function [y, sigsq] = gpfwd(net, x, cninv)%GPFWD	Forward propagation through Gaussian Process.%%	Description%	Y = GPFWD(NET, X) takes a Gaussian Process data structure NET%	together  with a matrix X of input vectors, and forward propagates%	the inputs through the model to generate a matrix Y of output%	vectors.  Each row of X corresponds to one input vector and each row%	of Y corresponds to one output vector.  This assumes that the%	training data (both inputs and targets) has been stored in NET by a%	call to GPINIT; these are needed to compute the training data%	covariance matrix.%%	[Y, SIGSQ] = GPFWD(NET, X) also generates a column vector SIGSQ of%	conditional variances (or squared error bars) where each value%	corresponds to a pattern.%%	[Y, SIGSQ] = GPFWD(NET, X, CNINV) uses the pre-computed inverse%	covariance matrix CNINV in the forward propagation.  This increases%	efficiency if several calls to GPFWD are made.%%	See also%	GP, DEMGP, GPINIT%%	Copyright (c) Ian T Nabney (1996-2001)errstring = consist(net, 'gp', x);if ~isempty(errstring);  error(errstring);endif ~(isfield(net, 'tr_in') & isfield(net, 'tr_targets'))   error('Require training inputs and targets');endif nargin == 2  % Inverse covariance matrix not supplied.  cninv = inv(gpcovar(net, net.tr_in));endktest = gpcovarp(net, x, net.tr_in);% Predict meany = ktest*cninv*net.tr_targets;if nargout >= 2  % Predict error bar  ndata = size(x, 1);  sigsq = (ones(ndata, 1) * gpcovarp(net, x(1,:), x(1,:))) ...    - sum((ktest*cninv).*ktest, 2); end