v_qrdotdiv

V_QRDOTDIV divides two real quaternions arrays elementwise q=[x,y]

 Inputs:  x(4n,...)
          y(4n,...)   Two real quaternion arrays of equal size

 Outputs: q(4n,...)    The Hadamard quaotient (i.e. ./) of the input arrays
                       If y is omitted then q = x^(-1)

      Copyright (C) Mike Brookes 2000-2012
      Version: $Id: v_qrdotdiv.m 10865 2018-09-21 17:22:45Z dmb $

   VOICEBOX is a MATLAB toolbox for speech processing.
   Home page: http://www.ee.ic.ac.uk/hp/staff/dmb/voicebox/voicebox.html

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
   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 can obtain a copy of the GNU General Public License from
   http://www.gnu.org/copyleft/gpl.html or by writing to
   Free Software Foundation, Inc.,675 Mass Ave, Cambridge, MA 02139, USA.
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0001 function q=v_qrdotdiv(x,y)
0002 %V_QRDOTDIV divides two real quaternions arrays elementwise q=[x,y]
0003 %
0004 % Inputs:  x(4n,...)
0005 %          y(4n,...)   Two real quaternion arrays of equal size
0006 %
0007 % Outputs: q(4n,...)    The Hadamard quaotient (i.e. ./) of the input arrays
0008 %                       If y is omitted then q = x^(-1)
0009 %
0010 %      Copyright (C) Mike Brookes 2000-2012
0011 %      Version: $Id: v_qrdotdiv.m 10865 2018-09-21 17:22:45Z dmb $
0012 %
0013 %   VOICEBOX is a MATLAB toolbox for speech processing.
0014 %   Home page: http://www.ee.ic.ac.uk/hp/staff/dmb/voicebox/voicebox.html
0015 %
0016 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
0017 %   This program is free software; you can redistribute it and/or modify
0018 %   it under the terms of the GNU General Public License as published by
0019 %   the Free Software Foundation; either version 2 of the License, or
0020 %   (at your option) any later version.
0021 %
0022 %   This program is distributed in the hope that it will be useful,
0023 %   but WITHOUT ANY WARRANTY; without even the implied warranty of
0024 %   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
0025 %   GNU General Public License for more details.
0026 %
0027 %   You can obtain a copy of the GNU General Public License from
0028 %   http://www.gnu.org/copyleft/gpl.html or by writing to
0029 %   Free Software Foundation, Inc.,675 Mass Ave, Cambridge, MA 02139, USA.
0030 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
0031 persistent a b c
0032 if isempty(a)
0033     a=[1 2 3 4 2 1 4 3 3 4 1 2 4 3 2 1];
0034     b=[1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4];
0035     c=[6 8 10 11 15 16];
0036 end
0037 s=size(x);
0038 x=reshape(x,4,[]);
0039 if nargin<2 % one argument - just invert x
0040     m=sum(x.^2,1);
0041     x=x./m(ones(4,1),:);
0042     x(2:4,:)=-x(2:4,:);
0043     q=reshape(x,s);
0044 else  % multiply by conjugate of y and then divide by |y|^2
0045     y=reshape(y,4,[]);
0046     m=sum(y.^2,1);
0047     q=x(a,:).*y(b,:);
0048     q(c,:)=-q(c,:);
0049     q=reshape(sum(reshape(q,4,[]),1),s)./m(ones(4,1),:);;
0050 end