/usr/share/gnudatalanguage/astrolib/permute.pro is in gdl-astrolib 2018.02.16+dfsg-1.
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; NAME:
; PERMUTE
;
; PURPOSE:
; This function returns an array containing the numbers
; [0, ..., N-1] in random order. They are useful as indices
; when permuting a dataset, for example in a balanced bootstrap
; Monte Carlo algorithm.
;
; CATEGORY:
; Statistics.
;
; CALLING SEQUENCE:
;
; Result = PERMUTE(N)
;
; INPUTS:
; N: The number of items to be permuted.
;
; OPTIONAL INPUTS:
; SEED: A random number seed, see RANDOMU.
;
; OUTPUTS:
; This function returns an N-element array containing a random
; permutation of the integers from 0 through N-1.
;
; SIDE EFFECTS:
; Unless Seed is specified, IDL's global random number
; seed is changed.
;
; PROCEDURE:
; This is an in-place swapping algorithm. It starts with an
; index array. For each position in the array, it swaps the
; occupant of that position with the occupant of a random
; position from there (inclusive) to the end of the array. The
; last iteration is not necessary to compute, since it swaps
; with itself.
;
; See http://www.techuser.net/randpermgen.html for a proof. The
; 2-line code there has been optimized for IDL's vector
; architecture. This is a linear-time algorithm.
;
; EXAMPLE:
; Show some permutations of 6 numbers:
; print, permute(6)
; 0 2 1 3 4 5
; print, permute(6)
; 2 4 3 5 1 0
; print, permute(6)
; 0 4 3 1 2 5
;
; Permute the array [2, 4, 6, 8]
; a = [2, 4, 6, 8]
; print, a[permute(4)]
; 4 8 6 2
;
; Test randomness (results should be close to k):
; m = 6l
; k = 10000l
; n = m * k
; a = lonarr(m, n)
; for i = 0l, n-1, 1 do a[*, i] = permute(m)
; for i = 0l, m-1, 1 do print, histogram(a[i, *])
; 9885 10062 10051 9915 10028 10059
; 10096 10087 10094 9913 9933 9877
; 10041 10013 9968 9958 9911 10109
; 9880 9858 10166 10049 10081 9966
; 10093 9915 9800 10166 9969 10057
; 10005 10065 9921 9999 10078 9932
;
; Time the algorithm:
; maxn = 7
; t = dblarr(maxn)
; n = 10L^(indgen(maxn)+1)
; for i = 0, maxn-1, 1 do begin &$
; t1 = systime(/s) &$
; print, n[i] &$
; a = permute(n[i]) &$
; t2 = systime(/s) &$
; t[i] = t2-t1 &$
; endfor
; print, ' Elements Seconds Elements Per Second'
; print, transpose([[n], [t], [t/n]])
;
; Elements Seconds Elements Per Second
; 10.000000 0.00012397766 1.2397766e-05
; 100.00000 0.00015020370 1.5020370e-06
; 1000.0000 0.0011651516 1.1651516e-06
; 10000.000 0.018178225 1.8178225e-06
; 100000.00 0.13504505 1.3504505e-06
; 1000000.0 1.3817160 1.3817160e-06
; 10000000. 14.609985 1.4609985e-06
;
; These times are for a 2.071 GHz AMD Athlon 2800+ CPU.
;
; MODIFICATION HISTORY:
; Written by: Joseph Harrington, Cornell. 2006-03-22
; jh@alum.mit.edu
;-
function PERMUTE, N, Seed
; Don't stop here!
on_error, 2
; test inputs
if n eq 1 then return, 0L
if n lt 1 then message, 'N = ' + strtrim(n, 2) + ', must be 1 or more.'
ar = lindgen(n)
rar = reverse(ar[0 : n - 2]) + 2
r = (n - 1) - long( randomu(seed, n - 1) * rar )
for i = 0L, n - 2, 1 do begin
t = ar[i]
ar[i] = ar[r[i]]
ar[r[i]] = t
endfor
return, ar
end
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