
"""simple docstring"""






import math as m






def 		_snake_case			(      lowercase__						:    Any ,	lowercase__						:    Any ,	lowercase__						:    Optional[int]=0.001						)    ->							Tuple:


			'''simple docstring'''





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






def 		_snake_case			(      lowercase__						:    Optional[Any] ,	lowercase__						:    List[str]=0 ,	lowercase__						:    Union[str, Any]=1_0_0 ,	lowercase__						:    Any=0.0001 ,	lowercase__						:    List[str]=1E-6 ,	lowercase__						:    str=False						)    ->							List[str]:


			'''simple docstring'''





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

				__UpperCAmelCase 					=    lambda x: m.tanh(x) ** 2 - m.exp(3 * x)  # noqa: E731
				__UpperCAmelCase					,					__UpperCAmelCase					,					__UpperCAmelCase 					=    newton_raphson(
				    f, xa=10, maxiter=10_00, 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 List, Optional, Tuple, Union

from . import logging
from .import_utils import is_torch_available, is_torch_version


if is_torch_available():
				import torch

__UpperCAmelCase 					=    logging.get_logger(__name__)  # pylint: disable=invalid-name

try:
				from torch._dynamo import allow_in_graph as maybe_allow_in_graph
except (ImportError, ModuleNotFoundError):






				def 		_snake_case			(      cls						:    Tuple						)    ->							List[Any]:


							'''simple docstring'''





							return cls






def 		_snake_case			(      lowercase__						:    Union[Tuple, List] ,	lowercase__						:    Optional[Union[List["torch.Generator"], "torch.Generator"]] = None ,	lowercase__						:    Optional["torch.device"] = None ,	lowercase__						:    Optional["torch.dtype"] = None ,	lowercase__						:    Optional["torch.layout"] = None ,	)    ->							Optional[Any]:


			'''simple docstring'''





			lowerCAmelCase_       :Any     	=    device
			lowerCAmelCase_       :Any     	=    shape[0]

			lowerCAmelCase_       :Dict     	=    layout or torch.strided
			lowerCAmelCase_       :List[str]     	=    device or torch.device("""cpu"""						)

			if generator is not None:
						lowerCAmelCase_       :Optional[Any]     	=    generator.device.type if not isinstance(lowercase__ ,	lowercase__						) else generator[0].device.type
						if gen_device_type != device.type and gen_device_type == "cpu":
									lowerCAmelCase_       :Optional[int]     	=    """cpu"""
									if device != "mps":
												logger.info(
												    f"""The passed generator was created on 'cpu' even though a tensor on {device} was expected."""
												    f""" Tensors will be created on 'cpu' and then moved to {device}. Note that one can probably"""
												    f""" slighly speed up this function by passing a generator that was created on the {device} device."""						)
						elif gen_device_type != device.type and gen_device_type == "cuda":
									raise ValueError(f"""Cannot generate a {device} tensor from a generator of type {gen_device_type}."""						)

			if isinstance(lowercase__ ,	lowercase__						):
						lowerCAmelCase_       :List[str]     	=    (1,) + shape[1:]
						lowerCAmelCase_       :Optional[Any]     	=    [
						    torch.randn(lowercase__ ,	generator=generator[i] ,	device=lowercase__ ,	dtype=lowercase__ ,	layout=lowercase__						)
						    for i in range(lowercase__						)
						]
						lowerCAmelCase_       :str     	=    torch.cat(lowercase__ ,	dim=0						).to(lowercase__						)
			else:
						lowerCAmelCase_       :Dict     	=    torch.randn(lowercase__ ,	generator=lowercase__ ,	device=lowercase__ ,	dtype=lowercase__ ,	layout=lowercase__						).to(lowercase__						)

			return latents






def 		_snake_case			(      lowercase__						:    Union[str, Any]						)    ->							int:


			'''simple docstring'''





			if is_torch_version("""<""" ,	"""2.0.0"""						) or not hasattr(lowercase__ ,	"""_dynamo"""						):
						return False
			return isinstance(lowercase__ ,	torch._dynamo.eval_frame.OptimizedModule						)






