% generate minimal representation for homogeneous vector xs = sugr_minimal_vector(x,Cxx) * x uncertain homogeneous vector * Cxx covariance matrix * xs = * .h spherically normalized * .Crr reduced CovM * .Jr Jacobian xr -> xs Wolfgang Förstner 1/2011 wfoerstn@uni-bonn.de See also sugr_minimal_3D_Line
0001 %% generate minimal representation for homogeneous vector 0002 % 0003 % xs = sugr_minimal_vector(x,Cxx) 0004 % 0005 % * x uncertain homogeneous vector 0006 % * Cxx covariance matrix 0007 % * xs = 0008 % * .h spherically normalized 0009 % * .Crr reduced CovM 0010 % * .Jr Jacobian xr -> xs 0011 % 0012 % Wolfgang Förstner 1/2011 0013 % wfoerstn@uni-bonn.de 0014 % 0015 % See also sugr_minimal_3D_Line 0016 0017 function xs = sugr_minimal_vector(x,Cxx) 0018 0019 n = norm(x); % norm 0020 xs.h = x/n; % spherical normalization 0021 Jr = null(xs.h'); % Jacobian xr -> xs 0022 Crr = Jr' * Cxx * Jr/n^2; % CovM of reduced vector 0023 xs.Crr = Crr; % Crr 0024 xs.Jr = Jr; 0025