public Min(Expression left, Expression right)
{
Symbol = "min";
Left = left;
Right = right;
_expr = 0.5 * (Left + Right - Sym.Abs(Left - Right));
EvalFunctional = (c) => Math.Min(Left.Eval(c), Right.Eval(c));
DiffFunctional = (c, var) =>
{
// var diffExpr = _expr.SymbolicDiff(var);
// return diffExpr.Eval(c);
// var u = Left.Diff(c, var);
// var v = Right.Diff(c, var);
if (Left.Eval(c) < Right.Eval(c))
{
return(Left.Diff(c, var));
}
else if (Left.Eval(c) > Right.Eval(c))
{
return(Right.Diff(c, var));
}
else
{
return(0.5 * (Left.Diff(c, var) + Right.Diff(c, var)));
}
};
}
public override Expression SymbolicDiff(Variable var)
{
var u = Parameter;
var dudx = Parameter.SymbolicDiff(var);
return(Sym.Cosh(u) * dudx);
}
public Max(Expression left, Expression right)
{
Symbol = "max";
Left = left;
Right = right;
_expr = 0.5 * (Left + Right + Sym.Abs(Left - Right));
EvalFunctional = (c) => Math.Max(Left.Eval(c), Right.Eval(c));
DiffFunctional = (c, var) =>
{
// var u = Left.Diff(c, var);
// var v = Right.Diff(c, var);
if (Left.Eval(c) > Right.Eval(c))
{
return(Left.Diff(c, var));
}
else if (Left.Eval(c) < Right.Eval(c))
{
return(Right.Diff(c, var));
}
else
{
return(0.5 * (Left.Diff(c, var) + Right.Diff(c, var)));
}
/* if (Left.Eval(c) > Right.Eval(c))
* return Left.Diff(c, var);
* else
* return Right.Diff(c, var);*/
};
}
public override Expression SymbolicDiff(Variable var)
{
var u = Left;
var v = Right;
var dudx = Left.SymbolicDiff(var);
var dvdx = Right.SymbolicDiff(var);
return((v * dudx - u * dvdx) / Sym.Pow(v, 2));
}
public override Expression SymbolicDiff(Variable var)
{
var u = Left;
var v = Right;
var dudx = Left.SymbolicDiff(var);
var dvdx = Right.SymbolicDiff(var);
return(v * Sym.Pow(u, v - 1) * dudx + Sym.Pow(u, v) * Sym.Ln(u) * dvdx);
}
public SmoothMin(Expression left, Expression right, double k = 10)
{
Symbol = "smin";
Left = left;
Right = right;
//_expr = 0.5 * (Left + Right + Sym.Abs(Left - Right));
_expr = Sym.Ln(Sym.Exp(-k * left) + Sym.Exp(-k * right)) / -k;
EvalFunctional = (c) => Math.Min(Left.Eval(c), Right.Eval(c));
DiffFunctional = (c, var) => _expr.Diff(c, var);
}
public override Expression SymbolicDiff(Variable var)
{
return(Sym.Sqrt(Sym.Pow(Child, 2) + 1e-12).SymbolicDiff(var));
}