






"""simple docstring"""




import torch
from torch import nn






class        UpperCamelCase			(	nn.Module      ):


 def __init__(     self		:						List[Any]							,						UpperCAmelCase__		:						Tuple							,						UpperCAmelCase__		:						List[Any]							,						UpperCAmelCase__		:						Dict							,						UpperCAmelCase__		:						List[Any]							,						UpperCAmelCase__		:						Any=1							,						UpperCAmelCase__		:						Any=False							)					->       Union[str, Any]:
   super().__init__()

   _a  :       Union[str, Any]             =	n_token
   _a  :       Optional[Any]             =	d_embed
   _a  :       Optional[Any]             =	d_proj

   _a  :       Dict             =	cutoffs + [n_token]
   _a  :       Union[str, Any]             =	[0] + self.cutoffs
   _a  :       Any             =	div_val

   _a  :       List[str]             =	self.cutoffs[0]
   _a  :       List[str]             =	len(self.cutoffs							) - 1
   _a  :       Optional[Any]             =	self.shortlist_size + self.n_clusters

   if self.n_clusters > 0:
     _a  :       int             =	nn.Parameter(torch.zeros(self.n_clusters							,						self.d_embed							)							)
     _a  :       Dict             =	nn.Parameter(torch.zeros(self.n_clusters							)							)

   _a  :       Optional[Any]             =	nn.ModuleList()
   _a  :       str             =	nn.ParameterList()

   if div_val == 1:
     for i in range(len(self.cutoffs							)							):
       if d_proj != d_embed:
         self.out_projs.append(nn.Parameter(torch.FloatTensor(UpperCAmelCase__							,						UpperCAmelCase__							)							)							)
       else:
         self.out_projs.append(UpperCAmelCase__							)

     self.out_layers.append(nn.Linear(UpperCAmelCase__							,						UpperCAmelCase__							)							)
   else:
     for i in range(len(self.cutoffs							)							):
       _a      ,  _a  :       Union[str, Any]             =	self.cutoff_ends[i], self.cutoff_ends[i + 1]
       _a  :       Optional[Any]             =	d_embed // (div_val**i)

       self.out_projs.append(nn.Parameter(torch.FloatTensor(UpperCAmelCase__							,						UpperCAmelCase__							)							)							)

       self.out_layers.append(nn.Linear(UpperCAmelCase__							,						r_idx - l_idx							)							)

   _a  :       List[Any]             =	keep_order


 def _lowercase	(     self		:						Tuple							,						UpperCAmelCase__		:						Optional[int]							,						UpperCAmelCase__		:						Optional[Any]							,						UpperCAmelCase__		:						Optional[Any]							,						UpperCAmelCase__		:						List[Any]							)					->       List[str]:
   if proj is None:
     _a  :       Optional[Any]             =	nn.functional.linear(UpperCAmelCase__							,						UpperCAmelCase__							,						bias=UpperCAmelCase__							)
   else:
     # if CUDA_MAJOR <= 9 and CUDA_MINOR <= 1:
     _a  :       str             =	nn.functional.linear(UpperCAmelCase__							,						proj.t().contiguous()							)
     _a  :       Tuple             =	nn.functional.linear(UpperCAmelCase__							,						UpperCAmelCase__							,						bias=UpperCAmelCase__							)
     # else:
     #     logit = torch.einsum('bd,de,ev->bv', (hidden, proj, weight.t()))
     #     if bias is not None:
     #         logit = logit + bias

   return logit


 def _lowercase	(     self		:						Optional[int]							,						UpperCAmelCase__		:						Union[str, Any]							,						UpperCAmelCase__		:						Dict=None							,						UpperCAmelCase__		:						Optional[Any]=False							)					->       Dict:

   if labels is not None:
     # Shift so that tokens < n predict n
     _a  :       Dict             =	hidden[..., :-1, :].contiguous()
     _a  :       Dict             =	labels[..., 1:].contiguous()
     _a  :       Optional[Any]             =	hidden.view(-1							,						hidden.size(-1							)							)
     _a  :       Union[str, Any]             =	labels.view(-1							)
     if hidden.size(0							) != labels.size(0							):
       raise RuntimeError("""Input and labels should have the same size in the batch dimension."""							)
   else:
     _a  :       Optional[int]             =	hidden.view(-1							,						hidden.size(-1							)							)

   if self.n_clusters == 0:
     _a  :       Any             =	self._compute_logit(UpperCAmelCase__							,						self.out_layers[0].weight							,						self.out_layers[0].bias							,						self.out_projs[0]							)
     if labels is not None:
       _a  :       Dict             =	labels != -100
       _a  :       Tuple             =	torch.zeros_like(UpperCAmelCase__							,						dtype=hidden.dtype							,						device=hidden.device							)
       _a  :       List[Any]             =	(
           -nn.functional.log_softmax(UpperCAmelCase__							,						dim=-1							)[mask].gather(1							,						labels[mask].unsqueeze(1							)							).squeeze(1							)
       )
     else:
       _a  :       Tuple             =	nn.functional.log_softmax(UpperCAmelCase__							,						dim=-1							)
   else:
     # construct weights and biases
     _a      ,  _a  :       Dict             =	[], []
     for i in range(len(self.cutoffs							)							):
       if self.div_val == 1:
         _a      ,  _a  :       Optional[Any]             =	self.cutoff_ends[i], self.cutoff_ends[i + 1]
         _a  :       Tuple             =	self.out_layers[0].weight[l_idx:r_idx]
         _a  :       Any             =	self.out_layers[0].bias[l_idx:r_idx]
       else:
         _a  :       Tuple             =	self.out_layers[i].weight
         _a  :       Dict             =	self.out_layers[i].bias

       if i == 0:
         _a  :       Dict             =	torch.cat([weight_i, self.cluster_weight]							,						dim=0							)
         _a  :       List[Any]             =	torch.cat([bias_i, self.cluster_bias]							,						dim=0							)

       weights.append(UpperCAmelCase__							)
       biases.append(UpperCAmelCase__							)

     _a      ,  _a      ,  _a  :       List[Any]             =	weights[0], biases[0], self.out_projs[0]

     _a  :       Optional[int]             =	self._compute_logit(UpperCAmelCase__							,						UpperCAmelCase__							,						UpperCAmelCase__							,						UpperCAmelCase__							)
     _a  :       str             =	nn.functional.log_softmax(UpperCAmelCase__							,						dim=1							)

     if labels is None:
       _a  :       int             =	hidden.new_empty((head_logit.size(0							), self.n_token)							)
     else:
       _a  :       List[Any]             =	torch.zeros_like(UpperCAmelCase__							,						dtype=hidden.dtype							,						device=hidden.device							)

     _a  :       List[Any]             =	0
     _a  :       Any             =	[0] + self.cutoffs
     for i in range(len(UpperCAmelCase__							) - 1							):
       _a      ,  _a  :       Tuple             =	cutoff_values[i], cutoff_values[i + 1]

       if labels is not None:
         _a  :       List[str]             =	(labels >= l_idx) & (labels < r_idx)
         _a  :       List[str]             =	mask_i.nonzero().squeeze()

         if indices_i.numel() == 0:
           continue

         _a  :       Optional[Any]             =	labels.index_select(0							,						UpperCAmelCase__							) - l_idx
         _a  :       str             =	head_logprob.index_select(0							,						UpperCAmelCase__							)
         _a  :       Dict             =	hidden.index_select(0							,						UpperCAmelCase__							)
       else:
         _a  :       Tuple             =	hidden

       if i == 0:
         if labels is not None:
           _a  :       Optional[int]             =	head_logprob_i.gather(1							,						target_i[:, None]							).squeeze(1							)
         else:
           _a  :       Optional[Any]             =	head_logprob[:, : self.cutoffs[0]]
       else:
         _a      ,  _a      ,  _a  :       int             =	weights[i], biases[i], self.out_projs[i]

         _a  :       Optional[int]             =	self._compute_logit(UpperCAmelCase__							,						UpperCAmelCase__							,						UpperCAmelCase__							,						UpperCAmelCase__							)
         _a  :       Any             =	nn.functional.log_softmax(UpperCAmelCase__							,						dim=1							)
         _a  :       Optional[int]             =	self.cutoffs[0] + i - 1  # No probability for the head cluster
         if labels is not None:
           _a  :       Optional[int]             =	head_logprob_i[:, cluster_prob_idx] + tail_logprob_i.gather(
               1							,						target_i[:, None]							).squeeze(1							)
         else:
           _a  :       str             =	head_logprob[:, cluster_prob_idx, None] + tail_logprob_i
           _a  :       Tuple             =	logprob_i

       if labels is not None:
         if (hasattr(self							,						"""keep_order"""							) and self.keep_order) or keep_order:
           out.index_copy_(0							,						UpperCAmelCase__							,						-logprob_i							)
         else:
           out[offset : offset + logprob_i.size(0							)].copy_(-logprob_i							)
         offset += logprob_i.size(0							)

   return out







 def _lowercase	(     self		:						int							,						UpperCAmelCase__		:						Tuple							)					->       int:
   if self.n_clusters == 0:
     _a  :       Tuple             =	self._compute_logit(UpperCAmelCase__							,						self.out_layers[0].weight							,						self.out_layers[0].bias							,						self.out_projs[0]							)
     return nn.functional.log_softmax(UpperCAmelCase__							,						dim=-1							)
   else:
     # construct weights and biases
     _a      ,  _a  :       List[str]             =	[], []
     for i in range(len(self.cutoffs							)							):
       if self.div_val == 1:
         _a      ,  _a  :       List[str]             =	self.cutoff_ends[i], self.cutoff_ends[i + 1]
         _a  :       Optional[int]             =	self.out_layers[0].weight[l_idx:r_idx]
         _a  :       Any             =	self.out_layers[0].bias[l_idx:r_idx]
       else:
         _a  :       Optional[int]             =	self.out_layers[i].weight
         _a  :       Optional[int]             =	self.out_layers[i].bias

       if i == 0:
         _a  :       List[str]             =	torch.cat([weight_i, self.cluster_weight]							,						dim=0							)
         _a  :       Dict             =	torch.cat([bias_i, self.cluster_bias]							,						dim=0							)

       weights.append(UpperCAmelCase__							)
       biases.append(UpperCAmelCase__							)

     _a      ,  _a      ,  _a  :       Tuple             =	weights[0], biases[0], self.out_projs[0]
     _a  :       Dict             =	self._compute_logit(UpperCAmelCase__							,						UpperCAmelCase__							,						UpperCAmelCase__							,						UpperCAmelCase__							)

     _a  :       Union[str, Any]             =	hidden.new_empty((head_logit.size(0							), self.n_token)							)
     _a  :       Optional[Any]             =	nn.functional.log_softmax(UpperCAmelCase__							,						dim=1							)

     _a  :       Optional[int]             =	[0] + self.cutoffs
     for i in range(len(UpperCAmelCase__							) - 1							):
       _a      ,  _a  :       Tuple             =	cutoff_values[i], cutoff_values[i + 1]

       if i == 0:
         _a  :       Any             =	head_logprob[:, : self.cutoffs[0]]
       else:
         _a      ,  _a      ,  _a  :       Optional[Any]             =	weights[i], biases[i], self.out_projs[i]

         _a  :       Union[str, Any]             =	self._compute_logit(UpperCAmelCase__							,						UpperCAmelCase__							,						UpperCAmelCase__							,						UpperCAmelCase__							)
         _a  :       Dict             =	nn.functional.log_softmax(UpperCAmelCase__							,						dim=1							)

         _a  :       List[Any]             =	head_logprob[:, -i] + tail_logprob_i
         _a  :       Optional[Any]             =	logprob_i

     return out









"""simple docstring"""




import unittest

import numpy as np

def 			lowerCAmelCase__     (     UpperCamelCase__     ,   UpperCamelCase__     ,   UpperCamelCase__     ,   UpperCamelCase__ = None     ,   ):



  '''simple docstring'''
  _a  :       List[Any]             =	np.shape(UpperCamelCase__				)
  _a  :       Any             =	np.shape(UpperCamelCase__				)
  _a  :       Union[str, Any]             =	np.shape(UpperCamelCase__				)

  if shape_a[0] != shape_b[0]:
    _a  :       int             =	(
        """Expected the same number of rows for A and B. """
        F"""Instead found A of size {shape_a} and B of size {shape_b}"""
    )
    raise ValueError(UpperCamelCase__				)

  if shape_b[1] != shape_c[1]:
    _a  :       Tuple             =	(
        """Expected the same number of columns for B and C. """
        F"""Instead found B of size {shape_b} and C of size {shape_c}"""
    )
    raise ValueError(UpperCamelCase__				)

  _a  :       int             =	pseudo_inv
  if a_inv is None:
    try:
      _a  :       Optional[int]             =	np.linalg.inv(UpperCamelCase__				)
    except np.linalg.LinAlgError:
      raise ValueError(
          """Input matrix A is not invertible. Cannot compute Schur complement."""				)

  return mat_c - mat_b.T @ a_inv @ mat_b






class        UpperCamelCase			(	unittest.TestCase      ):


 def _lowercase	(     self		:						int							)					->       None:
   _a  :       str             =	np.array([[1, 2, 1], [2, 1, 2], [3, 2, 4]]							)
   _a  :       Tuple             =	np.array([[0, 3], [3, 0], [2, 3]]							)
   _a  :       Optional[int]             =	np.array([[2, 1], [6, 3]]							)

   _a  :       Optional[Any]             =	schur_complement(UpperCAmelCase__							,						UpperCAmelCase__							,						UpperCAmelCase__							)

   _a  :       Union[str, Any]             =	np.block([[a, b], [b.T, c]]							)

   _a  :       int             =	np.linalg.det(UpperCAmelCase__							)
   _a  :       Union[str, Any]             =	np.linalg.det(UpperCAmelCase__							)
   _a  :       List[Any]             =	np.linalg.det(UpperCAmelCase__							)

   self.assertAlmostEqual(UpperCAmelCase__							,						det_a * det_s							)


 def _lowercase	(     self		:						int							)					->       None:
   _a  :       Optional[int]             =	np.array([[1, 2, 1], [2, 1, 2], [3, 2, 4]]							)
   _a  :       Optional[int]             =	np.array([[0, 3], [3, 0], [2, 3]]							)
   _a  :       Union[str, Any]             =	np.array([[2, 1], [6, 3]]							)

   with self.assertRaises(UpperCAmelCase__							):
     schur_complement(UpperCAmelCase__							,						UpperCAmelCase__							,						UpperCAmelCase__							)







 def _lowercase	(     self		:						List[Any]							)					->       None:
   _a  :       Any             =	np.array([[1, 2, 1], [2, 1, 2], [3, 2, 4]]							)
   _a  :       Dict             =	np.array([[0, 3], [3, 0], [2, 3]]							)
   _a  :       List[Any]             =	np.array([[2, 1, 3], [6, 3, 5]]							)

   with self.assertRaises(UpperCAmelCase__							):
     schur_complement(UpperCAmelCase__							,						UpperCAmelCase__							,						UpperCAmelCase__							)


if __name__ == "__main__":
 import doctest

 doctest.testmod()
 unittest.main()

