Perhaps a bit more messy than necessary, but: 
use strict;
use warnings;

my ($c, %k, %vals, %cols, @cols, @table, $row);

chomp($_ = <DATA>); s/\s+//g;
$c = 0; $k{$_} = $c++ for split /\|/, $_;

while (<DATA>) {
    s/\s+//g;
    @_ = split /\|/, $_;
    $vals{@_[$k{'v_id'}]}{@_[$k{'p_id'}]} = @_[$k{'s_id'}];
    $cols{@_[$k{'p_id'}]} = ();
}

@cols = sort { $a <=> $b } keys %cols;
push @table, ['', map { 'p_'.$_ } @cols];
for $row (sort { $a <=> $b } keys %vals) {
    push @table, ['v_'.$row, map { $vals{$row}{$_} ? 's_'.$vals{$row}{
+$_} : '' } @cols];
}

table(\@table);

sub table {
    my ($arr, $i, @lengths, $length, $format) = $_[0];

    for (@$arr) {
        for $i (0..$#$_) {
            $lengths[$i] = length($_->[$i]) if !$lengths[$i] || $lengt
+hs[$i] < length($_->[$i]);
        }
    }
    $length = 0;
    $length += $_ for @lengths;
    $length += 3 * $#lengths + 2;

    $format = join ' | ', map { '%-'.$_.'s' } @lengths;
    for ($i = 0; $i < $#$arr; $i++) {
        print ' ', sprintf($format, @{$arr->[$i]}), "\n",
              '-' x $length, "\n";
    }
    print ' ', sprintf($format, @{$arr->[-1]}), "\n";
}

__DATA__
p_id | v_id | s_id
  1  |  1   |  1
  2  |  1   |  2
  3  |  1   |  3
  4  |  1   |  4
  1  |  2   |  5
  2  |  2   |  6
  3  |  2   |  7
  4  |  2   |  8
  2  |  3   |  9
  4  |  3   |  10
  1  |  4   |  11
  2  |  4   |  12
  4  |  4   |  13
  3  |  5   |  14

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In reply to Re: Create a table from a matrix by TedPride
in thread Create a table from a matrix by Anonymous Monk

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