


"""simple docstring"""



import os
from typing import Optional

import fsspec
from fsspec.archive import AbstractArchiveFileSystem
from fsspec.utils import DEFAULT_BLOCK_SIZE
class 					__magic_name__		(			__UpperCAmelCase     ):
       __A			:      List[Any]        =   ""
       __A			:      str        =   (
           None  # protocol passed in prefix to the url. ex: "gzip", for gzip://file.txt::http://foo.bar/file.txt.gz
       )
       __A			:      str        =   None  # compression type in fsspec. ex: "gzip"
       __A			:      str        =   None  # extension of the filename to strip. ex: "".gz" to get file.txt from file.txt.gz






       def __init__(   self  :    Optional[Any]  ,     snake_case__  :    str = ""  ,     snake_case__  :    Optional[str] = None  ,     snake_case__  :    Optional[dict] = None  ,     **snake_case__  :    Any				):

              '''simple docstring'''






              super().__init__(self  ,     **snake_case__				)
              # always open as "rb" since fsspec can then use the TextIOWrapper to make it work for "r" mode
              lowercase		:str       							=				fsspec.open(
                  snake_case__  ,     mode='''rb'''  ,     protocol=snake_case__  ,     compression=self.compression  ,     client_kwargs={
                      '''requote_redirect_url''': False,  # see https://github.com/huggingface/datasets/pull/5459
                      '''trust_env''': True,  # Enable reading proxy env variables.
                      **(target_options or {}).pop('''client_kwargs'''  ,     {}				),  # To avoid issues if it was already passed.
                  }  ,     **(target_options or {})  ,     )
              lowercase		:Optional[int]       							=				os.path.basename(self.file.path.split('''::'''				)[0]				)
              lowercase		:str       							=				(
                  self.compressed_name[: self.compressed_name.rindex('''.'''				)]
                  if '''.''' in self.compressed_name
                  else self.compressed_name
              )
              lowercase		:int       							=				None






       @classmethod
       def  __snake_case						(   cls  :    Any  ,     snake_case__  :    Optional[int]				):

              '''simple docstring'''






              return super()._strip_protocol(snake_case__				).lstrip('''/'''				)






       def  __snake_case						(   self  :    int				):

              '''simple docstring'''






              if self.dir_cache is None:
                     lowercase		:Union[str, Any]       							=				{**self.file.fs.info(self.file.path				), '''name''': self.uncompressed_name}
                     lowercase		:Any       							=				{f['''name''']: f}






       def  __snake_case						(   self  :    Union[str, Any]  ,     snake_case__  :    str				):

              '''simple docstring'''






              return self.file.open().read()







       def  __snake_case						(   self  :    List[Any]  ,     snake_case__  :    str  ,     snake_case__  :    str = "rb"  ,     snake_case__  :    int=None  ,     snake_case__  :    List[str]=True  ,     snake_case__  :    int=None  ,     **snake_case__  :    Tuple  ,     ):

              '''simple docstring'''






              lowercase		:str       							=				self._strip_protocol(snake_case__				)
              if mode != "rb":
                     raise ValueError(f"""Tried to read with mode {mode} on file {self.file.path} opened with mode 'rb'"""				)
              return self.file.open()







class 					__magic_name__		(			__UpperCAmelCase     ):
       __A			:      str        =   "bz2"
       __A			:      Dict        =   "bz2"
       __A			:      Tuple        =   ".bz2"







class 					__magic_name__		(			__UpperCAmelCase     ):
       __A			:      Tuple        =   "gzip"
       __A			:      Union[str, Any]        =   "gzip"
       __A			:      Any        =   ".gz"







class 					__magic_name__		(			__UpperCAmelCase     ):
       __A			:      Optional[Any]        =   "lz4"
       __A			:      Tuple        =   "lz4"
       __A			:      Union[str, Any]        =   ".lz4"







class 					__magic_name__		(			__UpperCAmelCase     ):
       __A			:      Dict        =   "xz"
       __A			:      int        =   "xz"
       __A			:      int        =   ".xz"







class 					__magic_name__		(			__UpperCAmelCase     ):
       __A			:      Optional[Any]        =   "zstd"
       __A			:      str        =   "zstd"
       __A			:      Any        =   ".zst"






       def __init__(   self  :    List[Any]  ,     snake_case__  :    str  ,     snake_case__  :    str = "rb"  ,     snake_case__  :    Optional[str] = None  ,     snake_case__  :    Optional[dict] = None  ,     snake_case__  :    int = DEFAULT_BLOCK_SIZE  ,     **snake_case__  :    List[Any]  ,     ):

              '''simple docstring'''






              super().__init__(
                  fo=snake_case__  ,     mode=snake_case__  ,     target_protocol=snake_case__  ,     target_options=snake_case__  ,     block_size=snake_case__  ,     **snake_case__  ,     )
              # We need to wrap the zstd decompressor to avoid this error in fsspec==2021.7.0 and zstandard==0.15.2:
              #
              # File "/Users/user/.virtualenvs/hf-datasets/lib/python3.7/site-packages/fsspec/core.py", line 145, in open
              #     out.close = close
              # AttributeError: 'zstd.ZstdDecompressionReader' object attribute 'close' is read-only
              #
              # see https://github.com/intake/filesystem_spec/issues/725
              lowercase		:List[Any]       							=				self.file.__enter__
              class 					__magic_name__		:






                     def __init__(   self  :    Tuple  ,     snake_case__  :    List[Any]				):

                            '''simple docstring'''






                            lowercase		:Optional[Any]       							=				file_






                     def __enter__(   self  :    int				):

                            '''simple docstring'''






                            self._file.__enter__()
                            return self






                     def __exit__(   self  :    Any  ,     *snake_case__  :    Optional[Any]  ,     **snake_case__  :    str				):

                            '''simple docstring'''






                            self._file.__exit__(*snake_case__  ,     **snake_case__				)






                     def __iter__(   self  :    str				):

                            '''simple docstring'''






                            return iter(self._file				)






                     def  __snake_case						(   self  :    Dict				):

                            '''simple docstring'''






                            return next(self._file				)







                     def __getattr__(   self  :    List[str]  ,     snake_case__  :    Optional[int]				):

                            '''simple docstring'''






                            return getattr(self._file  ,     snake_case__				)

              def fixed_enter(*snake_case__  :    Optional[int]  ,     **snake_case__  :    Dict				):
                     return WrappedFile(_enter(*snake_case__  ,     **snake_case__				)				)

              lowercase		:Optional[Any]       							=				fixed_enter





"""simple docstring"""



import unittest

import numpy as np






def       lowerCamelCase					(a_						:np.ndarray				,				a_						:np.ndarray				,				a_						:np.ndarray				,				a_						:np.ndarray | None = None				,				)     ->							np.ndarray:
       lowercase		:str       							=				np.shape(a_)
       lowercase		:Dict       							=				np.shape(a_)
       lowercase		:Optional[int]       							=				np.shape(a_)

       if shape_a[0] != shape_b[0]:
              lowercase		:List[str]       							=				(
                  '''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]:
              lowercase		:List[str]       							=				(
                  '''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_)

       lowercase		:Optional[Any]       							=				pseudo_inv
       if a_inv is None:
              try:
                     lowercase		:int       							=				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 					__magic_name__		(			unittest.TestCase     ):






       def  __snake_case						(   self  :    int				):

              '''simple docstring'''






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

              lowercase		:Any       							=				schur_complement(snake_case__  ,     snake_case__  ,     snake_case__				)

              lowercase		:int       							=				np.block([[a, b], [b.T, c]]				)

              lowercase		:Tuple       							=				np.linalg.det(snake_case__				)
              lowercase		:Any       							=				np.linalg.det(snake_case__				)
              lowercase		:List[Any]       							=				np.linalg.det(snake_case__				)

              self.assertAlmostEqual(snake_case__  ,     det_a * det_s				)






       def  __snake_case						(   self  :    Optional[int]				):

              '''simple docstring'''






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

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







       def  __snake_case						(   self  :    List[Any]				):

              '''simple docstring'''






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

