
'''simple docstring'''







import unittest

import numpy as np





def 					UpperCAmelCase_		(__a      :    np.ndarray ,	__a      :    np.ndarray ,	__a      :    np.ndarray ,	__a      :    np.ndarray | None = None ,	):






   """simple docstring"""

   _a				:	Optional[int]			=   np.shape(__a )
   _a				:	Dict			=   np.shape(__a )
   _a				:	List[Any]			=   np.shape(__a )

   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(__a )

   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(__a )

   _a				:	Optional[Any]			=   pseudo_inv
   if a_inv is None:
      try:
         _a				:	Union[str, Any]			=   np.linalg.inv(__a )
      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	):





  """simple docstring"""

  def   __lowercase		(		self      :     List[str]       ):


     '''simple docstring'''






     _a				:	int			=   np.array([[1, 2, 1], [2, 1, 2], [3, 2, 4]]       )
     _a				:	Dict			=   np.array([[0, 3], [3, 0], [2, 3]]       )
     _a				:	List[str]			=   np.array([[2, 1], [6, 3]]       )

     _a				:	Any			=   schur_complement(_a							,_a							,_a       )

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

     _a				:	str			=   np.linalg.det(_a       )
     _a				:	Dict			=   np.linalg.det(_a       )
     _a				:	Union[str, Any]			=   np.linalg.det(_a       )

     self.assertAlmostEqual(_a							,det_a * det_s       )


  def   __lowercase		(		self      :     Optional[Any]       ):


     '''simple docstring'''






     _a				:	Optional[Any]			=   np.array([[1, 2, 1], [2, 1, 2], [3, 2, 4]]       )
     _a				:	Optional[Any]			=   np.array([[0, 3], [3, 0], [2, 3]]       )
     _a				:	str			=   np.array([[2, 1], [6, 3]]       )

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


  def   __lowercase		(		self      :     Union[str, Any]       ):


     '''simple docstring'''






     _a				:	Optional[Any]			=   np.array([[1, 2, 1], [2, 1, 2], [3, 2, 4]]       )
     _a				:	Optional[Any]			=   np.array([[0, 3], [3, 0], [2, 3]]       )
     _a				:	Optional[Any]			=   np.array([[2, 1, 3], [6, 3, 5]]       )

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


if __name__ == "__main__":
  import doctest

  doctest.testmod()
  unittest.main()





'''simple docstring'''







from __future__ import annotations

__lowerCAmelCase         =    [-1_0, -5, 0, 5, 5.1, 1_1, 1_3, 2_1, 3, 4, -2_1, -1_0, -5, -1, 0]
__lowerCAmelCase         =    [-5, 0, 5, 5.1, 1_1, 1_3, 2_1, -1, 4, -1, -1_0, -5, -1, 0, -1]





def 					UpperCAmelCase_		(__a      :    list[float] ):






   """simple docstring"""

   _a				:	Optional[int]			=   []
   _a				:	int			=   len(__a )

   for i in range(__a ):
      _a				:	float			=   -1
      for j in range(i + 1 ,	__a ):
         if arr[i] < arr[j]:
            _a				:	Any			=   arr[j]
            break
      result.append(__a )
   return result





def 					UpperCAmelCase_		(__a      :    list[float] ):






   """simple docstring"""

   _a				:	Tuple			=   []
   for i, outer in enumerate(__a ):
      _a				:	float			=   -1
      for inner in arr[i + 1 :]:
         if outer < inner:
            _a				:	Dict			=   inner
            break
      result.append(__a )
   return result





def 					UpperCAmelCase_		(__a      :    list[float] ):






   """simple docstring"""

   _a				:	int			=   len(__a )
   _a				:	list[float]			=   []
   _a				:	list[float]			=   [-1] * arr_size

   for index in reversed(range(__a ) ):
      if stack:
         while stack[-1] <= arr[index]:
            stack.pop()
            if not stack:
               break
      if stack:
         _a				:	Dict			=   stack[-1]
      stack.append(arr[index] )
   return result


if __name__ == "__main__":
  from doctest import testmod
  from timeit import timeit

  testmod()
  print(next_greatest_element_slow(arr))
  print(next_greatest_element_fast(arr))
  print(next_greatest_element(arr))

  __lowerCAmelCase         =    (
      """from __main__ import arr, next_greatest_element_slow, """
      """next_greatest_element_fast, next_greatest_element"""
  )
  print(
      """next_greatest_element_slow():""",
      timeit("""next_greatest_element_slow(arr)""", setup=setup),
  )
  print(
      """next_greatest_element_fast():""",
      timeit("""next_greatest_element_fast(arr)""", setup=setup),
  )
  print(
      """     next_greatest_element():""",
      timeit("""next_greatest_element(arr)""", setup=setup),
  )



