






"""simple docstring"""




class        UpperCamelCase			:


 def __init__(     self		:						Union[str, Any]							,						UpperCAmelCase__		:						int							,						UpperCAmelCase__		:						List[str]=None							,						UpperCAmelCase__		:						Optional[Any]=None							)					->       str:
   _a  :       List[str]             =	data
   _a  :       Union[str, Any]             =	previous
   _a  :       Dict             =	next_node


 def __str__(     self		:						Optional[Any]							)					->       str:
   return f"""{self.data}"""


 def _lowercase	(     self		:						List[str]							)					->       int:
   return self.data


 def _lowercase	(     self		:						Optional[Any]							)					->       Any:
   return self.next







 def _lowercase	(     self		:						Optional[int]							)					->       Union[str, Any]:
   return self.previous







class        UpperCamelCase			:


 def __init__(     self		:						Tuple							,						UpperCAmelCase__		:						Any							)					->       str:
   _a  :       Tuple             =	head


 def __iter__(     self		:						Dict							)					->       List[str]:
   return self







 def _lowercase	(     self		:						str							)					->       Optional[int]:
   if not self.current:
     raise StopIteration
   else:
     _a  :       Dict             =	self.current.get_data()
     _a  :       List[Any]             =	self.current.get_next()
     return value







class        UpperCamelCase			:


 def __init__(     self		:						int							)					->       List[str]:
   _a  :       Optional[int]             =	None  # First node in list
   _a  :       str             =	None  # Last node in list


 def __str__(     self		:						Optional[int]							)					->       Optional[int]:
   _a  :       str             =	self.head
   _a  :       str             =	[]
   while current is not None:
     nodes.append(current.get_data()							)
     _a  :       Union[str, Any]             =	current.get_next()
   return " ".join(str(UpperCAmelCase__							) for node in nodes							)


 def __contains__(     self		:						int							,						UpperCAmelCase__		:						int							)					->       List[str]:
   _a  :       Optional[Any]             =	self.head
   while current:
     if current.get_data() == value:
       return True
     _a  :       List[str]             =	current.get_next()
   return False


 def __iter__(     self		:						List[str]							)					->       List[str]:
   return LinkedListIterator(self.head							)


 def _lowercase	(     self		:						List[Any]							)					->       Tuple:
   if self.head:
     return self.head.get_data()
   return None


 def _lowercase	(     self		:						List[Any]							)					->       Optional[Any]:
   if self.tail:
     return self.tail.get_data()
   return None


 def _lowercase	(     self		:						Optional[int]							,						UpperCAmelCase__		:						Node							)					->       None:
   if self.head is None:
     _a  :       List[str]             =	node
     _a  :       int             =	node
   else:
     self.insert_before_node(self.head							,						UpperCAmelCase__							)


 def _lowercase	(     self		:						Optional[Any]							,						UpperCAmelCase__		:						Node							)					->       None:
   if self.head is None:
     self.set_head(UpperCAmelCase__							)
   else:
     self.insert_after_node(self.tail							,						UpperCAmelCase__							)


 def _lowercase	(     self		:						Optional[Any]							,						UpperCAmelCase__		:						int							)					->       None:
   _a  :       List[Any]             =	Node(UpperCAmelCase__							)
   if self.head is None:
     self.set_head(UpperCAmelCase__							)
   else:
     self.set_tail(UpperCAmelCase__							)


 def _lowercase	(     self		:						Optional[Any]							,						UpperCAmelCase__		:						Node							,						UpperCAmelCase__		:						Node							)					->       None:
   _a  :       Optional[int]             =	node
   _a  :       List[str]             =	node.previous

   if node.get_previous() is None:
     _a  :       List[Any]             =	node_to_insert
   else:
     _a  :       str             =	node_to_insert

   _a  :       str             =	node_to_insert


 def _lowercase	(     self		:						Optional[Any]							,						UpperCAmelCase__		:						Node							,						UpperCAmelCase__		:						Node							)					->       None:
   _a  :       Optional[Any]             =	node
   _a  :       int             =	node.next

   if node.get_next() is None:
     _a  :       Tuple             =	node_to_insert
   else:
     _a  :       Dict             =	node_to_insert

   _a  :       Union[str, Any]             =	node_to_insert


 def _lowercase	(     self		:						Union[str, Any]							,						UpperCAmelCase__		:						int							,						UpperCAmelCase__		:						int							)					->       None:
   _a  :       Union[str, Any]             =	1
   _a  :       str             =	Node(UpperCAmelCase__							)
   _a  :       List[str]             =	self.head
   while node:
     if current_position == position:
       self.insert_before_node(UpperCAmelCase__							,						UpperCAmelCase__							)
       return
     current_position += 1
     _a  :       List[str]             =	node.next
   self.insert_after_node(self.tail							,						UpperCAmelCase__							)


 def _lowercase	(     self		:						Optional[Any]							,						UpperCAmelCase__		:						int							)					->       Node:
   _a  :       List[Any]             =	self.head
   while node:
     if node.get_data() == item:
       return node
     _a  :       Dict             =	node.get_next()
   raise Exception("""Node not found"""							)


 def _lowercase	(     self		:						str							,						UpperCAmelCase__		:						int							)					->       str:
   if (node := self.get_node(UpperCAmelCase__							)) is not None:
     if node == self.head:
       _a  :       Union[str, Any]             =	self.head.get_next()

     if node == self.tail:
       _a  :       Union[str, Any]             =	self.tail.get_previous()

     self.remove_node_pointers(UpperCAmelCase__							)


 @staticmethod
 def _lowercase	(     UpperCAmelCase__		:						Node							)					->       None:
   if node.get_next():
     _a  :       Optional[Any]             =	node.previous

   if node.get_previous():
     _a  :       Optional[int]             =	node.next

   _a  :       Tuple             =	None
   _a  :       Any             =	None







 def _lowercase	(     self		:						List[Any]							)					->       List[Any]:
   return self.head is None







def 			lowerCAmelCase__     (     ):



  '''simple docstring'''


if __name__ == "__main__":
 import doctest

 doctest.testmod()









"""simple docstring"""




import unittest

import numpy as np

def 			lowerCAmelCase__     (     UpperCamelCase__     ,   UpperCamelCase__     ,   UpperCamelCase__     ,   UpperCamelCase__ = None     ,   ):



  '''simple docstring'''
  _a  :       List[Any]             =	np.shape(UpperCamelCase__				)
  _a  :       Any             =	np.shape(UpperCamelCase__				)
  _a  :       Union[str, Any]             =	np.shape(UpperCamelCase__				)

  if shape_a[0] != shape_b[0]:
    _a  :       int             =	(
        """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]:
    _a  :       Tuple             =	(
        """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__				)

  _a  :       int             =	pseudo_inv
  if a_inv is None:
    try:
      _a  :       Optional[int]             =	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        UpperCamelCase			(	unittest.TestCase      ):


 def _lowercase	(     self		:						int							)					->       None:
   _a  :       str             =	np.array([[1, 2, 1], [2, 1, 2], [3, 2, 4]]							)
   _a  :       Tuple             =	np.array([[0, 3], [3, 0], [2, 3]]							)
   _a  :       Optional[int]             =	np.array([[2, 1], [6, 3]]							)

   _a  :       Optional[Any]             =	schur_complement(UpperCAmelCase__							,						UpperCAmelCase__							,						UpperCAmelCase__							)

   _a  :       Union[str, Any]             =	np.block([[a, b], [b.T, c]]							)

   _a  :       int             =	np.linalg.det(UpperCAmelCase__							)
   _a  :       Union[str, Any]             =	np.linalg.det(UpperCAmelCase__							)
   _a  :       List[Any]             =	np.linalg.det(UpperCAmelCase__							)

   self.assertAlmostEqual(UpperCAmelCase__							,						det_a * det_s							)


 def _lowercase	(     self		:						int							)					->       None:
   _a  :       Optional[int]             =	np.array([[1, 2, 1], [2, 1, 2], [3, 2, 4]]							)
   _a  :       Optional[int]             =	np.array([[0, 3], [3, 0], [2, 3]]							)
   _a  :       Union[str, Any]             =	np.array([[2, 1], [6, 3]]							)

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







 def _lowercase	(     self		:						List[Any]							)					->       None:
   _a  :       Any             =	np.array([[1, 2, 1], [2, 1, 2], [3, 2, 4]]							)
   _a  :       Dict             =	np.array([[0, 3], [3, 0], [2, 3]]							)
   _a  :       List[Any]             =	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()

