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# rotqc2mc

## PURPOSE

ROTQC2MC converts a matrix of complex quaternion vectors to quaternion matrices

## SYNOPSIS

function mc=rotqc2mc(qc)

## DESCRIPTION

```ROTQC2MC converts a matrix of complex quaternion vectors to quaternion matrices
Inputs:

QC(2m,n,...)   array of complex quaternion vectors (each 2x1)

Outputs:

MC(2m,2n,...)   array of complex quaternion matrices (each 2x2)

Each quarternion, r+ai+bj+ck is a 2x1 complex vector in the input array of the
form [ r+bi ; a+ci ]. In the output array, this becomes a 2x2 complex matrix
of the form [ r+bi -a+ci ; a+ci r-bi ].

In matrix form, quaternions can be multiplied and added using normal matrix
arithmetic. The complex matrix form has 4 complex elements while the real
matrix form has 16 real elements.```

## CROSS-REFERENCE INFORMATION

This function calls:
This function is called by:

## SOURCE CODE

```0001 function mc=rotqc2mc(qc)
0002 %ROTQC2MC converts a matrix of complex quaternion vectors to quaternion matrices
0003 % Inputs:
0004 %
0005 %     QC(2m,n,...)   array of complex quaternion vectors (each 2x1)
0006 %
0007 % Outputs:
0008 %
0009 %     MC(2m,2n,...)   array of complex quaternion matrices (each 2x2)
0010 %
0011 % Each quarternion, r+ai+bj+ck is a 2x1 complex vector in the input array of the
0012 % form [ r+bi ; a+ci ]. In the output array, this becomes a 2x2 complex matrix
0013 % of the form [ r+bi -a+ci ; a+ci r-bi ].
0014 %
0015 % In matrix form, quaternions can be multiplied and added using normal matrix
0016 % arithmetic. The complex matrix form has 4 complex elements while the real
0017 % matrix form has 16 real elements.
0018
0019 %
0020 %      Copyright (C) Mike Brookes 2000-2012
0021 %      Version: \$Id: rotqc2mc.m 1616 2012-03-15 09:13:31Z dmb \$
0022 %
0023 %   VOICEBOX is a MATLAB toolbox for speech processing.
0025 %
0026 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
0027 %   This program is free software; you can redistribute it and/or modify
0029 %   the Free Software Foundation; either version 2 of the License, or
0030 %   (at your option) any later version.
0031 %
0032 %   This program is distributed in the hope that it will be useful,
0033 %   but WITHOUT ANY WARRANTY; without even the implied warranty of
0034 %   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
0035 %   GNU General Public License for more details.
0036 %
0037 %   You can obtain a copy of the GNU General Public License from
0038 %   http://www.gnu.org/copyleft/gpl.html or by writing to
0039 %   Free Software Foundation, Inc.,675 Mass Ave, Cambridge, MA 02139, USA.
0040 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
0041 s=size(qc);
0042 m=s(1);
0043 qa=reshape(qc,m,[]);
0044 n=2*size(qa,2);
0045 mc=zeros(m,n);
0046 ix=1:2:m;
0047 jx=2:2:n;
0048 mc(:,jx-1)=qa;
0049 mc(ix,jx)=-conj(qa(ix+1,:));
0050 mc(ix+1,jx)=conj(qa(ix,:));
0051 s(2)=2*s(2);
0052 mc=reshape(mc,s);```

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