python: generate unevenly spaced array

Question

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)

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.

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

EDIT:

I came up with following quick solution:

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

probably, because people want to see an attempt and help with errors than writing code for someone... — Lawrence Benson
– Lawrence Benson, Commented Sep 10, 2015 at 14:40
Sometimes it is hard to find the proper word like "harmonic series" and googling does not help. But I will update the question with my solution. — Moritz
– Moritz, Commented Sep 10, 2015 at 14:43

swenzel · Accepted Answer · 2015-09-10 15:46:29Z

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).

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)

Prints:

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

Now with the parameter spacing it works like this:

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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