
"""simple docstring"""

import numpy as np




def       lowercase__  (   lowerCAmelCase			:   Any	)	-> Optional[int]:






    """simple docstring"""




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

        # 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(lowercase_	), 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()








"""simple docstring"""

import torch
import torch.nn as nn
from transformers.modeling_utils import ModuleUtilsMixin
from transformers.models.ta.modeling_ta import (
    TaBlock,
    TaConfig,
    TaLayerNorm,
)

from ...configuration_utils import ConfigMixin, register_to_config
from ...models import ModelMixin
class        _UpperCAmelCase							(						SCREAMING_SNAKE_CASE_       ,     SCREAMING_SNAKE_CASE_       ,     SCREAMING_SNAKE_CASE_							):




      @register_to_config
      def __init__(							self				,    lowercase_				,    lowercase_				,    lowercase_				,    lowercase_				,    lowercase_				,    lowercase_				,    lowercase_				,    lowercase_				,    lowercase_				,    lowercase_ = False				,    )  ->   List[Any]:
          super().__init__()

          UpperCAmelCase       =   nn.Linear(lowercase_				,    lowercase_				,    bias=lowercase_							)

          UpperCAmelCase       =   nn.Embedding(lowercase_				,    lowercase_							)
          UpperCAmelCase       =   False

          UpperCAmelCase       =   nn.Dropout(p=lowercase_							)

          UpperCAmelCase       =   TaConfig(
              d_model=lowercase_				,    num_heads=lowercase_				,    d_kv=lowercase_				,    d_ff=lowercase_				,    feed_forward_proj=lowercase_				,    dropout_rate=lowercase_				,    is_decoder=lowercase_				,    is_encoder_decoder=lowercase_				,    )
          UpperCAmelCase       =   nn.ModuleList()
          for lyr_num in range(lowercase_							):
              UpperCAmelCase       =   TaBlock(lowercase_							)
              self.encoders.append(lowercase_							)

          UpperCAmelCase       =   TaLayerNorm(lowercase_							)
          UpperCAmelCase       =   nn.Dropout(p=lowercase_							)




      def       a_ (							self				,    lowercase_				,    lowercase_							)  ->   Union[str, Any]:
          UpperCAmelCase       =   self.input_proj(lowercase_							)

          # terminal relative positional encodings
          UpperCAmelCase       =   encoder_inputs.shape[1]
          UpperCAmelCase       =   torch.arange(lowercase_				,    device=encoder_inputs.device							)

          UpperCAmelCase       =   encoder_inputs_mask.sum(-1							)
          UpperCAmelCase       =   torch.roll(input_positions.unsqueeze(0							)				,    tuple(seq_lens.tolist()							)				,    dims=0							)
          x += self.position_encoding(lowercase_							)

          UpperCAmelCase       =   self.dropout_pre(lowercase_							)

          # inverted the attention mask
          UpperCAmelCase       =   encoder_inputs.size()
          UpperCAmelCase       =   self.get_extended_attention_mask(lowercase_				,    lowercase_							)

          for lyr in self.encoders:
              UpperCAmelCase       =   lyr(lowercase_				,    lowercase_							)[0]
          UpperCAmelCase       =   self.layer_norm(lowercase_							)

          return self.dropout_post(lowercase_							), encoder_inputs_mask



