You can easily modify your shuffling procedure to give you a shuffle in which no position remains fixed (this is called a derangement): 

sub fys {
    my $arr = shift;
    my $i = @{ $arr };
    while ( $i ) {
        my $j = int rand $i;
        @$arr[$i,$j] = @$arr[$j,$i];
        --$i;
    }
}

[download]
With this change, then all you need to shuffle the columns is this: 
@nums = map [ @{$_}[@cols] ], @nums;

[download]

The problem with this simple solution is that it cannot generate all possible derangements. For example, the modified FY misses the derangment 1,0,3,2 of 0,1,2,3.

I looked online for algorithms to fairly sample the space of all derangments of an input list, and the best I found was based on using the standard FY until a derangement is found (i.e. a rejection method). If you need to randomly sample from the space of all possible derangements of the columns, then keep your original FY procedure, but modify the creation of @cols to this: 

my @cols = 0..11;
do {
  fys( \@cols );
} until is_deranged( \@cols );

[download]
where 
sub is_deranged {
  my $arr = shift;
  $arr->[ $_ ] == $_ and return for 0..$#$arr;
  return 1;
}

[download]
The probability of getting a derangement from a random sample of permutations is ≈ 1/e (i.e. about three trials required per derangement, on average). Moreover, one can optimize the FY procedure around this problem (by having it automatically restart when it encounters a "trivial" swap, i.e. $i == $j), which obviates the need to have a specific rejection step. Therefore this approach has essentially the same time and space growth properties as FY.

Update: Added the stuff about fair sampling, and the rejection method for obtaining a random derangement.

the lowliest monk

In reply to Re: swap columns in a 2-dim array by tlm
in thread swap columns in a 2-dim array by davidj

Title:
Use:  <p> text here (a paragraph) </p>
and:  <code> code here </code>
to format your post, it's "PerlMonks-approved HTML":


  • Posts are HTML formatted. Put <p> </p> tags around your paragraphs. Put <code> </code> tags around your code and data!
  • Titles consisting of a single word are discouraged, and in most cases are disallowed outright.
  • Read Where should I post X? if you're not absolutely sure you're posting in the right place.
  • Please read these before you post! —
  • Posts may use any of the Perl Monks Approved HTML tags:
    a, abbr, b, big, blockquote, br, caption, center, col, colgroup, dd, del, details, div, dl, dt, em, font, h1, h2, h3, h4, h5, h6, hr, i, ins, li, ol, p, pre, readmore, small, span, spoiler, strike, strong, sub, summary, sup, table, tbody, td, tfoot, th, thead, tr, tt, u, ul, wbr
  • You may need to use entities for some characters, as follows. (Exception: Within code tags, you can put the characters literally.)
            For:     Use:
    & &amp;
    < &lt;
    > &gt;
    [ &#91;
    ] &#93;
  • Link using PerlMonks shortcuts! What shortcuts can I use for linking?
  • See Writeup Formatting Tips and other pages linked from there for more info.