Daniel@0: function [g, gdata, gprior] = rbfgrad(net, x, t)
Daniel@0: %RBFGRAD Evaluate gradient of error function for RBF network.
Daniel@0: %
Daniel@0: %	Description
Daniel@0: %	G = RBFGRAD(NET, X, T) takes a network data structure NET together
Daniel@0: %	with a matrix X of input vectors and a matrix T of target vectors,
Daniel@0: %	and evaluates the gradient G of the error function with respect to
Daniel@0: %	the network weights (i.e. including the hidden unit parameters). The
Daniel@0: %	error function is sum of squares. Each row of X corresponds to one
Daniel@0: %	input vector and each row of T contains the corresponding target
Daniel@0: %	vector. If the output function is 'NEUROSCALE' then the gradient is
Daniel@0: %	only computed for the output layer weights and biases.
Daniel@0: %
Daniel@0: %	[G, GDATA, GPRIOR] = RBFGRAD(NET, X, T) also returns separately  the
Daniel@0: %	data and prior contributions to the gradient. In the case of multiple
Daniel@0: %	groups in the prior, GPRIOR is a matrix with a row for each group and
Daniel@0: %	a column for each weight parameter.
Daniel@0: %
Daniel@0: %	See also
Daniel@0: %	RBF, RBFFWD, RBFERR, RBFPAK, RBFUNPAK, RBFBKP
Daniel@0: %
Daniel@0: 
Daniel@0: %	Copyright (c) Ian T Nabney (1996-2001)
Daniel@0: 
Daniel@0: % Check arguments for consistency
Daniel@0: switch net.outfn
Daniel@0: case 'linear'
Daniel@0:    errstring = consist(net, 'rbf', x, t);
Daniel@0: case 'neuroscale'
Daniel@0:    errstring = consist(net, 'rbf', x);
Daniel@0: otherwise
Daniel@0:    error(['Unknown output function ', net.outfn]);
Daniel@0: end
Daniel@0: if ~isempty(errstring);
Daniel@0:   error(errstring);
Daniel@0: end
Daniel@0: 
Daniel@0: ndata = size(x, 1);
Daniel@0: 
Daniel@0: [y, z, n2] = rbffwd(net, x);
Daniel@0: 
Daniel@0: switch net.outfn
Daniel@0: case 'linear'
Daniel@0: 
Daniel@0:    % Sum squared error at output units
Daniel@0:    delout = y - t;
Daniel@0: 
Daniel@0:    gdata = rbfbkp(net, x, z, n2, delout);
Daniel@0:    [g, gdata, gprior] = gbayes(net, gdata);
Daniel@0: 
Daniel@0: case 'neuroscale'
Daniel@0:    % Compute the error gradient with respect to outputs
Daniel@0:    y_dist = sqrt(dist2(y, y));
Daniel@0:    D = (t - y_dist)./(y_dist+diag(ones(ndata, 1)));
Daniel@0:    temp = y';
Daniel@0:    gradient = 2.*sum(kron(D, ones(1, net.nout)) .* ...
Daniel@0:       (repmat(y, 1, ndata) - repmat((temp(:))', ndata, 1)), 1);
Daniel@0:    gradient = (reshape(gradient, net.nout, ndata))';
Daniel@0:    % Compute the error gradient
Daniel@0:    gdata = rbfbkp(net, x, z, n2, gradient);
Daniel@0:    [g, gdata, gprior] = gbayes(net, gdata);
Daniel@0: otherwise
Daniel@0:    error(['Unknown output function ', net.outfn]);
Daniel@0: end
Daniel@0: