二分递归未按预期工作（Python）

Question

我已经确定了一个要使用的区间（从Python绘制的图中）——我的区间是[4,6]。我已经写了一个程序（没有完全完成），因此1）我取区间的中点（leftintervalwall，rightintervalwall），看看它是否给我0作为输出。2） 否则，该中点现在将成为新的leftintervalwall（RightIntervalWall保持不变）

我已经更新了代码：但是，当我在找到根时计算函数的输出时，得到的值为1.014，这是不正确的。它应该接近于0。所以我不确定代码中的漏洞在哪里。非常感谢

def continousfunction(xpoint):
    output = float(np.power(xpoint, 2) - np.log1p(1 + xpoint) - 30)
    return output;


                        
def processinterval(a, b):
    
        intervalmidpoint = (a + b) / 2
        return intervalmidpoint;
        

   
def findroot(a, b, accuracy):
    if(continousfunction(a) < 0 and continousfunction(b) > 0):
        bisection(a, b, accuracy)
        

        
def bisection(a, b, accuracy):
        
            
                intervalmidpoint = processinterval(a,b)
            
                if(continousfunction(intervalmidpoint) < 0):
                    a = intervalmidpoint
                    return bisection(intervalmidpoint, b, accuracy)
                    
                    
                
                print(continousfunction(intervalmidpoint))
   

def main():
    
    
    
    a = 4
    b = 6
    accuracy = 0.002
    findroot(a, b, accuracy)
    
    
main()     
    

Answer 1

这里是一个关于如何实现二分法的示例。为了避免递归错误，我添加了一个精度参数。我还对另一个函数test1做了额外的测试

[您的递归打印始终在同一时间间隔内]

def bisection(a, b, accuracy=0.002):
    midpoint = (a+b)/2
    f_m = func(midpoint)

    if abs(f_m) < accuracy:
        return midpoint
    
    # same sign
    if func(a) > 0 and f_m > 0 or func(a) < 0 and f_m < 0:
        return bisection(midpoint, b, accuracy=accuracy)
    if func(b) > 0 and f_m > 0 or func(b) < 0 and f_m < 0:
        return bisection(a, midpoint, accuracy=accuracy)
    # opposite sign
    if func(a) > 0 and f_m < 0 or func(a) < 0 and f_m > 0:
        return bisection(a, midpoint, accuracy=accuracy)
    if func(b) > 0 and f_m < 0 or func(b) < 0 and f_m > 0:
        return bisection(midpoint, b, accuracy=accuracy)


# test 1
def func(x):
    return x**3 -x -2

# initial boundaries of the interval
a, b = 1, 2
accuracy = .002

try:
    print(bisection(a, b, accuracy = .002))
except RecursionError:
    print('No root found with that accuracy limit')

# test 2
def func(x):
    return float(np.power(x, 2) - np.log1p(1 + x) - 30)

# initial boundaries of the interval
a, b = 4, 6
accuracy = .002

try:
    print(bisection(a, b, accuracy = .002))
except RecursionError:
    print('No root found with that accuracy limit')

输出

1.521484375 # for test 1
5.66015625  # for test 2