X-Git-Url: http://gitweb.michael.orlitzky.com/?p=octave.git;a=blobdiff_plain;f=random_orthogonal_matrix.m;fp=random_orthogonal_matrix.m;h=8c7cea5541e7aa8890893f9327b63934290cc7a7;hp=0000000000000000000000000000000000000000;hb=f7394188abd4c5ca3a8e6a74ac16b97a4966df5e;hpb=b1a89e6359bfef7a07ffe49bc703b51ef47574a9

diff --git a/random_orthogonal_matrix.m b/random_orthogonal_matrix.m
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+function U = random_orthogonal_matrix(integerN)
+  %
+  % Generate a random orthogonal matrix.
+  %
+  % INPUT:
+  %
+  %   - ``integerN`` -- The dimension of the resulting square matrix.
+  %
+  % OUTPUT:
+  %
+  %   - ``U`` -- An orthogonal matrix of dimension integerN.
+  %
+  % REFERENCES:
+  %
+  %   1. G.W. Stewart, Efficient Generation of Random Orthogonal Matrices,
+  %      SIAM J. Numer. Analysis, 1980, pp. 403--409, Section 3.
+  %
+
+  % We begin by computing a random matrix A.
+  A = rand(integerN);
+
+  % The Q-R decomposition of A will give us an orthogonal factor of A.
+  % See the reference for why this doesn't suck.
+  [U, R] = qr(A);
+end