




import unittest

import numpy as np







def lowerCamelCase__  (     _lowercase					,		_lowercase					,		_lowercase					,		_lowercase = None					,		):

     '''simple docstring'''


     UpperCAmelCase_     :				Dict  =     np.shape(_lowercase )
     UpperCAmelCase_     :				Optional[Any]  =     np.shape(_lowercase )
     UpperCAmelCase_     :				Tuple  =     np.shape(_lowercase )

     if shape_a[0] != shape_b[0]:
          UpperCAmelCase_     :				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(_lowercase )

     if shape_b[1] != shape_c[1]:
          UpperCAmelCase_     :				List[Any]  =     (
              '''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(_lowercase )

     UpperCAmelCase_     :				Dict  =     pseudo_inv
     if a_inv is None:
          try:
               UpperCAmelCase_     :				Any  =     np.linalg.inv(_lowercase )
          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     __a(	unittest.TestCase  ):






    """simple docstring"""





    def 				a__ ( self    )					->						None:
         UpperCAmelCase_     :				str  =     np.array([[1, 2, 1], [2, 1, 2], [3, 2, 4]]    )
         UpperCAmelCase_     :				Any  =     np.array([[0, 3], [3, 0], [2, 3]]    )
         UpperCAmelCase_     :				List[str]  =     np.array([[2, 1], [6, 3]]    )

         UpperCAmelCase_     :				Tuple  =     schur_complement(_SCREAMING_SNAKE_CASE  ,_SCREAMING_SNAKE_CASE  ,_SCREAMING_SNAKE_CASE    )

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

         UpperCAmelCase_     :				List[Any]  =     np.linalg.det(_SCREAMING_SNAKE_CASE    )
         UpperCAmelCase_     :				List[Any]  =     np.linalg.det(_SCREAMING_SNAKE_CASE    )
         UpperCAmelCase_     :				Any  =     np.linalg.det(_SCREAMING_SNAKE_CASE    )

         self.assertAlmostEqual(_SCREAMING_SNAKE_CASE  ,det_a * det_s    )





    def 				a__ ( self    )					->						None:
         UpperCAmelCase_     :				str  =     np.array([[1, 2, 1], [2, 1, 2], [3, 2, 4]]    )
         UpperCAmelCase_     :				Optional[int]  =     np.array([[0, 3], [3, 0], [2, 3]]    )
         UpperCAmelCase_     :				Optional[int]  =     np.array([[2, 1], [6, 3]]    )

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





    def 				a__ ( self    )					->						None:
         UpperCAmelCase_     :				Optional[int]  =     np.array([[1, 2, 1], [2, 1, 2], [3, 2, 4]]    )
         UpperCAmelCase_     :				Optional[Any]  =     np.array([[0, 3], [3, 0], [2, 3]]    )
         UpperCAmelCase_     :				int  =     np.array([[2, 1, 3], [6, 3, 5]]    )

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


if __name__ == "__main__":
     import doctest

     doctest.testmod()
     unittest.main()



'''simple docstring'''

# Lint as: python3
import sys
from collections.abc import Mapping
from typing import TYPE_CHECKING

import numpy as np
import pyarrow as pa

from .. import config
from ..utils.py_utils import map_nested
from .formatting import TensorFormatter


if TYPE_CHECKING:
 import torch
class     __lowerCAmelCase		(TensorFormatter[Mapping, """torch.Tensor""", Mapping]	):





      '''simple docstring'''






      def __init__(self       :       Optional[Any]  ,		UpperCamelCase       :       Tuple=None  ,		**UpperCamelCase       :       List[str]					):

             '''simple docstring'''







             super().__init__(features=UpperCamelCase					)
             lowercase__      =					torch_tensor_kwargs
             import torch  # noqa import torch at initialization



      def  UpperCamelCase__						(self       :       List[str]  ,		UpperCamelCase       :       Union[str, Any]					):

             '''simple docstring'''







             import torch

             if isinstance(UpperCamelCase  ,		UpperCamelCase					) and column:
                    if all(
                        isinstance(UpperCamelCase  ,		torch.Tensor					) and x.shape == column[0].shape and x.dtype == column[0].dtype
                        for x in column					):
                           return torch.stack(UpperCamelCase					)
             return column



      def  UpperCamelCase__						(self       :       List[Any]  ,		UpperCamelCase       :       Optional[Any]					):

             '''simple docstring'''







             import torch

             if isinstance(UpperCamelCase  ,		(str, bytes, type(UpperCamelCase					))					):
                    return value
             elif isinstance(UpperCamelCase  ,		(np.character, np.ndarray)					) and np.issubdtype(value.dtype  ,		np.character					):
                    return value.tolist()

             lowercase__      =					{}

             if isinstance(UpperCamelCase  ,		(np.number, np.ndarray)					) and np.issubdtype(value.dtype  ,		np.integer					):
                    lowercase__      =					{'''dtype''': torch.intaa}
             elif isinstance(UpperCamelCase  ,		(np.number, np.ndarray)					) and np.issubdtype(value.dtype  ,		np.floating					):
                    lowercase__      =					{'''dtype''': torch.floataa}
             elif config.PIL_AVAILABLE and "PIL" in sys.modules:
                    import PIL.Image

                    if isinstance(UpperCamelCase  ,		PIL.Image.Image					):
                           lowercase__      =					np.asarray(UpperCamelCase					)
             return torch.tensor(UpperCamelCase  ,		**{**default_dtype, **self.torch_tensor_kwargs}					)



      def  UpperCamelCase__						(self       :       Optional[int]  ,		UpperCamelCase       :       Dict					):

             '''simple docstring'''







             import torch

             # support for torch, tf, jax etc.
             if hasattr(UpperCamelCase  ,		'''__array__'''					) and not isinstance(UpperCamelCase  ,		torch.Tensor					):
                    lowercase__      =					data_struct.__array__()
             # support for nested types like struct of list of struct
             if isinstance(UpperCamelCase  ,		np.ndarray					):
                    if data_struct.dtype == object:  # torch tensors cannot be instantied from an array of objects
                           return self._consolidate([self.recursive_tensorize(UpperCamelCase					) for substruct in data_struct]					)
             elif isinstance(UpperCamelCase  ,		(list, tuple)					):
                    return self._consolidate([self.recursive_tensorize(UpperCamelCase					) for substruct in data_struct]					)
             return self._tensorize(UpperCamelCase					)



      def  UpperCamelCase__						(self       :       List[str]  ,		UpperCamelCase       :       dict					):

             '''simple docstring'''







             return map_nested(self._recursive_tensorize  ,		UpperCamelCase  ,		map_list=UpperCamelCase					)



      def  UpperCamelCase__						(self       :       Dict  ,		UpperCamelCase       :       pa.Table					):

             '''simple docstring'''







             lowercase__      =					self.numpy_arrow_extractor().extract_row(UpperCamelCase					)
             lowercase__      =					self.python_features_decoder.decode_row(UpperCamelCase					)
             return self.recursive_tensorize(UpperCamelCase					)



      def  UpperCamelCase__						(self       :       List[Any]  ,		UpperCamelCase       :       pa.Table					):

             '''simple docstring'''







             lowercase__      =					self.numpy_arrow_extractor().extract_column(UpperCamelCase					)
             lowercase__      =					self.python_features_decoder.decode_column(UpperCamelCase  ,		pa_table.column_names[0]					)
             lowercase__      =					self.recursive_tensorize(UpperCamelCase					)
             lowercase__      =					self._consolidate(UpperCamelCase					)
             return column






      def  UpperCamelCase__						(self       :       Tuple  ,		UpperCamelCase       :       pa.Table					):

             '''simple docstring'''







             lowercase__      =					self.numpy_arrow_extractor().extract_batch(UpperCamelCase					)
             lowercase__      =					self.python_features_decoder.decode_batch(UpperCamelCase					)
             lowercase__      =					self.recursive_tensorize(UpperCamelCase					)
             for column_name in batch:
                    lowercase__      =					self._consolidate(batch[column_name]					)
             return batch




