function g = mlpbkp(net, x, z, deltas)%MLPBKP	Backpropagate gradient of error function for 2-layer network.%%	Description%	G = MLPBKP(NET, X, Z, DELTAS) takes a network data structure NET%	together with a matrix X of input vectors, a matrix  Z of hidden unit%	activations, 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 multi-layer perceptron network models to%	compute gradients for mixture density networks as well as standard%	error functions.%%	See also%	MLP, MLPGRAD, MLPDERIV, MDNGRAD%%	Copyright (c) Ian T Nabney (1996-2001)% Evaluate second-layer gradients.gw2 = z'*deltas;gb2 = sum(deltas, 1);% Now do the backpropagation.delhid = deltas*net.w2';delhid = delhid.*(1.0 - z.*z);% Finally, evaluate the first-layer gradients.gw1 = x'*delhid;gb1 = sum(delhid, 1);g = [gw1(:)', gb1, gw2(:)', gb2];