code: 
  
  from typing import TYPE_CHECKING
  
  from ...utils import OptionalDependencyNotAvailable, _LazyModule, is_sentencepiece_available, is_torch_available
  
  
  A_		:			Optional[int]										=   {
      'configuration_xlm_prophetnet': ['XLM_PROPHETNET_PRETRAINED_CONFIG_ARCHIVE_MAP', 'XLMProphetNetConfig'],
  }
  
  try:
         if not is_sentencepiece_available():
                raise OptionalDependencyNotAvailable()
  except OptionalDependencyNotAvailable:
         pass
  else:
         A_		:			Optional[Any]										=   ['XLMProphetNetTokenizer']
  
  try:
         if not is_torch_available():
                raise OptionalDependencyNotAvailable()
  except OptionalDependencyNotAvailable:
         pass
  else:
         A_		:			Any										=   [
             'XLM_PROPHETNET_PRETRAINED_MODEL_ARCHIVE_LIST',
             'XLMProphetNetDecoder',
             'XLMProphetNetEncoder',
             'XLMProphetNetForCausalLM',
             'XLMProphetNetForConditionalGeneration',
             'XLMProphetNetModel',
             'XLMProphetNetPreTrainedModel',
         ]
  
  
  if TYPE_CHECKING:
         from .configuration_xlm_prophetnet import XLM_PROPHETNET_PRETRAINED_CONFIG_ARCHIVE_MAP, XLMProphetNetConfig
  
         try:
                if not is_sentencepiece_available():
                       raise OptionalDependencyNotAvailable()
         except OptionalDependencyNotAvailable:
                pass
         else:
                from .tokenization_xlm_prophetnet import XLMProphetNetTokenizer
  
         try:
                if not is_torch_available():
                       raise OptionalDependencyNotAvailable()
         except OptionalDependencyNotAvailable:
                pass
         else:
                from .modeling_xlm_prophetnet import (
                    XLM_PROPHETNET_PRETRAINED_MODEL_ARCHIVE_LIST,
                    XLMProphetNetDecoder,
                    XLMProphetNetEncoder,
                    XLMProphetNetForCausalLM,
                    XLMProphetNetForConditionalGeneration,
                    XLMProphetNetModel,
                    XLMProphetNetPreTrainedModel,
                )
  
  else:
         import sys
  
         A_		:			str										=   _LazyModule(__name__, globals()['__file__'], _import_structure, module_spec=__spec__)
  
  
  
  
style_context: 
  
  import numpy as np
  
  
  def       __a       (   SCREAMING_SNAKE_CASE      )      ->     Tuple:
  
  
  
  
  
  
      '''simple docstring'''
      __UpperCAmelCase					,     __UpperCAmelCase									=			a.shape
      __UpperCAmelCase									=			min(SCREAMING_SNAKE_CASE       ,   SCREAMING_SNAKE_CASE      )
      __UpperCAmelCase									=			np.eye(SCREAMING_SNAKE_CASE      )
      __UpperCAmelCase									=			a.copy()
  
      for k in range(t - 1      ):
          # select a column of modified matrix A':
          __UpperCAmelCase									=			r[k:, [k]]
          # construct first basis vector
          __UpperCAmelCase									=			np.zeros_like(SCREAMING_SNAKE_CASE      )
          __UpperCAmelCase									=			1.0
          # determine scaling factor
          __UpperCAmelCase									=			np.linalg.norm(SCREAMING_SNAKE_CASE      )
          # construct vector v for Householder reflection
          __UpperCAmelCase									=			x + np.sign(x[0]      ) * alpha * ea
          v /= np.linalg.norm(SCREAMING_SNAKE_CASE      )
  
          # construct the Householder matrix
          __UpperCAmelCase									=			np.eye(m - k      ) - 2.0 * v @ v.T
          # pad with ones and zeros as necessary
          __UpperCAmelCase									=			np.block([[np.eye(SCREAMING_SNAKE_CASE      ), np.zeros((k, m - k)      )], [np.zeros((m - k, k)      ), q_k]]      )
  
          __UpperCAmelCase									=			q @ q_k.T
          __UpperCAmelCase									=			q_k @ r
  
      return q, r
  
  
  if __name__ == "__main__":
         import doctest
  
         doctest.testmod()
  
  
  
  
  