sugr_uncondition_Projection

% Uncondition Projection

 P = sugr_uncondition_Projection(Pc, Ml, Mr) 

 Pc = struct, projection conditioned
      Pc.P   3 x 4-matrix
      Pc.Crr reduced CovM
 Ml = 3 x 3 condition matrix
 Mr = 4 x 4 condition matrix
 
 P  = struct, unconditioned matrix P = inv(Ml) * Pc * Mr, 

 Wolfgang Förstner 2/2013
 wfoerstn@uni-bonn.de

 See also sugr_condition_Points

0001 %% Uncondition Projection
0002 %
0003 % P = sugr_uncondition_Projection(Pc, Ml, Mr)
0004 %
0005 % Pc = struct, projection conditioned
0006 %      Pc.P   3 x 4-matrix
0007 %      Pc.Crr reduced CovM
0008 % Ml = 3 x 3 condition matrix
0009 % Mr = 4 x 4 condition matrix
0010 %
0011 % P  = struct, unconditioned matrix P = inv(Ml) * Pc * Mr,
0012 %
0013 % Wolfgang Förstner 2/2013
0014 % wfoerstn@uni-bonn.de
0015 %
0016 % See also sugr_condition_Points
0017 
0018 function P = sugr_uncondition_Projection(Pc, Ml, Mr)
0019 
0020 % Matrix
0021 Pmc = Pc.P;
0022 
0023 % unconditioned matrix
0024 Pm =  inv(Ml) * Pmc * Mr;                                                  %#ok<MINV>
0025 % Pm_unconditioned = Pm;
0026 
0027 % uncondition CovM
0028 pc  = Pmc(:);
0029 p   = Pm(:);
0030 % dpu    =                    (Mr' kron inv(Ml)) * dpc
0031 % dp_r   =          J'(dp') * (Mr' kron inv(Ml)) * J(pc') dpc_r
0032 % dp_h   = J(dp') * J'(dp') * (Mr' kron inv(Ml)) * J(pc') dpc_r
0033 J = null(p') * null(p')' * kron(Mr',inv(Ml)) * null(pc');
0034 Chh = J * Pc.Crr * J';
0035 
0036 P = sugr_Projection_3D_2D(Pm,Chh);
0037 
0038