random_orthogonal_matrix.m

   1 function U = random_orthogonal_matrix(integerN)
   2   %
   3   % Generate a random orthogonal matrix.
   4   %
   5   % INPUT:
   6   %
   7   %   - ``integerN`` -- The dimension of the resulting square matrix.
   8   %
   9   % OUTPUT:
  10   %
  11   %   - ``U`` -- An orthogonal matrix of dimension integerN.
  12   %
  13   % REFERENCES:
  14   %
  15   %   1. G.W. Stewart, Efficient Generation of Random Orthogonal Matrices,
  16   %      SIAM J. Numer. Analysis, 1980, pp. 403--409, Section 3.
  17   %
  18
  19   % We begin by computing a random matrix A.
  20   A = rand(integerN);
  21
  22   % The Q-R decomposition of A will give us an orthogonal factor of A.
  23   % See the reference for why this doesn't suck.
  24   [U, R] = qr(A);
  25 end