% TOEP3_DERV_STDEV      Calculates the standard deviation of derivative
% observation in Gaussian process.
%
% [STD_DEV_DERV] = TOEP3_DERV_STDEV(M,p)
%
% This calculates the STANDARD DEVIATION for derivative observation in
% Gaussian Process, where SD = A - B'/Q*B ie. Q is the covariance between
% function inputs and itself, B is the covariance between the derivative
% point and the function point, while A is the covariance between the
% derivative and itself. The prior covariance function used is of the form,
%
%                   C(zi,zj) = a*exp([zi-zj]'*g*[zi-zj]) + v
%
% Inputs:
%       M   = Input explanatory variable, of dimension {N0 x 1}
%       p   = Hyperparameters, [a g v]
%
% Output:
%       STD_DEV_DERV    = Standard deviation of derivative observation
%
% The fast algorithm uses Yule-Walker equation with Trench Algorithm, to
% calculate the diagonal elements only, henceforth only N-squared speed.
%
%
% 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