





'''simple docstring'''

from typing import Any






class        UpperCAmelCase     :
 def __init__(    self				:Any						,	lowercase_				:List[str]							)->							Any:
     A__    =      data
     A__    =      None






class        UpperCAmelCase     :
 def __init__(    self				:Optional[int]							)->							Dict:
     A__    =      None
 def 					UpperCAmelCase_							(    self				:Dict							)->							str:
     A__    =      self.head
     while temp is not None:
         print(temp.data						,	end=" "							)
         A__    =      temp.next
     print()
 def 					UpperCAmelCase_							(    self				:Optional[int]						,	lowercase_				:Any							)->							Any:
     A__    =      Node(_a							)
     A__    =      self.head
     A__    =      new_node



 def 					UpperCAmelCase_							(    self				:str						,	lowercase_				:str						,	lowercase_				:int							)->							Optional[Any]:
     if node_data_a == node_data_a:
         return
     else:
         A__    =      self.head
         while node_a is not None and node_a.data != node_data_a:
             A__    =      node_a.next

         A__    =      self.head
         while node_a is not None and node_a.data != node_data_a:
             A__    =      node_a.next

         if node_a is None or node_a is None:
             return

         A__    =      node_a.data, node_a.data


if __name__ == "__main__":
  __lowerCAmelCase							:     Optional[int]		     =LinkedList()
  for i in range(5, 0, -1):
    ll.push(i)

  ll.print_list()

  ll.swap_nodes(1, 4)
  print("After swapping")
  ll.print_list()









'''simple docstring'''

import unittest

import numpy as np





def 						UpperCamelCase    (							_lowerCamelCase : np.ndarray						,	_lowerCamelCase : np.ndarray						,	_lowerCamelCase : np.ndarray						,	_lowerCamelCase : np.ndarray | None = None						,	):
    A__    =      np.shape(_lowerCamelCase	)
    A__    =      np.shape(_lowerCamelCase	)
    A__    =      np.shape(_lowerCamelCase	)

    if shape_a[0] != shape_b[0]:
        A__    =      (
            "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(_lowerCamelCase	)

    if shape_b[1] != shape_c[1]:
        A__    =      (
            "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(_lowerCamelCase	)

    A__    =      pseudo_inv
    if a_inv is None:
        try:
            A__    =      np.linalg.inv(_lowerCamelCase	)
        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 					UpperCAmelCase_							(    self				:Any							)->							None:
     A__    =      np.array([[1, 2, 1], [2, 1, 2], [3, 2, 4]]							)
     A__    =      np.array([[0, 3], [3, 0], [2, 3]]							)
     A__    =      np.array([[2, 1], [6, 3]]							)

     A__    =      schur_complement(lowercase_						,	lowercase_						,	lowercase_							)

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

     A__    =      np.linalg.det(lowercase_							)
     A__    =      np.linalg.det(lowercase_							)
     A__    =      np.linalg.det(lowercase_							)

     self.assertAlmostEqual(lowercase_						,	det_a * det_s							)
 def 					UpperCAmelCase_							(    self				:Dict							)->							None:
     A__    =      np.array([[1, 2, 1], [2, 1, 2], [3, 2, 4]]							)
     A__    =      np.array([[0, 3], [3, 0], [2, 3]]							)
     A__    =      np.array([[2, 1], [6, 3]]							)

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



 def 					UpperCAmelCase_							(    self				:Union[str, Any]							)->							None:
     A__    =      np.array([[1, 2, 1], [2, 1, 2], [3, 2, 4]]							)
     A__    =      np.array([[0, 3], [3, 0], [2, 3]]							)
     A__    =      np.array([[2, 1, 3], [6, 3, 5]]							)

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


if __name__ == "__main__":
  import doctest

  doctest.testmod()
  unittest.main()



