[Numpy-discussion] puzzle: generate index with many ranges

[Rick White]

Here's a technique that works:

Python 2.4.2 (#5, Nov 21 2005, 23:08:11)
[GCC 4.0.0 20041026 (Apple Computer, Inc. build 4061)] on darwin
Type "help", "copyright", "credits" or "license" for more information.
 >>> import numpy as np
 >>> a = np.array([0,4,0,11])
 >>> b = np.array([-1,11,4,15])
 >>> rangelen = b-a+1
 >>> cumlen = rangelen.cumsum()
 >>> c = np.arange(cumlen[-1],dtype=np.int32)
 >>> c += np.repeat(a[1:]-c[cumlen[0:-1]], rangelen[1:])
 >>> print c
[ 4  5  6  7  8  9 10 11  0  1  2  3  4 11 12 13 14 15]

The basic idea is that the difference of your desired output from a  
simple range is an array with a bunch of constant values appended  
together, and that is what repeat() does.  I'm assuming that you'll  
never have b < a.  Notice the slight ugliness of prepending the  
elements at the beginning so that the cumsum starts with zero.   
(Maybe there is a cleaner way to do that.)

This does create a second array (via the repeat) that is the same  
length as the result.  If that uses too much memory, you could break  
up the repeat and update of c into segments using a loop.  (You  
wouldn't need a loop for every a,b element -- do a bunch in each  
iteration.)

-- Rick

Raik Gruenberg wrote:

> Hi there,
>
> perhaps someone has a bright idea for this one:
>
> I want to concatenate ranges of numbers into a single array (for  
> indexing). So I
> have generated an array "a" with starting positions, for example:
>
> a = [4, 0, 11]
>
> I have an array b with stop positions:
>
> b = [11, 4, 15]
>
> and I would like to generate an index array that takes 4..11, then  
> 0..4, then
> 11..15.
>
> In reality, a and b have 10000+ elements and the arrays to be  
> "sliced" are very
> large so I want to avoid any for loops etc. Any idea how this could  
> be done? I
> thought some combination of *repeat* and adding of *arange* should  
> do the trick
> but just cannot nail it down.
>
> Thanks in advance for any hints!
>
> Greetings,
> Raik