wolffd@0: function g = rbfbkp(net, x, z, n2, deltas)
wolffd@0: %RBFBKP	Backpropagate gradient of error function for RBF network.
wolffd@0: %
wolffd@0: %	Description
wolffd@0: %	G = RBFBKP(NET, X, Z, N2, DELTAS) takes a network data structure NET
wolffd@0: %	together with a matrix X of input vectors, a matrix  Z of hidden unit
wolffd@0: %	activations, a matrix N2 of the squared distances between centres and
wolffd@0: %	inputs, and a matrix DELTAS of the  gradient of the error function
wolffd@0: %	with respect to the values of the output units (i.e. the summed
wolffd@0: %	inputs to the output units, before the activation function is
wolffd@0: %	applied). The return value is the gradient G of the error function
wolffd@0: %	with respect to the network weights. Each row of X corresponds to one
wolffd@0: %	input vector.
wolffd@0: %
wolffd@0: %	This function is provided so that the common backpropagation
wolffd@0: %	algorithm can be used by RBF network models to compute gradients for
wolffd@0: %	the output values (in RBFDERIV) as well as standard error functions.
wolffd@0: %
wolffd@0: %	See also
wolffd@0: %	RBF, RBFGRAD, RBFDERIV
wolffd@0: %
wolffd@0: 
wolffd@0: %	Copyright (c) Ian T Nabney (1996-2001)
wolffd@0: 
wolffd@0: % Evaluate second-layer gradients.
wolffd@0: gw2 = z'*deltas;
wolffd@0: gb2 = sum(deltas);
wolffd@0: 
wolffd@0: % Evaluate hidden unit gradients
wolffd@0: delhid = deltas*net.w2';
wolffd@0: 
wolffd@0: gc = zeros(net.nhidden, net.nin);
wolffd@0: ndata = size(x, 1);
wolffd@0: t1 = ones(ndata, 1);
wolffd@0: t2 = ones(1, net.nin);
wolffd@0: % Switch on activation function type
wolffd@0: switch net.actfn
wolffd@0:       
wolffd@0: case 'gaussian' % Gaussian
wolffd@0:    delhid = (delhid.*z);
wolffd@0:    % A loop seems essential, so do it with the shortest index vector
wolffd@0:    if (net.nin < net.nhidden)
wolffd@0:       for i = 1:net.nin
wolffd@0:          gc(:,i) = (sum(((x(:,i)*ones(1, net.nhidden)) - ...
wolffd@0:             (ones(ndata, 1)*(net.c(:,i)'))).*delhid, 1)./net.wi)';
wolffd@0:       end
wolffd@0:    else
wolffd@0:       for i = 1:net.nhidden
wolffd@0:          gc(i,:) = sum((x - (t1*(net.c(i,:)))./net.wi(i)).*(delhid(:,i)*t2), 1);
wolffd@0:       end
wolffd@0:    end
wolffd@0:    gwi = sum((n2.*delhid)./(2.*(ones(ndata, 1)*(net.wi.^2))), 1);
wolffd@0:    
wolffd@0: case 'tps'	% Thin plate spline activation function
wolffd@0:    delhid = delhid.*(1+log(n2+(n2==0)));
wolffd@0:    for i = 1:net.nhidden
wolffd@0:       gc(i,:) = sum(2.*((t1*(net.c(i,:)) - x)).*(delhid(:,i)*t2), 1);
wolffd@0:    end
wolffd@0:    % widths are not adjustable in this model
wolffd@0:    gwi = [];
wolffd@0: case 'r4logr' % r^4 log r activation function
wolffd@0:    delhid = delhid.*(n2.*(1+2.*log(n2+(n2==0))));
wolffd@0:    for i = 1:net.nhidden
wolffd@0:       gc(i,:) = sum(2.*((t1*(net.c(i,:)) - x)).*(delhid(:,i)*t2), 1);
wolffd@0:    end
wolffd@0:    % widths are not adjustable in this model
wolffd@0:    gwi = [];
wolffd@0: otherwise
wolffd@0:    error('Unknown activation function in rbfgrad')
wolffd@0: end
wolffd@0:    
wolffd@0: g = [gc(:)', gwi, gw2(:)', gb2];