



"""simple docstring"""






import unittest

import numpy as np






def        snake_case_  (      A_					:		np.ndarray,				A_					:		np.ndarray,				A_					:		np.ndarray,				A_					:		np.ndarray | None = None,				):


       '''simple docstring'''





       _lowerCamelCase						:				Union[str, Any]    			= np.shape(A_						)
       _lowerCamelCase						:				List[str]    			= np.shape(A_						)
       _lowerCamelCase						:				List[str]    			= np.shape(A_						)

       if shape_a[0] != shape_b[0]:
              _lowerCamelCase						:				Tuple    			= (
                  '''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]:
              _lowerCamelCase						:				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_						)

       _lowerCamelCase						:				List[str]    			= pseudo_inv
       if a_inv is None:
              try:
                     _lowerCamelCase						:				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        __snake_case       (	unittest.TestCase):




  def 						SCREAMING_SNAKE_CASE				( self     :						Any		):






         """simple docstring"""






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

         _lowerCamelCase						:				List[Any]    			= schur_complement(__lowerCAmelCase						,					__lowerCAmelCase						,					__lowerCAmelCase		)

         _lowerCamelCase						:				Dict    			= np.block([[a, b], [b.T, c]]		)

         _lowerCamelCase						:				Tuple    			= np.linalg.det(__lowerCAmelCase		)
         _lowerCamelCase						:				List[str]    			= np.linalg.det(__lowerCAmelCase		)
         _lowerCamelCase						:				Any    			= np.linalg.det(__lowerCAmelCase		)

         self.assertAlmostEqual(__lowerCAmelCase						,					det_a * det_s		)




  def 						SCREAMING_SNAKE_CASE				( self     :						Optional[Any]		):






         """simple docstring"""






         _lowerCamelCase						:				List[Any]    			= np.array([[1, 2, 1], [2, 1, 2], [3, 2, 4]]		)
         _lowerCamelCase						:				Optional[int]    			= np.array([[0, 3], [3, 0], [2, 3]]		)
         _lowerCamelCase						:				int    			= np.array([[2, 1], [6, 3]]		)

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




  def 						SCREAMING_SNAKE_CASE				( self     :						List[str]		):






         """simple docstring"""






         _lowerCamelCase						:				str    			= np.array([[1, 2, 1], [2, 1, 2], [3, 2, 4]]		)
         _lowerCamelCase						:				List[str]    			= np.array([[0, 3], [3, 0], [2, 3]]		)
         _lowerCamelCase						:				Union[str, Any]    			= 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 dataclasses import dataclass, field
from typing import ClassVar, Dict

from ..features import Features, Value
from .base import TaskTemplate







@dataclass(frozen=a			)
class 			__A( a			):
				snake_case_						   =    field(default='''language-modeling'''  ,   metadata={'''include_in_asdict_even_if_is_default''': True}			)

				snake_case_						   =    Features({'''text''': Value('''string'''			)}			)
				snake_case_						   =    Features({}			)
				snake_case_						   =    "text"




				@property
				def 				SCREAMING_SNAKE_CASE_		(     self				)    ->      Dict[str, str]:


								'''simple docstring'''




								return {self.text_column: "text"}