
import torch
from torch import nn







class        lowerCAmelCase__      (   nn.Module	):

						def __init__(			self       ,							a       ,							a       ,							a       ,							a       ,							a=1       ,							a=False				)					->      Tuple:


								'''simple docstring'''

								super().__init__()

								_UpperCamelCase						    =	n_token
								_UpperCamelCase						    =	d_embed
								_UpperCamelCase						    =	d_proj

								_UpperCamelCase						    =	cutoffs + [n_token]
								_UpperCamelCase						    =	[0] + self.cutoffs
								_UpperCamelCase						    =	div_val

								_UpperCamelCase						    =	self.cutoffs[0]
								_UpperCamelCase						    =	len(self.cutoffs				) - 1
								_UpperCamelCase						    =	self.shortlist_size + self.n_clusters

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

								_UpperCamelCase						    =	nn.ModuleList()
								_UpperCamelCase						    =	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(a       ,							a				)				)				)
												else:
														self.out_projs.append(a				)

										self.out_layers.append(nn.Linear(a       ,							a				)				)
								else:
										for i in range(len(self.cutoffs				)				):
												_UpperCamelCase    ,	_UpperCamelCase						    =	self.cutoff_ends[i], self.cutoff_ends[i + 1]
												_UpperCamelCase						    =	d_embed // (div_val**i)

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

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

								_UpperCamelCase						    =	keep_order

						def  A_				(			self       ,							a       ,							a       ,							a       ,							a				)					->      Optional[Any]:


								'''simple docstring'''

								if proj is None:
										_UpperCamelCase						    =	nn.functional.linear(a       ,							a       ,							bias=a				)
								else:
										# if CUDA_MAJOR <= 9 and CUDA_MINOR <= 1:
										_UpperCamelCase						    =	nn.functional.linear(a       ,							proj.t().contiguous()				)
										_UpperCamelCase						    =	nn.functional.linear(a       ,							a       ,							bias=a				)
										# else:
										#     logit = torch.einsum('bd,de,ev->bv', (hidden, proj, weight.t()))
										#     if bias is not None:
										#         logit = logit + bias

								return logit

						def  A_				(			self       ,							a       ,							a=None       ,							a=False				)					->      Tuple:


								'''simple docstring'''

								if labels is not None:
										# Shift so that tokens < n predict n
										_UpperCamelCase						    =	hidden[..., :-1, :].contiguous()
										_UpperCamelCase						    =	labels[..., 1:].contiguous()
										_UpperCamelCase						    =	hidden.view(-1       ,							hidden.size(-1				)				)
										_UpperCamelCase						    =	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:
										_UpperCamelCase						    =	hidden.view(-1       ,							hidden.size(-1				)				)

								if self.n_clusters == 0:
										_UpperCamelCase						    =	self._compute_logit(a       ,							self.out_layers[0].weight       ,							self.out_layers[0].bias       ,							self.out_projs[0]				)
										if labels is not None:
												_UpperCamelCase						    =	labels != -1_00
												_UpperCamelCase						    =	torch.zeros_like(a       ,							dtype=hidden.dtype       ,							device=hidden.device				)
												_UpperCamelCase						    =	(
												    -nn.functional.log_softmax(a       ,							dim=-1				)[mask].gather(1       ,							labels[mask].unsqueeze(1				)				).squeeze(1				)
												)
										else:
												_UpperCamelCase						    =	nn.functional.log_softmax(a       ,							dim=-1				)
								else:
										# construct weights and biases
										_UpperCamelCase    ,	_UpperCamelCase						    =	[], []
										for i in range(len(self.cutoffs				)				):
												if self.div_val == 1:
														_UpperCamelCase    ,	_UpperCamelCase						    =	self.cutoff_ends[i], self.cutoff_ends[i + 1]
														_UpperCamelCase						    =	self.out_layers[0].weight[l_idx:r_idx]
														_UpperCamelCase						    =	self.out_layers[0].bias[l_idx:r_idx]
												else:
														_UpperCamelCase						    =	self.out_layers[i].weight
														_UpperCamelCase						    =	self.out_layers[i].bias

												if i == 0:
														_UpperCamelCase						    =	torch.cat([weight_i, self.cluster_weight]       ,							dim=0				)
														_UpperCamelCase						    =	torch.cat([bias_i, self.cluster_bias]       ,							dim=0				)

												weights.append(a				)
												biases.append(a				)

										_UpperCamelCase    ,	_UpperCamelCase    ,	_UpperCamelCase						    =	weights[0], biases[0], self.out_projs[0]

										_UpperCamelCase						    =	self._compute_logit(a       ,							a       ,							a       ,							a				)
										_UpperCamelCase						    =	nn.functional.log_softmax(a       ,							dim=1				)

										if labels is None:
												_UpperCamelCase						    =	hidden.new_empty((head_logit.size(0				), self.n_token)				)
										else:
												_UpperCamelCase						    =	torch.zeros_like(a       ,							dtype=hidden.dtype       ,							device=hidden.device				)

										_UpperCamelCase						    =	0
										_UpperCamelCase						    =	[0] + self.cutoffs
										for i in range(len(a				) - 1				):
												_UpperCamelCase    ,	_UpperCamelCase						    =	cutoff_values[i], cutoff_values[i + 1]

												if labels is not None:
														_UpperCamelCase						    =	(labels >= l_idx) & (labels < r_idx)
														_UpperCamelCase						    =	mask_i.nonzero().squeeze()

														if indices_i.numel() == 0:
																continue

														_UpperCamelCase						    =	labels.index_select(0       ,							a				) - l_idx
														_UpperCamelCase						    =	head_logprob.index_select(0       ,							a				)
														_UpperCamelCase						    =	hidden.index_select(0       ,							a				)
												else:
														_UpperCamelCase						    =	hidden

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

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

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

								return out







						def  A_				(			self       ,							a				)					->      Optional[int]:


								'''simple docstring'''

								if self.n_clusters == 0:
										_UpperCamelCase						    =	self._compute_logit(a       ,							self.out_layers[0].weight       ,							self.out_layers[0].bias       ,							self.out_projs[0]				)
										return nn.functional.log_softmax(a       ,							dim=-1				)
								else:
										# construct weights and biases
										_UpperCamelCase    ,	_UpperCamelCase						    =	[], []
										for i in range(len(self.cutoffs				)				):
												if self.div_val == 1:
														_UpperCamelCase    ,	_UpperCamelCase						    =	self.cutoff_ends[i], self.cutoff_ends[i + 1]
														_UpperCamelCase						    =	self.out_layers[0].weight[l_idx:r_idx]
														_UpperCamelCase						    =	self.out_layers[0].bias[l_idx:r_idx]
												else:
														_UpperCamelCase						    =	self.out_layers[i].weight
														_UpperCamelCase						    =	self.out_layers[i].bias

												if i == 0:
														_UpperCamelCase						    =	torch.cat([weight_i, self.cluster_weight]       ,							dim=0				)
														_UpperCamelCase						    =	torch.cat([bias_i, self.cluster_bias]       ,							dim=0				)

												weights.append(a				)
												biases.append(a				)

										_UpperCamelCase    ,	_UpperCamelCase    ,	_UpperCamelCase						    =	weights[0], biases[0], self.out_projs[0]
										_UpperCamelCase						    =	self._compute_logit(a       ,							a       ,							a       ,							a				)

										_UpperCamelCase						    =	hidden.new_empty((head_logit.size(0				), self.n_token)				)
										_UpperCamelCase						    =	nn.functional.log_softmax(a       ,							dim=1				)

										_UpperCamelCase						    =	[0] + self.cutoffs
										for i in range(len(a				) - 1				):
												_UpperCamelCase    ,	_UpperCamelCase						    =	cutoff_values[i], cutoff_values[i + 1]

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

														_UpperCamelCase						    =	self._compute_logit(a       ,							a       ,							a       ,							a				)
														_UpperCamelCase						    =	nn.functional.log_softmax(a       ,							dim=1				)

														_UpperCamelCase						    =	head_logprob[:, -i] + tail_logprob_i
														_UpperCamelCase						    =	logprob_i

										return out





def 							__A(lowerCAmelCase						,  lowerCAmelCase )		->				tuple[float, float]:

		"""simple docstring"""






		if not len(lowerCAmelCase ) == len(lowerCAmelCase ) == 3:
				raise ValueError("""Please enter a valid equation.""" )
		if equationa[0] == equationa[1] == equationa[0] == equationa[1] == 0:
				raise ValueError("""Both a & b of two equations can't be zero.""" )

		# Extract the coefficients
		_UpperCamelCase    ,	_UpperCamelCase    ,	_UpperCamelCase						    =	equationa
		_UpperCamelCase    ,	_UpperCamelCase    ,	_UpperCamelCase						    =	equationa

		# Calculate the determinants of the matrices
		_UpperCamelCase						    =	aa * ba - aa * ba
		_UpperCamelCase						    =	ca * ba - ca * ba
		_UpperCamelCase						    =	aa * ca - aa * ca

		# Check if the system of linear equations has a solution (using Cramer's rule)
		if determinant == 0:
				if determinant_x == determinant_y == 0:
						raise ValueError("""Infinite solutions. (Consistent system)""" )
				else:
						raise ValueError("""No solution. (Inconsistent system)""" )
		else:
				if determinant_x == determinant_y == 0:
						# Trivial solution (Inconsistent system)
						return (0.0, 0.0)
				else:
						_UpperCamelCase						    =	determinant_x / determinant
						_UpperCamelCase						    =	determinant_y / determinant
						# Non-Trivial Solution (Consistent system)
						return (x, y)



