I want to make the upper half a symmetrical one to the lower.

Ah! Thought it was too easy. That'll take 2 lines :)

#! perl -slw
use strict;
use Data::Dump qw[ pp ];

sub fillLTM {
    my @lt;
    my $n = 1;
    push @lt, [ splice @_, 0, $n++ ] while @_;
    return @lt;
}

## read raw data
while( my $rawData = <DATA> ) {
    ## Populate LT matrix
    my @lt = fillLTM( split ' ', $rawData );
    pp \@lt;;

    for my $y ( 0 .. $#lt -1 ) {
        push @{ $lt[$y] }, $lt[$_][$y] for $y+1 .. $#{ $lt[-1] };
    }
    pp \@lt;;
}

__DATA__
1 2 3 4 5 6 7 8 9 10
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
[download]

Produces:

C:\test>junk
[
    [1], 
    [2, 3], 
    [4, 5, 6], 
    [7, 8, 9, 10]
]
[
    [1, 2, 4,  7], 
    [2, 3, 5,  8], 
    [4, 5, 6,  9], 
    [7, 8, 9, 10]
]

[
    [ 1], 
    [ 2,  3], 
    [ 4,  5,  6], 
    [ 7,  8,  9, 10], 
    [11, 12, 13, 14, 15]
]
[
    [ 1,  2,  4,  7, 11], 
    [ 2,  3,  5,  8, 12], 
    [ 4,  5,  6,  9, 13], 
    [ 7,  8,  9, 10, 14], 
    [11, 12, 13, 14, 15]
]
[download]