


"""simple docstring"""

import unittest

import numpy as np


def lowerCAmelCase_      (				UpperCamelCase__	: np.ndarray				,   UpperCamelCase__	: np.ndarray				,   UpperCamelCase__	: np.ndarray				,   UpperCamelCase__	: np.ndarray | None = None				,   ):






 """simple docstring"""







 __lowercase									=	np.shape(UpperCamelCase__ )
 __lowercase									=	np.shape(UpperCamelCase__ )
 __lowercase									=	np.shape(UpperCamelCase__ )

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

 if shape_b[1] != shape_c[1]:
  __lowercase									=	(
      """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(UpperCamelCase__ )

 __lowercase									=	pseudo_inv
 if a_inv is None:
  try:
   __lowercase									=	np.linalg.inv(UpperCamelCase__ )
  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    lowerCamelCase__						(		unittest.TestCase    ):
      def SCREAMING_SNAKE_CASE_	(		self	:	int							):






       '''simple docstring'''


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

       __lowercase									=	schur_complement(A_      ,       A_      ,       A_							)

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

       __lowercase									=	np.linalg.det(A_							)
       __lowercase									=	np.linalg.det(A_							)
       __lowercase									=	np.linalg.det(A_							)

       self.assertAlmostEqual(A_      ,       det_a * det_s							)
      def SCREAMING_SNAKE_CASE_	(		self	:	Optional[Any]							):






       '''simple docstring'''


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

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






      def SCREAMING_SNAKE_CASE_	(		self	:	Optional[Any]							):






       '''simple docstring'''


       __lowercase									=	np.array([[1, 2, 1], [2, 1, 2], [3, 2, 4]]							)
       __lowercase									=	np.array([[0, 3], [3, 0], [2, 3]]							)
       __lowercase									=	np.array([[2, 1, 3], [6, 3, 5]]							)

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


if __name__ == "__main__":
       import doctest

       doctest.testmod()
       unittest.main()




"""simple docstring"""

import pytest

from datasets import Dataset, DatasetDict, Features, NamedSplit, Value
from datasets.io.text import TextDatasetReader

from ..utils import assert_arrow_memory_doesnt_increase, assert_arrow_memory_increases


def lowerCAmelCase_      (				UpperCamelCase__	: List[str]				,   UpperCamelCase__	: Any ):






 """simple docstring"""







 assert isinstance(UpperCamelCase__				,   UpperCamelCase__ )
 assert dataset.num_rows == 4
 assert dataset.num_columns == 1
 assert dataset.column_names == ["text"]
 for feature, expected_dtype in expected_features.items():
  assert dataset.features[feature].dtype == expected_dtype


@pytest.mark.parametrize("""keep_in_memory"""				,   [False, True] )
def lowerCAmelCase_      (				UpperCamelCase__	: Dict				,   UpperCamelCase__	: Optional[int]				,   UpperCamelCase__	: List[str] ):






 """simple docstring"""







 __lowercase									=	tmp_path / """cache"""
 __lowercase									=	{"""text""": """string"""}
 with assert_arrow_memory_increases() if keep_in_memory else assert_arrow_memory_doesnt_increase():
  __lowercase									=	TextDatasetReader(UpperCamelCase__				,   cache_dir=UpperCamelCase__				,   keep_in_memory=UpperCamelCase__ ).read()
 _check_text_dataset(UpperCamelCase__				,   UpperCamelCase__ )


@pytest.mark.parametrize(
    """features"""				,   [
        None,
        {"""text""": """string"""},
        {"""text""": """int32"""},
        {"""text""": """float32"""},
    ]				,   )
def lowerCAmelCase_      (				UpperCamelCase__	: List[Any]				,   UpperCamelCase__	: List[str]				,   UpperCamelCase__	: Union[str, Any] ):






 """simple docstring"""







 __lowercase									=	tmp_path / """cache"""
 __lowercase									=	{"""text""": """string"""}
 __lowercase									=	features.copy() if features else default_expected_features
 __lowercase									=	(
     Features({feature: Value(UpperCamelCase__ ) for feature, dtype in features.items()} ) if features is not None else None
 )
 __lowercase									=	TextDatasetReader(UpperCamelCase__				,   features=UpperCamelCase__				,   cache_dir=UpperCamelCase__ ).read()
 _check_text_dataset(UpperCamelCase__				,   UpperCamelCase__ )


@pytest.mark.parametrize("""split"""				,   [None, NamedSplit("""train""" ), """train""", """test"""] )
def lowerCAmelCase_      (				UpperCamelCase__	: Union[str, Any]				,   UpperCamelCase__	: str				,   UpperCamelCase__	: Tuple ):






 """simple docstring"""







 __lowercase									=	tmp_path / """cache"""
 __lowercase									=	{"""text""": """string"""}
 __lowercase									=	TextDatasetReader(UpperCamelCase__				,   cache_dir=UpperCamelCase__				,   split=UpperCamelCase__ ).read()
 _check_text_dataset(UpperCamelCase__				,   UpperCamelCase__ )
 assert dataset.split == split if split else "train"


@pytest.mark.parametrize("""path_type"""				,   [str, list] )
def lowerCAmelCase_      (				UpperCamelCase__	: Union[str, Any]				,   UpperCamelCase__	: List[str]				,   UpperCamelCase__	: Any ):






 """simple docstring"""







 if issubclass(UpperCamelCase__				,   UpperCamelCase__ ):
  __lowercase									=	text_path
 elif issubclass(UpperCamelCase__				,   UpperCamelCase__ ):
  __lowercase									=	[text_path]
 __lowercase									=	tmp_path / """cache"""
 __lowercase									=	{"""text""": """string"""}
 __lowercase									=	TextDatasetReader(UpperCamelCase__				,   cache_dir=UpperCamelCase__ ).read()
 _check_text_dataset(UpperCamelCase__				,   UpperCamelCase__ )


def lowerCAmelCase_      (				UpperCamelCase__	: str				,   UpperCamelCase__	: str				,   UpperCamelCase__	: Any=("train",) ):






 """simple docstring"""







 assert isinstance(UpperCamelCase__				,   UpperCamelCase__ )
 for split in splits:
  __lowercase									=	dataset_dict[split]
  assert dataset.num_rows == 4
  assert dataset.num_columns == 1
  assert dataset.column_names == ["text"]
  for feature, expected_dtype in expected_features.items():
   assert dataset.features[feature].dtype == expected_dtype


@pytest.mark.parametrize("""keep_in_memory"""				,   [False, True] )
def lowerCAmelCase_      (				UpperCamelCase__	: int				,   UpperCamelCase__	: List[str]				,   UpperCamelCase__	: List[Any] ):






 """simple docstring"""







 __lowercase									=	tmp_path / """cache"""
 __lowercase									=	{"""text""": """string"""}
 with assert_arrow_memory_increases() if keep_in_memory else assert_arrow_memory_doesnt_increase():
  __lowercase									=	TextDatasetReader({"""train""": text_path}				,   cache_dir=UpperCamelCase__				,   keep_in_memory=UpperCamelCase__ ).read()
 _check_text_datasetdict(UpperCamelCase__				,   UpperCamelCase__ )


@pytest.mark.parametrize(
    """features"""				,   [
        None,
        {"""text""": """string"""},
        {"""text""": """int32"""},
        {"""text""": """float32"""},
    ]				,   )
def lowerCAmelCase_      (				UpperCamelCase__	: Optional[Any]				,   UpperCamelCase__	: Dict				,   UpperCamelCase__	: Union[str, Any] ):






 """simple docstring"""







 __lowercase									=	tmp_path / """cache"""
 # CSV file loses col_1 string dtype information: default now is "int64" instead of "string"
 __lowercase									=	{"""text""": """string"""}
 __lowercase									=	features.copy() if features else default_expected_features
 __lowercase									=	(
     Features({feature: Value(UpperCamelCase__ ) for feature, dtype in features.items()} ) if features is not None else None
 )
 __lowercase									=	TextDatasetReader({"""train""": text_path}				,   features=UpperCamelCase__				,   cache_dir=UpperCamelCase__ ).read()
 _check_text_datasetdict(UpperCamelCase__				,   UpperCamelCase__ )


@pytest.mark.parametrize("""split"""				,   [None, NamedSplit("""train""" ), """train""", """test"""] )
def lowerCAmelCase_      (				UpperCamelCase__	: Dict				,   UpperCamelCase__	: int				,   UpperCamelCase__	: int ):






 """simple docstring"""







 if split:
  __lowercase									=	{split: text_path}
 else:
  __lowercase									=	"""train"""
  __lowercase									=	{"""train""": text_path, """test""": text_path}
 __lowercase									=	tmp_path / """cache"""
 __lowercase									=	{"""text""": """string"""}
 __lowercase									=	TextDatasetReader(UpperCamelCase__				,   cache_dir=UpperCamelCase__ ).read()
 _check_text_datasetdict(UpperCamelCase__				,   UpperCamelCase__				,   splits=list(path.keys() ) )
 assert all(dataset[split].split == split for split in path.keys() )
