




'''simple docstring'''

import numpy as np





def 				A_					(	snake_case	):
  SCREAMING_SNAKE_CASE:Dict   =   a.shape
  SCREAMING_SNAKE_CASE:Union[str, Any]   =   min(_SCREAMING_SNAKE_CASE ,    _SCREAMING_SNAKE_CASE	)
  SCREAMING_SNAKE_CASE:Union[str, Any]   =   np.eye(_SCREAMING_SNAKE_CASE	)
  SCREAMING_SNAKE_CASE:List[Any]   =   a.copy()

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

    # construct the Householder matrix
    SCREAMING_SNAKE_CASE:List[Any]   =   np.eye(m - k	) - 2.0 * v @ v.T
    # pad with ones and zeros as necessary
    SCREAMING_SNAKE_CASE:Union[str, Any]   =   np.block([[np.eye(_SCREAMING_SNAKE_CASE	), np.zeros((k, m - k)	)], [np.zeros((m - k, k)	), q_k]]	)

    SCREAMING_SNAKE_CASE:Any   =   q @ q_k.T
    SCREAMING_SNAKE_CASE:List[Any]   =   q_k @ r

  return q, r


if __name__ == "__main__":
    import doctest

    doctest.testmod()









'''simple docstring'''

from typing import TYPE_CHECKING

from ...utils import OptionalDependencyNotAvailable, _LazyModule, is_tokenizers_available, is_torch_available


A_      =							{"configuration_yoso": ["YOSO_PRETRAINED_CONFIG_ARCHIVE_MAP", "YosoConfig"]}

try:
    if not is_torch_available():
        raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
    pass
else:
    A_      =							[
        "YOSO_PRETRAINED_MODEL_ARCHIVE_LIST",
        "YosoForMaskedLM",
        "YosoForMultipleChoice",
        "YosoForQuestionAnswering",
        "YosoForSequenceClassification",
        "YosoForTokenClassification",
        "YosoLayer",
        "YosoModel",
        "YosoPreTrainedModel",
    ]


if TYPE_CHECKING:
    from .configuration_yoso import YOSO_PRETRAINED_CONFIG_ARCHIVE_MAP, YosoConfig

    try:
        if not is_torch_available():
            raise OptionalDependencyNotAvailable()
    except OptionalDependencyNotAvailable:
        pass
    else:
        from .modeling_yoso import (
            YOSO_PRETRAINED_MODEL_ARCHIVE_LIST,
            YosoForMaskedLM,
            YosoForMultipleChoice,
            YosoForQuestionAnswering,
            YosoForSequenceClassification,
            YosoForTokenClassification,
            YosoLayer,
            YosoModel,
            YosoPreTrainedModel,
        )


else:
    import sys

    A_      =							_LazyModule(__name__, globals()["__file__"], _import_structure)






