# v_rotqr2mr

## PURPOSE V_ROTQR2MR converts a matrix of real quaternion vectors to quaternion matrices

## SYNOPSIS function mr=v_rotqr2mr(qr)

## DESCRIPTION ```V_ROTQR2MR converts a matrix of real quaternion vectors to quaternion matrices
Inputs:

QR(4m,n,...)   mxn matrix of real quaternion vectors (each 4x1)

Outputs:

MR(4m,4n,...)   mxn matrix of real quaternion matrices (each 4x4)

In matrix form, quaternions can be multiplied and added using normal matrix
arithmetic. Each element of an mxn matrix of quaternions is itself a 4x4 block
so the total dimension of MR is 4m x 4n.```

## CROSS-REFERENCE INFORMATION This function calls:
• v_rotqr2ro ROTQR2RO converts a real quaternion to a 3x3 rotation matrix
This function is called by:
• v_qrmult V_QRMULT multiplies together two real quaternions matrices q=[q1,q2]

## SOURCE CODE ```0001 function mr=v_rotqr2mr(qr)
0002 %V_ROTQR2MR converts a matrix of real quaternion vectors to quaternion matrices
0003 % Inputs:
0004 %
0005 %     QR(4m,n,...)   mxn matrix of real quaternion vectors (each 4x1)
0006 %
0007 % Outputs:
0008 %
0009 %     MR(4m,4n,...)   mxn matrix of real quaternion matrices (each 4x4)
0010 %
0011 % In matrix form, quaternions can be multiplied and added using normal matrix
0012 % arithmetic. Each element of an mxn matrix of quaternions is itself a 4x4 block
0013 % so the total dimension of MR is 4m x 4n.
0014
0015 %
0016 %      Copyright (C) Mike Brookes 2000-2018
0017 %      Version: \$Id: v_rotqr2mr.m 10865 2018-09-21 17:22:45Z dmb \$
0018 %
0019 %   VOICEBOX is a MATLAB toolbox for speech processing.
0021 %
0022 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
0023 %   This program is free software; you can redistribute it and/or modify
0025 %   the Free Software Foundation; either version 2 of the License, or
0026 %   (at your option) any later version.
0027 %
0028 %   This program is distributed in the hope that it will be useful,
0029 %   but WITHOUT ANY WARRANTY; without even the implied warranty of
0030 %   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
0031 %   GNU General Public License for more details.
0032 %
0033 %   You can obtain a copy of the GNU General Public License from
0034 %   http://www.gnu.org/copyleft/gpl.html or by writing to
0035 %   Free Software Foundation, Inc.,675 Mass Ave, Cambridge, MA 02139, USA.
0036 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
0037 persistent a b c
0038 if isempty(a)
0039     a=[1 2 3 3 1 2];    % destination row of +ve entries (from 0)
0040     b=[1 2 3 2 3 1];    % destination col of +ve entries (from 0)
0041     c=[0 0 0 1 2 3];    % source row of +ve entries (from 0)
0042 end
0043 s=size(qr);
0044 m=s(1);
0045 mr=repmat(reshape(qr,s(1),[]),4,1);
0046 n=size(mr,2);
0047 mn=s(1)*n;
0048 j=repmat(4*m*(0:n-1),m/4,1);
0049 i=repmat((1:4:m)',n,1)+j(:);
0050 ni=length(i);
0051 i6=repmat(i,1,6);
0052 mr(i6+repmat(a+m*b,ni,1))=mr(i6+repmat(c,ni,1));
0053 mr(i6+repmat(c+m*b,ni,1))=-mr(i6+repmat(a,ni,1));
0054 s(2)=4*s(2); % output array size
0055 mr=reshape(mr,s);
0056 if ~nargout
0057     qr=qr(1:4);
0058     v_rotqr2ro(qr(:)); % plot a rotated cube
0059 end```