function Qkm1 = example_4_2_2_compute_qkm1(a,b, L_Qc_LT, deltaT, Npts)
% EXAMPLE_4_2_2_COMPUTE_QKM1 - Computes the discretization process noise matrix Q_{k-1}
%   
% Our system matrix we integrate is given by 
%
% F = [ 0, 1; a, b ]; 
%
% L_Qc_LT = the combined expression of L * Q_c' * L^T as matrix 
% 
% Written by:
% -- 
% John L. Weatherwax                2006-08-28
% 
% email: wax@alum.mit.edu
% 
% Please send comments and especially bug reports to the
% above email address.
% 
%-----

F  = [ 0, 1; a, b ];
FT = F';

tRange = linspace(0,deltaT,Npts);

V = [];
for ti = tRange, 
  tmp = expm( F*ti ) * L_Qc_LT * expm( FT*ti );
  V = [ V, tmp(:) ];
end

Qkm1 = (tRange(2)-tRange(1))*reshape( trapz(V')', size(F) );