




import unittest

import numpy as np


def    A						(__A   :    np.ndarray   ,				__A   :    np.ndarray   ,				__A   :    np.ndarray   ,				__A   :    np.ndarray | None = None   ,				)   ->      np.ndarray:







     """simple docstring"""


     UpperCAmelCase_          =							np.shape(__A       )
     UpperCAmelCase_          =							np.shape(__A       )
     UpperCAmelCase_          =							np.shape(__A       )

     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(__A       )

     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(__A       )

     UpperCAmelCase_          =							pseudo_inv
     if a_inv is None:
          try:
               UpperCAmelCase_          =							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 lowerCamelCase						(      self		:						Any):

        """simple docstring"""


        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(_snake_case					,						_snake_case					,						_snake_case)

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

        UpperCAmelCase_          =							np.linalg.det(_snake_case)
        UpperCAmelCase_          =							np.linalg.det(_snake_case)
        UpperCAmelCase_          =							np.linalg.det(_snake_case)

        self.assertAlmostEqual(_snake_case					,						det_a * det_s)







   def lowerCamelCase						(      self		:						List[str]):

        """simple docstring"""


        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(_snake_case):
             schur_complement(_snake_case					,						_snake_case					,						_snake_case)







   def lowerCamelCase						(      self		:						List[str]):

        """simple docstring"""


        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(_snake_case):
             schur_complement(_snake_case					,						_snake_case					,						_snake_case)


if __name__ == "__main__":
    import doctest

    doctest.testmod()
    unittest.main()












from typing import List, Optional, TypeVar

from .arrow_dataset import Dataset, _concatenate_map_style_datasets, _interleave_map_style_datasets
from .dataset_dict import DatasetDict, IterableDatasetDict
from .info import DatasetInfo
from .iterable_dataset import IterableDataset, _concatenate_iterable_datasets, _interleave_iterable_datasets
from .splits import NamedSplit
from .utils import logging
from .utils.py_utils import Literal


snake_case_ : Any    		=       logging.get_logger(__name__)


snake_case_ : Optional[int]    		=       TypeVar("DatasetType", Dataset, IterableDataset)


def    A						(__A   :    List[DatasetType]   ,				__A   :    Optional[List[float]] = None   ,				__A   :    Optional[int] = None   ,				__A   :    Optional[DatasetInfo] = None   ,				__A   :    Optional[NamedSplit] = None   ,				__A   :    Literal["first_exhausted", "all_exhausted"] = "first_exhausted"   ,				)   ->      DatasetType:







     """simple docstring"""


     from .arrow_dataset import Dataset
     from .iterable_dataset import IterableDataset

     if not datasets:
          raise ValueError('''Unable to interleave an empty list of datasets.'''       )
     for i, dataset in enumerate(__A       ):
          if not isinstance(__A   ,				(Dataset, IterableDataset)       ):
               if isinstance(__A   ,				(DatasetDict, IterableDatasetDict)       ):
                    if not dataset:
                         raise ValueError(
                             F"""Expected a list of Dataset objects or a list of IterableDataset objects, but element at position {i} """
                             '''is an empty dataset dictionary.'''       )
                    raise ValueError(
                        F"""Dataset at position {i} has at least one split: {list(__A       )}\n"""
                        F"""Please pick one to interleave with the other datasets, for example: dataset['{next(iter(__A       )       )}']"""       )
               raise ValueError(
                   F"""Expected a list of Dataset objects or a list of IterableDataset objects, but element at position {i} is a {type(__A       ).__name__}."""       )
          if i == 0:
               UpperCAmelCase_     ,       UpperCAmelCase_          =							(
                   (Dataset, IterableDataset) if isinstance(__A   ,				__A       ) else (IterableDataset, Dataset)
               )
          elif not isinstance(__A   ,				__A       ):
               raise ValueError(
                   F"""Unable to interleave a {dataset_type.__name__} (at position 0) with a {other_type.__name__} (at position {i}). Expected a list of Dataset objects or a list of IterableDataset objects."""       )
     if stopping_strategy not in ["first_exhausted", "all_exhausted"]:
          raise ValueError(F"""{stopping_strategy} is not supported. Please enter a valid stopping_strategy."""       )
     if dataset_type is Dataset:
          return _interleave_map_style_datasets(
              __A   ,				__A   ,				__A   ,				info=__A   ,				split=__A   ,				stopping_strategy=__A       )
     else:
          return _interleave_iterable_datasets(
              __A   ,				__A   ,				__A   ,				info=__A   ,				split=__A   ,				stopping_strategy=__A       )


def    A						(__A   :    List[DatasetType]   ,				__A   :    Optional[DatasetInfo] = None   ,				__A   :    Optional[NamedSplit] = None   ,				__A   :    int = 0   ,				)   ->      DatasetType:







     """simple docstring"""


     if not dsets:
          raise ValueError('''Unable to concatenate an empty list of datasets.'''       )
     for i, dataset in enumerate(__A       ):
          if not isinstance(__A   ,				(Dataset, IterableDataset)       ):
               if isinstance(__A   ,				(DatasetDict, IterableDatasetDict)       ):
                    if not dataset:
                         raise ValueError(
                             F"""Expected a list of Dataset objects or a list of IterableDataset objects, but element at position {i} """
                             '''is an empty dataset dictionary.'''       )
                    raise ValueError(
                        F"""Dataset at position {i} has at least one split: {list(__A       )}\n"""
                        F"""Please pick one to interleave with the other datasets, for example: dataset['{next(iter(__A       )       )}']"""       )
               raise ValueError(
                   F"""Expected a list of Dataset objects or a list of IterableDataset objects, but element at position {i} is a {type(__A       ).__name__}."""       )
          if i == 0:
               UpperCAmelCase_     ,       UpperCAmelCase_          =							(
                   (Dataset, IterableDataset) if isinstance(__A   ,				__A       ) else (IterableDataset, Dataset)
               )
          elif not isinstance(__A   ,				__A       ):
               raise ValueError(
                   F"""Unable to interleave a {dataset_type.__name__} (at position 0) with a {other_type.__name__} (at position {i}). Expected a list of Dataset objects or a list of IterableDataset objects."""       )
     if dataset_type is Dataset:
          return _concatenate_map_style_datasets(__A   ,				info=__A   ,				split=__A   ,				axis=__A       )
     else:
          return _concatenate_iterable_datasets(__A   ,				info=__A   ,				split=__A   ,				axis=__A       )






