




import unittest

import numpy as np



def 						lowerCAmelCase		(		_lowerCAmelCase							:   np.ndarray						,							_lowerCAmelCase							:   np.ndarray						,							_lowerCAmelCase							:   np.ndarray						,							_lowerCAmelCase							:   np.ndarray | None = None						,							):




 """simple docstring"""







 UpperCAmelCase__							 =						np.shape(_lowerCAmelCase	)
 UpperCAmelCase__							 =						np.shape(_lowerCAmelCase	)
 UpperCAmelCase__							 =						np.shape(_lowerCAmelCase	)

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

 UpperCAmelCase__							 =						pseudo_inv
 if a_inv is None:
  try:
   UpperCAmelCase__							 =						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   :Dict      )     ->			None:
       UpperCAmelCase__							 =						np.array([[1, 2, 1], [2, 1, 2], [3, 2, 4]]      )
       UpperCAmelCase__							 =						np.array([[0, 3], [3, 0], [2, 3]]      )
       UpperCAmelCase__							 =						np.array([[2, 1], [6, 3]]      )

       UpperCAmelCase__							 =						schur_complement(lowerCamelCase ,      lowerCamelCase ,      lowerCamelCase      )

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

       UpperCAmelCase__							 =						np.linalg.det(lowerCamelCase      )
       UpperCAmelCase__							 =						np.linalg.det(lowerCamelCase      )
       UpperCAmelCase__							 =						np.linalg.det(lowerCamelCase      )

       self.assertAlmostEqual(lowerCamelCase ,      det_a * det_s      )
      def 	UpperCAmelCase_						(			self   :Optional[Any]      )     ->			None:
       UpperCAmelCase__							 =						np.array([[1, 2, 1], [2, 1, 2], [3, 2, 4]]      )
       UpperCAmelCase__							 =						np.array([[0, 3], [3, 0], [2, 3]]      )
       UpperCAmelCase__							 =						np.array([[2, 1], [6, 3]]      )

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







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

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


if __name__ == "__main__":
  import doctest

  doctest.testmod()
  unittest.main()











from ..utils import DummyObject, requires_backends
class 			_UpperCamelCase      (				metaclass=lowerCAmelCase		):
      UpperCAmelCase_        =		["""flax"""]
      def __init__(			self   :List[Any] ,      *lowerCamelCase   :int ,      **lowerCamelCase   :List[Any]      )     ->			Dict:
       requires_backends(self ,      ["flax"]      )
      @classmethod
      def 	UpperCAmelCase_						(			cls   :Union[str, Any] ,      *lowerCamelCase   :Any ,      **lowerCamelCase   :List[str]      )     ->			int:
       requires_backends(cls ,      ["flax"]      )







      @classmethod
      def 	UpperCAmelCase_						(			cls   :Optional[int] ,      *lowerCamelCase   :List[str] ,      **lowerCamelCase   :List[Any]      )     ->			Dict:
       requires_backends(cls ,      ["flax"]      )



class 			_UpperCamelCase      (				metaclass=lowerCAmelCase		):
      UpperCAmelCase_        =		["""flax"""]
      def __init__(			self   :Dict ,      *lowerCamelCase   :int ,      **lowerCamelCase   :str      )     ->			str:
       requires_backends(self ,      ["flax"]      )
      @classmethod
      def 	UpperCAmelCase_						(			cls   :Optional[int] ,      *lowerCamelCase   :Tuple ,      **lowerCamelCase   :List[Any]      )     ->			Optional[int]:
       requires_backends(cls ,      ["flax"]      )







      @classmethod
      def 	UpperCAmelCase_						(			cls   :Optional[Any] ,      *lowerCamelCase   :Dict ,      **lowerCamelCase   :Optional[int]      )     ->			List[Any]:
       requires_backends(cls ,      ["flax"]      )



class 			_UpperCamelCase      (				metaclass=lowerCAmelCase		):
      UpperCAmelCase_        =		["""flax"""]
      def __init__(			self   :List[str] ,      *lowerCamelCase   :Union[str, Any] ,      **lowerCamelCase   :Any      )     ->			Union[str, Any]:
       requires_backends(self ,      ["flax"]      )
      @classmethod
      def 	UpperCAmelCase_						(			cls   :List[Any] ,      *lowerCamelCase   :str ,      **lowerCamelCase   :List[Any]      )     ->			Tuple:
       requires_backends(cls ,      ["flax"]      )







      @classmethod
      def 	UpperCAmelCase_						(			cls   :str ,      *lowerCamelCase   :Any ,      **lowerCamelCase   :Dict      )     ->			int:
       requires_backends(cls ,      ["flax"]      )



class 			_UpperCamelCase      (				metaclass=lowerCAmelCase		):
      UpperCAmelCase_        =		["""flax"""]
      def __init__(			self   :Union[str, Any] ,      *lowerCamelCase   :int ,      **lowerCamelCase   :Dict      )     ->			List[Any]:
       requires_backends(self ,      ["flax"]      )
      @classmethod
      def 	UpperCAmelCase_						(			cls   :int ,      *lowerCamelCase   :Union[str, Any] ,      **lowerCamelCase   :str      )     ->			Optional[int]:
       requires_backends(cls ,      ["flax"]      )







      @classmethod
      def 	UpperCAmelCase_						(			cls   :List[str] ,      *lowerCamelCase   :Optional[int] ,      **lowerCamelCase   :Tuple      )     ->			Dict:
       requires_backends(cls ,      ["flax"]      )



class 			_UpperCamelCase      (				metaclass=lowerCAmelCase		):
      UpperCAmelCase_        =		["""flax"""]
      def __init__(			self   :Union[str, Any] ,      *lowerCamelCase   :Any ,      **lowerCamelCase   :List[str]      )     ->			Union[str, Any]:
       requires_backends(self ,      ["flax"]      )
      @classmethod
      def 	UpperCAmelCase_						(			cls   :Optional[Any] ,      *lowerCamelCase   :Union[str, Any] ,      **lowerCamelCase   :Optional[Any]      )     ->			Optional[int]:
       requires_backends(cls ,      ["flax"]      )







      @classmethod
      def 	UpperCAmelCase_						(			cls   :List[Any] ,      *lowerCamelCase   :Dict ,      **lowerCamelCase   :Optional[int]      )     ->			List[str]:
       requires_backends(cls ,      ["flax"]      )



class 			_UpperCamelCase      (				metaclass=lowerCAmelCase		):
      UpperCAmelCase_        =		["""flax"""]
      def __init__(			self   :Tuple ,      *lowerCamelCase   :str ,      **lowerCamelCase   :List[str]      )     ->			List[Any]:
       requires_backends(self ,      ["flax"]      )
      @classmethod
      def 	UpperCAmelCase_						(			cls   :Any ,      *lowerCamelCase   :List[str] ,      **lowerCamelCase   :Any      )     ->			int:
       requires_backends(cls ,      ["flax"]      )







      @classmethod
      def 	UpperCAmelCase_						(			cls   :List[Any] ,      *lowerCamelCase   :List[Any] ,      **lowerCamelCase   :Optional[Any]      )     ->			Tuple:
       requires_backends(cls ,      ["flax"]      )



class 			_UpperCamelCase      (				metaclass=lowerCAmelCase		):
      UpperCAmelCase_        =		["""flax"""]
      def __init__(			self   :Any ,      *lowerCamelCase   :List[Any] ,      **lowerCamelCase   :List[str]      )     ->			List[str]:
       requires_backends(self ,      ["flax"]      )
      @classmethod
      def 	UpperCAmelCase_						(			cls   :Optional[Any] ,      *lowerCamelCase   :Optional[int] ,      **lowerCamelCase   :Dict      )     ->			Union[str, Any]:
       requires_backends(cls ,      ["flax"]      )







      @classmethod
      def 	UpperCAmelCase_						(			cls   :int ,      *lowerCamelCase   :List[Any] ,      **lowerCamelCase   :str      )     ->			str:
       requires_backends(cls ,      ["flax"]      )



class 			_UpperCamelCase      (				metaclass=lowerCAmelCase		):
      UpperCAmelCase_        =		["""flax"""]
      def __init__(			self   :str ,      *lowerCamelCase   :Any ,      **lowerCamelCase   :Union[str, Any]      )     ->			Optional[Any]:
       requires_backends(self ,      ["flax"]      )
      @classmethod
      def 	UpperCAmelCase_						(			cls   :Optional[Any] ,      *lowerCamelCase   :Any ,      **lowerCamelCase   :List[str]      )     ->			int:
       requires_backends(cls ,      ["flax"]      )







      @classmethod
      def 	UpperCAmelCase_						(			cls   :List[Any] ,      *lowerCamelCase   :Union[str, Any] ,      **lowerCamelCase   :Union[str, Any]      )     ->			List[Any]:
       requires_backends(cls ,      ["flax"]      )



class 			_UpperCamelCase      (				metaclass=lowerCAmelCase		):
      UpperCAmelCase_        =		["""flax"""]
      def __init__(			self   :Dict ,      *lowerCamelCase   :Dict ,      **lowerCamelCase   :int      )     ->			List[Any]:
       requires_backends(self ,      ["flax"]      )
      @classmethod
      def 	UpperCAmelCase_						(			cls   :Tuple ,      *lowerCamelCase   :Optional[Any] ,      **lowerCamelCase   :Optional[int]      )     ->			Dict:
       requires_backends(cls ,      ["flax"]      )







      @classmethod
      def 	UpperCAmelCase_						(			cls   :Any ,      *lowerCamelCase   :Optional[int] ,      **lowerCamelCase   :List[str]      )     ->			List[Any]:
       requires_backends(cls ,      ["flax"]      )



class 			_UpperCamelCase      (				metaclass=lowerCAmelCase		):
      UpperCAmelCase_        =		["""flax"""]
      def __init__(			self   :List[Any] ,      *lowerCamelCase   :int ,      **lowerCamelCase   :Optional[Any]      )     ->			List[str]:
       requires_backends(self ,      ["flax"]      )
      @classmethod
      def 	UpperCAmelCase_						(			cls   :int ,      *lowerCamelCase   :List[Any] ,      **lowerCamelCase   :List[Any]      )     ->			Any:
       requires_backends(cls ,      ["flax"]      )







      @classmethod
      def 	UpperCAmelCase_						(			cls   :str ,      *lowerCamelCase   :Optional[int] ,      **lowerCamelCase   :str      )     ->			List[str]:
       requires_backends(cls ,      ["flax"]      )



class 			_UpperCamelCase      (				metaclass=lowerCAmelCase		):
      UpperCAmelCase_        =		["""flax"""]
      def __init__(			self   :List[Any] ,      *lowerCamelCase   :str ,      **lowerCamelCase   :int      )     ->			List[Any]:
       requires_backends(self ,      ["flax"]      )
      @classmethod
      def 	UpperCAmelCase_						(			cls   :List[str] ,      *lowerCamelCase   :List[Any] ,      **lowerCamelCase   :Any      )     ->			List[Any]:
       requires_backends(cls ,      ["flax"]      )







      @classmethod
      def 	UpperCAmelCase_						(			cls   :Optional[Any] ,      *lowerCamelCase   :Any ,      **lowerCamelCase   :Tuple      )     ->			int:
       requires_backends(cls ,      ["flax"]      )



class 			_UpperCamelCase      (				metaclass=lowerCAmelCase		):
      UpperCAmelCase_        =		["""flax"""]
      def __init__(			self   :Any ,      *lowerCamelCase   :List[Any] ,      **lowerCamelCase   :Tuple      )     ->			Dict:
       requires_backends(self ,      ["flax"]      )
      @classmethod
      def 	UpperCAmelCase_						(			cls   :List[Any] ,      *lowerCamelCase   :int ,      **lowerCamelCase   :Union[str, Any]      )     ->			List[Any]:
       requires_backends(cls ,      ["flax"]      )







      @classmethod
      def 	UpperCAmelCase_						(			cls   :str ,      *lowerCamelCase   :int ,      **lowerCamelCase   :List[str]      )     ->			List[str]:
       requires_backends(cls ,      ["flax"]      )



class 			_UpperCamelCase      (				metaclass=lowerCAmelCase		):
      UpperCAmelCase_        =		["""flax"""]
      def __init__(			self   :int ,      *lowerCamelCase   :Dict ,      **lowerCamelCase   :Optional[int]      )     ->			str:
       requires_backends(self ,      ["flax"]      )
      @classmethod
      def 	UpperCAmelCase_						(			cls   :Union[str, Any] ,      *lowerCamelCase   :Any ,      **lowerCamelCase   :Union[str, Any]      )     ->			Optional[int]:
       requires_backends(cls ,      ["flax"]      )







      @classmethod
      def 	UpperCAmelCase_						(			cls   :int ,      *lowerCamelCase   :Union[str, Any] ,      **lowerCamelCase   :Any      )     ->			Optional[Any]:
       requires_backends(cls ,      ["flax"]      )





