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PERMUTE

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.

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

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