From octave-sources-request at bevo dot che dot wisc dot edu Fri Apr  4 00:21:25 2003
Subject: hadamard.m
From: "Quentin H. Spencer" <qspencer at ieee dot org>
To: octave-sources at bevo dot che dot wisc dot edu
Date: Thu, 3 Apr 2003 23:16:41 -0600

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I just noticed Octave does not have the function hadamard.m for 
generating Hadamard matrices, so I wrote it. For those interested in 
duplicating the organization of "the leading brand" software, I believe 
this is in the statistics toolbox. I don't know whether this should be 
added directly to octave or octave-forge. By the way, what is the 
general philosophy on this (adding contributed functions to octave or 
octave-forge)?

regards,

Quentin Spencer

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## Copyright (C) 2003, Quentin H. Spencer
##
## This program is free software; you can redistribute it and/or modify
## it under the terms of the GNU General Public License as published by
## the Free Software Foundation; either version 2 of the License, or
## (at your option) any later version.
##
## This program is distributed in the hope that it will be useful,
## but WITHOUT ANY WARRANTY; without even the implied warranty of
## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
## GNU General Public License for more details.
##
## You should have received a copy of the GNU General Public License
## along with this program; if not, write to the Free Software
## Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA

## -*- texinfo -*-
##  at deftypefn {Function File} {} hadamard(@var{N})
##
## Generate a Hadamard matrix of dimension  at var{N} dot  While Hadamard
## matrices exist for  at var{N}=2, and 4*K for integer values of K,
## this function only supports values of  at var{N} where @var{N},
##  at var{N}/12, or @var{N}/20 is a power of 2.
##  at end deftypefn

function H = hadamard(N);

H2 = [1, 1; 1,-1];

if(2^(logN=floor(log2(N)))==N)
    H = H2;
    for n = 1:logN-1
	H = kron(H,H2);
    end

elseif(2^(logN=floor(log2(N/12)))*12==N)
    H =[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, 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,-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, 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];
    for n = 1:logN
	H = kron(H,H2);
    end
    
elseif(2^(logN=floor(log2(N/20)))*20==N)
    H =[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,-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, 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, 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, 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, 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, 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, 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, 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,-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;
	1,-1,-1,-1, 1, 1, 1, 1,-1,-1, 1, 1, 1,-1,-1,-1,-1, 1, 1,-1];
    for n = 1:logN
	H = kron(H,H2);
    end

else
    warning(["incorrect or unsupported dimension argument: ",int2str(N)]);
end

endfunction

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