1 function [ D1, D2, td ] = Aufgabe1(X)
   2 %Aufgabe1 - compute distance matrix.
   3 %
   4 %usage
   5 %  [D1, D2, td] = Aufgabe1(X)
   6 %
   7 %input
   8 %  X : (d,n)-matrix of column vectors.
   9 %
  10 %output
  11 %  D1 : (n,n)-matrix of L_2 distances, computed by for-loop.
  12 %  D2 : (n,n)-matrix of L_2 distances, computed by matrix algebra.
  13 %  td : run-time difference between computation of D1 and D2
  14 %
  15 %description
  16 %  Aufgabe1 computes the pairwise L_2 distances between the column vectors
  17 %  of X using two different algorithms: D1 by explicit for-loops, D2 by matrix
  18 %  algebra. td reports the difference in runtime between the two implementations, where
  19 %  td is positive, if the first method (D1) took longer than the second. 
  20 %
  21 %author
  22 %  buenau@cs.tu-berlin.de
  23 
  24 [d, n] = size(X);
  25 
  26 % Speicher für Distanzmatrizen reservieren. 
  27 D1 = zeros(n, n);
  28 D2 = zeros(n, n);
  29 
  30 % Timer starten. 
  31 tic; 
  32 
  33 % Distanzmatrix mit for-Schleifen berechnen. 
  34 for j = 2:n
  35     for i = 1:j-1  % Nur obere Dreiecksmatrix berechnen, da die Distanzmatrix symmetrisch ist.
  36         D1(i, j) = sqrt( sum ( ( X(:,i) - X(:,j) ) .^ 2 ) );
  37     end
  38 end
  39 D1 = D1 + D1';  % Untere Dreiecksmatrix hinzufügen. 
  40 
  41 % Timer stoppen. 
  42 time_D1 = toc; 
  43 
  44 % Timer starten. 
  45 tic;
  46 
  47 % Distanzmatrix ohne for-Schleifen berechnen. 
  48 xx = sum(X .^ 2, 1);    % (1, n)-Vektor der quadratischen Terme x'*x. 
  49 xy = X'*X;              % (n, n)-Matrix der gemischten Terme x'*y.
  50 D2 = sqrt(repmat(xx, [n 1]) - 2*xy + repmat(xx', [1 n]));
  51 
  52 % Timer stoppen. 
  53 time_D2 = toc; 
  54 
  55 % Zeitdifferenz errechnen. 
  56 td = time_D1 - time_D2;