public static FunctionBinder.ParamsFunction <X> FiniteDifference_ <X>(IList <IVar> inputs, Scalar <X> output, Tensor <X> .Shared x, IDictionary givens = null)
{
var epsilon = Scalar <X>("epsilon");
var i_ = Scalar <int>("i");
var j_ = Scalar <int>("j");
var k_ = Scalar <int>("k");
var indexes = new Scalar <int> .Var[0];
if (x.NDim == 1)
{
indexes = new[] { i_ }
}
;
if (x.NDim == 2)
{
indexes = new[] { i_, j_ }
}
;
if (x.NDim == 3)
{
indexes = new[] { i_, j_, k_ }
}
;
var inputSet = new List <IVar>();
foreach (var i in inputs)
{
inputSet.Add(i);
}
foreach (var i in indexes)
{
inputSet.Add(i);
}
inputSet.Add(epsilon);
var eps = Op.OneHot(x.Shape, indexes, epsilon);
var out_m_eps = (Scalar <X>)output.Patch(new Patch {
[x] = x - eps
});
var out_p_eps = (Scalar <X>)output.Patch(new Patch {
[x] = x + eps
});
var delta = (out_p_eps - out_m_eps) / (Numeric <X> .Two * epsilon);
return(Function(inputSet, delta, givens: givens));
}
public static Tensor <Type> operator -(Tensor <Type> x)
{
switch (x)
{
case Elementwise unary when unary.Abstraction is Scalars.Neg <Type> :
return(unary.Inputs[0]); // -(-x) = x
case Elementwise binary when binary.Abstraction is Scalars.Sub <Type> :
return(binary.Inputs[1] - binary.Inputs[0]); // -(x - y) = y - x
case Fill <Type> fill:
return(Op.Const(-fill.x, fill.Shape));
case OneHot <Type> oneHot:
return(Op.OneHot(oneHot.Shape, oneHot.Index, -oneHot.Content));
default:
return(Op.Apply(x, _x => - _x));
}
}