public override Expr Substitute(VariableExpr target, Expr expression)
{
var argument = target.Equals(Argument) ? expression : Argument.Substitute(target, expression);
if (argument.Equals(Argument))
{
return(this);
}
return(Unary(Op, argument));
}
public override Expr Substitute(VariableExpr target, Expr expression)
{
return(new ArrayExpr(Elements.Select((item) => item.Substitute(target, expression)).ToArray()));
}
/// <summary>
/// Get the partial derivative of the expression with respect to a variable.
/// </summary>
/// <param name="variable">The variable.</param>
/// </example>
public override Expr Partial(VariableExpr variable)
{
return(new ArrayExpr(Elements.Select((item) => item.Partial(variable)).ToArray()));
}
public override Expr Partial(VariableExpr variable)
{
return(0);
}
public override Expr Substitute(VariableExpr target, Expr expression)
{
return(this);
}
public override Expr Partial(VariableExpr variable)
{
Expr x = Argument, xp = Argument.Partial(variable);
switch (Op)
{
case UnaryOp.Identity: return(xp);
case UnaryOp.Negate: return(-xp);
case UnaryOp.Inverse: return(-xp / (x ^ 2));
case UnaryOp.Rnd: return(0);
case UnaryOp.Pi: return(Math.PI * xp);
case UnaryOp.Abs: return(Sign(x) * xp);
case UnaryOp.Sign: return(0);
case UnaryOp.Exp: return(Exp(x) * xp);
case UnaryOp.Log: return(xp / x);
case UnaryOp.Log2: return(xp / (Math.Log(2) * x));
case UnaryOp.Log10: return(xp / (Math.Log(10) * x));
case UnaryOp.Sqr: return(x * (2 * xp));
case UnaryOp.Cub: return((x ^ 2) * (3 * xp));
case UnaryOp.Sqrt: return(xp / (2 * Sqrt(x)));
case UnaryOp.Cbrt: return(xp / (3 * (x ^ (2.0 / 3))));
case UnaryOp.Floor: return(0);
case UnaryOp.Ceiling: return(0);
case UnaryOp.Round: return(0);
case UnaryOp.Sin: return(Cos(x) * xp);
case UnaryOp.Cos: return((-Sin(x)) * xp);
case UnaryOp.Tan: return(2 * xp / (1 + Cos(2 * x)));
case UnaryOp.Sinh: return(Cosh(x) * xp);
case UnaryOp.Cosh: return(Sinh(x) * xp);
case UnaryOp.Tanh: return(xp / (0.5 * (1 + Cosh(2 * x))));
case UnaryOp.Asin: return(xp / Sqrt(1 - (x ^ 2)));
case UnaryOp.Acos: return(-xp / Sqrt(1 - (x ^ 2)));
case UnaryOp.Atan: return(xp / (1 + (x ^ 2)));
case UnaryOp.Asinh: return(xp / Sqrt((x ^ 2) + 1));
case UnaryOp.Acosh: return(xp / Sqrt((x ^ 2) - 1));
case UnaryOp.Atanh: return(xp / (1 - (x ^ 2)));
case UnaryOp.Sum: return(Sum(xp));
case UnaryOp.Transpose: return(Transpose(xp));
default:
throw new NotImplementedException($"Operator {Key} does not have slope defined.");
}
}