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) ]
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
