循环使用，而在第一次迭代中停止

Question

我用带循环条件的python进行了二分计算。循环以两个条件停止，达到最大迭代或最大误差。

但是当我运行时，它总是以两个迭代结束。

当我删除最大错误需求时，迭代运行到最大迭代，而当我删除迭代需求时，迭代只重复2次。

请帮帮我。谢谢。

def bisection(f, Xl, Xu, max_eA, iteration):
    x_l = Xl
    x_u = Xu
    eA = 0
    Xr = (x_l + x_u)/2
    total_iter = 0

    if f(Xl)*f(Xu) >= 0:
        print("Bisection method fails.")
        return None

    while eA < max_eA and total_iter < iteration+1:
        print("iteration", total_iter+1)
        xr_old = Xr
        print("xr old",xr_old)
        Xr = (x_l + x_u)/2
        print("Xr now", Xr)
        f_xr = f(Xr)
        if     f_xr == 0:
            print("Found exact solution.")
            print("Xr fix", Xr)
            return Xr
        elif f(x_l)*f_xr < 0:
            x_l = x_l
            x_u = Xr
            print("x_l use",x_l)
            print("x_u use",x_u)
        elif f(x_l)*f_xr > 0:
            x_l = Xr
            x_u = x_u
        else:
            print("Bisection method fails.")
            return None
        xr_new = Xr
        print("xr new",xr_new)
        print("xr old 2", xr_old)
        print("ea use",eA)
        eA = abs((xr_new-xr_old)/xr_new)
        print("max ea",max_eA)
        print("eA after calculate", eA)
        total_iter=total_iter+1
    return (x_l + x_u)/2

f = lambda x:  ((10000000 * (1.2 ** x)) / ((1.2 ** x) - 1))\
           +\
           ((-10000000*x) / ((1.2 ** x) - 1))\
           +\
           10000000
bisection(f,5,10,0.0001,20)

Answer 1

代码只迭代两次，因为在第二次迭代中，eA的值比max_eA大，这是显而易见的。在从while循环中删除eA的条件后，您将获得21次迭代所需的输出。

代码的输出是

iteration 1
xr old 7.5
Xr now 7.5
xr new 7.5
xr old 2 7.5
ea use 0
max ea 0.0001
eA after calculate 0.0
iteration 2
xr old 7.5
Xr now 8.75
x_l use 7.5
x_u use 8.75
xr new 8.75
xr old 2 7.5
ea use 0.0
max ea 0.0001
eA after calculate 0.14285714285714285

从输出中可以看到，在第二次迭代中，eA的值是0.14285714285714285，max_ea的值是0.0001。所以，while循环失败了。