Question

我想使用导数的定义找到函数（x）（x - 1）的导数。我希望我的增量为1e-2。这样它就可以模拟限制为零。我在Range for Floats上看到我可以使用用户定义的函数来创建带浮点变量的范围函数。

def frange(x, y, jump):
    while x < y:
        yield x
        x += jump

    def drange(start, stop, step):
     r = start
     while r < stop:
        yield r
        r += step

i = frange(1e-14,1e-2,2)

for k in i:
    set  = []
    x = 1
    dvt = ((x + k ) * (x + k - 1) - x*(x - 1))/k

    set.append(dvt)
    print(set)

当我运行程序时，我只得到

[0.9992007221626509]

发生了什么我没有在列表中添加多个衍生物？

Answer 1

设置你说

x += jump

这将x的值设置为2 + 1e-14，其大于1e-2

当我阅读代码时，似乎您可能意味着

myjump = pow(10, jump) #outside the loop

x *= myjump # inside the loop

这将在示例中将每个循环乘以100，并且过程1e-14,1e-12,1e-10 ... 1e-2

或者，如果您想添加它，那么您应该说

x += myjump # inside the loop

或者你需要测试跳跃实际上是一个小到足以被处理的分数。

Answer 2

这是一个清理版本：

def fn(x):
    return x * (x - 1)

def numerical_diff(fn, x, delta):
    return (fn(x + delta) - fn(x)) / delta

def geometric_series(a, r, n):
    value = a
    for i in range(n):
        yield value     # a * r ** i
        value *= r

def main():
    x = 1.
    for delta in geometric_series(0.01, 0.01, 7):
        print(
            "x = {:5.3f}  f(x) = {:5.3f}  delta = {:16.14f}  f'(x) = {:16.14f}"
            .format(x, fn(x), delta, numerical_diff(fn, x, delta))
        )

if __name__ == "__main__":
    main()

产生

x = 1.000  f(x) = 0.000  delta = 0.01000000000000  f'(x) = 1.01000000000000
x = 1.000  f(x) = 0.000  delta = 0.00010000000000  f'(x) = 1.00009999999989
x = 1.000  f(x) = 0.000  delta = 0.00000100000000  f'(x) = 1.00000099991773
x = 1.000  f(x) = 0.000  delta = 0.00000001000000  f'(x) = 1.00000000392253
x = 1.000  f(x) = 0.000  delta = 0.00000000010000  f'(x) = 1.00000008284037
x = 1.000  f(x) = 0.000  delta = 0.00000000000100  f'(x) = 1.00008890058334
x = 1.000  f(x) = 0.000  delta = 0.00000000000001  f'(x) = 0.99920072216265

小间隔浮子的范围功能

2 个答案: