#!/usr/bin/perl5.6.1 -w
# Another Algorithm we learned in school as Perl code (-;
# It is used for solving equations, and I put it here hoping 
# for some hints what could be improved, because concerning 
# elegance I do not like it and would be glad to have the 
# possibilitie to learn from more experienced folks (-;
# (especially readability is a problem for me)

use strict;
my (@MatrixA,@MatrixB,@MatrixX);
# MatrixA will include the left-side of the equation,MatrixB the right, MatrixX the solutions

my $line_counter=0;
# Input are equations of the Form: a*x1+b*x2+c*x3+..=A
# Written as:a b c=A
# Either in a file or just entered or line by line.
# Input of the left side, has to be quadratic!
while(<>)
{  
    my @line_array;
    chomp;
    die "Wrong Character in Input, $_" unless /^[0123456789 -=]+$/;
    die "No B-Val found" unless s/=(-?\d+)$//;
    @line_array=(split / /);           
    $MatrixB[$line_counter]=$1;      
    $MatrixA[$line_counter]=\@line_array;
    $line_counter++;
}
#Check if all input lines have the same number of elements
foreach (0..($line_counter-2))
{
    my $line_length_1=@{$MatrixA[$_]};
    my $line_length_2=@{$MatrixA[$_+1]};
    die "ERROR:(Columns 1/Columns 2: $line_length_1/$line_length_2)\n" unless ($line_length_1==$line_length_2);
}

my $input_lines=@MatrixB;
my $input_columns=@{$MatrixA[0]};

die "Matrix not quadratic"
    unless ($input_lines==$input_columns);

my $format=$input_columns-1;

sub Print_Matrix
{
    print join(" ",@{$MatrixA[$_]})."=".$MatrixB[$_]."\n" foreach (0..$input_columns-1); 
    print "\n";
}


&Print_Matrix;
{
    # Creation of a compareable Matrix
    # To check if two lines are equivalent
    my (@Norm_MatrixA,@Norm_MatrixB);
    foreach my $current_line (0..$format)
    {  
	my $factor=$MatrixA[$current_line][0];
	foreach (0..($format))
	{
	    $Norm_MatrixA[$current_line][$_]=$MatrixA[$current_line][$_]/$factor;
	    $Norm_MatrixB[$current_line]=$MatrixB[$current_line]/$factor;
	}  	
    }
    # Compare the Lines of the Matrix:
    foreach (0..($format))
    {
	my $upper_line=$_;
	my $eq_counter=0;
	foreach(($upper_line+1)..($format))
	{
	    my $lower_line=$_;
	    foreach(0..($format))
	    {
	        $eq_counter++ if ($Norm_MatrixA[$upper_line][$_]==$Norm_MatrixA[$lower_line][$_]);
	    }
	    $eq_counter++ if ($Norm_MatrixB[$upper_line]==$Norm_MatrixB[$lower_line]);
	    die "Two Lines of Matrix ident: $upper_line/$lower_line" if($eq_counter>=$input_columns)
	}
    }
}

# Now here comes the Gauss Algorithm
foreach my $SubMatrix (0..($input_lines-2))
{
    foreach my $line (($SubMatrix+1)..($format))
    {	
	my $pivot=$MatrixA[$SubMatrix][$SubMatrix];
	my $first=$MatrixA[$line][$SubMatrix];
	foreach my $Spalte (0..($format))
	{
	    $MatrixA[$line][$Spalte]=$MatrixA[$SubMatrix][$Spalte]+($MatrixA[$line][$Spalte]*$pivot/$first*-1);
	}    
	$MatrixB[$line]=$MatrixB[$SubMatrix]+($MatrixB[$line]*$pivot/$first*-1);
    } 
    &Print_Matrix;
}

# Get the solutions
foreach my $solve_line (reverse (0..($format)))
{
    my $leftsum=0;
    ($leftsum+=($MatrixA[$solve_line][$_]*$MatrixX[$_]))foreach ($solve_line+1..$format);  
    $MatrixX[$solve_line]=($MatrixB[$solve_line]-$leftsum)/($MatrixA[$solve_line][$solve_line]);    
}
print "x_$_=$MatrixX[$_-1]\n"foreach(1..$format+1);