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
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--- /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