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Re: Sorting a matrix [message #83565 is a reply to message #83475]

Fri, 08 March 2013 15:51

Jeremy Bailin
Messages: 618
Registered: April 2008

Senior Member

On 3/8/13 4:24 PM, Gianguido Cianci wrote:
> I was curious to compare this method with a more straightforward way. multisort.pro below does both.
> Jeremy's method is twice as fast for large arrays. However, the two methods only give the same result for smallish arrays.
>
> Any ideas what's going on?
>
> ;;;;;;;;;;;;;; EXAMPLES ;;;;;;;;;;;;;
> multisort, round(randomu(s,20,1e1)*10)
> ; 1
> ; 0.00027489662 0.00026106834
>
> multisort, round(randomu(s,20,1e2)*10)
> ; 0
> ; 0.00072312355 0.00039005280
>
>
> ;;;;;;;;;;;;;; CODE ;;;;;;;;;;;;;;;
> PRO multisort, matrix
>
> compile_opt idl2
>
>
> matrixshape = size(matrix, /dimen)
>
> t1 = systime(1)
>
>
> ; this gives you the range of each column:
> matrixord = lonarr(matrixshape)
> for i=0l,matrixshape[0]-1 do matrixord[i,*] = ord(matrix[i,*])
> ordmax = max(matrixord, dimen=2)
>
> ; what do you need to multiply by to get a unique range?
> column_multiply = [reverse(product(reverse(ordmax[1:*]+1), /int, /cumul)), 1]
>
> ; create a unique key and sort on it
> sortkey = total(matrixord * rebin(column_multiply,matrixshape, /sample), /int, 1)
> newmatrix = matrix[*, sort(sortkey)]
> t2 = systime(1)
>
>
> newmatrix2 = matrix
> FOR i = matrixshape[0]-1, 0, -1 DO BEGIN
> s = bsort(newmatrix2[i, *]);use bsort which maintains order of identical elements
> newmatrix2 = newmatrix2[*, s]
> ENDFOR
> t3 = systime(1)
>
> print,array_equal( newmatrix, newmatrix2)
>
> print, t3-t2, t2-t1
>
>
> RETURN
> END
>

Bwahahah.... oh dear.

The problem is that in this case, column_multiply ends up being a LONG64
in order to fit the maximum value of the PRODUCT. But when you multiply:
matrixord * rebin(column_multiply, matrixshape, /sample)
the values are larger than the maximum LONG64... and wrap around to
become negative numbers!

IDL> print, minmax(matrixord)
0 10
IDL> print, minmax(column_multiply)
1 5054470284992937710
IDL> print, minmax(matrixord * rebin(column_multiply, matrixshape, /sample))
-8337803503723676196 8596744417517336158
IDL> help, matrixord, column_multiply
MATRIXORD LONG = Array[20, 100]
COLUMN_MULTIPLY LONG64 = Array[20]

In principle there are 10^20 possible rows, and it's trying to make sure
it has a unique integer for each possibility.

I guess my advice is to cap it at 19 columns and maybe do it in chunks
if there are more columns.

-Jeremy.

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[Message index]

		Sorting a matrix By: Mats Löfdahl on Fri, 01 March 2013 04:45
		Re: Sorting a matrix By: Mats Löfdahl on Fri, 01 March 2013 08:49
		Re: Sorting a matrix By: Jeremy Bailin on Tue, 05 March 2013 21:22
		Re: Sorting a matrix By: Jeremy Bailin on Fri, 01 March 2013 08:28
		Re: Sorting a matrix By: Mats Löfdahl on Thu, 07 March 2013 05:32
		Re: Sorting a matrix By: Jeremy Bailin on Thu, 07 March 2013 16:34
		Re: Sorting a matrix By: Mats Löfdahl on Fri, 08 March 2013 16:14
		Re: Sorting a matrix By: cgguido on Fri, 08 March 2013 16:24
		Re: Sorting a matrix By: cgguido on Fri, 08 March 2013 14:24
		Re: Sorting a matrix By: Jeremy Bailin on Fri, 08 March 2013 15:51
		Re: Sorting a matrix By: Mats Löfdahl on Fri, 08 March 2013 16:31

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