newton_sqrt.py

# newton_sqrt.py: Newton法による平方根計算
import math  # math.sqrt, math.fabs


# Newton法による平方根計算
def newton_sqrt(x, rtol, atol):
    old_sqrt = x
    for times in range(0, 10):  # 最大10回
        new_sqrt = (old_sqrt + x / old_sqrt) / 2.0
        if math.fabs(new_sqrt - old_sqrt) <= math.fabs(old_sqrt) * rtol + atol:
            return new_sqrt, times

        old_sqrt = new_sqrt

    return new_sqrt, times


# 収束条件
rel_tol = 1.0e-10
abs_tol = 1.0e-50

# x = 3
x = 3.0
true_val = math.sqrt(x)
newton_val, iter_times = newton_sqrt(x, rel_tol, abs_tol)
print('math.sqrt(', x, ') = ', true_val)
print('newton   (', x, ') = ', newton_val, ', Iter.Times = ', iter_times)
print('Relative Error     = ', math.fabs((true_val - newton_val) / true_val))

# x = 12
x = 12.0
true_val = math.sqrt(x)
newton_val, iter_times = newton_sqrt(x, rel_tol, abs_tol)
print('math.sqrt(', x, ') = ', true_val)
print('newton   (', x, ') = ', newton_val, ', Iter.Times = ', iter_times)
print('Relative Error     = ', math.fabs((true_val - newton_val) / true_val))

# x = 123
x = 123.0 # 2022-05-09 fixed!
true_val = math.sqrt(x)
newton_val, iter_times = newton_sqrt(x, rel_tol, abs_tol)
print('math.sqrt(', x, ') = ', true_val)
print('newton   (', x, ') = ', newton_val, ', Iter.Times = ', iter_times)
print('Relative Error     = ', math.fabs((true_val - newton_val) / true_val))

# x = 12345
x = 12345.0
true_val = math.sqrt(x)
newton_val, iter_times = newton_sqrt(x, rel_tol, abs_tol)
print('math.sqrt(', x, ') = ', true_val)
print('newton   (', x, ') = ', newton_val, ', Iter.Times = ', iter_times)
print('Relative Error     = ', math.fabs((true_val - newton_val) / true_val))



# -------------------------------------
# Copyright (c) 2021 Tomonori Kouya
# All rights reserved.
# -------------------------------------