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Update newton_raphson.py

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Rohan Anand 2023-07-16 13:21:38 +05:30 committed by GitHub
parent 588de45cf3
commit bf53be27ca
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1 changed files with 15 additions and 12 deletions
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arithmetic_analysis/newton_raphson.py
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@ -7,7 +7,7 @@ from __future__ import annotations
from sympy import diff, symbols, sympify from sympy import diff, symbols, sympify
def newton_raphson(func: str, a: float, precision: float = 10**-10) -> float: def newton_raphson(func: str, start_point: float, precision: float = 10**-10) -> float:
"""Finds root from the point 'a' onwards by Newton-Raphson method """Finds root from the point 'a' onwards by Newton-Raphson method
>>> newton_raphson("sin(x)", 2) >>> newton_raphson("sin(x)", 2)
3.1415926536808043 3.1415926536808043
@ -18,22 +18,25 @@ def newton_raphson(func: str, a: float, precision: float = 10**-10) -> float:
>>> newton_raphson("log(x)- 1", 2) >>> newton_raphson("log(x)- 1", 2)
2.718281828458938 2.718281828458938
""" """
x = a x = start_point
symbol = symbols("x") symbol = symbols('x')
# expressions to be represented symbolically and manipulated algebraically # expressions to be represented symbolically and manipulated algebraically
exp = sympify(func) expression = sympify(func)
# calculate the derivative value at the current x value
exp_diff = diff(exp, symbol)
maximum_iterations = 100
for _ in range(maximum_iterations): # calculates the derivative value at the current x value
val = exp.subs(symbol, x) derivative = diff(expression, symbol)
diff_val = exp_diff.subs(symbol, x)
if abs(val) < precision: max_iterations = 100
for _ in range(max_iterations):
function_value = expression.subs(symbol, x)
derivative_value = derivative.subs(symbol, x)
if abs(function_value) < precision:
return float(x) return float(x)
x -= val / diff_val x = x - (function_value / derivative_value)
return float(x) return float(x)