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69 lines
2.3 KiB
Python
69 lines
2.3 KiB
Python
# Implementing Newton Raphson method in Python
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# Author: Syed Haseeb Shah (github.com/QuantumNovice)
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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 real-valued function.
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# https://en.wikipedia.org/wiki/Newton%27s_method
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from __future__ import annotations
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from sympy import diff, symbols, sympify
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def newton_raphson(
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func: str, start_point: float, precision: float = 10**-10
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) -> float:
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"""Finds root from the point 'a' onwards by Newton-Raphson method
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>>> newton_raphson("sin(x)", 2)
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3.1415926536808043
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>>> newton_raphson("x**2 - 5*x +2", 0.4)
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0.4384471871911696
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>>> newton_raphson("x**2 - 5", 0.1)
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2.23606797749979
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>>> newton_raphson("log(x)- 1", 2)
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2.718281828458938
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>>> from scipy.optimize import newton
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>>> all(newton_raphson("log(x)- 1", 2) == newton("log(x)- 1", 2) for precision in 10, 100, 1000, 10000))
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True
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>>> newton_raphson("log(x)- 1", 2, 0)
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Traceback (most recent call last):
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...
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ValueError: precision must be greater than zero
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>>> newton_raphson("log(x)- 1", 2, -1)
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Traceback (most recent call last):
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...
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ValueError: precision must be greater than zero
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"""
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x = start_point
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symbol = symbols("x")
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# expressions to be represented symbolically and manipulated algebraically
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expression = sympify(func)
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# calculates the derivative value at the current x value
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derivative = diff(expression, symbol)
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max_iterations = 100
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for _ in range(max_iterations):
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function_value = expression.subs(symbol, x)
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derivative_value = derivative.subs(symbol, x)
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if abs(function_value) < precision:
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return float(x)
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x = x - (function_value / derivative_value)
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return float(x)
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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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print(f"The root of x**2 - 5*x + 2 = 0 is {newton_raphson('x**2 - 5*x + 2', 0.4)}")
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# Find Square Root of 5
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print(f"The root of log(x) - 1 = 0 is {newton_raphson('log(x) - 1', 2)}")
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# Exponential Roots
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print(f"The root of exp(x) - 1 = 0 is {newton_raphson('exp(x) - 1', 0)}")
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