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