Mercurial > matrix-functions
diff toolbox/hadamard.m @ 2:c124219d7bfa draft
Re-add the 1995 toolbox after noticing the statement in the ~higham/mctoolbox/ webpage.
author | Antonio Pino Robles <data.script93@gmail.com> |
---|---|
date | Thu, 07 May 2015 18:36:24 +0200 |
parents | 8f23314345f4 |
children |
line wrap: on
line diff
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/toolbox/hadamard.m Thu May 07 18:36:24 2015 +0200 @@ -0,0 +1,41 @@ +function H = hadamard(n) +%HADAMARD Hadamard matrix. +% HADAMARD(N) is a Hadamard matrix of order N, that is, +% a matrix H with elements 1 or -1 such that H*H' = N*EYE(N). +% An N-by-N Hadamard matrix with N>2 exists only if REM(N,4) = 0. +% This function handles only the cases where N, N/12 or N/20 +% is a power of 2. + +% Reference: +% S.W. Golomb and L.D. Baumert, The search for Hadamard matrices, +% Amer. Math. Monthly, 70 (1963) pp. 12-17. + +% History: +% NJH (11/14/91), revised by CBM, 6/24/92, +% comment lines revised by NJH, August 1993. + +[f,e] = log2([n n/12 n/20]); +k = find(f==1/2 & e>0); +if isempty(k) + error(['N, N/12 or N/20 must be a power of 2.']); +end +e = e(k)-1; + +if k == 1 % N = 1 * 2^e; + H = [1]; + +elseif k == 2 % N = 12 * 2^e; + H = [ones(1,12); ones(11,1) ... + toeplitz([-1 -1 1 -1 -1 -1 1 1 1 -1 1],[-1 1 -1 1 1 1 -1 -1 -1 1 -1])]; + +elseif k == 3 % N = 20 * 2^e; + H = [ones(1,20); ones(19,1) ... + hankel([-1 -1 1 1 -1 -1 -1 -1 1 -1 1 -1 1 1 1 1 -1 -1 1], ... + [1 -1 -1 1 1 -1 -1 -1 -1 1 -1 1 -1 1 1 1 1 -1 -1])]; +end + +% Kronecker product construction. +for i = 1:e + H = [H H + H -H]; +end