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