## [24b7af]: inst / @quaternion / mpower.m  Maximize  Restore  History

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 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60``` ```## 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 . ## -*- texinfo -*- ## Matrix power operator of quaternions. Used by Octave for "q^x". ## Author: Lukas Reichlin ## 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 ```