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);

end



if ~(isfield(net, 'tr_in') & isfield(net, 'tr_targets'))

   error('Require training inputs and targets');

end



if nargin == 2

  % Inverse covariance matrix not supplied.

  cninv = inv(gpcovar(net, net.tr_in));

end

ktest = gpcovarp(net, x, net.tr_in);



% Predict mean

y = 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



end