fpermute

Derives a matrix of all possible permutations of natural numbers 1, 2, ... , N for a given N

Description

I faced a stupid problem of getting all possible orders of variables for Cholesky decomposition of a covariance matrix. Web search offered advertisements of 60-line codes as a solution, so I decided to crack it myself. Enjoy.

• MATLAB release: MATLAB 6.5.1 (R13SP1)

[Tim Davis]

A few suggestions. First and foremost, this code needs commenting. You have to look at the output matrix to figure out what matrix it's computing. This code has no comments at all. That's really the main reason I give it a rating of 3.

The second reason is that it needs to be redesigned. Wouldn't it make more sense to provide a function that returns each of the n! permutations one at a time? The matrix itself is huge. fpermute(10) returns a (10!)-by-10 matrix, about 3.6 million by 10. Surely an application doesn't need all 3.6 million permutations at the same time.

Something like:

k = 1
[p,k] = next_permutation(n,k)

which increments k. k=1 gives the first one (p=1:n), k=2 the next one, etc.

That would be a useful function. This one is limited by memory requirement to small values of n.