All,

I have no experience with Perl modules that do linear algebra. I've

searched CPAN and see several.

Can someone advise me on what to use? I'd like to have the ability to

start with a matrix with integer entries, put it in reduced row

echelon form, with all of the entries as rational numbers, such as:

A =

4 0 0 2

-1 -3 0 1

0 2 0 -1

ans =

1 0 0 1/2

0 1 0 -1/2

0 0 0 0

Suggestions? This has to be in perl.

D.

Try this, only tested on your matrix.

And the swapped rows (redo) didn't come into

play on your matrix. I just guess its a redo

but don't know.

Code is based on Pseudo code from wikipedia.

-sln

---------------------------

use strict;

use warnings;

#

my

@matrix = (

[ 4, 0, 0, 2 ],

[ -1, -3, 0, 1 ],

[ 0, 2, 0, -1 ],

);

my @Mreduced = GetReducedRowEchelonForm(

@matrix);

print "\n";

print "@{$_}\n" for (

@matrix);

print "------ \n";

print "@{$_}\n" for (@Mreduced);

exit;

#

sub GetReducedRowEchelonForm

{

return () unless

@_ && ref $_[0] eq "ARRAY";

my @M;

for my $k (0 .. $#_) {

$M[$k] = [@{$_[$k]}];

}

my $lead = 0;

my $rowCount = @M - 1;

my $columnCount = @{$M[0]} - 1;

FUNC:

for my $r (0 .. $rowCount)

{

last FUNC if $columnCount <= $lead;

my $i = $r;

while( $M[$i][$lead] == 0) {

$i++;

if ( $rowCount == $i) {

$i = $r;

$lead++;

last FUNC if $columnCount == $lead;

}

last FUNC if $i > $rowCount;

}

if ($i != $r) {

my $irow = $M[$i];

$M[$i] = $M[$r];

$M[$r] = $irow;

redo FUNC; # swapped rows, should we redo? Don't know.

}

my $divisor = $M[$r][$lead];

foreach my $rowval ( @{$M[$r]} ) {

$rowval /= $divisor;

}

for $i (0 .. $rowCount) {

if ($i != $r) {

my $multiplier = $M[$i][$lead];

for my $ndx (0 .. $columnCount) {

$M[$i][$ndx] -= $multiplier * $M[$r][$ndx];

}

}

}

$lead++;

}

return @M;

}

__END__

http://en.wikipedia.org/wiki/Row_echelon_form
The following pseudocode converts a matrix to reduced row-echelon form:

function ToReducedRowEchelonForm(Matrix M) is

lead := 0

rowCount := the number of rows in M

columnCount := the number of columns in M

for 0 <= r < rowCount do

if columnCount <= lead then

stop function

end if

i = r

while M[i, lead] = 0 do

i = i + 1

if rowCount = i then

i = r

lead = lead + 1

if columnCount = lead then

stop function

end if

end if

end while

if i != r then Swap rows i and r

Divide row r by M[r, lead]

for 0 <= i < rowCount do

if i != r do

Subtract M[i, lead] multiplied by row r from row i

end if

end for

lead = lead + 1

end for

end function