问题描述:

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