// i(t) = sigmoid(W(i)*x(t) + U(i)*h(t-1)) input gate
// f(t) = sigmoid(W(f)*x(t) + U(f)*h(t-1)) forget gate
// o(t) = sigmoid(W(o)*x(t) + U(o)*h(t-1)) output exposure gate
// c tilde(t) = tanh(W(c)*x(t) + U(c)*h(t-1)) new memory cell
// c(t) = f(t).*c tilde(t-1) + i(t).*c tilde(t) final memory cell
// h(t) = o(t).*tanh(c(t))
public Tensor Step(Graph.Graph f, Tensor x, Tensor h)
{
// input gate
var inputGate = f.Sigmoid(f.AddBias(f.Add(f.Multiply(x, _wix), f.Multiply(h, _wih)), _bi));
// forget gate
var forgetGate = f.Sigmoid(f.AddBias(f.Add(f.Multiply(x, _wfx), f.Multiply(h, _wfh)), _bf));
var newInput = f.Tanh(f.Multiply(x, _wcx));
return(f.Add(f.ElementwiseMultiply(inputGate, newInput), f.ElementwiseMultiply(forgetGate, f.Tanh(h))));
}
// i(t) = sigmoid(W(i)*x(t) + U(i)*h(t-1)) input gate
// f(t) = sigmoid(W(f)*x(t) + U(f)*h(t-1)) forget gate
// o(t) = sigmoid(W(o)*x(t) + U(o)*h(t-1)) output exposure gate
// c tilde(t) = tanh(W(c)*x(t) + U(c)*h(t-1)) new memory cell
// c(t) = f(t).*c tilde(t-1) + i(t).*c tilde(t) final memory cell
// h(t) = o(t).*tanh(c(t))
public Tensor Step(Graph.Graph f, Tensor x, Tensor c, Tensor h, out Tensor nc)
{
// input gate
var inputGate = f.Sigmoid(f.AddBias(f.Add(f.Multiply(x, _wix), f.Multiply(h, _wih)), _bi));
// forget gate
var forgetGate = f.Sigmoid(f.AddBias(f.Add(f.Multiply(x, _wfx), f.Multiply(h, _wfh)), _bf));
// output gate
var outputGate = f.Sigmoid(f.AddBias(f.Add(f.Multiply(x, _wox), f.Multiply(h, _woh)), _bo));
// new cell
var newInfo = f.Tanh(f.AddBias(f.Add(f.Multiply(x, _wcx), f.Multiply(h, _wch)), _bc));
// final cell
var retainCell = f.ElementwiseMultiply(forgetGate, c);
var writeCell = f.ElementwiseMultiply(inputGate, newInfo);
var finalCell = f.Add(retainCell, writeCell);
// hidden unit
nc = finalCell;
return(f.ElementwiseMultiply(outputGate, f.Tanh(finalCell)));
}