






import math as m



def      UpperCAmelCase						( lowerCAmelCase__					,     lowerCAmelCase__					,     lowerCAmelCase__=0.001	):


		'''simple docstring'''

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



def      UpperCAmelCase						( lowerCAmelCase__					,     lowerCAmelCase__=0					,     lowerCAmelCase__=100					,     lowerCAmelCase__=0.0_001					,     lowerCAmelCase__=1E-6					,     lowerCAmelCase__=False	):


		'''simple docstring'''

		__A    =							xa  # set the initial guess
		__A    =							[a]
		__A    =							abs(f(lowerCAmelCase__	)	)
		__A    =							lambda lowerCAmelCase__	: calc_derivative(lowerCAmelCase__					,     lowerCAmelCase__					,     h=lowerCAmelCase__	)  # noqa: E731  Derivative of f(x)
		for _ in range(lowerCAmelCase__	):
				if fa(lowerCAmelCase__	) == 0:
						raise ValueError("No converging solution found"	)
				__A    =							a - f(lowerCAmelCase__	) / fa(lowerCAmelCase__	)  # Calculate the next estimate
				if logsteps:
						steps.append(lowerCAmelCase__	)
				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

					snake_case_   :	Tuple							      =lambda x: m.tanh(x) ** 2 - m.exp(3 * x)  # noqa: E731
					snake_case_      ,	snake_case_      ,	snake_case_   :	str							      =newton_raphson(
					    f, xa=10, maxiter=1000, 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}}}""")









'''simple docstring'''







from typing import TYPE_CHECKING

from ...utils import OptionalDependencyNotAvailable, _LazyModule, is_tokenizers_available, is_torch_available


_A      :     Optional[Any]       	={
    '''configuration_realm''': ['''REALM_PRETRAINED_CONFIG_ARCHIVE_MAP''', '''RealmConfig'''],
    '''tokenization_realm''': ['''RealmTokenizer'''],
}

try:
			if not is_tokenizers_available():
						raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
			pass
else:
			_A      :     str       	=['''RealmTokenizerFast''']

try:
			if not is_torch_available():
						raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
			pass
else:
			_A      :     List[Any]       	=[
			    '''REALM_PRETRAINED_MODEL_ARCHIVE_LIST''',
			    '''RealmEmbedder''',
			    '''RealmForOpenQA''',
			    '''RealmKnowledgeAugEncoder''',
			    '''RealmPreTrainedModel''',
			    '''RealmReader''',
			    '''RealmScorer''',
			    '''load_tf_weights_in_realm''',
			]
			_A      :     Union[str, Any]       	=['''RealmRetriever''']


if TYPE_CHECKING:
			from .configuration_realm import REALM_PRETRAINED_CONFIG_ARCHIVE_MAP, RealmConfig
			from .tokenization_realm import RealmTokenizer

			try:
						if not is_tokenizers_available():
									raise OptionalDependencyNotAvailable()
			except OptionalDependencyNotAvailable:
						pass
			else:
						from .tokenization_realm import RealmTokenizerFast

			try:
						if not is_torch_available():
									raise OptionalDependencyNotAvailable()
			except OptionalDependencyNotAvailable:
						pass
			else:
						from .modeling_realm import (
						    REALM_PRETRAINED_MODEL_ARCHIVE_LIST,
						    RealmEmbedder,
						    RealmForOpenQA,
						    RealmKnowledgeAugEncoder,
						    RealmPreTrainedModel,
						    RealmReader,
						    RealmScorer,
						    load_tf_weights_in_realm,
						)
						from .retrieval_realm import RealmRetriever


else:
			import sys

			_A      :     int       	=_LazyModule(__name__, globals()['''__file__'''], _import_structure, module_spec=__spec__)

