/// <summary>
/// Applies the chain rule on a function.
/// </summary>
/// <param name="function">The function definition.</param>
/// <param name="dargs">The derivatives of the arguments.</param>
/// <param name="format">The format of the new function. {0} denotes the old name, while {1} will hold the index to which the function should be derived.</param>
/// <returns></returns>
public static Node ChainRule(FunctionNode function, IReadOnlyList <Node> dargs, string format)
{
Node result = null;
for (var i = 0; i < dargs.Count; i++)
{
if (dargs[i] == null)
{
break;
}
var b = Node.Function(format.FormatString(function.Name, i), function.Arguments) * dargs[i];
result = result == null ? b : Node.Add(result, b);
}
return(result);
}
private static Node DPwr(FunctionNode f, IReadOnlyList <Node> dargs)
{
dargs.Check(2);
Node result = null;
if (dargs[0] != null)
{
result = Node.Function("sgn", f.Arguments[0]) * f.Arguments[1] * dargs[0] * Node.Function(f.Name, f.Arguments[0], f.Arguments[1] - 1.0);
}
if (dargs[1] != null)
{
result += dargs[1] * Node.Function("log", f.Arguments[0]) * f;
}
return(result);
}
private static Node Limit(FunctionNode f, IReadOnlyList <Node> dargs)
{
dargs.Check(3);
var x = f.Arguments[0];
var y = f.Arguments[1];
var z = f.Arguments[2];
Node result = null;
if (dargs[0] != null)
{
result = Node.Conditional(
Node.And(
Node.GreaterThan(x, Node.Function("min", y, z)),
Node.LessThan(x, Node.Function("max", y, z))),
dargs[0],
Node.Zero);
}
if (dargs[1] != null)
{
result += Node.Conditional(
Node.And(
Node.LessThanOrEqual(y, z),
Node.LessThanOrEqual(x, Node.Function("min", y, z))),
dargs[1],
Node.Zero);
}
if (dargs[2] != null)
{
result += Node.Conditional(
Node.And(
Node.LessThan(y, z),
Node.GreaterThanOrEqual(x, Node.Function("max", y, z))),
dargs[2],
Node.Zero);
}
return(result);
}
private static Node DHypot(FunctionNode f, IReadOnlyList <Node> dargs)
{
dargs.Check(2);
if (dargs[1] == null)
{
if (dargs[0] == null)
{
return(null);
}
return(0.5 * f.Arguments[0] * dargs[0] / f);
}
else if (dargs[0] == null)
{
return(0.5 * f.Arguments[1] * dargs[1] / f);
}
else
{
return(0.5 * (f.Arguments[0] * dargs[0] + f.Arguments[1] * dargs[1]) / f);
}
}
private static Node DAtan2(FunctionNode f, IReadOnlyList <Node> dargs)
{
dargs.Check(2);
if (dargs[1] == null)
{
if (dargs[0] == null)
{
return(null);
}
return(f.Arguments[1] * dargs[0] / (Node.Function("square", f.Arguments[0]) + Node.Function("square", f.Arguments[1])));
}
else if (dargs[0] == null)
{
return(-f.Arguments[0] * dargs[1] / (Node.Function("square", f.Arguments[0]) + Node.Function("square", f.Arguments[1])));
}
else
{
return((f.Arguments[1] * dargs[0] - f.Arguments[0] * dargs[1]) / (Node.Function("square", f.Arguments[0]) + Node.Function("square", f.Arguments[1])));
}
}
private static Node DAtan(FunctionNode f, IReadOnlyList <Node> dargs) => dargs.Check(1)[0] / (Node.One + Node.Power(f.Arguments[0], Node.Two));
private static Node DAsin(FunctionNode f, IReadOnlyList <Node> dargs) => dargs.Check(1)[0] / Node.Function("sqrt", Node.One - Node.Power(f.Arguments[0], Node.Two));
private static Node Zero(FunctionNode f, IReadOnlyList <Node> dargs) => null;
private static Node DPassThrough(FunctionNode f, IReadOnlyList <Node> dargs) => Node.Function(f.Name, dargs);
private static Node DAtanh(FunctionNode f, IReadOnlyList <Node> dargs) => dargs.Check(1)[0] / (1 - Node.Function("square", f.Arguments[0]));
/// <include file='docs.xml' path='docs/members/Function/*'/> public static FunctionNode Function(string name, params Node[] arguments) => FunctionNode.Function(name, arguments);
/// <include file='docs.xml' path='docs/members/Function/*'/> public static FunctionNode Function(string name, IReadOnlyList <Node> arguments) => FunctionNode.Function(name, arguments);
