function [Q,Z,L,D,z] = decorrel (Q,a);%DECORREL: Decorrelate a (co)variance matrix of ambiguities%% This routine creates a decorrelated Q-matrix, by finding the% Z-matrix and performing the corresponding transformation.%% The method is described in:% The routine is based on Fortran routines written by Paul de Jonge (TUD)% and on Matlab-routines written by Kai Borre.% The resulting Z-matrix can be used as follows:% z = Zt * a; \hat(z) = Zt * \hat(a);% Q_\hat(z) = Zt * Q_\hat(a) * Z%% Input arguments:%   a: Original ambiguities%   Q: Variance/covariance matrux of ambiguities (original)%% Output arguments:%   Q: Decorrelated variance/covariance matrix%   Z: Z-transformation matrix%   L: L matrix (from LtDL-decomposition of Q, optional)%   D: D matrix (from LtDL-decomposition of Q, optional)%   z: Transformed ambiguities (optional)% ----------------------------------------------------------------------% Function.: decorrel% Date.....: 19-MAY-1999% Author...: Peter Joosten%            Mathematical Geodesy and Positioning%            Delft University of Technology% ----------------------------------------------------------------------% -----------------------% --- Initialisations ---% -----------------------n    = size(Q,1);Zti  = eye(n);i1   = n - 1;sw   = 1;% --------------------------% --- LtDL decomposition ---% --------------------------[L,D] = ldldecom (Q);% ------------------------------------------% --- The actual decorrelation procedure ---% ------------------------------------------while sw;   i  = n;   sw = 0;   while ( ~sw ) & (i > 1)      i = i - 1;      if (i <= i1);                for j = i+1:n            mu = round(L(j,i));            if mu ~= 0               L(j:n,i) = L(j:n,i) - mu * L(j:n,j);               Zti(1:n,j) = Zti(1:n,j) + mu * Zti(1:n,i);            end         end      end;      delta = D(i) + L(i+1,i)^2 * D(i+1);      if (delta < D(i+1))         lambda(3)    = D(i+1) * L(i+1,i) / delta;         eta          = D(i) / delta;         D(i)         = eta * D(i+1);         D(i+1)       = delta;         Help         = L(i+1,1:i-1) - L(i+1,i) .* L(i,1:i-1);         L(i+1,1:i-1) = lambda(3) * L(i+1,1:i-1) + eta * L(i,1:i-1);         L(i,1:i-1)   = Help;         L(i+1,i)     = lambda(3);         Help         = L(i+2:n,i);         L(i+2:n,i)   = L(i+2:n,i+1);         L(i+2:n,i+1) = Help;                  Help         = Zti(1:n,i);         Zti(1:n,i)   = Zti(1:n,i+1);         Zti(1:n,i+1) = Help;         i1           = i;         sw           = 1;      end;   end;end;% ---------------------------------------------------------------------% --- Return the transformed Q-matrix and the transformation-matrix ---% --- Return the decorrelated ambiguities, if they were supplied    ---% ---------------------------------------------------------------------Z = round(inv(Zti'));Q = Z' * Q * Z;if nargin == 2 & nargout >= 5;  z = Z' * a;end;% ----------------------------------------------------------------------% End of routine: decorrel% ----------------------------------------------------------------------