3]] )
												SCREAMING_SNAKE_CASE           =    np.array([[2, 1], [6, 3]] )

												SCREAMING_SNAKE_CASE           =    schur_complement(_UpperCamelCase		,							_UpperCamelCase		,							_UpperCamelCase )

												SCREAMING_SNAKE_CASE           =    np.block([[a, b], [b.T, c]] )

												SCREAMING_SNAKE_CASE           =    np.linalg.det(_UpperCamelCase )
												SCREAMING_SNAKE_CASE           =    np.linalg.det(_UpperCamelCase )
												SCREAMING_SNAKE_CASE           =    np.linalg.det(_UpperCamelCase )

												self.assertAlmostEqual(_UpperCamelCase		,							det_a * det_s )




							def 		__snake_case(  self				:   Tuple )   ->			None:



												'''simple docstring'''

												SCREAMING_SNAKE_CASE           =    np.array([[1, 2, 1], [2, 1, 2], [3, 2, 4]] )
												SCREAMING_SNAKE_CASE           =    np.array([[0, 3], [3, 0], [2, 3]] )
												SCREAMING_SNAKE_CASE           =    np.array([[2, 1], [6, 3]] )

												with self.assertRaises(_UpperCamelCase ):
																	schur_complement(_UpperCamelCase		,							_UpperCamelCase		,							_UpperCamelCase )





							def 		__snake_case(  self				:   List[Any] )   ->			None:



												'''simple docstring'''

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

												with self.assertRaises(_UpperCamelCase ):
																	schur_complement(_UpperCamelCase		,							_UpperCamelCase		,							_UpperCamelCase )


if __name__ == "__main__":
							import doctest

							doctest.testmod()
							unittest.main()





# Author: OMKAR PATHAK, Nwachukwu Chidiebere

# Use a Python dictionary to construct the graph.
from __future__ import annotations

from pprint import pformat
from typing import Generic, TypeVar

_lowerCamelCase   :				Union[str, Any]     			=						TypeVar('''T''')


class   lowercase      (       Generic[T]       ):




							def __init__(  self				:   int		,							_UpperCamelCase				:   bool = True )   ->			None:



												'''simple docstring'''

												SCREAMING_SNAKE_CASE           =    {}  # dictionary of lists
												SCREAMING_SNAKE_CASE           =    directed




							def 		__snake_case(  self				:   int		,							_UpperCamelCase				:   T		,							_UpperCamelCase				:   T )   ->			GraphAdjacencyList[T]:



												'''simple docstring'''

												if not self.directed:  # For undirected graphs
																	# if both source vertex and destination vertex are both present in the
																	# adjacency list, add destination vertex to source vertex list of adjacent
																	# vertices and add source vertex to destination vertex list of adjacent
																	# vertices.
																	if source_vertex in self.adj_list and destination_vertex in self.adj_list:
																						self.adj_list[source_vertex].append(_UpperCamelCase )
																						self.adj_list[destination_vertex].append(_UpperCamelCase )
																	# if only source vertex is present in adjacency list, add destination vertex
																	# to source vertex list of adjacent vertices, then create a new vertex with
																	# destination vertex as key and assign a list containing the source vertex
																	# as it's first adjacent vertex.
																	elif source_vertex in self.adj_list:
																						self.adj_list[source_vertex].append(_UpperCamelCase )
																						SCREAMING_SNAKE_CASE           =    [source_vertex]
																	# if only destination vertex is present in adjacency list, add source vertex
																	# to destination vertex list of adjacent vertices, then create a new vertex
																	# with source vertex as key and assign a list containing the source vertex
																	# as it's first adjacent vertex.
																	elif destination_vertex in self.adj_list:
																						self.adj_list[destination_vertex].append(_UpperCamelCase )
																						SCREAMING_SNAKE_CASE           =    [destination_vertex]
																	# if both source vertex and destination vertex are not present in adjacency
																	# list, create a new vertex with source vertex as key and assign a list
																	# containing the destination vertex as it's first adjacent vertex also
																	# create a new vertex with destination vertex as key and assign a list
																	# containing the source vertex as it's first adjacent vertex.
																	else:
																						SCREAMING_SNAKE_CASE           =    [destination_vertex]
																						SCREAMING_SNAKE_CASE           =    [source_vertex]
												else:  # For directed graphs
																	# if both source vertex and destination vertex are present in adjacency
																	# list, add destination vertex to source vertex list of adjacent vertices.
																	if source_vertex in self.adj_list and destination_vertex in self.adj_list:
																						self.adj_list[source_vertex].append(_UpperCamelCase )
																	# if only source vertex is present in adjacency list, add destination
																	# vertex to source vertex list of adjacent vertices and create a new vertex
																	# with destination vertex as key, which has no adjacent vertex
																	elif source_vertex in self.adj_list:
																						self.adj_list[source_vertex].append(_UpperCamelCase )
																						SCREAMING_SNAKE_CASE           =    []
																	# if only destination vertex is present in adjacency list, create a new
																	# vertex with source vertex as key and assign a list containing destination
																	# vertex as first adjacent vertex
																	elif destination_vertex in self.adj_list:
																						SCREAMING_SNAKE_CASE           =    [destination_vertex]
																	# if both source vertex and destination vertex are not present in adjacency
																	# list, create a new vertex with source vertex as key and a list containing
																	# destination vertex as it's first adjacent vertex. Then create a new vertex
																	# with destination vertex as key, which has no adjacent vertex
																	else:
																						SCREAMING_SNAKE_CASE           =    [destination_vertex]
																						SCREAMING_SNAKE_CASE           =    []

												return self





							def __repr__(  self				:   Union[str, Any] )   ->			str:



												'''simple docstring'''

												return pformat(self.adj_list )




