% TOEP2_TRACE           Obtain the trace of an inverse Toeplitz matrix.
%
% [TR] = TOEP2_TRACE(ds,vn1,dt)
%
% This function uses the modified Durbin-Levinson's algorithm to calculate
% the trace of inverse-matrix product, i.e.[inv(Q)*T], where that Q and T
% are strictly Toeplitz matrix, with dt defined as the top row of  T. The 
% component of Q is obtained from the function toep_logdet, returning ds 
% (vector) and vn1 (reflection coefficient) as its by-products.
%
% Inputs:
%       ds  = Vector form for <toep2_trace> calculation
%       vs1 = Reflection coefficient for <toep2_trace> calculation
%       dt  = Top row of Toeplitz matrix, T, of dimension {1 x N}
%
% Output:
%       TR  = Returns the trace of inverse-matrix product, tr{inv(Q)*T}
%
%
% The computation is written in C code for execution of fast algorithm.
% The origin of the fast algorithm is contributed by Y. Zhang
% (2005) for the use in Gaussian Process Prior Models.
%
%
% (C) Gaussian Process Toeplitz Toolbox 1.0
% (C) Copyright 2005-2007, Keith Neo <keith.neo@nuim.ie>
%                          http://www.hamilton.ie