Hi, everybody, In addition to all comments, just as a pleasure to remind an old-fashion "no computer" way to calculate the rotation angle. The trace of a rotation matrix (the sum of its diagonal elements) is always equal to 2*cos(kappa)+1. Calculate it yourself for kappa = 180° and compare with the trace of the Francis's matrix.
ROTA 1: -0.5444 -0.2202 0.8094 ROTA 2: 0.8330 -0.0278 0.5526 ROTA 3: -0.0991 0.9751 0.1985 One can easily reject (still without a computer) other "crystallographic" angles. Best regards, Sasha Urzhumtsev -----Message d'origine----- De : CCP4 bulletin board [mailto:CCP4BB@JISCMAIL.AC.UK] De la part de Ian Tickle Envoyé : mardi 21 février 2012 15:13 À : CCP4BB@JISCMAIL.AC.UK Objet : Re: [ccp4bb] proper or improper ncs? Francis, It's very easy to spot a 2-fold rotation or screw because the matrix must be symmetric (or nearly so)**. Your matrix very obviously is not (i,e, A12 ne A21, A13 ne A31 etc). ** Proof: A rotation matrix is orthogonal, which implies inverse = transpose: A^-1 = A~. A 2-fold rotation is proper which implies AA = I or A^-1 = A. Take these together and you get A = A~ i.e. A is symmetric. Surprising how many people aren't aware of this! Cheers -- Iann On 21 February 2012 13:47, Francis E Reyes <francis.re...@colorado.edu> wrote: > Hi all > > This structure has the following ncs (output via > phenix.simple_ncs_from_pdb) OPERATOR 1 > CENTER: 18.3443 -55.4605 23.0986 > > ROTA 1: 1.0000 0.0000 0.0000 > ROTA 2: 0.0000 1.0000 0.0000 > ROTA 3: 0.0000 0.0000 1.0000 > TRANS: 0.0000 0.0000 0.0000 > > OPERATOR 2 > CENTER: 37.0405 -23.8676 -14.9388 > > ROTA 1: -0.5444 -0.2202 0.8094 > ROTA 2: 0.8330 -0.0278 0.5526 > ROTA 3: -0.0991 0.9751 0.1985 > TRANS: 45.3456 -78.7231 53.0085 > > > It looks two-foldish but I'm not sure if it's proper or improper. (I'm trying > to rationalize the lack of peaks on the self rotation maps). > > > Any help would be appreciated. > > F > > > > --------------------------------------------- > Francis E. Reyes M.Sc. > 215 UCB > University of Colorado at Boulder
