
import tensorflow as tf

from ...tf_utils import shape_list

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






			'''simple docstring'''

			def __init__(       self :       Any						,	snake_case_ :       int						,	snake_case_ :       Any						,	snake_case_ :       Dict						,	snake_case_ :       Any						,	snake_case_ :       int=1						,	snake_case_ :       Dict=False						,	**snake_case_ :       str      ):
							super().__init__(**snake_case_      )

							UpperCamelCase_:							int	=						vocab_size
							UpperCamelCase_:							List[Any]	=						d_embed
							UpperCamelCase_:							Any	=						d_proj

							UpperCamelCase_:							Any	=						cutoffs + [vocab_size]
							UpperCamelCase_:							Any	=						[0] + self.cutoffs
							UpperCamelCase_:							List[Any]	=						div_val

							UpperCamelCase_:							Tuple	=						self.cutoffs[0]
							UpperCamelCase_:							Tuple	=						len(self.cutoffs      ) - 1
							UpperCamelCase_:							Dict	=						self.shortlist_size + self.n_clusters
							UpperCamelCase_:							int	=						keep_order

							UpperCamelCase_:							Dict	=						[]
							UpperCamelCase_:							Tuple	=						[]

			def       lowerCAmelCase__	(       self :       int						,	snake_case_ :       Optional[Any]      ):
							if self.n_clusters > 0:
											UpperCamelCase_:							Dict	=						self.add_weight(
											    shape=(self.n_clusters, self.d_embed)						,	initializer="""zeros"""						,	trainable=snake_case_						,	name="""cluster_weight"""      )
											UpperCamelCase_:							Union[str, 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:
																			UpperCamelCase_:							Optional[int]	=						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_      )
															UpperCamelCase_:							Tuple	=						self.add_weight(
															    shape=(self.vocab_size, self.d_embed)						,	initializer="""zeros"""						,	trainable=snake_case_						,	name=f'''out_layers_._{i}_._weight'''						,	)
															UpperCamelCase_:							int	=						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      )      ):
															UpperCamelCase_:							List[str]	=						self.cutoff_ends[i], self.cutoff_ends[i + 1]
															UpperCamelCase_:							str	=						self.d_embed // (self.div_val**i)

															UpperCamelCase_:							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_      )
															UpperCamelCase_:							List[str]	=						self.add_weight(
															    shape=(r_idx - l_idx, d_emb_i)						,	initializer="""zeros"""						,	trainable=snake_case_						,	name=f'''out_layers_._{i}_._weight'''						,	)
															UpperCamelCase_:							str	=						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       lowerCAmelCase__	(       snake_case_ :       Tuple						,	snake_case_ :       Dict						,	snake_case_ :       Union[str, Any]						,	snake_case_ :       str=None      ):
							UpperCamelCase_:							Optional[int]	=						x
							if proj is not None:
											UpperCamelCase_:							Optional[Any]	=						tf.einsum("""ibd,ed->ibe"""						,	snake_case_						,	snake_case_      )
							return tf.einsum("""ibd,nd->ibn"""						,	snake_case_						,	snake_case_      ) + b

			@staticmethod
			def       lowerCAmelCase__	(       snake_case_ :       Any						,	snake_case_ :       List[str]      ):
							UpperCamelCase_:							str	=						shape_list(snake_case_      )
							UpperCamelCase_:							Optional[int]	=						tf.range(lp_size[0]						,	dtype=target.dtype      )
							UpperCamelCase_:							Dict	=						tf.stack([r, target]						,	1      )
							return tf.gather_nd(snake_case_						,	snake_case_      )




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

															if self.div_val == 1:
																			UpperCamelCase_:							str	=						self.out_layers[0][0][l_idx:r_idx]
																			UpperCamelCase_:							Optional[Any]	=						self.out_layers[0][1][l_idx:r_idx]
															else:
																			UpperCamelCase_:							Union[str, Any]	=						self.out_layers[i][0]
																			UpperCamelCase_:							Dict	=						self.out_layers[i][1]

															if i == 0:
																			UpperCamelCase_:							Tuple	=						tf.concat([cur_W, self.cluster_weight]						,	0      )
																			UpperCamelCase_:							int	=						tf.concat([cur_b, self.cluster_bias]						,	0      )

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

							if target is not None:
											if return_mean:
															UpperCamelCase_:							Optional[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






from sympy import diff, lambdify, symbols
from sympy.functions import *  # noqa: F403







def        A__					(						lowerCamelCase     ,    lowerCamelCase     ,    lowerCamelCase = "x"     ,    lowerCamelCase = 10**-10     ,    lowerCamelCase = 1     ,    )  ->	complex:
				UpperCamelCase_:							Optional[Any]	=						symbols(lowerCamelCase						)
				UpperCamelCase_:							int	=						lambdify(lowerCamelCase     ,    lowerCamelCase						)
				UpperCamelCase_:							Optional[Any]	=						lambdify(lowerCamelCase     ,    diff(lowerCamelCase     ,    lowerCamelCase						)						)

				UpperCamelCase_:							Tuple	=						starting_point

				while True:
								if diff_function(lowerCamelCase						) != 0:
												UpperCamelCase_:							List[Any]	=						prev_guess - multiplicity * func(lowerCamelCase						) / diff_function(
												    lowerCamelCase						)
								else:
												raise ZeroDivisionError("""Could not find root"""						) from None

								# Precision is checked by comparing the difference of consecutive guesses
								if abs(next_guess - prev_guess						) < precision:
												return next_guess

								UpperCamelCase_:							Any	=						next_guess


# Let's Execute
if __name__ == "__main__":
							# Find root of trigonometric function
							# Find value of pi
							print(F"""The root of sin(x) = 0 is {newton_raphson('sin(x)', 2)}""")

							# Find root of polynomial
							# Find fourth Root of 5
							print(F"""The root of x**4 - 5 = 0 is {newton_raphson('x**4 -5', 0.4 +5J)}""")

							# Find value of e
							print(
							    """The root of log(y) - 1 = 0 is """,
							    F"""{newton_raphson('log(y) - 1', 2, variable='y')}""",
							)

							# Exponential Roots
							print(
							    """The root of exp(x) - 1 = 0 is""",
							    F"""{newton_raphson('exp(x) - 1', 10, precision=0.005)}""",
							)

							# Find root of cos(x)
							print(F"""The root of cos(x) = 0 is {newton_raphson('cos(x)', 0)}""")






