Last active
August 29, 2015 14:05
-
-
Save dutc/1686573cbd49599610fb to your computer and use it in GitHub Desktop.
Netwon's method (or any other iterative solving technique) with numpy
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
from numpy.random import randint | |
from numpy import sqrt | |
# Newton's method: | |
# `x' is input, `y' is iteratively refined answer | |
# solve for square root of x: y**2 = x | |
# f (y) = y^2 - x | |
# f'(y) = 2y | |
# y[1] = y[0] - f(y[0]) / f'(y[0]) | |
xs = randint(1, 100, size=10).astype(float) # 10 numbers on [1,100) | |
ys = xs / 2 # first guess | |
unsolved = lambda xs, ys, accuracy = 0.01: abs(xs - ys ** 2) > accuracy | |
print '<{}>'.format(''.join('{:>4.0f}'.format(x) for x in xs)) | |
us = unsolved(xs, ys) | |
while us.any(): | |
ys[us] = ys[us] - (ys[us] ** 2 - xs[us])/(2 * ys[us]) | |
us = unsolved(xs, ys) | |
print ' {} '.format(''.join(' {} '.format(' ' if u else '✓') for u in us)) | |
for x, y, z, e in zip(xs, ys, sqrt(xs), abs(sqrt(xs) - ys)): | |
print '√{:2.0f} = {:>5.2f} = {:>5.2f} err: {:>6.4f}'.format(x, y, z, e) |
Sign up for free
to join this conversation on GitHub.
Already have an account?
Sign in to comment