python - 如何随机生成非常小的数字？

Question

假设我想在 [10^-20, 0.1] 范围内抽取一个随机数，我该怎么做？

如果我使用 numpy.random.uniform，我似乎不会低于 10^-2:

In [2]: np.random.uniform(0.1, 10**(-20))
Out[2]: 0.02506361878539856

In [3]: np.random.uniform(0.1, 10**(-20))
Out[3]: 0.04035553250149768

In [4]: np.random.uniform(0.1, 10**(-20))
Out[4]: 0.09801074888377342

In [5]: np.random.uniform(0.1, 10**(-20))
Out[5]: 0.09778150831277296

In [6]: np.random.uniform(0.1, 10**(-20))
Out[6]: 0.08486347093110456

In [7]: np.random.uniform(0.1, 10**(-20))
Out[7]: 0.04206753781952958

或者我可以生成一个数组，而不是像:

In [44]: fac = np.linspace(10**(-20),10**(-1),100)

In [45]: fac
Out[45]: 
array([  1.00000000e-20,   1.01010101e-03,   2.02020202e-03,
         3.03030303e-03,   4.04040404e-03,   5.05050505e-03,
         6.06060606e-03,   7.07070707e-03,   8.08080808e-03,
         9.09090909e-03,   1.01010101e-02,   1.11111111e-02,
         1.21212121e-02,   1.31313131e-02,   1.41414141e-02,
         1.51515152e-02,   1.61616162e-02,   1.71717172e-02,
         1.81818182e-02,   1.91919192e-02,   2.02020202e-02,
         2.12121212e-02,   2.22222222e-02,   2.32323232e-02,
         2.42424242e-02,   2.52525253e-02,   2.62626263e-02,
         2.72727273e-02,   2.82828283e-02,   2.92929293e-02,
         3.03030303e-02,   3.13131313e-02,   3.23232323e-02,
         3.33333333e-02,   3.43434343e-02,   3.53535354e-02,
         3.63636364e-02,   3.73737374e-02,   3.83838384e-02,
         3.93939394e-02,   4.04040404e-02,   4.14141414e-02,
         4.24242424e-02,   4.34343434e-02,   4.44444444e-02,
         4.54545455e-02,   4.64646465e-02,   4.74747475e-02,
         4.84848485e-02,   4.94949495e-02,   5.05050505e-02,
         5.15151515e-02,   5.25252525e-02,   5.35353535e-02,
         5.45454545e-02,   5.55555556e-02,   5.65656566e-02,
         5.75757576e-02,   5.85858586e-02,   5.95959596e-02,
         6.06060606e-02,   6.16161616e-02,   6.26262626e-02,
         6.36363636e-02,   6.46464646e-02,   6.56565657e-02,
         6.66666667e-02,   6.76767677e-02,   6.86868687e-02,
         6.96969697e-02,   7.07070707e-02,   7.17171717e-02,
         7.27272727e-02,   7.37373737e-02,   7.47474747e-02,
         7.57575758e-02,   7.67676768e-02,   7.77777778e-02,
         7.87878788e-02,   7.97979798e-02,   8.08080808e-02,
         8.18181818e-02,   8.28282828e-02,   8.38383838e-02,
         8.48484848e-02,   8.58585859e-02,   8.68686869e-02,
         8.78787879e-02,   8.88888889e-02,   8.98989899e-02,
         9.09090909e-02,   9.19191919e-02,   9.29292929e-02,
         9.39393939e-02,   9.49494949e-02,   9.59595960e-02,
         9.69696970e-02,   9.79797980e-02,   9.89898990e-02,
         1.00000000e-01])

并从该数组中随机选择一个元素，但无论如何我都想澄清第一个选项是否可行，因为我可能会遗漏一些明显的东西。

Answer 1

您需要仔细考虑您正在做的事情。您要求在几乎 0.0 和 0.1 之间均匀分布。平均结果为 0.05。这正是你得到的。您似乎想要指数的随机分布。

以下可能会做你想做的事:

import random

def rnd():
    exp = random.randint(-19, -1)
    significand = 0.9 * random.random() + 0.1
    return significand * 10**exp

[rnd() for _ in range(20)]

最低可能值是 exp=-19和 significand=0.1给予 0.1*10**-19 = 1**-20 .最高可能值是 exp=-1和 significand=1.0给予 1.0*10**-1 = 0.1 .

注意:从技术上讲，significand只能将 1.0 作为 random() is bounded to [0.0, 1.0)，即包含0.0，不包含1.0。

输出:

[2.3038280595190108e-11,
 0.02658855644891981,
 4.104572641101877e-11,
 3.638231824527544e-19,
 6.220040206106022e-17,
 7.207472203268789e-06,
 6.244626749598619e-17,
 2.299282102612733e-18,
 0.0013251357609258432,
 3.118805901868378e-06,
 6.585606992344938e-05,
 0.005955900790586139,
 1.72779538837876e-08,
 7.556972406280229e-13,
 3.887023124444594e-15,
 0.0019965330694999488,
 1.7732147730252207e-08,
 8.920398286274208e-17,
 4.4422869312622194e-08,
 2.4815949527034027e-18]

请参阅维基百科上的“scientific notation”以了解有效数和指数的定义。