


'''simple docstring'''




import tensorflow as tf

from ...tf_utils import shape_list



class  lowerCAmelCase				(				tf.keras.layers.Layer							):



	def __init__(					self ,					snake_case__ ,					snake_case__ ,					snake_case__ ,					snake_case__ ,					snake_case__=1 ,					snake_case__=False ,					**snake_case__    ):
		super().__init__(**_snake_case    )

		lowerCAmelCase					:    List[Any]      							= vocab_size
		lowerCAmelCase					:    Any      							= d_embed
		lowerCAmelCase					:    Union[str, Any]      							= d_proj

		lowerCAmelCase					:    Optional[int]      							= cutoffs + [vocab_size]
		lowerCAmelCase					:    Optional[int]      							= [0] + self.cutoffs
		lowerCAmelCase					:    Optional[int]      							= div_val

		lowerCAmelCase					:    Any      							= self.cutoffs[0]
		lowerCAmelCase					:    Union[str, Any]      							= len(self.cutoffs    ) - 1
		lowerCAmelCase					:    Any      							= self.shortlist_size + self.n_clusters
		lowerCAmelCase					:    List[str]      							= keep_order

		lowerCAmelCase					:    Dict      							= []
		lowerCAmelCase					:    Dict      							= []



	def 				lowercase     (					self ,					snake_case__    ):


		if self.n_clusters > 0:
			lowerCAmelCase					:    List[Any]      							= self.add_weight(
			    shape=(self.n_clusters, self.d_embed) ,					initializer='zeros' ,					trainable=_snake_case ,					name='cluster_weight'    )
			lowerCAmelCase					:    Optional[Any]      							= self.add_weight(
			    shape=(self.n_clusters,) ,					initializer='zeros' ,					trainable=_snake_case ,					name='cluster_bias'    )

		if self.div_val == 1:
			for i in range(len(self.cutoffs    )    ):
				if self.d_proj != self.d_embed:
					lowerCAmelCase					:    Dict      							= self.add_weight(
					    shape=(self.d_embed, self.d_proj) ,					initializer='zeros' ,					trainable=_snake_case ,					name=f"out_projs_._{i}" ,					)
					self.out_projs.append(_snake_case    )
				else:
					self.out_projs.append(_snake_case    )
				lowerCAmelCase					:    List[Any]      							= self.add_weight(
				    shape=(self.vocab_size, self.d_embed) ,					initializer='zeros' ,					trainable=_snake_case ,					name=f"out_layers_._{i}_._weight" ,					)
				lowerCAmelCase					:    Optional[Any]      							= self.add_weight(
				    shape=(self.vocab_size,) ,					initializer='zeros' ,					trainable=_snake_case ,					name=f"out_layers_._{i}_._bias" ,					)
				self.out_layers.append((weight, bias)    )
		else:
			for i in range(len(self.cutoffs    )    ):
				lowerCAmelCase							,   lowerCAmelCase					:    Optional[Any]      							= self.cutoff_ends[i], self.cutoff_ends[i + 1]
				lowerCAmelCase					:    Union[str, Any]      							= self.d_embed // (self.div_val**i)

				lowerCAmelCase					:    str      							= self.add_weight(
				    shape=(d_emb_i, self.d_proj) ,					initializer='zeros' ,					trainable=_snake_case ,					name=f"out_projs_._{i}"    )
				self.out_projs.append(_snake_case    )
				lowerCAmelCase					:    Tuple      							= self.add_weight(
				    shape=(r_idx - l_idx, d_emb_i) ,					initializer='zeros' ,					trainable=_snake_case ,					name=f"out_layers_._{i}_._weight" ,					)
				lowerCAmelCase					:    Optional[int]      							= self.add_weight(
				    shape=(r_idx - l_idx,) ,					initializer='zeros' ,					trainable=_snake_case ,					name=f"out_layers_._{i}_._bias" ,					)
				self.out_layers.append((weight, bias)    )
		super().build(_snake_case    )



	@staticmethod
	def 				lowercase     (					snake_case__ ,					snake_case__ ,					snake_case__ ,					snake_case__=None    ):
		lowerCAmelCase					:    Dict      							= x
		if proj is not None:
			lowerCAmelCase					:    Optional[Any]      							= tf.einsum('ibd,ed->ibe' ,					_snake_case ,					_snake_case    )
		return tf.einsum('ibd,nd->ibn' ,					_snake_case ,					_snake_case    ) + b



	@staticmethod
	def 				lowercase     (					snake_case__ ,					snake_case__    ):
		lowerCAmelCase					:    List[Any]      							= shape_list(_snake_case    )
		lowerCAmelCase					:    Any      							= tf.range(lp_size[0] ,					dtype=target.dtype    )
		lowerCAmelCase					:    Optional[int]      							= tf.stack([r, target] ,					1    )
		return tf.gather_nd(_snake_case ,					_snake_case    )



	def 				lowercase     (					self ,					snake_case__ ,					snake_case__ ,					snake_case__=True ,					snake_case__=False    ):
		lowerCAmelCase					:    Any      							= 0
		if self.n_clusters == 0:
			lowerCAmelCase					:    List[str]      							= self._logit(_snake_case ,					self.out_layers[0][0] ,					self.out_layers[0][1] ,					self.out_projs[0]    )
			if target is not None:
				lowerCAmelCase					:    Optional[int]      							= tf.nn.sparse_softmax_cross_entropy_with_logits(labels=_snake_case ,					logits=_snake_case    )
			lowerCAmelCase					:    Any      							= tf.nn.log_softmax(_snake_case ,					axis=-1    )
		else:
			lowerCAmelCase					:    Optional[int]      							= shape_list(_snake_case    )
			lowerCAmelCase					:    Optional[Any]      							= []
			lowerCAmelCase					:    Any      							= tf.zeros(hidden_sizes[:2]    )
			for i in range(len(self.cutoffs    )    ):
				lowerCAmelCase							,   lowerCAmelCase					:    Any      							= self.cutoff_ends[i], self.cutoff_ends[i + 1]
				if target is not None:
					lowerCAmelCase					:    Any      							= (target >= l_idx) & (target < r_idx)
					lowerCAmelCase					:    Union[str, Any]      							= tf.where(_snake_case    )
					lowerCAmelCase					:    Any      							= tf.boolean_mask(_snake_case ,					_snake_case    ) - l_idx

				if self.div_val == 1:
					lowerCAmelCase					:    int      							= self.out_layers[0][0][l_idx:r_idx]
					lowerCAmelCase					:    List[str]      							= self.out_layers[0][1][l_idx:r_idx]
				else:
					lowerCAmelCase					:    Dict      							= self.out_layers[i][0]
					lowerCAmelCase					:    Any      							= self.out_layers[i][1]

				if i == 0:
					lowerCAmelCase					:    Union[str, Any]      							= tf.concat([cur_W, self.cluster_weight] ,					0    )
					lowerCAmelCase					:    Union[str, Any]      							= tf.concat([cur_b, self.cluster_bias] ,					0    )

					lowerCAmelCase					:    str      							= self._logit(_snake_case ,					_snake_case ,					_snake_case ,					self.out_projs[0]    )
					lowerCAmelCase					:    Dict      							= tf.nn.log_softmax(_snake_case    )
					out.append(head_logprob[..., : self.cutoffs[0]]    )
					if target is not None:
						lowerCAmelCase					:    List[Any]      							= tf.boolean_mask(_snake_case ,					_snake_case    )
						lowerCAmelCase					:    int      							= self._gather_logprob(_snake_case ,					_snake_case    )
				else:
					lowerCAmelCase					:    Any      							= self._logit(_snake_case ,					_snake_case ,					_snake_case ,					self.out_projs[i]    )
					lowerCAmelCase					:    Optional[Any]      							= tf.nn.log_softmax(_snake_case    )
					lowerCAmelCase					:    int      							= self.cutoffs[0] + i - 1  # No probability for the head cluster
					lowerCAmelCase					:    Dict      							= head_logprob[..., cluster_prob_idx, None] + tail_logprob
					out.append(_snake_case    )
					if target is not None:
						lowerCAmelCase					:    Union[str, Any]      							= tf.boolean_mask(_snake_case ,					_snake_case    )
						lowerCAmelCase					:    Dict      							= tf.boolean_mask(_snake_case ,					_snake_case    )
						lowerCAmelCase					:    Optional[int]      							= self._gather_logprob(_snake_case ,					_snake_case    )
						cur_logprob += cur_head_logprob[:, self.cutoff_ends[1] + i - 1]
				if target is not None:
					loss += tf.scatter_nd(_snake_case ,					-cur_logprob ,					shape_list(_snake_case    )    )
			lowerCAmelCase					:    int      							= tf.concat(_snake_case ,					axis=-1    )

		if target is not None:
			if return_mean:
				lowerCAmelCase					:    Union[str, Any]      							= tf.reduce_mean(_snake_case    )
			# Add the training-time loss value to the layer using `self.add_loss()`.
			self.add_loss(_snake_case    )

			# Log the loss as a metric (we could log arbitrary metrics,
			# including different metrics for training and inference.
			self.add_metric(_snake_case ,					name=self.name ,					aggregation='mean' if return_mean else ''    )

		return out



'''simple docstring'''




import math

def 			__UpperCamelCase    (    _A    :				int = 1_00				)    ->      int:




	"""simple docstring"""





	lowerCAmelCase					:    List[Any]      							= sum(i * i for i in range(1					,   n + 1				)				)
	lowerCAmelCase					:    Optional[Any]      							= int(math.pow(sum(range(1					,   n + 1				)				)					,   2				)				)
	return square_of_sum - sum_of_squares


if __name__ == "__main__":
				print(f"""{solution() = }""")
