
'''simple docstring'''







from math import atan, cos, radians, sin, tan

from .haversine_distance import haversine_distance

lowercase					:							int   =      6378137.0
lowercase					:							Any   =      6356752.314245
lowercase					:							List[str]   =      637_8137







def        SCREAMING_SNAKE_CASE__			(     __A    ,       __A    ,       __A    ,       __A			) ->			float:
	_snake_case     		=	(AXIS_A - AXIS_B) / AXIS_A
	# Parametric latitudes
	# https://en.wikipedia.org/wiki/Latitude#Parametric_(or_reduced)_latitude
	_snake_case     		=	atan((1 - flattening) * tan(radians(__A			)			)			)
	_snake_case     		=	atan((1 - flattening) * tan(radians(__A			)			)			)

	# Compute central angle between two points
	# using haversine theta. sigma =  haversine_distance / equatorial radius
	_snake_case     		=	haversine_distance(__A    ,       __A    ,       __A    ,       __A			) / EQUATORIAL_RADIUS

	# Intermediate P and Q values
	_snake_case     		=	(b_lata + b_lata) / 2
	_snake_case     		=	(b_lata - b_lata) / 2

	# Intermediate X value
	# X = (sigma - sin(sigma)) * sin^2Pcos^2Q / cos^2(sigma/2)
	_snake_case     		=	(sin(__A			) ** 2) * (cos(__A			) ** 2)
	_snake_case     		=	cos(sigma / 2			) ** 2
	_snake_case     		=	(sigma - sin(__A			)) * (x_numerator / x_demonimator)

	# Intermediate Y value
	# Y = (sigma + sin(sigma)) * cos^2Psin^2Q / sin^2(sigma/2)
	_snake_case     		=	(cos(__A			) ** 2) * (sin(__A			) ** 2)
	_snake_case     		=	sin(sigma / 2			) ** 2
	_snake_case     		=	(sigma + sin(__A			)) * (y_numerator / y_denominator)

	return EQUATORIAL_RADIUS * (sigma - ((flattening / 2) * (x_value + y_value)))


if __name__ == "__main__":
					import doctest

					doctest.testmod()



'''simple docstring'''







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







def        SCREAMING_SNAKE_CASE__			(     __A    ,       __A    ,       __A = "x"    ,       __A = 10**-10    ,       __A = 1    ,       ) ->			complex:
	_snake_case     		=	symbols(__A			)
	_snake_case     		=	lambdify(__A    ,       __A			)
	_snake_case     		=	lambdify(__A    ,       diff(__A    ,       __A			)			)

	_snake_case     		=	starting_point

	while True:
		if diff_function(__A			) != 0:
			_snake_case     		=	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

		_snake_case     		=	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)}''')

