madM has asked for the wisdom of the Perl Monks concerning the following question:

Hi Monks.. I am trying to multiply matrices but i want someway to calculate the matrix to the power of x .. like matrix ^4 or something like this... i have build a subroutine that accepts a matrix as argument and can multiply itself.. the matrix structure looks like this(just an example) 
my %data = (
A => { A => 5,  R => -2, N => -1 },
R => { A => -2, R => 7,  N => -1 },
N => { A => -1, R => -1, N => 7 },
);

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any ideas? 
my @aminos= qw(A R N D C Q E G H I L K M F P S T W Y V B Z X);
sub multiplyRates {
    my $M1= @_ ;
    foreach my $key1 (@aminos) {
        foreach my $key2 (@aminos) {
            my $prod;
            foreach my $key (@aminos) {
                $prod += $M1->{$key1}->{$key} * $M1->{$key}->{$key2};
            }
            $multiplyrate->{$key1}->{$key2} = $prod;
        }
        $multiplyrate1->{$key1} = $newMutationmatrix1->{$key1};
    }
    return \%$multiplyrate;
}

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Re: Multiplying matrices
by moritz (Cardinal) on Mar 10, 2014 at 10:28 UTC
    Hi Monks.. I am trying to multiply matrices but i want someway to calculate the matrix to the power of x

    If your matrices are square, you can decompose your matrix into a product of the form M = U * D * U^T where U is a unitary matrix, U^T is its transposition, and D is a diagonal matrix. Calculating M^x then becomes M^x = U * D^x * U^T, and since D is diagonal calculating the xth power is the same as taking each component to the xth power.

    How does the magical decomposition work? My linear algebra fu is a bit rusty, but Matrix decomposition says the singular value decomposition (SVD) can help.

    Perl 6 - the future is here, just unevenly distributed
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Re: Multiplying matrices
by zentara (Cardinal) on Mar 10, 2014 at 10:00 UTC
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      For many years, I too have suggested people look at PDL, but it's only now reflecting on zentara's suggestion that I see PDL could really use some example code up on perlmonks. Unfortunately, I'm not a big PDL user, so you might want to jump onto the PDL mailing list or peruse the Quantified Onion for more knowledgeable answers.

      Taking a stab at an example, would the PDL code look something like this? 

      use PDL;

# amino acids in this order in the reaction rates pdl
# A R N D C Q E G H I L K M F P S T W Y V B Z X
$rates = pdl [
    [ 5, -2, -1 ],
    [ -2, 7, -1 ],
    [ -1, -1, 7 ],
];

$multiplied_rates = $rates x $rates;
print $multiplied_rates;

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      My calculation by hand seems to agree with the first two values. The rest is left as an exercise for the user.

      Looks a lot easier than the OP's code, if you can overcome the fear of the new. And it's kinda cool :)

      Edit:If I'd checked before posting, I would have linked to The Perl Data Language (PDL): A Quick Reference Guide or RFC: Getting Started with PDL (the Perl Data Language) both of which have lots of examples.

      Sometimes I can think of 6 impossible LDAP attributes before breakfast.
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Re: Multiplying matrices
by Bloodnok (Vicar) on Mar 10, 2014 at 12:44 UTC
    Hmmm, I wonder how far you've looked - I would refer you to Chapter 7 of Mastering Algorithms with Perl (referred to directly in Mastering Algorithms with Perl) - which refers to Math::MatrixReal & PDL (PDL having been mentioned elsewhere (Re: Multiplying matrices by zentara) in this thread) and I also found this (Math::GSL::Matrix) on the 3rd page of a search within CPAN - but these all concern mathematical matrices i.e. grids of numbers, whereas your example data isn't actually a matrix.

    A user level that continues to overstate my experience :-))
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Re: Multiplying matrices
by Lennotoecom (Pilgrim) on Mar 10, 2014 at 14:58 UTC
    I know this is super ugly, though working.
    @a = qw/2 2 2 5/;
#@a = qw/3 3 3 2 2 2 4 4 4/;
$n = 4;

powMatrix(\@a, $n);

sub powMatrix {
    $m = shift;
    @f = @$m;
    $i = shift;
    $l = sqrt(@$m);
    while(--$i){
        for($k = 0; $k < @$m; $k+=$l){        
            for($c = 0; $c < $l; $c++){
            $o = $c; $z = 0;
                for($b = $k; $b < $k+$l; $b++){
                $z += $f[$b] * $m->[$o];
                $o += $l;    
                }
            push (@g, $z);
            }
        }
    @f = @g; @g = ();
    }
    print "@f\n";
}

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