



"""simple docstring"""







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

def       _lowerCamelCase				(							UpperCAmelCase_ :       str,	UpperCAmelCase_ :       complex,	UpperCAmelCase_ :       str = "x",	UpperCAmelCase_ :       float = 10**-10,	UpperCAmelCase_ :       int = 1,	)	-> complex:






	"""simple docstring"""





	A__											=					symbols(UpperCAmelCase_     )
	A__											=					lambdify(UpperCAmelCase_,	UpperCAmelCase_     )
	A__											=					lambdify(UpperCAmelCase_,	diff(UpperCAmelCase_,	UpperCAmelCase_     )     )

	A__											=					starting_point

	while True:
		if diff_function(UpperCAmelCase_     ) != 0:
			A__											=					prev_guess - multiplicity * func(UpperCAmelCase_     ) / diff_function(
			    UpperCAmelCase_     )
		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__											=					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)}')









"""simple docstring"""







from ..utils import (
    OptionalDependencyNotAvailable,
    is_flax_available,
    is_scipy_available,
    is_torch_available,
    is_torchsde_available,
)


try:
			if not is_torch_available():
						raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
			from ..utils.dummy_pt_objects import *  # noqa F403
else:
			from .scheduling_consistency_models import CMStochasticIterativeScheduler
			from .scheduling_ddim import DDIMScheduler
			from .scheduling_ddim_inverse import DDIMInverseScheduler
			from .scheduling_ddim_parallel import DDIMParallelScheduler
			from .scheduling_ddpm import DDPMScheduler
			from .scheduling_ddpm_parallel import DDPMParallelScheduler
			from .scheduling_deis_multistep import DEISMultistepScheduler
			from .scheduling_dpmsolver_multistep import DPMSolverMultistepScheduler
			from .scheduling_dpmsolver_multistep_inverse import DPMSolverMultistepInverseScheduler
			from .scheduling_dpmsolver_singlestep import DPMSolverSinglestepScheduler
			from .scheduling_euler_ancestral_discrete import EulerAncestralDiscreteScheduler
			from .scheduling_euler_discrete import EulerDiscreteScheduler
			from .scheduling_heun_discrete import HeunDiscreteScheduler
			from .scheduling_ipndm import IPNDMScheduler
			from .scheduling_k_dpm_2_ancestral_discrete import KDPMaAncestralDiscreteScheduler
			from .scheduling_k_dpm_2_discrete import KDPMaDiscreteScheduler
			from .scheduling_karras_ve import KarrasVeScheduler
			from .scheduling_pndm import PNDMScheduler
			from .scheduling_repaint import RePaintScheduler
			from .scheduling_sde_ve import ScoreSdeVeScheduler
			from .scheduling_sde_vp import ScoreSdeVpScheduler
			from .scheduling_unclip import UnCLIPScheduler
			from .scheduling_unipc_multistep import UniPCMultistepScheduler
			from .scheduling_utils import KarrasDiffusionSchedulers, SchedulerMixin
			from .scheduling_vq_diffusion import VQDiffusionScheduler

try:
			if not is_flax_available():
						raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
			from ..utils.dummy_flax_objects import *  # noqa F403
else:
			from .scheduling_ddim_flax import FlaxDDIMScheduler
			from .scheduling_ddpm_flax import FlaxDDPMScheduler
			from .scheduling_dpmsolver_multistep_flax import FlaxDPMSolverMultistepScheduler
			from .scheduling_karras_ve_flax import FlaxKarrasVeScheduler
			from .scheduling_lms_discrete_flax import FlaxLMSDiscreteScheduler
			from .scheduling_pndm_flax import FlaxPNDMScheduler
			from .scheduling_sde_ve_flax import FlaxScoreSdeVeScheduler
			from .scheduling_utils_flax import (
			    FlaxKarrasDiffusionSchedulers,
			    FlaxSchedulerMixin,
			    FlaxSchedulerOutput,
			    broadcast_to_shape_from_left,
			)


try:
			if not (is_torch_available() and is_scipy_available()):
						raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
			from ..utils.dummy_torch_and_scipy_objects import *  # noqa F403
else:
			from .scheduling_lms_discrete import LMSDiscreteScheduler

try:
			if not (is_torch_available() and is_torchsde_available()):
						raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
			from ..utils.dummy_torch_and_torchsde_objects import *  # noqa F403
else:
			from .scheduling_dpmsolver_sde import DPMSolverSDEScheduler




