Mercurial > forge
changeset 2660:068affeed38b octave-forge
zagzig & zigzag functions from Fredrik Bulow, for use with matrix processing
author | gnumuthu |
---|---|
date | Tue, 10 Oct 2006 19:24:34 +0000 |
parents | 6af5e46abef9 |
children | efc472a6e3fe |
files | main/miscellaneous/inst/zagzig.m main/miscellaneous/inst/zigzag.m |
diffstat | 2 files changed, 181 insertions(+), 0 deletions(-) [+] |
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--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/main/miscellaneous/inst/zagzig.m Tue Oct 10 19:24:34 2006 +0000 @@ -0,0 +1,92 @@ +## Copyright (C) 2006, October, 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 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 -*- +## @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} + +## Author: Fredrik Bulow, <fredrik.bulow@gmail.com> + +function rval = zagzig(mtrx) + + if nargin != 1 #Checking arguments. + error('usage: zagzig(matrix); see help zagzig'); + 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]) +%!
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/main/miscellaneous/inst/zigzag.m Tue Oct 10 19:24:34 2006 +0000 @@ -0,0 +1,89 @@ +## Copyright (C) 2006, October, 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 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 -*- +## @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} + +## Author: Fredrik Bulow, <fredrik.bulow@gmail.com> + +function rval = zigzag(mtrx) + if nargin < 1 + error('usage: zigzag(matrix); see help zigzag'); + end + 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]) +%!