





import sys
from collections.abc import Mapping

import numpy as np
import pyarrow as pa

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







class 						_lowerCAmelCase(						TensorFormatter[Mapping, np.ndarray, Mapping]):

		"""simple docstring"""







		def __init__( self  ,    UpperCAmelCase=None  ,    **UpperCAmelCase     )-> int:
					super().__init__(features=UpperCAmelCase     )
					__A				 =       np_array_kwargs

		def 		SCREAMING_SNAKE_CASE__	( self  ,    UpperCAmelCase     )-> Dict:
					if isinstance(UpperCAmelCase  ,    UpperCAmelCase     ):
								if column and all(
								    isinstance(UpperCAmelCase  ,    np.ndarray     ) and x.shape == column[0].shape and x.dtype == column[0].dtype for x in column     ):
											return np.stack(UpperCAmelCase     )
								else:
											# don't use np.array(column, dtype=object)
											# since it fails in certain cases
											# see https://stackoverflow.com/q/51005699
											__A				 =       np.empty(len(UpperCAmelCase     )  ,    dtype=UpperCAmelCase     )
											__A				 =       column
											return out
					return column

		def 		SCREAMING_SNAKE_CASE__	( self  ,    UpperCAmelCase     )-> List[str]:
					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
					elif isinstance(UpperCAmelCase  ,    np.number     ):
								return value

					__A				 =       {}

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

								if isinstance(UpperCAmelCase  ,    PIL.Image.Image     ):
											return np.asarray(UpperCAmelCase  ,    **self.np_array_kwargs     )

					return np.asarray(UpperCAmelCase  ,    **{**default_dtype, **self.np_array_kwargs}     )

		def 		SCREAMING_SNAKE_CASE__	( self  ,    UpperCAmelCase     )-> Tuple:
					# support for torch, tf, jax etc.
					if config.TORCH_AVAILABLE and "torch" in sys.modules:
								import torch

								if isinstance(UpperCAmelCase  ,    torch.Tensor     ):
											return self._tensorize(data_struct.detach().cpu().numpy()[()]     )
					if hasattr(UpperCAmelCase  ,    '''__array__'''     ) and not isinstance(UpperCAmelCase  ,    (np.ndarray, np.character, np.number)     ):
								__A				 =       data_struct.__array__()
					# support for nested types like struct of list of struct
					if isinstance(UpperCAmelCase  ,    np.ndarray     ):
								if data_struct.dtype == object:
											return self._consolidate([self.recursive_tensorize(UpperCAmelCase     ) for substruct in data_struct]     )
					if isinstance(UpperCAmelCase  ,    (list, tuple)     ):
								return self._consolidate([self.recursive_tensorize(UpperCAmelCase     ) for substruct in data_struct]     )
					return self._tensorize(UpperCAmelCase     )

		def 		SCREAMING_SNAKE_CASE__	( self  ,    UpperCAmelCase     )-> List[Any]:
					return map_nested(self._recursive_tensorize  ,    UpperCAmelCase  ,    map_list=UpperCAmelCase     )

		def 		SCREAMING_SNAKE_CASE__	( self  ,    UpperCAmelCase     )-> Mapping:
					__A				 =       self.numpy_arrow_extractor().extract_row(UpperCAmelCase     )
					__A				 =       self.python_features_decoder.decode_row(UpperCAmelCase     )
					return self.recursive_tensorize(UpperCAmelCase     )

		def 		SCREAMING_SNAKE_CASE__	( self  ,    UpperCAmelCase     )-> np.ndarray:
					__A				 =       self.numpy_arrow_extractor().extract_column(UpperCAmelCase     )
					__A				 =       self.python_features_decoder.decode_column(UpperCAmelCase  ,    pa_table.column_names[0]     )
					__A				 =       self.recursive_tensorize(UpperCAmelCase     )
					__A				 =       self._consolidate(UpperCAmelCase     )
					return column





		def 		SCREAMING_SNAKE_CASE__	( self  ,    UpperCAmelCase     )-> Mapping:
					__A				 =       self.numpy_arrow_extractor().extract_batch(UpperCAmelCase     )
					__A				 =       self.python_features_decoder.decode_batch(UpperCAmelCase     )
					__A				 =       self.recursive_tensorize(UpperCAmelCase     )
					for column_name in batch:
								__A				 =       self._consolidate(batch[column_name]     )
					return batch








import numpy as np
def 				__UpperCamelCase  (		snake_case     )  ->						Any:


   '''simple docstring'''







   __A ,						__A				 =       a.shape
   __A				 =       min(snake_case    ,	snake_case     )
   __A				 =       np.eye(snake_case     )
   __A				 =       a.copy()

   for k in range(t - 1     ):
      # select a column of modified matrix A':
      __A				 =       r[k:, [k]]
      # construct first basis vector
      __A				 =       np.zeros_like(snake_case     )
      __A				 =       1.0
      # determine scaling factor
      __A				 =       np.linalg.norm(snake_case     )
      # construct vector v for Householder reflection
      __A				 =       x + np.sign(x[0]     ) * alpha * ea
      v /= np.linalg.norm(snake_case     )

      # construct the Householder matrix
      __A				 =       np.eye(m - k     ) - 2.0 * v @ v.T
      # pad with ones and zeros as necessary
      __A				 =       np.block([[np.eye(snake_case     ), np.zeros((k, m - k)     )], [np.zeros((m - k, k)     ), q_k]]     )

      __A				 =       q @ q_k.T
      __A				 =       q_k @ r

   return q, r


if __name__ == "__main__":
    import doctest

    doctest.testmod()

