function g = mlpbkp(net, x, z, deltas)
%MLPBKP Backpropagate gradient of error function for 2-layer network.
% 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];