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Generating a grid in the 3D,4D,5D...N space - Advice/Combinatory/Matrices [message #94864] Mon, 13 November 2017 06:50 Go to previous message
clement.feller@obspm. is currently offline  clement.feller@obspm.
Messages: 5
Registered: March 2017
Junior Member
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

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