




import numpy as np





def 							lowerCamelCase    (							UpperCAmelCase_	:      Tuple      )->			Tuple:

       """simple docstring"""




       a   ,      a			   =a.shape
       a			   =min(UpperCAmelCase_   ,       UpperCAmelCase_      )
       a			   =np.eye(UpperCAmelCase_      )
       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(UpperCAmelCase_      )
              a			   =1.0
              # determine scaling factor
              a			   =np.linalg.norm(UpperCAmelCase_      )
              # construct vector v for Householder reflection
              a			   =x + np.sign(x[0]      ) * alpha * ea
              v /= np.linalg.norm(UpperCAmelCase_      )

              # 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(UpperCAmelCase_      ), 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()






from typing import TYPE_CHECKING

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


_lowerCamelCase							=      {'''configuration_cvt''': ['''CVT_PRETRAINED_CONFIG_ARCHIVE_MAP''', '''CvtConfig''']}


try:
    if not is_torch_available():
        raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
    pass
else:
    _lowerCamelCase							=      [
        '''CVT_PRETRAINED_MODEL_ARCHIVE_LIST''',
        '''CvtForImageClassification''',
        '''CvtModel''',
        '''CvtPreTrainedModel''',
    ]

try:
    if not is_tf_available():
        raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
    pass
else:
    _lowerCamelCase							=      [
        '''TF_CVT_PRETRAINED_MODEL_ARCHIVE_LIST''',
        '''TFCvtForImageClassification''',
        '''TFCvtModel''',
        '''TFCvtPreTrainedModel''',
    ]

if TYPE_CHECKING:
    from .configuration_cvt import CVT_PRETRAINED_CONFIG_ARCHIVE_MAP, CvtConfig

    try:
        if not is_torch_available():
            raise OptionalDependencyNotAvailable()
    except OptionalDependencyNotAvailable:
        pass
    else:
        from .modeling_cvt import (
            CVT_PRETRAINED_MODEL_ARCHIVE_LIST,
            CvtForImageClassification,
            CvtModel,
            CvtPreTrainedModel,
        )

    try:
        if not is_tf_available():
            raise OptionalDependencyNotAvailable()
    except OptionalDependencyNotAvailable:
        pass
    else:
        from .modeling_tf_cvt import (
            TF_CVT_PRETRAINED_MODEL_ARCHIVE_LIST,
            TFCvtForImageClassification,
            TFCvtModel,
            TFCvtPreTrainedModel,
        )


else:
    import sys

    _lowerCamelCase							=      _LazyModule(__name__, globals()['''__file__'''], _import_structure, module_spec=__spec__)
