





'''simple docstring'''





from __future__ import annotations

import numpy as np





def     _UpperCamelCase     (a__   :np.ndarray       ):






							"""simple docstring"""





							UpperCamelCase__     ,     UpperCamelCase__				     =			np.shape(a__       )
							if rows != columns:
														UpperCamelCase__				     =			(
														    """'table' has to be of square shaped array but got a """
														    f"""{rows}x{columns} array:\n{table}"""
														)
														raise ValueError(a__       )

							UpperCamelCase__				     =			np.zeros((rows, columns)       )
							UpperCamelCase__				     =			np.zeros((rows, columns)       )
							for i in range(a__       ):
														for j in range(a__       ):
																					UpperCamelCase__				     =			sum(lower[i][k] * upper[k][j] for k in range(a__       )       )
																					if upper[j][j] == 0:
																												raise ArithmeticError("""No LU decomposition exists"""       )
																					UpperCamelCase__				     =			(table[i][j] - total) / upper[j][j]
														UpperCamelCase__				     =			1
														for j in range(a__   ,			a__       ):
																					UpperCamelCase__				     =			sum(lower[i][k] * upper[k][j] for k in range(a__       )       )
																					UpperCamelCase__				     =			table[i][j] - total
							return lower, upper


if __name__ == "__main__":
					import doctest

					doctest.testmod()











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





def     _UpperCamelCase     (a__   :str   ,			a__   :complex   ,			a__   :str = "x"   ,			a__   :float = 10**-10   ,			a__   :int = 1   ,			):






							"""simple docstring"""





							UpperCamelCase__				     =			symbols(a__       )
							UpperCamelCase__				     =			lambdify(a__   ,			a__       )
							UpperCamelCase__				     =			lambdify(a__   ,			diff(a__   ,			a__       )       )

							UpperCamelCase__				     =			starting_point

							while True:
														if diff_function(a__       ) != 0:
																					UpperCamelCase__				     =			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

														UpperCamelCase__				     =			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=0.0_05)}""",
					)

					# Find root of cos(x)
					print(f"""The root of cos(x) = 0 is {newton_raphson('cos(x)', 0)}""")




