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84 lines
2.5 KiB
Python
84 lines
2.5 KiB
Python
# Implementing Newton Raphson method in Python
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# Author: Saksham Gupta
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#
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# The Newton-Raphson method (also known as Newton's method) is a way to
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# quickly find a good approximation for the root of a functreal-valued ion
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# The method can also be extended to complex functions
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#
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# Newton's Method - https://en.wikipedia.org/wiki/Newton's_method
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from sympy import diff, lambdify, symbols
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from sympy.functions import * # noqa: F401, F403
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def newton_raphson(
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function: str,
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starting_point: complex,
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variable: str = "x",
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precision: float = 10**-10,
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multiplicity: int = 1,
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) -> complex:
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"""Finds root from the 'starting_point' onwards by Newton-Raphson method
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Refer to https://docs.sympy.org/latest/modules/functions/index.html
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for usable mathematical functions
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>>> newton_raphson("sin(x)", 2)
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3.141592653589793
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>>> newton_raphson("x**4 -5", 0.4 + 5j)
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(-7.52316384526264e-37+1.4953487812212207j)
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>>> newton_raphson('log(y) - 1', 2, variable='y')
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2.7182818284590455
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>>> newton_raphson('exp(x) - 1', 10, precision=0.005)
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1.2186556186174883e-10
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>>> newton_raphson('cos(x)', 0)
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Traceback (most recent call last):
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...
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ZeroDivisionError: Could not find root
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"""
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x = symbols(variable)
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func = lambdify(x, function)
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diff_function = lambdify(x, diff(function, x))
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prev_guess = starting_point
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while True:
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if diff_function(prev_guess) != 0:
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next_guess = prev_guess - multiplicity * func(prev_guess) / diff_function(
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prev_guess
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)
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else:
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raise ZeroDivisionError("Could not find root") from None
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# Precision is checked by comparing the difference of consecutive guesses
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if abs(next_guess - prev_guess) < precision:
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return next_guess
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prev_guess = next_guess
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# Let's Execute
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if __name__ == "__main__":
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# Find root of trigonometric function
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# Find value of pi
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print(f"The root of sin(x) = 0 is {newton_raphson('sin(x)', 2)}")
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# Find root of polynomial
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# Find fourth Root of 5
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print(f"The root of x**4 - 5 = 0 is {newton_raphson('x**4 -5', 0.4 +5j)}")
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# Find value of e
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print(
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"The root of log(y) - 1 = 0 is ",
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f"{newton_raphson('log(y) - 1', 2, variable='y')}",
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)
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# Exponential Roots
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print(
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"The root of exp(x) - 1 = 0 is",
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f"{newton_raphson('exp(x) - 1', 10, precision=0.005)}",
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)
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# Find root of cos(x)
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print(f"The root of cos(x) = 0 is {newton_raphson('cos(x)', 0)}")
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