【算法 | Python】二分法求函数在区间[a,b]中的根

末蓝、 2022-12-03 05:22 146阅读 0赞

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程序来源：[Bisection][]

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### Arithmetic Analysis ###

*   *   *  原理说明
         *  源代码
         *  代码说明

### 原理说明 ###

*  [二分法-百度百科][-]

### 源代码 ###

import math
    
    ''' 二分法求函数在区间[a,b]中的根 '''
    
    def bisection(
        function, a, b
    ):  # finds where the function becomes 0 in [a,b] using bolzano
    
        start = a
        end = b
        if function(a) == 0:  # one of the a or b is a root for the function
            return a
        elif function(b) == 0:
            return b
        elif (
            function(a) * function(b) > 0
        ):  # if none of these are root and they are both positive or negative,
            # then his algorithm can't find the root
            print("couldn't find root in [a,b]")
            return
        else:
            mid = start + (end - start) / 2.0
            while abs(start - mid) > 10 ** -7:  # until we achieve precise equals to 10^-7
                if function(mid) == 0:
                    return mid
                elif function(mid) * function(start) < 0:
                    end = mid
                else:
                    start = mid
                mid = start + (end - start) / 2.0
            return mid
    
    
    def f(x):
        return math.pow(x, 3) - 2 * x - 5
    
    
    if __name__ == "__main__":
        print(bisection(f, 1, 1000))

### 代码说明 ###

*  本程序较为简单，说明略，有问题请留言。

[Bisection]: https://github.com/TheAlgorithms/Python/blob/master/arithmetic_analysis/bisection.py
[-]: https://baike.baidu.com/item/%E4%BA%8C%E5%88%86%E6%B3%95/1364267?fr=aladdin