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* Remove eval from arithmetic_analysis/newton_raphson.py
* Relocate contents of arithmetic_analysis/
Delete the arithmetic_analysis/ directory and relocate its files because
the purpose of the directory was always ill-defined. "Arithmetic
analysis" isn't a field of math, and the directory's files contained
algorithms for linear algebra, numerical analysis, and physics.
Relocated the directory's linear algebra algorithms to linear_algebra/,
its numerical analysis algorithms to a new subdirectory called
maths/numerical_analysis/, and its single physics algorithm to physics/.
* updating DIRECTORY.md
---------
Co-authored-by: github-actions <${GITHUB_ACTOR}@users.noreply.github.com>
46 lines
1.5 KiB
Python
46 lines
1.5 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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from __future__ import annotations
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from decimal import Decimal
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from sympy import diff, lambdify, symbols
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def newton_raphson(func: str, a: float | Decimal, precision: float = 1e-10) -> 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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0.4384471871911695
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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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"""
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x = symbols("x")
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f = lambdify(x, func, "math")
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f_derivative = lambdify(x, diff(func), "math")
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x_curr = a
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while True:
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x_curr = Decimal(x_curr) - Decimal(f(x_curr)) / Decimal(f_derivative(x_curr))
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if abs(f(x_curr)) < precision:
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return float(x_curr)
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if __name__ == "__main__":
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import doctest
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doctest.testmod()
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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 value of e
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print(f"The root of log(x) - 1 = 0 is {newton_raphson('log(x) - 1', 2)}")
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# Find root of exponential function
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print(f"The root of exp(x) - 1 = 0 is {newton_raphson('exp(x) - 1', 0)}")
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