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Happy Coding
Newton's Method
寻找函数零点：Quickly finds accurate approximations to zeros of differenciable functions.
只要问题是可微的，则问题是可解的。
Wikipedia上操作演示
https://en.wikipedia.org/wiki/Newton's_method#/media/File:NewtonIteration_Ani.gif
实现指南：
高阶函数为的是抽象出功能，不要被参数混乱思路
python中整数相除会返回整数，所以注意传入浮点数做参数
def square_root(a):
def f(x):
return x * x - a
def df(x):
return 2 * x
return find_zero(f, df)
def find_zero(f, df):
def near_zero(x):
return appro_equal(f(x), 0)
return improve(update(f, df), near_zero, guess=1.0, max_update=100)
def update(f, df):
def u(x):
return x - f(x)/df(x)
return u
def improve(update, close, guess, max_update):
k = 0
while not close(guess) and k < max_update:
print guess, k
guess = update(guess)
k += 1
return guess # the guess improved
def appro_equal(x, y, tolerance=1e-15):
print abs(x-y) < tolerance
return abs(x-y) < tolerance
推广至求n次根
>>> def power(x, n):
"""Return x * x * x * ... * x for x repeated n times."""
product, k = 1, 0
while k < n:
product, k = product * x, k + 1
return product
>>> def nth_root_of_a(n, a):
def f(x):
return power(x, n) - a
def df(x):
return n * power(x, n-1)
return find_zero(f, df)
实际应用 Function Decorator
def trace(fn):
def t(x):
print "Calling", fn, "on argument", x
return fn(x)
return t
@trace
def square(x):
return x * x
2022年8月30日 21:47
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2023年2月02日 03:02
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2024年1月11日 21:52
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