



from collections import OrderedDict
from typing import Any, Mapping, Optional

from ... import PreTrainedTokenizer
from ...configuration_utils import PretrainedConfig
from ...file_utils import TensorType, is_torch_available
from ...onnx import OnnxConfig, OnnxConfigWithPast, OnnxSeqaSeqConfigWithPast
from ...onnx.utils import compute_effective_axis_dimension
from ...utils import logging


A__    :    Any        =   logging.get_logger(__name__)

A__    :    str        =   {
    '''facebook/blenderbot_small-90M''': '''https://huggingface.co/facebook/blenderbot_small-90M/resolve/main/config.json''',
    # See all BlenderbotSmall models at https://huggingface.co/models?filter=blenderbot_small
}



class 							__snake_case		(	_lowercase		):
							_a      =					'''blenderbot-small'''
							_a      =					['''past_key_values''']
							_a      =					{'''num_attention_heads''': '''encoder_attention_heads''', '''hidden_size''': '''d_model'''}




							def __init__(			self	:			Optional[Any]							,							A_	:			Union[str, Any]=5_0_2_6_5							,							A_	:			str=5_1_2							,							A_	:			Any=8							,							A_	:			str=2_0_4_8							,							A_	:			List[Any]=1_6							,							A_	:			Dict=8							,							A_	:			Union[str, Any]=2_0_4_8							,							A_	:			Union[str, Any]=1_6							,							A_	:			Optional[int]=0.0							,							A_	:			Dict=0.0							,							A_	:			Dict=True							,							A_	:			Any=True							,							A_	:			Dict="gelu"							,							A_	:			int=5_1_2							,							A_	:			str=0.1							,							A_	:			Optional[int]=0.0							,							A_	:			Union[str, Any]=0.0							,							A_	:			Optional[int]=0.02							,							A_	:			Union[str, Any]=1							,							A_	:			str=False							,							A_	:			Tuple=0							,							A_	:			Union[str, Any]=1							,							A_	:			Tuple=2							,							A_	:			Optional[int]=2							,							**A_	:			List[Any]							,							):
									lowerCAmelCase_     :	List[str]							   =					vocab_size
									lowerCAmelCase_     :	int							   =					max_position_embeddings
									lowerCAmelCase_     :	int							   =					d_model
									lowerCAmelCase_     :	int							   =					encoder_ffn_dim
									lowerCAmelCase_     :	Any							   =					encoder_layers
									lowerCAmelCase_     :	Any							   =					encoder_attention_heads
									lowerCAmelCase_     :	List[Any]							   =					decoder_ffn_dim
									lowerCAmelCase_     :	Any							   =					decoder_layers
									lowerCAmelCase_     :	int							   =					decoder_attention_heads
									lowerCAmelCase_     :	int							   =					dropout
									lowerCAmelCase_     :	str							   =					attention_dropout
									lowerCAmelCase_     :	Any							   =					activation_dropout
									lowerCAmelCase_     :	List[str]							   =					activation_function
									lowerCAmelCase_     :	Optional[int]							   =					init_std
									lowerCAmelCase_     :	int							   =					encoder_layerdrop
									lowerCAmelCase_     :	List[str]							   =					decoder_layerdrop
									lowerCAmelCase_     :	List[str]							   =					use_cache
									lowerCAmelCase_     :	int							   =					encoder_layers
									lowerCAmelCase_     :	int							   =					scale_embedding  # scale factor will be sqrt(d_model) if True

									super().__init__(
									    pad_token_id=__A							,							bos_token_id=__A							,							eos_token_id=__A							,							is_encoder_decoder=__A							,							decoder_start_token_id=__A							,							forced_eos_token_id=__A							,							**__A							,							)





class 							__snake_case		(	_lowercase		):




							@property
							def   UpperCAmelCase__     (			self	:			Optional[int]):
									if self.task in ["default", "seq2seq-lm"]:
											lowerCAmelCase_     :	Dict							   =					OrderedDict(
											    [
											        ('''input_ids''', {0: '''batch''', 1: '''encoder_sequence'''}),
											        ('''attention_mask''', {0: '''batch''', 1: '''encoder_sequence'''}),
											    ])

											if self.use_past:
													lowerCAmelCase_     :	Optional[Any]							   =					{0: """batch"""}
													lowerCAmelCase_     :	Union[str, Any]							   =					{0: """batch""", 1: """past_decoder_sequence + sequence"""}
											else:
													lowerCAmelCase_     :	Tuple							   =					{0: """batch""", 1: """decoder_sequence"""}
													lowerCAmelCase_     :	str							   =					{0: """batch""", 1: """decoder_sequence"""}

											if self.use_past:
													self.fill_with_past_key_values_(__A							,							direction='''inputs''')
									elif self.task == "causal-lm":
											# TODO: figure this case out.
											lowerCAmelCase_     :	Union[str, Any]							   =					OrderedDict(
											    [
											        ('''input_ids''', {0: '''batch''', 1: '''encoder_sequence'''}),
											        ('''attention_mask''', {0: '''batch''', 1: '''encoder_sequence'''}),
											    ])
											if self.use_past:
													lowerCAmelCase_     :	Dict							   =					self.num_layers
													for i in range(__A):
															lowerCAmelCase_     :	Dict							   =					{0: """batch""", 2: """past_sequence + sequence"""}
															lowerCAmelCase_     :	Union[str, Any]							   =					{0: """batch""", 2: """past_sequence + sequence"""}
									else:
											lowerCAmelCase_     :	int							   =					OrderedDict(
											    [
											        ('''input_ids''', {0: '''batch''', 1: '''encoder_sequence'''}),
											        ('''attention_mask''', {0: '''batch''', 1: '''encoder_sequence'''}),
											        ('''decoder_input_ids''', {0: '''batch''', 1: '''decoder_sequence'''}),
											        ('''decoder_attention_mask''', {0: '''batch''', 1: '''decoder_sequence'''}),
											    ])

									return common_inputs




							@property
							def   UpperCAmelCase__     (			self	:			Any):
									if self.task in ["default", "seq2seq-lm"]:
											lowerCAmelCase_     :	Any							   =					super().outputs
									else:
											lowerCAmelCase_     :	Dict							   =					super(__A							,							self).outputs
											if self.use_past:
													lowerCAmelCase_     :	Tuple							   =					self.num_layers
													for i in range(__A):
															lowerCAmelCase_     :	Tuple							   =					{0: """batch""", 2: """past_sequence + sequence"""}
															lowerCAmelCase_     :	int							   =					{0: """batch""", 2: """past_sequence + sequence"""}
									return common_outputs




							def   UpperCAmelCase__     (			self	:			List[Any]							,							A_	:			PreTrainedTokenizer							,							A_	:			int = -1							,							A_	:			int = -1							,							A_	:			bool = False							,							A_	:			Optional[TensorType] = None							,							):
									lowerCAmelCase_     :	str							   =					self._generate_dummy_inputs_for_sequence_classification_and_question_answering(
									    __A							,							__A							,							__A							,							__A							,							__A)

									# Generate decoder inputs
									lowerCAmelCase_     :	str							   =					seq_length if not self.use_past else 1
									lowerCAmelCase_     :	Any							   =					self._generate_dummy_inputs_for_sequence_classification_and_question_answering(
									    __A							,							__A							,							__A							,							__A							,							__A)
									lowerCAmelCase_     :	Dict							   =					{F"""decoder_{name}""": tensor for name, tensor in decoder_inputs.items()}
									lowerCAmelCase_     :	str							   =					dict(**__A							,							**__A)

									if self.use_past:
											if not is_torch_available():
													raise ValueError('''Cannot generate dummy past_keys inputs without PyTorch installed.''')
											else:
													import torch
											lowerCAmelCase_     :	List[Any]							   =					common_inputs["""input_ids"""].shape
											lowerCAmelCase_     :	List[str]							   =					common_inputs["""decoder_input_ids"""].shape[1]
											lowerCAmelCase_     :	int							   =					self.num_attention_heads
											lowerCAmelCase_     :	Optional[Any]							   =					(
											    batch,
											    num_encoder_attention_heads,
											    encoder_seq_length,
											    self._config.hidden_size // num_encoder_attention_heads,
											)
											lowerCAmelCase_     :	Optional[Any]							   =					decoder_seq_length + 3
											lowerCAmelCase_     :	str							   =					(
											    batch,
											    num_decoder_attention_heads,
											    decoder_past_length,
											    self._config.hidden_size // num_decoder_attention_heads,
											)

											lowerCAmelCase_     :	List[str]							   =					torch.cat(
											    [common_inputs['''decoder_attention_mask'''], torch.ones(__A							,							__A)]							,							dim=1)

											lowerCAmelCase_     :	int							   =					[]
											# If the number of encoder and decoder layers are present in the model configuration, both are considered
											lowerCAmelCase_     :	Any							   =					self.num_layers
											lowerCAmelCase_     :	int							   =					min(__A							,							__A)
											lowerCAmelCase_     :	Tuple							   =					max(__A							,							__A) - min_num_layers
											lowerCAmelCase_     :	Dict							   =					"""encoder""" if num_encoder_layers > num_decoder_layers else """decoder"""

											for _ in range(__A):
													common_inputs["past_key_values"].append(
													    (
													        torch.zeros(__A),
													        torch.zeros(__A),
													        torch.zeros(__A),
													        torch.zeros(__A),
													    ))
											# TODO: test this.
											lowerCAmelCase_     :	List[str]							   =					encoder_shape if remaining_side_name == """encoder""" else decoder_shape
											for _ in range(__A							,							__A):
													common_inputs["past_key_values"].append((torch.zeros(__A), torch.zeros(__A)))
									return common_inputs




							def   UpperCAmelCase__     (			self	:			List[str]							,							A_	:			PreTrainedTokenizer							,							A_	:			int = -1							,							A_	:			int = -1							,							A_	:			bool = False							,							A_	:			Optional[TensorType] = None							,							):
									lowerCAmelCase_     :	str							   =					self._generate_dummy_inputs_for_sequence_classification_and_question_answering(
									    __A							,							__A							,							__A							,							__A							,							__A)

									if self.use_past:
											if not is_torch_available():
													raise ValueError('''Cannot generate dummy past_keys inputs without PyTorch installed.''')
											else:
													import torch
											lowerCAmelCase_     :	Union[str, Any]							   =					common_inputs["""input_ids"""].shape
											# Not using the same length for past_key_values
											lowerCAmelCase_     :	int							   =					seqlen + 2
											lowerCAmelCase_     :	Optional[Any]							   =					self.num_layers
											lowerCAmelCase_     :	Optional[Any]							   =					self.num_attention_heads
											lowerCAmelCase_     :	List[str]							   =					(
											    batch,
											    num_encoder_attention_heads,
											    past_key_values_length,
											    self._config.hidden_size // num_encoder_attention_heads,
											)

											lowerCAmelCase_     :	Union[str, Any]							   =					common_inputs["""attention_mask"""].dtype
											lowerCAmelCase_     :	int							   =					torch.cat(
											    [common_inputs['''attention_mask'''], torch.ones(__A							,							__A							,							dtype=__A)]							,							dim=1)
											lowerCAmelCase_     :	Tuple							   =					[
											    (torch.zeros(__A), torch.zeros(__A)) for _ in range(__A)
											]
									return common_inputs




							def   UpperCAmelCase__     (			self	:			int							,							A_	:			PreTrainedTokenizer							,							A_	:			int = -1							,							A_	:			int = -1							,							A_	:			bool = False							,							A_	:			Optional[TensorType] = None							,							):
									# Copied from OnnxConfig.generate_dummy_inputs
									# Did not use super(OnnxConfigWithPast, self).generate_dummy_inputs for code clarity.
									# If dynamic axis (-1) we forward with a fixed dimension of 2 samples to avoid optimizations made by ONNX
									lowerCAmelCase_     :	List[str]							   =					compute_effective_axis_dimension(
									    __A							,							fixed_dimension=OnnxConfig.default_fixed_batch							,							num_token_to_add=0)

									# If dynamic axis (-1) we forward with a fixed dimension of 8 tokens to avoid optimizations made by ONNX
									lowerCAmelCase_     :	List[str]							   =					tokenizer.num_special_tokens_to_add(__A)
									lowerCAmelCase_     :	Tuple							   =					compute_effective_axis_dimension(
									    __A							,							fixed_dimension=OnnxConfig.default_fixed_sequence							,							num_token_to_add=__A)

									# Generate dummy inputs according to compute batch and sequence
									lowerCAmelCase_     :	Any							   =					[""" """.join([tokenizer.unk_token]) * seq_length] * batch_size
									lowerCAmelCase_     :	Any							   =					dict(tokenizer(__A							,							return_tensors=__A))
									return common_inputs




							def   UpperCAmelCase__     (			self	:			List[str]							,							A_	:			PreTrainedTokenizer							,							A_	:			int = -1							,							A_	:			int = -1							,							A_	:			bool = False							,							A_	:			Optional[TensorType] = None							,							):
									if self.task in ["default", "seq2seq-lm"]:
											lowerCAmelCase_     :	Any							   =					self._generate_dummy_inputs_for_default_and_seqaseq_lm(
											    __A							,							batch_size=__A							,							seq_length=__A							,							is_pair=__A							,							framework=__A)

									elif self.task == "causal-lm":
											lowerCAmelCase_     :	List[str]							   =					self._generate_dummy_inputs_for_causal_lm(
											    __A							,							batch_size=__A							,							seq_length=__A							,							is_pair=__A							,							framework=__A)
									else:
											lowerCAmelCase_     :	List[Any]							   =					self._generate_dummy_inputs_for_sequence_classification_and_question_answering(
											    __A							,							batch_size=__A							,							seq_length=__A							,							is_pair=__A							,							framework=__A)

									return common_inputs







							def   UpperCAmelCase__     (			self	:			int							,							A_	:			int							,							A_	:			Dict							,							A_	:			str							,							A_	:			Dict):
									if self.task in ["default", "seq2seq-lm"]:
											lowerCAmelCase_     :	Union[str, Any]							   =					super()._flatten_past_key_values_(__A							,							__A							,							__A							,							__A)
									else:
											lowerCAmelCase_     :	Union[str, Any]							   =					super(__A							,							self)._flatten_past_key_values_(
											    __A							,							__A							,							__A							,							__A)








from sympy import diff, lambdify, symbols
from sympy.functions import *  # noqa: F403
def 							__SCREAMING_SNAKE_CASE     (   a__    :   str			,a__    :   complex			,a__    :   str = "x"			,a__    :   float = 10**-10			,a__    :   int = 1			,)					->				complex:
	__A :			Tuple		    =			symbols(a__       )
	__A :			List[str]		    =			lambdify(a__			,a__       )
	__A :			Any		    =			lambdify(a__			,diff(a__			,a__       )       )

	__A :			Dict		    =			starting_point

	while True:
		if diff_function(a__       ) != 0:
			__A :			Optional[int]		    =			prev_guess - multiplicity * func(a__       ) / diff_function(
			    a__       )
		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

		__A :			List[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)}""")





