| Re: Generating a grid in the 3D,4D,5D...N space - Advice/Combinatory/Matrices [message #94878 is a reply to message #94873] |
Tue, 14 November 2017 10:13   |
Dick Jackson
Messages: 347
Registered: August 1998
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Senior Member |
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Hi Clement,
I found a few efficiencies to improve Markus' method a little, and I think I have a working method to allow unequal numbers of rows and columns—it could be improved, but I have to leave this for the moment.
Report from running the tests:
Markus' method
% Time elapsed: 0.15960312 seconds.
n = 7
Memory used (MB): 12.5667
Dick's method 1
% Time elapsed: 0.19358516 seconds.
n = 7
Memory used (MB): 5.49789
Arrays match!
Dick's method 2
% Time elapsed: 0.34163213 seconds.
nc = 7
nr = 7
Memory used (MB): 12.5669
Arrays match!
Here is the code:
PRO MultiDimCombos
; https://groups.google.com/forum/#!topic/comp.lang.idl-pvwave /FV6s1s19BJc
n = 7
; Markus
startMem = Memory(/CURRENT)
Tic
array=bindgen(n,long(n)^n)
for k=0,n-1 do $
array[k,*]=rebin(byte((n*lindgen(long(n)^(k+1))+k) mod (n^2) ), $
long(n)^n, /sample)
Print
Print, 'Markus'' method'
Toc
highMem = Memory(/HIGHWATER)
Print, 'n = '+StrTrim(n, 2)
Print, 'Memory used (MB): ', (highMem-startMem)/1024./1024
arrayM = array
IF n LE 3 THEN Print, array
; Dick 1
startMem = Memory(/CURRENT)
Tic
array=bytarr(n,long(n)^n, /NOZERO) ; Changed from bindgen to bytarr(/NOZERO)
for k=0,n-1 do $ ; Removed '*' from destination subscripts
array[k,0]=Reform(rebin(byte((n*lindgen(long(n)^(k+1))+k) mod (n^2) ), $
long(n)^n, /sample), $
[1, long(n)^n], /OVERWRITE)
Print
Print, 'Dick''s method 1'
Toc
highMem = Memory(/HIGHWATER)
Print, 'n = '+StrTrim(n, 2)
Print, 'Memory used (MB): ', (highMem-startMem)/1024./1024
arrayD1 = array
IF n LE 3 THEN Print, array
Print, 'Arrays'+([' do not', ''])[Array_Equal(arrayD1, arrayM)]+' match!'
; Dick 2 -- method for unequal numbers of columns and rows
startMem = Memory(/CURRENT)
Tic
; To compare with Markus and Dick1:
nc = n
nr = n
; To test unequal nc and nr:
;nc = 4
;nr = 3
a = bindgen(nc, nr) ; bindgen is OK to nr = 8
i = lindgen([1, Long(nr)^nc]) ; indgen is OK to nr = 8
array=bytarr(nc,long(nr)^nc, /NOZERO)
for k=0,nc-1 do $
array[k,0]=a[k,i/(Long(nr)^(nc-1-k)) MOD nr]
Print
Print, 'Dick''s method 2'
Toc
highMem = Memory(/HIGHWATER)
Print, 'nc = '+StrTrim(nc, 2)
Print, 'nr = '+StrTrim(nr, 2)
Print, 'Memory used (MB): ', (highMem-startMem)/1024./1024
arrayD2 = array
IF nr * nc LE 12 THEN Print, array
IF nc EQ n and nr EQ n THEN $
Print, 'Arrays'+([' do not', ''])[Array_Equal(arrayD2, arrayM)]+' match!'
END
Hope this helps!
Cheers,
-Dick
Dick Jackson Software Consulting Inc.
Victoria, BC, Canada --- http://www.d-jackson.com
On Tuesday, 14 November 2017 05:16:47 UTC-8, clement...@obspm.fr wrote:
> Hello again,
>
> Thanks both of you for your replies.
>
> @Mike: I had looked into this before (I think Jeremy Bailin has published a code similar to yours called combigen.pro), but I then meet difficulties in selecting part of the generated combinations.
>
> @Markus: I say, your code is sleek and nifty. I like your solution.
>
> In the meantime, I had given this problem some more thoughts and I had come up with another slow ugly one that doesn't work for all cases:
>
> function gen_indices_comb, m, n
> ;d I/O:
> ;d m -> long integer corresponds to the number of row in original table
> ;d n -> long integer corresponds to the number of columns in original table
> ;d
> ;d vals -> long array listing the vectors of indices to extract the
> ;d different possible combinations from the values of the original
> ;d table
> ;d
> ;d NOTES: SLOW CODE, a mitigation of the values of m and n is REQUIRED
> ;d Cases, where m & n are greater than 9, are not to considered
> ;d with this code
>
> nmax = m^n
>
> ;c Assemble command generating vector of indices
> cmd = 'tmp = ['
> for ijk=(m-1L),1L,-1L do $
> cmd += ' (lmn/n^'+string(ijk,format='(I03)')+') mod n,'
> cmd += 'lmn mod n ]'
>
> ;c initialiase memory
> ini = indgen(m,n)
> tmp = lonarr(m)
> val = lonarr(m, m^n)
>
> ;c execute command for each type of combination
> for lmn=0L,(n^m-1L) do begin
> void = execute(cmd)
> if void ne 1 then message, ' > Error generating indices.'
> val[*,ijk] = ini+tmp*m
> endfor
>
> return, val
> end
>
> Afn I'm considering this post solved, I'll update it with a definitive version of my solution.
>
> Again thanks your replies,
> /C
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