Daniel@0: function [y, sigsq] = gpfwd(net, x, cninv)
Daniel@0: %GPFWD	Forward propagation through Gaussian Process.
Daniel@0: %
Daniel@0: %	Description
Daniel@0: %	Y = GPFWD(NET, X) takes a Gaussian Process data structure NET
Daniel@0: %	together  with a matrix X of input vectors, and forward propagates
Daniel@0: %	the inputs through the model to generate a matrix Y of output
Daniel@0: %	vectors.  Each row of X corresponds to one input vector and each row
Daniel@0: %	of Y corresponds to one output vector.  This assumes that the
Daniel@0: %	training data (both inputs and targets) has been stored in NET by a
Daniel@0: %	call to GPINIT; these are needed to compute the training data
Daniel@0: %	covariance matrix.
Daniel@0: %
Daniel@0: %	[Y, SIGSQ] = GPFWD(NET, X) also generates a column vector SIGSQ of
Daniel@0: %	conditional variances (or squared error bars) where each value
Daniel@0: %	corresponds to a pattern.
Daniel@0: %
Daniel@0: %	[Y, SIGSQ] = GPFWD(NET, X, CNINV) uses the pre-computed inverse
Daniel@0: %	covariance matrix CNINV in the forward propagation.  This increases
Daniel@0: %	efficiency if several calls to GPFWD are made.
Daniel@0: %
Daniel@0: %	See also
Daniel@0: %	GP, DEMGP, GPINIT
Daniel@0: %
Daniel@0: 
Daniel@0: %	Copyright (c) Ian T Nabney (1996-2001)
Daniel@0: 
Daniel@0: errstring = consist(net, 'gp', x);
Daniel@0: if ~isempty(errstring);
Daniel@0:   error(errstring);
Daniel@0: end
Daniel@0: 
Daniel@0: if ~(isfield(net, 'tr_in') & isfield(net, 'tr_targets'))
Daniel@0:    error('Require training inputs and targets');
Daniel@0: end
Daniel@0: 
Daniel@0: if nargin == 2
Daniel@0:   % Inverse covariance matrix not supplied.
Daniel@0:   cninv = inv(gpcovar(net, net.tr_in));
Daniel@0: end
Daniel@0: ktest = gpcovarp(net, x, net.tr_in);
Daniel@0: 
Daniel@0: % Predict mean
Daniel@0: y = ktest*cninv*net.tr_targets;
Daniel@0: 
Daniel@0: if nargout >= 2
Daniel@0:   % Predict error bar
Daniel@0:   ndata = size(x, 1);
Daniel@0:   sigsq = (ones(ndata, 1) * gpcovarp(net, x(1,:), x(1,:))) ...
Daniel@0:     - sum((ktest*cninv).*ktest, 2); 
Daniel@0: end