Created
February 13, 2013 16:09
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According the Lecture 6 of Berkeley Computer Science 61A – Fall 2012 ,i modify the newton method code for performance improve.
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""" | |
INPUT: float, float, float | |
OUTPUT: bool | |
""" | |
def approx_eq_1(x, y, tolerance=1e-18): | |
return abs(x - y) <= tolerance | |
""" | |
INPUT: float, float, float | |
OUTPUT: bool | |
""" | |
def approx_eq_2(x, y, tolerance=1e-7): | |
return abs(x - y) <= abs(x) * tolerance | |
""" | |
INPUT: float, float | |
OUTPUT: bool | |
""" | |
def approx_eq(x, y): | |
if x == y: | |
return True | |
return approx_eq_1(x, y) or approx_eq_2(x, y) | |
""" | |
INPUT: function, function, int(float), int | |
OUTPUT: float | |
""" | |
def iter_improve(update, done, guess=1, max_updates=1000): | |
k = 0 | |
last_guess = 0 | |
while not done(guess) and k < max_updates and not approx_eq(guess, last_guess): | |
last_guess = guess | |
guess = update(guess) | |
k = k + 1 | |
print 'iterate times: %s' % k | |
return guess | |
""" | |
INPUT: function, float, float | |
OUTPUT: float | |
""" | |
def deriv(f, x, delta=1e-5): | |
df = f(x + delta) - f(x) | |
return df / delta | |
""" | |
INPUT: function | |
OUTPUT: function | |
""" | |
def newton_update(f): | |
def update(x): | |
return x - f(x) / deriv(f, x) | |
return update | |
""" | |
INPUT: function, int(float) | |
OUTPUT: float | |
""" | |
def find_root(f, guess=1): | |
done = lambda x: f(x) == 0 | |
return iter_improve(newton_update(f), done, guess) |
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