public static DualNumber Pow(DualNumber a, double b)
{
var pow = Math.Pow(a.Value, b);
var frac = a.Diff / a.Value;
return(new DualNumber(pow, b * pow * frac, b * pow * (a.Diff2 / a.Value + (b - 1) * frac * frac)));
}
public static DualNumber Sin(DualNumber a)
{
var sin = Math.Sin(a.Value);
var cos = Math.Cos(a.Value);
return(new DualNumber(sin, cos * a.Diff, cos * a.Diff2 - sin * a.Diff * a.Diff));
}
public static DualNumber Cosh(DualNumber a)
{
var sin = Math.Sinh(a.Value);
var cos = Math.Cosh(a.Value);
return(new DualNumber(cos, sin * a.Diff, sin * a.Diff2 + cos * a.Diff * a.Diff));
}
public static DualNumber Atan(DualNumber a)
{
var tmp = 1 / (1 + a.Value * a.Value);
var tmpDiff = a.Diff * tmp;
return(new DualNumber(Math.Atan(a.Value), tmpDiff, a.Diff2 * tmp - 2 * a.Value * tmpDiff * tmpDiff));
}
public static DualNumber Acos(DualNumber a)
{
var tmp = 1 / Math.Sqrt(1 - a.Value * a.Value);
var tmpDiff = a.Diff * tmp;
return(new DualNumber(Math.Acos(a.Value), -tmpDiff, -(a.Diff2 + a.Value * tmpDiff * tmpDiff) * tmp));
}
public static DualNumber Pow(DualNumber a, DualNumber b) => Exp(b * Log(a));
public static DualNumber Log(DualNumber a)
{
return(new DualNumber(Math.Log(a.Value), a.Diff / a.Value, (a.Diff2 - a.Diff * a.Diff / a.Value) / a.Value));
}
public static DualNumber Exp(DualNumber a)
{
var exp = Math.Exp(a.Value);
return(new DualNumber(exp, exp * a.Diff, exp * (a.Diff2 + a.Diff * a.Diff)));
}
public static DualNumber Sqrt(DualNumber a)
{
var r = Math.Sqrt(a.Value);
return(new DualNumber(r, 0.5 * a.Diff / r, 0.5 * a.Diff2 / r - 0.25 * a.Diff * a.Diff / (a.Value * r)));
}
public static DualNumber Inverse(DualNumber a)
{
return(new DualNumber(1 / a.Value, -a.Diff / (a.Value * a.Value), (2 * a.Diff * a.Diff / a.Value - a.Diff2) / (a.Value * a.Value)));
}
public static DualVector Vec(DualNumber x, DualNumber y, DualNumber z) => new DualVector(x, y, z);
public DualVector(Vector v)
{
X = v.X;
Y = v.Y;
Z = v.Z;
}
public DualVector(DualNumber x, DualNumber y, DualNumber z)
{
X = x;
Y = y;
Z = z;
}
public static DualNumber Abs(DualNumber a) => a.Value >= 0 ? a : -a;
public static DualNumber Tanh(DualNumber a)
{
var tan = Math.Tanh(a.Value);
return(new DualNumber(tan, (1 - tan * tan) * a.Diff, (1 - tan * tan) * (a.Diff2 - 2 * tan * a.Diff * a.Diff)));
}