rank_k_approximation.m

   1 function Ak = rank_k_approximation(A,k)
   2   %
   3   % Compute the rank-k approximation to A from the ``k`` largest
   4   % singular values of A.
   5   %
   6   % INPUT:
   7   %
   8   %   - ``A`` -- The matrix to approximate.
   9   %
  10   %   - ``k`` -- The rank of the resulting matrix; i.e. the number
  11   %              of (large) singular values to keep.
  12   %
  13   % OUTPUT:
  14   %
  15   %   - ``Ak`` -- The rank-k approximation to ``A``.
  16   %
  17   [m,n] = size(A);
  18
  19   if (k >= min(m,n))
  20     % We're keeping greater than or equal to the maximum number of
  21     % singular values that can exist.
  22     Ak = A;
  23     return;
  24   end
  25
  26   [U, S, V, flag] = svds(A, k);
  27
  28   if (flag == 0)
  29     Ak = U*S*V';
  30   else
  31     error('Could not compute the rank-k approximation.');
  32   end
  33 end