;    Copyright (C) 2006  Will M. Farr <farr@mit.edu>
;
;    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 2 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, write to the Free Software Foundation, Inc.,
;    51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.


(module lie-group-SO3-test "generics.ss"
  (require "lie-group-SO3.ss" 
           (all-except "lie-groups.ss" phi psi) 
           "manifolds.ss" "tuples.ss" "test.ss"
           (lib "math.ss"))
  
  (provide lie-group-SO3-test-suite)
  
  (define-named-coordinates (phi theta psi) SO3-euler-angles-chart)
  
  (define lie-group-SO3-test-suite 
    (test-suite
     "lie-group-SO3.ss"
     (test-case 
      "Euler-angle structure constants."
      (check-equals? (structure-constants SO3 SO3-euler-angles-chart)
                     (down (down (up 0 0 0)
                                 (up 0 0 1)
                                 (up 0 -1 0))
                           (down (up 0 0 -1)
                                 (up 0 0 0)
                                 (up 1 0 0))
                           (down (up 0 1 0)
                                 (up -1 0 0)
                                 (up 0 0 0)))))
     (test-case 
      "Coordinate vectors commute."
      (check-equals? ((vector-field->component-field (lie-bracket d/dphi d/dtheta) 
                                                     SO3-euler-angles-chart)
                      (slot-ref SO3 'identity))
                     (up 0 0 0)))
     (test-case 
      "Lie algebra bracket of coordinate vectors does not commute."
      (check-equals? ((vector-field->component-field 
                       ((lie-algebra-bracket SO3) d/dphi d/dtheta)
                       SO3-euler-angles-chart)
                      (slot-ref SO3 'identity))
                     (up 0 0 1)))
     (test-case 
      "Extended tangent vectors are really left-invariant"
      (check-tuple-close? 
       1e-6
       ((vector-field->component-field 
         (- ((lie-algebra-bracket SO3) d/dphi d/dtheta)
            ((natural-extension SO3) d/dpsi))
         SO3-euler-angles-chart)
        ((slot-ref SO3-euler-angles-chart 'chiinv)
         (up 0.02345453 0.0349587 0.0435897)))
       (up 0 0 0)))
     (test-case 
      "Rectangular angles correct"
      (let ((x-y-z (up (random) (random) (random))))
        (check-tuple-close? 1e-6
                            ((slot-ref SO3-rectangular-angles-chart 'chi)
                             ((slot-ref SO3-rectangular-angles-chart 'chiinv) x-y-z))
                            x-y-z)
        (check-tuple-close? 1e-3
                            ((slot-ref SO3-rectangular-angles-chart 'chi)
                             (* ((slot-ref SO3-rectangular-angles-chart 'chiinv)
                                 (up (/ pi 4) 0 0))
                                ((slot-ref SO3-rectangular-angles-chart 'chiinv)
                                 (up 0 (/ pi 4) 0))
                                ((slot-ref SO3-rectangular-angles-chart 'chiinv)
                                 (up 0 0 (/ pi 4)))))
                            (up 1.04089 -0.146975 1.04089)))))))