Re: Help setting up an array

[JD Smith <jdsmith(at)astro.cornell.edu>]

Peter Thorne wrote:
> 
> Apologies if this is trivial, but I have been working for about 8 hours
> on it and can't even begin to see how to code it in IDL. Any help very
> gratefully received. I am setting up a function which receives the
> location of points in n-dimensional space for m fields, as well as their
> weights. On call the function does not know the size of any of these
> dimensions.
> 
> Simplifying to m=1 (this m dimension should be trivial) the input is:
> 
> an array of size (n x npoints) locations of each point in the
> n-dimensional space
> 
> a vector of size (npoints) the weights.
> 
> Now, what I want to be able to do is re-bin these points into an
> n-dimensional discretized space array which encloses all points. I can
> work out the limits of this space by simply finding min and max in each
> of the n dimensions of the location array. I then need to split this
> grid into nbox n-dimensional discrete boxes (say 50 divisions per
> dimension, boxes need not be of equal size in each dimension) and place
> the respective points in their boxes in this finite representation,
> weighted by weight (trivial).
> 
> At present I am having two major problems:
> 
> 1. How to declare this discretized array and the limits in n-dimensional
> space of each box into which I bin my values given that I know n and
> nbox.
> 
> and doubtless much more difficult to overcome:
> 
> 2. How to sensibly code selection criteria to ascertain whether a
> particular value belongs to a particular grid box.
> 
> Perhaps it is not possible to code without an a priori knowledge of n -
> the dimensionality of the problem to know how many for loops to use? I
> can't see how where statements could be used.

It seems what you are trying to do is take a list of coordinates and
values and construct a data cube or hyper-cube.  For a concrete example,
consider a list of tuples of the form:

x,y,z,density

You'd like to create a 3-d array with enough elements to adequately
represent the density cube.  This immediately begs the question:  how is
the density sampled, regularly or irregularly?  If the answer is
regularly, the solution is trivial:

  s=size(c,/DIMENSIONS)
  n=intarr(s[0])
  for i=s[0]-1,0,-1 do begin 
     ind=(c[i,*]-min(c[i,*]))/spacing[i]
     n[i]=max(ind)+1
     inds=n_elements(inds) eq 0?ind:ind+n[i]*inds
  endfor 
  array=make_array(DIMENSION=n,type=size(w,/TYPE))
  array[inds]=w

where "c" is the 3xn array of x,y,z coordinates (or dxn for your
dimensionality), "w" is the n point vector of densities or weights,
etc.  And "spacing" is the n point vector of the regular spacing in each
dimension. 

E.g. suppose x runs from 0 to 20 with spacing .5, y runs from 0 to 50
with spacing 1, and z runs from 10 20 with spacing 2.

You'd set spacing=[.5,1,2] and you'd get a 41x51x6 array, with all the
values plugged into the right place.  Note that all this is doing is
rearranging data which could otherwise have been constructed into a data
cube in the first place.

If, as I suspect, you'd like to resample irregularly gridded
higher-dimensional data, you'll need to think about what sort of
sampling, and onto what size mesh you'd like to sample.  There is no
fundamental answer to these questions within the dataset itself, though
you could of course come up with quantitative heuristics.

JD