~ubuntu-branches/ubuntu/wily/octave-miscellaneous/wily-proposed

## 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} {} zigzag (@var{mtrx})

## Returns zigzag 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 zigzag(mat) gives the output,

## [1   2   4   7   5   3   6   8   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 

##

## An example of zagzig use:

## @example

## @group

## mat = reshape(1:9,3,3);

## zigzag(mat)

## ans =[1   2   4   7   5   3   6   8   9]

##

## @end group

## @end example

##

## @end deftypefn

## @seealso{zagzig}

function rval = zigzag(mtrx)

  if nargin != 1

    print_usage;

  endif

  n=size(mtrx);

  if(issquare(mtrx)) #Square matrix (quick case)

    ##We create a matrix of the same size as mtrx where odd elements are

    ##1, others 0.

    odd=kron(ones(ceil(n/2)),eye(2))((1:n(1)),(1:n(2)));

    ##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(2)-1:-1:1-n(1)

      rval=[rval diag(mtrx,i)'];

    endfor

  else #Not square (Slow cases)

    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'];

      else                ##Odd!

        rval=[rval new((1+length(new))-(1:length(new)))'];

      endif

    endfor

  endif

endfunction

%!assert(zigzag(reshape(1:9,3,3)),[1   2   4   7   5   3   6   8   9])