使用二分法(Bisection Method)求平方根。

使用二分法(Bisection Method)求平方根。

def sqrtBI(x, epsilon):
    assert x>0, 'X must be non-nagtive, not ' + str(x)
    assert epsilon > 0, 'epsilon must be postive, not ' + str(epsilon)
 
    low = 0
    high = x
    guess = (low + high)/2.0
    counter = 1
    while (abs(guess ** 2 - x) > epsilon) and (counter <= 100):
        if guess ** 2 < x:
            low = guess
        else :
            high = guess
        guess = (low + high)/2.0
        counter += 1
    return guess

验证一下。

>>> sqrtBI(2,0.000001)

>>> 1.41421365738

上面的方法,如果 X<1 ,就会有问题。因为 X (X<1)的平方根不在 [0, x] 的范围内。例如,0.25,它的平方根——0.5 不在 [0, 0.25] 的区间内。

>>> sqrtBI(0.25,0.000001)

>>> 0.25

那如何求0.25的平方根呢?

只要略微改动上面的代码即可。注意6行和7行的代码。

def sqrtBI(x, epsilon):
    assert x>0, 'X must be non-nagtive, not ' + str(x)
    assert epsilon > 0, 'epsilon must be postive, not ' + str(epsilon)
 
    low = 0
    high = max(x, 1.0)
    ## high = x
    guess = (low + high)/2.0
    counter = 1
    while (abs(guess ** 2 - x) > epsilon) and (counter <= 100):
        if guess ** 2 < x:
            low = guess
        else :
            high = guess
        guess = (low + high)/2.0
        counter += 1
    return guess

验证一下:

>>> sqrtBI(0.25,0.000001)

>>> 0.5


上一篇:Mac OS 中的 Python(和 NumPy)开发环境设置
下一篇:谈谈Python中对象拷贝

版权声明:本站文章除非注明,均为原创内容,如需转载请务必注明出处,违者本站保留追究其法律责任之权利。