my @sparse = () ;
  while (...whatever...) {
    my $value = ... ;  # next value
    my $col   = ... ;  # in this column
    my $row   = ... ;  # and this row
    if ($value) {      # keep only the non-zeros
      push @sparse, [$col, $row, $value] ;
    } ;
  } ;

  @sparse = sort { ($$a[0] <=> $$b[0]) || ($$a[1] <=> $$b[1]) || die } @sparse ;

##</code><code>##

use strict ;
use warnings ;

my @sparse = () ;
my $col = 0 ;  # emerges from loop set to # of columns
my $row = 0 ;  # emerges from loop set to # of rows

while (<DATA>) {
  s/\s+/ /g ; s/^ // ; s/ $// ;
  $col = 0 ;
  foreach my $val (split / /) {
    if ($val) { push @sparse, [$col, $row, $val] ; } ;
    ++$col ;
  } ;
  ++$row ;
} ;

@sparse = sort { ($$a[0] <=> $$b[0]) || ($$a[1] <=> $$b[1]) || die } @sparse ;

my $Ap = 0 ;
print "Ap = $Ap" ;
my $c = 0 ;
foreach my $a (@sparse) {
  while ($c < $$a[0]) {
    print " $Ap" ;
    ++$c ;
  } ;
  ++$Ap ;
} ;
while ($c++ < $col) { print " $Ap" ; } ;
print "\n" ;

print "Ai =" ;
foreach my $a (@sparse) {
  print " $$a[1]" ;
} ;
print "\n" ;

print "Ax =" ;
foreach my $a (@sparse) {
  print " $$a[2]" ;
} ;
print "\n" ;

__DATA__
       2   3   0   0   0
       3   0   4   0   6
       0  -1  -3   2   0
       0   0   1   0   0
       0   4   2   0   1