





'''simple docstring'''

from importlib import import_module

from .logging import get_logger


__lowerCAmelCase							:     List[str]		     =get_logger(__name__)






class        UpperCAmelCase     :
 def __init__(    self				:Optional[Any]						,	lowercase_				:List[Any]						,	lowercase_				:str=None							)->							List[str]:
     A__    =      attrs or []
     if module is not None:
         for key in module.__dict__:
             if key in attrs or not key.startswith("__"							):
                 setattr(self						,	lowercase_						,	getattr(lowercase_						,	lowercase_							)							)
     A__    =      module._original_module if isinstance(lowercase_						,	_PatchedModuleObj							) else module






class        UpperCAmelCase     :
 __lowercase       		=    []
 def __init__(    self				:List[str]						,	lowercase_				:List[str]						,	lowercase_				:str						,	lowercase_				:Optional[Any]						,	lowercase_				:Tuple=None							)->							Any:
     A__    =      obj
     A__    =      target
     A__    =      new
     A__    =      target.split("."							)[0]
     A__    =      {}
     A__    =      attrs or []
 def __enter__(    self				:Any							)->							Optional[Any]:
     *A__,     A__    =      self.target.split("."							)

     # Patch modules:
     # it's used to patch attributes of submodules like "os.path.join";
     # in this case we need to patch "os" and "os.path"

     for i in range(len(lowercase_							)							):
         try:
             A__    =      import_module(".".join(submodules[: i + 1]							)							)
         except ModuleNotFoundError:
             continue
         # We iterate over all the globals in self.obj in case we find "os" or "os.path"
         for attr in self.obj.__dir__():
             A__    =      getattr(self.obj						,	lowercase_							)
             # We don't check for the name of the global, but rather if its value *is* "os" or "os.path".
             # This allows to patch renamed modules like "from os import path as ospath".
             if obj_attr is submodule or (
                 (isinstance(lowercase_						,	_PatchedModuleObj							) and obj_attr._original_module is submodule)
             ):
                 A__    =      obj_attr
                 # patch at top level
                 setattr(self.obj						,	lowercase_						,	_PatchedModuleObj(lowercase_						,	attrs=self.attrs							)							)
                 A__    =      getattr(self.obj						,	lowercase_							)
                 # construct lower levels patches
                 for key in submodules[i + 1 :]:
                     setattr(lowercase_						,	lowercase_						,	_PatchedModuleObj(getattr(lowercase_						,	lowercase_						,	lowercase_							)						,	attrs=self.attrs							)							)
                     A__    =      getattr(lowercase_						,	lowercase_							)
                 # finally set the target attribute
                 setattr(lowercase_						,	lowercase_						,	self.new							)

        # Patch attribute itself:
        # it's used for builtins like "open",
        # and also to patch "os.path.join" we may also need to patch "join"
        # itself if it was imported as "from os.path import join".

     if submodules:  # if it's an attribute of a submodule like "os.path.join"
         try:
             A__    =      getattr(import_module(".".join(lowercase_							)							)						,	lowercase_							)
         except (AttributeError, ModuleNotFoundError):
             return
         # We iterate over all the globals in self.obj in case we find "os.path.join"
         for attr in self.obj.__dir__():
             # We don't check for the name of the global, but rather if its value *is* "os.path.join".
             # This allows to patch renamed attributes like "from os.path import join as pjoin".
             if getattr(self.obj						,	lowercase_							) is attr_value:
                 A__    =      getattr(self.obj						,	lowercase_							)
                 setattr(self.obj						,	lowercase_						,	self.new							)
     elif target_attr in globals()["__builtins__"]:  # if it'a s builtin like "open"
         A__    =      globals()["__builtins__"][target_attr]
         setattr(self.obj						,	lowercase_						,	self.new							)
     else:
         raise RuntimeError(F"Tried to patch attribute {target_attr} instead of a submodule."							)
 def __exit__(    self				:Optional[int]						,	*lowercase_				:List[Any]							)->							List[str]:
     for attr in list(self.original							):
         setattr(self.obj						,	lowercase_						,	self.original.pop(lowercase_							)							)
 def 					UpperCAmelCase_							(    self				:Union[str, Any]							)->							Any:
     self.__enter__()
     self._active_patches.append(self							)



 def 					UpperCAmelCase_							(    self				:Tuple							)->							Tuple:
     try:
         self._active_patches.remove(self							)
     except ValueError:
         # If the patch hasn't been started this will fail
         return None

     return self.__exit__()










'''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()



