#!/usr/bin/perl

# Distancia de Mahalanobis
# Autor: Hermano Pereira
# www.hermano.com.br
# 14/07/2011

# Kardi Teknomo
# http://people.revoledu.com/kardi/tutorial/Similarity/MahalanobisDistance.html
# Group 1
my @g1 = ([2,2],[2,5],[6,5],[7,3],[4,7],[6,4],[5,3],[4,6],[2,5],[1,3]);
# Group 2
my @g2 = ([6,5],[7,4],[8,7],[5,6],[5,4]);

&mahalanobis(\@g1,\@g2);

####################################################################################

sub mahalanobis {
   my ($ref_a,$ref_b) = @_;
   my @a = @{$ref_a};
   my @b = @{$ref_b};

   print "\n\nValores de entrada para distancia de Mahalanobis:\n\n";
   print "a = ";
   &mahalanobis_mprint(@a);
   print "\n\nb = ";
   &mahalanobis_mprint(@b);
   print "\n";
   <STDIN>;

   print "Subtraindo o valor de cada coluna com sua media aritmetica:\n\n";
   print "a -> a2 = ";
   my @a2 = &mahalanobis_mean(@a);
   &mahalanobis_mprint(@a2);
   print "\n\nb -> b2 = ";
   my @b2 = &mahalanobis_mean(@b);
   &mahalanobis_mprint(@b2);
   print "\n";
   <STDIN>;

   print "Calculando a matriz de covariancia:\n\n";
   print "a2 -> ac = ";
   my @ac = &mahalanobis_mcov(@a2);
   &mahalanobis_mprint(@ac);
   print "\n\nb2 -> bc = ";
   my @bc = &mahalanobis_mcov(@b2);
   &mahalanobis_mprint(@bc);
   print "\n";
   <STDIN>;

   print "Juncao (pooled) das matrizes de acordo com seus pesos:\n\n";
   print "ac + bc -> mp = ";
   my @mp = &mahalanobis_mpooled(\@ac,\@bc,scalar(@a),scalar(@b));
   &mahalanobis_mprint(@mp);
   print "\n";
   <STDIN>;
   
   print "Calcular matriz inversa:\n\n";
   print "mp -> mpi = ";
   my @mpi = &mahalanobis_mpoolinv(@mp);
   &mahalanobis_mprint(@mpi);
   print "\n";
   <STDIN>;

   print "Calcular diferenca da media aritmetica entre as matrizes:\n\n";
   print "a <-> b -> mmd = ";
   my @mmd = &mahalanobis_meandiff(\@a,\@b);
   &mahalanobis_mprint(@mmd);
   print "\n";
   <STDIN>;

   print "Transposta da matriz de diferencas de medias:\n\n";
   print "mmd -> mmdt = ";
   my @mmdt = &mahalanobis_mtransp(@mmd);
   &mahalanobis_mprint(@mmdt);
   print "\n";
   <STDIN>;

  
   print "Multiplicar matriz transposta da diferencas de medias com a matriz inversa (pooled):\n\n";  
   print "mmdt * mpi -> mm1 = ";
   my @mm1 = &mahalanobis_mprod(\@mmdt,\@mpi);
   &mahalanobis_mprint(@mm1);
   print "\n";
   <STDIN>;

   print "Multiplicar matriz do resultado anterior com a matriz de diferenca de medias:\n\n";
   print "mm1 * mmd -> mm2 = ";
   my @mm2 = &mahalanobis_mprod(\@mm1,\@mmd);
   &mahalanobis_mprint(@mm2);
   print "\n";
   <STDIN>;

   print "E com a raiz quadrada do resultado anterior:\n\n";
   my $mahalanobis = sqrt($mm2[0][0]);
   print "Mahalanobis entre a e b = ".$mahalanobis."\n\n";

   return $mahalanobis;
}

sub mahalanobis_mean {
   my @m = @_;
   my @sum;
   for (my $i = 0; $i < scalar(@m); $i++) {
      for (my $j = 0; $j < scalar(@{$m[$i]}); $j++) {
         $sum[$j] += $m[$i][$j];
      }
   }
   my @avg;
   for (my $j = 0; $j < scalar(@{$m[0]}); $j++) {
      $avg[$j] = $sum[$j] / scalar(@m);
   }
   my @m2;
   for (my $i = 0; $i < scalar(@m); $i++) {
      for (my $j = 0; $j < scalar(@{$m[$i]}); $j++) {
         $m2[$i][$j] = $m[$i][$j] - $avg[$j];
      }
   }
   return @m2;
}

sub mahalanobis_mprint {
   my @m = @_;
   print "(";
   for (my $i = 0; $i < scalar(@m); $i++) {
      print "["; 
      for (my $j = 0; $j < scalar(@{$m[$i]}); $j++) {
         print $m[$i][$j];
         print "," if (! ($j == scalar(@{$m[$i]}) -1));
      }
      print "]";
      print "," if (! ($i == scalar(@m) - 1));
   }
   print ")";
}

sub mahalanobis_mcov {
   my @m = @_;
   my $cols = scalar(@{$m[0]});
   my @m2;
   for (my $i = 0; $i < $cols; $i++) {
      for (my $j = 0; $j < $cols; $j++) {
         $m2[$i][$j] = &mahalanobis_mcov_cov(\@m,$i,$j);
      }
   }
   return @m2;
}

sub mahalanobis_mcov_cov {
   my ($ref_m,$c1,$c2) = @_;
   my @m = @{$ref_m};
   my $sprod = 0;
   for (my $i = 0; $i < scalar(@m); $i++) {
      $sprod += ($m[$i][$c1] * $m[$i][$c2]);
   }
   my $cov = $sprod / scalar(@m);
   return $cov;
}

sub mahalanobis_mpooled {
   my ($ref_m1,$ref_m2,$s1,$s2) = @_;
   my @m1 = @{$ref_m1};
   my @m2 = @{$ref_m2};
   my @m3;
   for (my $i = 0; $i < scalar(@m1); $i++) {
      for (my $j = 0; $j < scalar(@m2); $j++) {
         $m3[$i][$j] = ($s1/($s1+$s2) * $m1[$i][$j]) + ($s2/($s1+$s2) * $m2[$i][$j]);
      }
   }
   return @m3;
}

sub mahalanobis_mpoolinv {
   my @m = @_;
   # append
   for (my $i = 0; $i < scalar(@m); $i++) {
      for (my $j = 0; $j < scalar(@m); $j++) {
         if ($i == $j) {
            $m[$i][$j + scalar(@m)] = 1;
         } else {
            $m[$i][$j + scalar(@m)] = 0;
         }
      }
   }
   # inverse
   for (my $i = 0; $i < scalar(@m); $i++) {
      my $p = 1 / $m[$i][$i];
      for (my $j = $i; $j <= scalar(@m) + $i; $j++) {
         $m[$i][$j] *= $p;
      }
      for (my $i2 = 0; $i2 < scalar(@m); $i2++) {
         if ($i != $i2) {
            for (my $j = scalar(@m) + $i; $j >= $i; $j--) {
               $m[$i2][$j] += (($m[$i2][$i] * -1) * $m[$i][$j]);
            }
         }
      }
   }
   # result
   my @m2;
   for (my $i = 0; $i < scalar(@m); $i++) {
      for (my $j = scalar(@{$m[$i]}) / 2; $j < scalar(@{$m[$i]}); $j++) {
         $m2[$i][$j - scalar(@{$m[$i]}) / 2] = $m[$i][$j];
      }
   }
   return @m2;
}

sub mahalanobis_meandiff {
   my ($ref_a,$ref_b) = @_;
   my @a = @{$ref_a};
   my @b = @{$ref_b};
   my @a_avg = &mahalanobis_meandiff_avg(@a);
   my @b_avg = &mahalanobis_meandiff_avg(@b);
   my @m;
   for (my $i = 0; $i < scalar(@a_avg); $i++) {
      $m[$i][0] = $a_avg[$i] - $b_avg[$i];
   }
   return @m;
}

sub mahalanobis_meandiff_avg {
   my @m = @_;
   my @sum;
   for (my $i = 0; $i < scalar(@m); $i++) {
      for (my $j = 0; $j < scalar(@{$m[$i]}); $j++) {
         $sum[$j] += $m[$i][$j];
      }
   }
   my @avg;
   for (my $j = 0; $j < scalar(@{$m[0]}); $j++) {
      $avg[$j] = $sum[$j] / scalar(@m);
   }
   return @avg;
}

sub mahalanobis_mtransp {
   my @m = @_;
   my @m2;
   for (my $i = 0; $i < scalar(@m); $i++) {
      for (my $j = 0; $j < scalar(@{$m[$i]}); $j++) {
         $m2[$j][$i] = $m[$i][$j];
      }
   }
   return @m2;
}

sub mahalanobis_mprod {
   my ($ref_a,$ref_b) = @_;
   my @a = @{$ref_a};
   my @b = @{$ref_b};
   my @m;
   for (my $i = 0; $i < scalar(@a); $i++) {
      for (my $j = 0; $j < scalar(@{$b[0]}); $j++) {
         for (my $k = 0; $k < scalar(@b); $k++) {
               $m[$i][$j] += $a[$i][$k] * $b[$k][$j];
         }
      }
   }
   return @m;
}

####################################################################################