Add a useful package (from Source forge) for octave

[CreaPhase.git] / octave_packages / miscellaneous-1.1.0 / zagzig.m

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+## Copyright (C) 2006 Fredrik Bulow <fredrik.bulow@gmail.com>
+##
+## 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 3 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, see <http://www.gnu.org/licenses/>.
+
+## -*- texinfo -*-
+## @deftypefn {Function File} {} zagzig (@var{mtrx})
+## Returns zagzig walk-off of the elements of @var{mtrx}.
+## Essentially it walks the matrix in a Z-fashion.
+##  
+## mat = 
+##   1   4   7
+##   2   5   8
+##   3   6   9
+## then zagzag(mat) gives the output,
+## [1 4 2 3 5 7 8 6 9], by walking as
+## shown in the figure from pt 1 in that order of output.
+## The argument @var{mtrx} should be a MxN matrix. One use of
+## zagzig the use with picking up DCT coefficients
+## like in the JPEG algorithm for compression.
+##
+## An example of zagzig use:
+## @example
+## @group
+## mat = reshape(1:9,3,3);
+## zagzag(mat)
+## ans =[1 4 2 3 5 7 8 6 9]
+##
+## @end group
+## @end example
+##
+## @end deftypefn
+## @seealso{zigzag}
+
+function rval = zagzig(mtrx)
+
+  if nargin != 1 #Checking arguments.
+    print_usage;
+  endif
+
+  if issquare(mtrx) #Square matrix (quick case)
+    n=length(mtrx);
+    ##We create a matrix of the same size as mtrx where odd elements are
+    ##1, others 0.
+    odd=kron(ones(n,n),eye(2))((1:n),(1:n));
+
+    ##We transpose even elements only.
+    mtrx = (mtrx.*odd)' + (mtrx.*(1-odd));
+
+    ##Now we mirror the matrix. The desired vector is now the
+    ##concatenation of the diagonals.
+    mtrx=mtrx(:,1+size(mtrx,2)-(1:size(mtrx,2)));
+
+    ##Picking out the diagonals.
+    rval  = [];
+    for i = n-1:-1:1-n
+      rval=[rval diag(mtrx,i)'];
+    endfor
+
+  else #Not square (Slow cases)
+    n=size(mtrx);
+    mtrx=mtrx(:,1+size(mtrx,2)-(1:size(mtrx,2)));
+
+    ##Picking out the diagonals and reversing odd ones manually.
+    rval  = [];
+    for i = n(2)-1:-1:1-n(1)
+      new = diag(mtrx,i);
+      if floor(i/2)==i/2 ##Even?
+        rval=[rval new((1+length(new))-(1:length(new)))'];
+      else                ##Odd!
+        rval=[rval new'];
+      endif
+    endfor
+  endif
+endfunction
+
+%!assert(zagzig(reshape(1:9,3,3)),[1 4 2 3 5 7 8 6 9])