# HG changeset patch
# User Rik <octave@nomad.inbox5.com>
# Date 1321764089 28800
# Node ID 5b1ddcf5ede1593a123f142ea7d1c6294aa472de
# Parent  dd01f0bfd78d235d81ccd6539331d20b58dc8126
hadamard.m: Embed hadamard28 matrix as constant rather than computed value.

* hadamard.m: Embed hadamard28 matrix as constant rather than computed value.

diff --git a/scripts/special-matrix/hadamard.m b/scripts/special-matrix/hadamard.m
--- a/scripts/special-matrix/hadamard.m
+++ b/scripts/special-matrix/hadamard.m
@@ -66,9 +66,9 @@
 
   ## Find k if n = 2^k*p.
   k = 0;
-  while (n > 1 && floor (n/2) == n/2)
+  while (n > 1 && fix (n/2) == n/2)
     k++;
-    n = n/2;
+    n /= 2;
   endwhile
 
   ## Find base hadamard.
@@ -98,15 +98,16 @@
   ## Build H(2^k*n) from kron(H(2^k),H(n)).
   h2 = [1,1;1,-1];
   while (true)
-    if (floor (k/2) != k/2)
+    if (fix (k/2) != k/2)
       h = kron (h2, h);
     endif
-    k = floor (k/2);
+    k = fix (k/2);
     if (k == 0)
       break;
     endif
     h2 = kron (h2, h2);
   endwhile
+
 endfunction
 
 function h = h12 ()
@@ -117,7 +118,6 @@
   h(2:end,2:end) = toeplitz (tu, tl);
 endfunction
 
-
 function h = h20 ()
   tu = [+1,-1,-1,+1,+1,+1,+1,-1,+1,-1,+1,-1,-1,-1,-1,+1,+1,-1,-1];
   tl = [+1,-1,-1,+1,+1,-1,-1,-1,-1,+1,-1,+1,-1,+1,+1,+1,+1,-1,-1];
@@ -126,53 +126,50 @@
   h(2:end,2:end) = fliplr (toeplitz (tu, tl));
 endfunction
 
-function h = hnormalize (h)
-  ## Make sure each row and column starts with +1.
-  h(h(:,1)==-1,:) *= -1;
-  h(:,h(1,:)==-1) *= -1;
-endfunction
-
 function h = h28 ()
   ## Williamson matrix construction from
   ## http://www.research.att.com/~njas/hadamard/had.28.will.txt
-  s = ["+------++----++-+--+-+--++--";
-       "-+-----+++-----+-+--+-+--++-";
-       "--+-----+++---+-+-+----+--++";
-       "---+-----+++---+-+-+-+--+--+";
-       "----+-----+++---+-+-+++--+--";
-       "-----+-----++++--+-+--++--+-";
-       "------++----++-+--+-+--++--+";
-       "--++++-+-------++--+++-+--+-";
-       "---++++-+-----+-++--+-+-+--+";
-       "+---+++--+----++-++--+-+-+--";
-       "++---++---+----++-++--+-+-+-";
-       "+++---+----+----++-++--+-+-+";
-       "++++--------+-+--++-++--+-+-";
-       "-++++--------+++--++--+--+-+";
-       "-+-++-++--++--+--------++++-";
-       "+-+-++--+--++--+--------++++";
-       "-+-+-++--+--++--+----+---+++";
-       "+-+-+-++--+--+---+---++---++";
-       "++-+-+-++--+------+--+++---+";
-       "-++-+-+-++--+------+-++++---";
-       "+-++-+---++--+------+-++++--";
-       "-++--++-+-++-+++----++------";
-       "+-++--++-+-++-+++-----+-----";
-       "++-++---+-+-++-+++-----+----";
-       "-++-++-+-+-+-+--+++-----+---";
-       "--++-++++-+-+----+++-----+--";
-       "+--++-+-++-+-+----+++-----+-";
-       "++--++-+-++-+-+----++------+"];
-  ## Without this, the assignment of -1 will not work properly
-  ## (compatibility forces LHS(idx) = ANY_VAL to keep the LHS logical
-  ## instead of widening to a type that can represent ANY_VAL).
-  h = double (s == "+");
-  h(!h) = -1;
+  ## Normalized so that each row and column starts with +1
+  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 1 -1 1 1 -1 1 -1 -1 1 -1 -1 1 -1 1 -1 1 -1 -1 1 -1
+       1 1 -1 1 -1 -1 1 -1 1 1 1 -1 -1 -1 -1 -1 -1 1 1 -1 1 -1 1 1 1 1 -1 -1
+       1 1 -1 1 -1 1 1 1 1 1 -1 -1 1 -1 1 -1 -1 -1 -1 1 -1 -1 -1 -1 1 -1 1 1
+       1 1 -1 1 -1 1 -1 1 -1 1 -1 1 1 1 -1 1 -1 -1 1 -1 1 1 -1 1 -1 -1 -1 -1
+       1 -1 1 -1 1 -1 1 1 1 1 1 -1 1 -1 -1 1 -1 1 -1 -1 1 1 -1 -1 -1 -1 1 -1
+       1 1 1 -1 1 -1 1 1 -1 1 -1 -1 1 1 1 -1 1 -1 -1 -1 -1 -1 1 1 -1 1 -1 -1
+       1 1 -1 -1 1 -1 1 -1 -1 -1 -1 1 1 1 -1 1 -1 1 1 -1 -1 -1 -1 -1 1 1 1 1
+       1 1 1 -1 -1 1 1 1 -1 -1 1 1 -1 -1 -1 1 1 -1 -1 1 1 -1 -1 -1 1 1 -1 -1
+       1 1 -1 -1 1 1 -1 1 -1 -1 1 -1 -1 -1 1 -1 1 1 1 -1 1 -1 -1 1 -1 -1 1 1
+       1 -1 1 -1 -1 1 1 -1 1 1 -1 1 -1 1 -1 -1 1 -1 1 -1 1 -1 1 -1 -1 -1 1 1
+       1 1 1 -1 1 1 -1 -1 1 1 -1 1 -1 -1 1 -1 -1 1 1 1 -1 1 -1 -1 -1 1 -1 -1
+       1 -1 1 1 -1 1 1 -1 -1 -1 1 -1 1 1 1 -1 1 1 1 -1 -1 1 -1 -1 1 -1 -1 -1
+       1 1 1 -1 -1 1 -1 -1 1 -1 1 -1 1 1 -1 1 -1 1 -1 1 -1 -1 1 1 -1 -1 -1 1
+       1 -1 1 1 -1 -1 1 1 -1 -1 -1 1 -1 -1 1 1 -1 1 1 1 -1 -1 1 1 -1 -1 1 -1];
 endfunction
 
-%!assert(hadamard(1),1)
-%!assert(hadamard(2),[1,1;1,-1])
+
+%!assert (hadamard (1), 1)
+%!assert (hadamard (2), [1,1;1,-1])
 %!test
-%!  for n=[1,2,4,8,12,24,48,20,28,2^9]
-%!    h=hadamard(n); assert(norm(h*h'-n*eye(n)),0);
-%!  end
+%! for n = [1,2,4,8,12,24,48,20,28,2^9]
+%!   h = hadamard(n);
+%!   assert (norm (h*h'-n*eye (n)), 0);
+%! endfor
+
+%!error hadamard ()
+%!error hadamard (1,2)
+%!error <N must be 2^k*p> hadamard (5)
+