






import math as m






def    UpperCamelCase__  (   UpperCAmelCase    ,	UpperCAmelCase    ,	UpperCAmelCase=0.0_0_1     )     ->		Union[str, Any]:







							"""simple docstring"""





							return (f(a + h     ) - f(a - h     )) / (2 * h)






def    UpperCamelCase__  (   UpperCAmelCase    ,	UpperCAmelCase=0    ,	UpperCAmelCase=100    ,	UpperCAmelCase=0.0_0_0_1    ,	UpperCAmelCase=1e-6    ,	UpperCAmelCase=False     )     ->		Optional[int]:







							"""simple docstring"""





							_a  :    Optional[int]			=						xa  # set the initial guess
							_a  :    Union[str, Any]			=						[a]
							_a  :    str			=						abs(f(UpperCAmelCase     )     )
							_a  :    Optional[int]			=						lambda UpperCAmelCase     : calc_derivative(UpperCAmelCase    ,	UpperCAmelCase    ,	h=UpperCAmelCase     )  # noqa: E731  Derivative of f(x)
							for _ in range(UpperCAmelCase     ):
														if fa(UpperCAmelCase     ) == 0:
																					raise ValueError('''No converging solution found'''     )
														_a  :    List[str]			=						a - f(UpperCAmelCase     ) / fa(UpperCAmelCase     )  # Calculate the next estimate
														if logsteps:
																					steps.append(UpperCAmelCase     )
														if error < maxerror:
																					break
							else:
														raise ValueError('''Iteration limit reached, no converging solution found'''     )
							if logsteps:
														# If logstep is true, then log intermediate steps
														return a, error, steps
							return a, error


if __name__ == "__main__":
						from matplotlib import pyplot as plt

						__lowerCamelCase						= lambda x: m.tanh(x) ** 2 - m.exp(3 * x)  # noqa: E731
						__lowerCamelCase						,  __lowerCamelCase						,  __lowerCamelCase						= newton_raphson(
						    f, xa=10, maxiter=1_000, step=1e-6, logsteps=True
						)
						plt.plot([abs(f(x)) for x in steps])
						plt.xlabel('step')
						plt.ylabel('error')
						plt.show()
						print(F'''solution = {{{solution:f}}}, error = {{{error:f}}}''')







from typing import TYPE_CHECKING

from ...utils import (
    OptionalDependencyNotAvailable,
    _LazyModule,
    is_flax_available,
    is_tf_available,
    is_tokenizers_available,
    is_torch_available,
)


__lowerCamelCase						= {
    'configuration_bart': ['BART_PRETRAINED_CONFIG_ARCHIVE_MAP', 'BartConfig', 'BartOnnxConfig'],
    'tokenization_bart': ['BartTokenizer'],
}

try:
						if not is_tokenizers_available():
												raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
						pass
else:
						__lowerCamelCase						= ['BartTokenizerFast']

try:
						if not is_torch_available():
												raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
						pass
else:
						__lowerCamelCase						= [
						    'BART_PRETRAINED_MODEL_ARCHIVE_LIST',
						    'BartForCausalLM',
						    'BartForConditionalGeneration',
						    'BartForQuestionAnswering',
						    'BartForSequenceClassification',
						    'BartModel',
						    'BartPretrainedModel',
						    'PretrainedBartModel',
						]

try:
						if not is_tf_available():
												raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
						pass
else:
						__lowerCamelCase						= [
						    'TFBartForConditionalGeneration',
						    'TFBartForSequenceClassification',
						    'TFBartModel',
						    'TFBartPretrainedModel',
						]

try:
						if not is_flax_available():
												raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
						pass
else:
						__lowerCamelCase						= [
						    'FlaxBartDecoderPreTrainedModel',
						    'FlaxBartForCausalLM',
						    'FlaxBartForConditionalGeneration',
						    'FlaxBartForQuestionAnswering',
						    'FlaxBartForSequenceClassification',
						    'FlaxBartModel',
						    'FlaxBartPreTrainedModel',
						]

if TYPE_CHECKING:
						from .configuration_bart import BART_PRETRAINED_CONFIG_ARCHIVE_MAP, BartConfig, BartOnnxConfig
						from .tokenization_bart import BartTokenizer

						try:
												if not is_tokenizers_available():
																		raise OptionalDependencyNotAvailable()
						except OptionalDependencyNotAvailable:
												pass
						else:
												from .tokenization_bart_fast import BartTokenizerFast

						try:
												if not is_torch_available():
																		raise OptionalDependencyNotAvailable()
						except OptionalDependencyNotAvailable:
												pass
						else:
												from .modeling_bart import (
												    BART_PRETRAINED_MODEL_ARCHIVE_LIST,
												    BartForCausalLM,
												    BartForConditionalGeneration,
												    BartForQuestionAnswering,
												    BartForSequenceClassification,
												    BartModel,
												    BartPretrainedModel,
												    PretrainedBartModel,
												)

						try:
												if not is_tf_available():
																		raise OptionalDependencyNotAvailable()
						except OptionalDependencyNotAvailable:
												pass
						else:
												from .modeling_tf_bart import (
												    TFBartForConditionalGeneration,
												    TFBartForSequenceClassification,
												    TFBartModel,
												    TFBartPretrainedModel,
												)

						try:
												if not is_flax_available():
																		raise OptionalDependencyNotAvailable()
						except OptionalDependencyNotAvailable:
												pass
						else:
												from .modeling_flax_bart import (
												    FlaxBartDecoderPreTrainedModel,
												    FlaxBartForCausalLM,
												    FlaxBartForConditionalGeneration,
												    FlaxBartForQuestionAnswering,
												    FlaxBartForSequenceClassification,
												    FlaxBartModel,
												    FlaxBartPreTrainedModel,
												)

else:
						import sys

						__lowerCamelCase						= _LazyModule(__name__, globals()['__file__'], _import_structure, module_spec=__spec__)