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## Copyright (C) 2010-2014 Lukas F. Reichlin
##
## 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 -*-
## Matrix power operator of quaternions. Used by Octave for "q^x".
## Author: Lukas Reichlin <lukas.reichlin@gmail.com>
## Created: May 2010
## Version: 0.2
function q = mpower (a, b)
if (nargin != 2)
error ("quaternion: mpower: this is a binary operator");
endif
[r, c] = size (a);
if (r != c)
error ("quaternion: mpower: quaternion matrix must be square");
endif
if (r == 1 && c == 1) # a scalar, b?
q = a .^ b; # b could be a quaternion
elseif (is_real_array (b) && isscalar (b) && fix (b) == b)
e = fix (abs (b));
switch (sign (b))
case -1 # q^-e
a = inv (a);
q = a;
case 0 # q^0
q = eye (r); # alternative: q = quaternion (eye (r))
return;
case 1; # q^e
q = a;
endswitch
for k = 2 : e
q *= a; # improvement?: q^8 = ((q^2)^2)^2, q^9 = (((q^2)^2)^2)*q
endfor
else
error ("quaternion: mpower: case not implemented yet");
q = expm (logm (a) * b); # don't know whether this formula is correct
endif
## TODO: - q1 ^ q2
## - arrays
endfunction

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