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Re: Generating a grid in the 3D,4D,5D...N space - Advice/Combinatory/Matrices [message #94865 is a reply to message #94864] Mon, 13 November 2017 16:04 Go to previous messageGo to previous message
Michael Galloy is currently offline  Michael Galloy
Messages: 1114
Registered: April 2006
Senior Member
On 11/13/17 7:50 AM, clement.feller@obspm.fr wrote:
> Hello everyone,
>
> I coming back to you for some advice on how to properly generate a grid in an N-D space. I hope that this expression is the proper one in english, but in any case, let me illustrate this by the following exemple:
>> a = indgen(3,3) & print, a
> 0 1 2
> 3 4 5
> 6 7 8
>
> What I am looking for would be to find the clean and proper IDL way to generate the following sets of combinations:
> 0,1,2
> 0,1,5
> 0,1,8
> 0,4,2
> 0,4,5
> .....
> .....
>
> 6,7,2
> 6,7,5
> 6,7,8
>
> Now, I have found ways to do this for a 2D,3D,4D,5D space with either nested loops (yuck! I know), or with combinations of rebin, reform and transpose.
> I've been successfully using those solutions for several weeks, yet I wonder on how to expand this to a general case and in the proper IDL way.
>
> Why and how this is useful to me ?
> I am actually trying to evaluate a function with several parameters. Let's call it f(x, p_0, ..., p_n). Given x, I want to evaluate f with multiple sets of parameters.
> E.g. to generate a regular grid I can use INTERPOLATE, e.g. for a 2D space with 10 evaluations for each dimension:
>
>> p = [[0.,1.], [0,100]]
>> p = transpose(p)
>> interpolate(p,1./9.*findgen(10))
> 0.0000000 0.0000000
> 0.11111111 11.111112
> 0.22222222 22.222223
> 0.33333334 33.333336
> 0.44444445 44.444447
> 0.55555558 55.555557
> 0.66666669 66.666672
> 0.77777779 77.777779
> 0.88888890 88.888893
> 1.0000000 100.00000
>
> If one wants an irregular grid (with 10 evaluations in the first dimension and 5 in the second one), one can use a nested loop and play with indices.
>
> So, once you have this table, how can one generate the proper sets of combinations of indices ?
> Another way to look at it is that you just want to "multiply" or chunk index your table, i.e. to generate the n vector used in the histogram's i-vector example (http://www.idlcoyote.com/tips/histogram_tutorial.html).
>
> I've playing around with nested indgen, looking for a repetitive motive from the 2D to the 5D space when using rebin, reform, transpose to assemble a generic command. But nothing much so far....
>
> Does anybody out there already had a go with such problem before or any advice ?
>
> I thank you all in advance for your replies.
> Cheers,
> /C
>

I don't have a good solution. I think the below routine is general, but
slow solution:

https://github.com/mgalloy/mglib/blob/master/src/analysis/mg _find_combinations.pro

Mike
--
Michael Galloy
www.michaelgalloy.com
Modern IDL: A Guide to IDL Programming (http://modernidl.idldev.com)

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