% TOE_UNSYM_TIMES_Y     Computes the unsymmetrical Toeplitz matrix-vector
% multiplication.
%
% [X] = TOE_UNSYM_TIMES_Y(cxt,y)
%
% This function calculates the matrix-vector multiplication between X and
% y, where y is a column vector and X is an unsymmetical toeplitz matrix.
%
% Inputs:
%       cxt = Top row of unsymmetrical Toeplitz matrix, Q, with dim{1 x N}
%       y   = Column vector of dimension {N x 1}
%
% Output:
%       X   = Returns the matrix-vector product of Q*y
%
% Q is an unsymmetrical toeplitz matrix, of the form:
%
%                   [a      b       c       d       e]
%                   [-b     a       b       c       d]
%                   [-c     -b      a       b       c]
%                   [-d     -c      -b      a       b]
%                   [-e     -d      -c      -b      a]
%
%
% 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