Add a useful package (from Source forge) for octave

[CreaPhase.git] / octave_packages / quaternion-2.0.0 / @quaternion / log.m

diff --git a/octave_packages/quaternion-2.0.0/@quaternion/log.m b/octave_packages/quaternion-2.0.0/@quaternion/log.m
new file mode 100644 (file)
index 0000000..457e7a9
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+++ b/octave_packages/quaternion-2.0.0/@quaternion/log.m
@@ -0,0 +1,61 @@
+## Copyright (C) 2011   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 -*-
+## @deftypefn {Function File} {@var{qlog} =} log (@var{q})
+## Logarithmus naturalis of a quaternion.
+## @end deftypefn
+
+## Author: Lukas Reichlin <lukas.reichlin@gmail.com>
+## Created: November 2011
+## Version: 0.1
+
+function q = log (q)
+
+  if (nargin != 1)
+    print_usage ();
+  endif
+
+  normq = abs (q);
+  normv = normv (q);
+  acossq = acos (q.w ./ normq);
+
+  q.w = log (normq);    
+  q.x = (q.x ./ normv) .* acossq;
+  q.y = (q.y ./ normv) .* acossq;
+  q.z = (q.z ./ normv) .* acossq;
+  
+  ## FIXME: q = quaternion (2, 3, 4, 5)
+  ##        p = log (exp (q))
+  ##        p.v is wrong, probably somehow related to acos
+  ## NOTE:  p = exp (log (q)) is calculated correctly
+  ## NOTE:  qtfm 1.9 returns the same "wrong" result
+
+endfunction
+
+
+%!shared A, B
+%! Aw = [2, 6, 10; 14, 18, 22];
+%! Ax = [3, 7, 11; 15, 19, 23];
+%! Ay = [4, 8, 12; 16, 20, 24];
+%! Az = [5, 9, 13; 17, 21, 25];
+%! A = quaternion (Aw, Ax, Ay, Az);
+%!
+%! B = exp (log (A));
+%!
+%!assert (A.w, B.w, 1e-4);
+%!assert (A.x, B.x, 1e-4);
+%!assert (A.y, B.y, 1e-4);
+%!assert (A.z, B.z, 1e-4);