/// Sigmoid関数
public static AutoDiff Sigmoid(AutoDiff x)
{
var z = new AutoDiff(1 / (1 + Math.Exp(-x.Val)), 1);
z.AddInput(0, x, (1 - z.Val) * z.Val);
return(z);
}
/// 絶対値関数
public static AutoDiff Abs(AutoDiff x)
{
var z = new AutoDiff(Math.Abs(x.Val), 1);
z.AddInput(0, x, x.Val < 0 ? -1 : 1);
return(z);
}
/// Rectified Linear Unit
/// <param name="x"></param>
/// <returns></returns>
public static AutoDiff ReLU(AutoDiff x)
{
var z = new AutoDiff(Math.Max(0, x.Val), 1);
z.AddInput(0, x, x.Val > 0 ? 1 : 0);
return(z);
}
/// Exp関数
public static AutoDiff Exp(AutoDiff x)
{
var z = new AutoDiff(Math.Exp(x.Val), 1);
z.AddInput(0, x, z.Val);
return(z);
}
/// Cos関数
public static AutoDiff Cos(AutoDiff x)
{
var z = new AutoDiff(Math.Cos(x.Val), 1);
z.AddInput(0, x, -Math.Sin(x.Val));
return(z);
}
/// Sqrt関数
public static AutoDiff Sqrt(AutoDiff x)
{
var z = new AutoDiff(Math.Sqrt(x.Val), 1);
z.AddInput(0, x, 0.5 / z.Val);
return(z);
}
/// -単項演算子のオーバーロード
public static AutoDiff operator -(AutoDiff x)
{
var z = new AutoDiff(-x.Val, 1);
z.AddInput(0, x, -1);
return(z);
}
/// Tanh関数
public static AutoDiff Tanh(AutoDiff x)
{
var z = new AutoDiff(Math.Tanh(x.Val), 1);
z.AddInput(0, x, 1 - z.Val * z.Val);
return(z);
}
/// 累乗関数 x^y
public static AutoDiff Pow(AutoDiff x, AutoDiff y)
{
var z = new AutoDiff(Math.Pow(x.Val, y.Val), 2);
z.AddInput(0, x, y.Val * Math.Pow(x.Val, y.Val - 1));
z.AddInput(1, y, z.Val * Math.Log(x.Val));
return(z);
}
/// *演算子のオーバーロード
public static AutoDiff operator *(AutoDiff x, AutoDiff y)
{
var z = new AutoDiff(x.Val * y.Val, 2);
z.AddInput(0, x, y.Val);
z.AddInput(1, y, x.Val);
return(z);
}
/// Tan関数
public static AutoDiff Tan(AutoDiff x)
{
var z = new AutoDiff(Math.Tan(x.Val), 1);
double cos = Math.Cos(x.Val);
z.AddInput(0, x, 1 / (cos * cos));
return(z);
}
/// Log関数
public static AutoDiff Log(AutoDiff x, double a)
{
const double delta = 1e-13;
var z = new AutoDiff(Math.Log(x.Val + delta, a), 1);
z.AddInput(0, x, 1 / ((x.Val + delta) * Math.Log(a)));
return(z);
}
/// /演算子のオーバーロード
public static AutoDiff operator /(AutoDiff x, AutoDiff y)
{
var z = new AutoDiff(x.Val / y.Val, 2);
z.AddInput(0, x, 1 / y.Val);
z.AddInput(1, y, -x.Val / (y.Val * y.Val));
return(z);
}
/// -演算子のオーバーロード
public static AutoDiff operator -(AutoDiff x, AutoDiff y)
{
var z = new AutoDiff(x.Val - y.Val, 2);
z.AddInput(0, x, 1);
z.AddInput(1, y, -1);
return(z);
}
/// 合計関数
public static AutoDiff Sum(AutoDiff[] x)
{
var z = new AutoDiff(0, x.Length);
for (int i = 0; i < x.Length; i++)
{
z.Val += x[i].Val;
z.AddInput(i, x[i], 1);
}
return(z);
}
/// 平均関数
public static AutoDiff Average(AutoDiff[] x)
{
var z = new AutoDiff(0, x.Length);
for (int i = 0; i < x.Length; i++)
{
z.Val += x[i].Val;
z.AddInput(i, x[i], 1.0 / x.Length);
}
z.Val /= x.Length;
return(z);
}
/// 内積関数
public static AutoDiff InnerProd(AutoDiff[] x, AutoDiff[] y)
{
var N = Math.Min(x.Length, y.Length);
var z = new AutoDiff(0, 2 * N);
for (int i = 0; i < N; i++)
{
z.Val += x[i].Val * y[i].Val;
z.AddInput(i, x[i], y[i].Val);
z.AddInput(i + N, y[i], x[i].Val);
}
return(z);
}
/// Max関数
public static AutoDiff Max(AutoDiff x, AutoDiff y)
{
return(x.Val > y.Val ? +x : +y);
}
/// 入力変数と対応する偏微分値を追加する
public void AddInput(int index, AutoDiff input, double diff)
{
this.Inputs[index] = input;
this.Differentials[index] = diff;
}
/// Min関数
public static AutoDiff Min(AutoDiff x, AutoDiff y)
{
return(x.Val < y.Val ? +x : +y);
}
