





import unittest

import numpy as np



def    __lowercase   (      _SCREAMING_SNAKE_CASE ,						_SCREAMING_SNAKE_CASE ,						_SCREAMING_SNAKE_CASE ,						_SCREAMING_SNAKE_CASE = None ,						) ->   np.ndarray:


      '''simple docstring'''


      SCREAMING_SNAKE_CASE		=						np.shape(_SCREAMING_SNAKE_CASE	)
      SCREAMING_SNAKE_CASE		=						np.shape(_SCREAMING_SNAKE_CASE	)
      SCREAMING_SNAKE_CASE		=						np.shape(_SCREAMING_SNAKE_CASE	)

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

      if shape_b[1] != shape_c[1]:
            SCREAMING_SNAKE_CASE		=						(
                """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(_SCREAMING_SNAKE_CASE	)

      SCREAMING_SNAKE_CASE		=						pseudo_inv
      if a_inv is None:
            try:
                  SCREAMING_SNAKE_CASE		=						np.linalg.inv(_SCREAMING_SNAKE_CASE	)
            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 				SCREAMING_SNAKE_CASE__  (							self						:    int       )     ->		None:




           '''simple docstring'''


           SCREAMING_SNAKE_CASE		=						np.array([[1, 2, 1], [2, 1, 2], [3, 2, 4]]       )
           SCREAMING_SNAKE_CASE		=						np.array([[0, 3], [3, 0], [2, 3]]       )
           SCREAMING_SNAKE_CASE		=						np.array([[2, 1], [6, 3]]       )

           SCREAMING_SNAKE_CASE		=						schur_complement(lowerCamelCase__						,lowerCamelCase__						,lowerCamelCase__       )

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

           SCREAMING_SNAKE_CASE		=						np.linalg.det(lowerCamelCase__       )
           SCREAMING_SNAKE_CASE		=						np.linalg.det(lowerCamelCase__       )
           SCREAMING_SNAKE_CASE		=						np.linalg.det(lowerCamelCase__       )

           self.assertAlmostEqual(lowerCamelCase__						,det_a * det_s       )






     def 				SCREAMING_SNAKE_CASE__  (							self						:    str       )     ->		None:




           '''simple docstring'''


           SCREAMING_SNAKE_CASE		=						np.array([[1, 2, 1], [2, 1, 2], [3, 2, 4]]       )
           SCREAMING_SNAKE_CASE		=						np.array([[0, 3], [3, 0], [2, 3]]       )
           SCREAMING_SNAKE_CASE		=						np.array([[2, 1], [6, 3]]       )

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






     def 				SCREAMING_SNAKE_CASE__  (							self						:    List[str]       )     ->		None:




           '''simple docstring'''


           SCREAMING_SNAKE_CASE		=						np.array([[1, 2, 1], [2, 1, 2], [3, 2, 4]]       )
           SCREAMING_SNAKE_CASE		=						np.array([[0, 3], [3, 0], [2, 3]]       )
           SCREAMING_SNAKE_CASE		=						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 typing import Callable, Optional

from .. import Features
from ..packaged_modules.generator.generator import Generator
from .abc import AbstractDatasetInputStream

class 		UpperCamelCase__ (      lowerCAmelCase_   ):



     '''simple docstring'''

     def __init__(							self						:    Union[str, Any]						,lowerCamelCase__						:    Callable						,lowerCamelCase__						:    Optional[Features] = None						,lowerCamelCase__						:    str = None						,lowerCamelCase__						:    bool = False						,lowerCamelCase__						:    bool = False						,lowerCamelCase__						:    Optional[dict] = None						,lowerCamelCase__						:    Optional[int] = None						,**lowerCamelCase__						:    Optional[Any]						,)     ->		List[str]:




           '''simple docstring'''


           super().__init__(
               features=lowerCamelCase__						,cache_dir=lowerCamelCase__						,keep_in_memory=lowerCamelCase__						,streaming=lowerCamelCase__						,num_proc=lowerCamelCase__						,**lowerCamelCase__						,)
           SCREAMING_SNAKE_CASE		=						Generator(
               cache_dir=lowerCamelCase__						,features=lowerCamelCase__						,generator=lowerCamelCase__						,gen_kwargs=lowerCamelCase__						,**lowerCamelCase__						,)






     def 				SCREAMING_SNAKE_CASE__  (							self						:    Union[str, Any]       )     ->		Optional[Any]:




           '''simple docstring'''


           if self.streaming:
                 SCREAMING_SNAKE_CASE		=						self.builder.as_streaming_dataset(split="""train"""       )
           # Build regular (map-style) dataset
           else:
                 SCREAMING_SNAKE_CASE		=						None
                 SCREAMING_SNAKE_CASE		=						None
                 SCREAMING_SNAKE_CASE		=						None
                 SCREAMING_SNAKE_CASE		=						None

                 self.builder.download_and_prepare(
                     download_config=lowerCamelCase__						,download_mode=lowerCamelCase__						,verification_mode=lowerCamelCase__						,base_path=lowerCamelCase__						,num_proc=self.num_proc						,)
                 SCREAMING_SNAKE_CASE		=						self.builder.as_dataset(
                     split="""train"""						,verification_mode=lowerCamelCase__						,in_memory=self.keep_in_memory       )
           return dataset


