1: #!/usr/bin/perl5.6.1 -w
   2: # Another Algorithm we learned in school as Perl code (-;
   3: # It is used for solving equations, and I put it here hoping 
   4: # for some hints what could be improved, because concerning 
   5: # elegance I do not like it and would be glad to have the 
   6: # possibilitie to learn from more experienced folks (-;
   7: # (especially readability is a problem for me)
   8: 
   9: use strict;
  10: my (@MatrixA,@MatrixB,@MatrixX);
  11: # MatrixA will include the left-side of the equation,MatrixB the right, MatrixX the solutions
  12: 
  13: my $line_counter=0;
  14: # Input are equations of the Form: a*x1+b*x2+c*x3+..=A
  15: # Written as:a b c=A
  16: # Either in a file or just entered or line by line.
  17: # Input of the left side, has to be quadratic!
  18: while(<>)
  19: {  
  20:     my @line_array;
  21:     chomp;
  22:     die "Wrong Character in Input, $_" unless /^[0123456789 -=]+$/;
  23:     die "No B-Val found" unless s/=(-?\d+)$//;
  24:     @line_array=(split / /);           
  25:     $MatrixB[$line_counter]=$1;      
  26:     $MatrixA[$line_counter]=\@line_array;
  27:     $line_counter++;
  28: }
  29: #Check if all input lines have the same number of elements
  30: foreach (0..($line_counter-2))
  31: {
  32:     my $line_length_1=@{$MatrixA[$_]};
  33:     my $line_length_2=@{$MatrixA[$_+1]};
  34:     die "ERROR:(Columns 1/Columns 2: $line_length_1/$line_length_2)\n" unless ($line_length_1==$line_length_2);
  35: }
  36: 
  37: my $input_lines=@MatrixB;
  38: my $input_columns=@{$MatrixA[0]};
  39: 
  40: die "Matrix not quadratic"
  41:     unless ($input_lines==$input_columns);
  42: 
  43: my $format=$input_columns-1;
  44: 
  45: sub Print_Matrix
  46: {
  47:     print join(" ",@{$MatrixA[$_]})."=".$MatrixB[$_]."\n" foreach (0..$input_columns-1); 
  48:     print "\n";
  49: }
  50: 
  51: 
  52: &Print_Matrix;
  53: {
  54:     # Creation of a compareable Matrix
  55:     # To check if two lines are equivalent
  56:     my (@Norm_MatrixA,@Norm_MatrixB);
  57:     foreach my $current_line (0..$format)
  58:     {  
  59: 	my $factor=$MatrixA[$current_line][0];
  60: 	foreach (0..($format))
  61: 	{
  62: 	    $Norm_MatrixA[$current_line][$_]=$MatrixA[$current_line][$_]/$factor;
  63: 	    $Norm_MatrixB[$current_line]=$MatrixB[$current_line]/$factor;
  64: 	}  	
  65:     }
  66:     # Compare the Lines of the Matrix:
  67:     foreach (0..($format))
  68:     {
  69: 	my $upper_line=$_;
  70: 	my $eq_counter=0;
  71: 	foreach(($upper_line+1)..($format))
  72: 	{
  73: 	    my $lower_line=$_;
  74: 	    foreach(0..($format))
  75: 	    {
  76: 	        $eq_counter++ if ($Norm_MatrixA[$upper_line][$_]==$Norm_MatrixA[$lower_line][$_]);
  77: 	    }
  78: 	    $eq_counter++ if ($Norm_MatrixB[$upper_line]==$Norm_MatrixB[$lower_line]);
  79: 	    die "Two Lines of Matrix ident: $upper_line/$lower_line" if($eq_counter>=$input_columns)
  80: 	}
  81:     }
  82: }
  83: 
  84: # Now here comes the Gauss Algorithm
  85: foreach my $SubMatrix (0..($input_lines-2))
  86: {
  87:     foreach my $line (($SubMatrix+1)..($format))
  88:     {	
  89: 	my $pivot=$MatrixA[$SubMatrix][$SubMatrix];
  90: 	my $first=$MatrixA[$line][$SubMatrix];
  91: 	foreach my $Spalte (0..($format))
  92: 	{
  93: 	    $MatrixA[$line][$Spalte]=$MatrixA[$SubMatrix][$Spalte]+($MatrixA[$line][$Spalte]*$pivot/$first*-1);
  94: 	}    
  95: 	$MatrixB[$line]=$MatrixB[$SubMatrix]+($MatrixB[$line]*$pivot/$first*-1);
  96:     } 
  97:     &Print_Matrix;
  98: }
  99: 
 100: # Get the solutions
 101: foreach my $solve_line (reverse (0..($format)))
 102: {
 103:     my $leftsum=0;
 104:     ($leftsum+=($MatrixA[$solve_line][$_]*$MatrixX[$_]))foreach ($solve_line+1..$format);  
 105:     $MatrixX[$solve_line]=($MatrixB[$solve_line]-$leftsum)/($MatrixA[$solve_line][$solve_line]);    
 106: }
 107: print "x_$_=$MatrixX[$_-1]\n"foreach(1..$format+1);
 108: