python：生成间距不均匀的数组 [英] python: generate unevenly spaced array

问题描述

我想生成一个由下限值和上限值限制的数组，该数组具有n个元素，类似于：

I would like to generate an array bounded by a lower and upper value with n elements similar to:

def my_lin(lb, ub, steps):
    dx = (ub-lb) / (steps-1)
    return [lb + i*dx for i in range(steps)]

my_lin(0,10,11)

但我希望更多的值更接近较低的值值。某种谐波间隔。我不想有一个对数间距。

But I would like to have more values closer to the lower value. Some kind of harmonic spacing. I do not want to have a logarithmic spacing.

我想这很简单，但我无法弄清楚。非常感谢您的帮助。

I guess it is rather simple but I cannot figure it out. Any help is highly appreciated.

编辑：

我想出了以下快速解决方案：

I came up with following quick solution:

def harm_series(lb,n):
    return [float(lb)/float(i) for i in range(1,n) ]

推荐答案

查找函数 f ，它在 [0,1] 内具有您想要的间距（请注意 f（0）== 0和f（1）== 1 应该保留），然后应用 f（i * dx /（ub-lb））*（ub-lb）。

Find a function f which has your desired spacing within [0,1] (note that f(0)==0 and f(1)==1 should hold) and then apply f(i*dx/(ub-lb))*(ub-lb).

我个人喜欢此功能，但还有更多功能。
例如，尝试以下操作：

I personally like power functions for this but there is many more. For example, try this:

def my_lin(lb, ub, steps, spacing=1.1):
    span = (ub-lb)
    dx = 1.0 / (steps-1)
    return [lb + (i*dx)**spacing*span for i in range(steps)]

lin = my_lin(0, 10, 11)
print lin
# visualize the spacing
print ''.join(' '*int(2*a)+'*' for a in lin)

打印：

[0.0, 0.7943282347242814, 1.702679845041569, 2.6597044516956405, 3.6497741462219233, 4.665164957684037, 5.701201299034059, 6.754727665838724, 7.823462148343428, 8.905673323855929, 10.0]
* *   *     *       *         *           *             *               *                 *                    *

现在使用参数 spacing 可以正常工作像这样：

Now with the parameter spacing it works like this:

• 离零越近，您在 ub


• 从1到另一个方向越远，mo它们是否聚集在 lb


• 如果 spacing 正好为1，则它们是等距

• The closer you get to zero, the more your values gather around ub
• The farther you go away from 1 into the other direction, the more they gather around lb
• If spacing is exactly 1, they are equally spaced

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