/// <summary>
/// Gives the value of the derivative using the quotient formula
/// </summary>
/// <param name="input"></param>
/// <returns></returns>
public double ProcessDerivative_Quotient(double input, BaseNode root)
{
BaseNode @base = root;
double x1 = input - h;
double x2 = input + h;
double y1 = @base.Calculate(x1);
double y2 = @base.Calculate(x2);
return((y2 - y1) / (x2 - x1));
}
/// <summary>
/// Creates a MacLaurien series based off the function
/// </summary>
/// <param name="mcLaurienRoot">Where the McLaurien Series will be outputted</param>
/// <param name="order">Nth order of a series</param>
public void CreateMcLaurienSeries(out BaseNode mcLaurienRoot, int order = 5)
{
if (derivativeRoot == null)
{
CreateDerivativeTree(); derivativeRoot.Simplify();
}
// we made sure that there is a derivative
BaseNode myDerivative = Plotter.CloneTree(derivativeRoot);
myDerivative.derivativeRoot = myDerivative;
double[] values = new double[order + 1]; // values for functions (f(0), derivative of f(0), second derivative of f(0), etc..)
values[0] = root.Calculate(0); // set up a value for f(0)
if (values.Length >= 2)
{
values[1] = derivativeRoot.Calculate(0); // set up a value of the first derivative of f(0)
}
if (values.Length >= 3)
{
for (int i = 2; i < values.Length; i++)
{
myDerivative.CreateDerivativeTree(null);
values[i] = myDerivative.derivativeRoot.Calculate(0);
myDerivative = myDerivative.derivativeRoot;
}
}
List <BaseNode> mcLaurienItems = new List <BaseNode> ();
SumNode result = new SumNode(null, null, null);
result.left = new NumberNode(null, values[0]);
for (int i = 1; i < values.Length; i++)
{
DivisionNode item = new DivisionNode(null, null, null);
FactorialNode denominator = new FactorialNode(new NumberNode(null, i), null); // not sure about this line
MultiplicationNode numerator = new MultiplicationNode(
new NumberNode(null, values[i]),
new PowerNode(new BasicFunctionXNode("", null), new NumberNode(null, i), null), null
);
item.left = numerator;
item.right = denominator;
mcLaurienItems.Add(item);
}
foreach (var item in mcLaurienItems)
{
result.PutToRightNode(item);
}
mcLaurienRoot = result;
}
/// <summary>
/// Returns the y-value for x-value based on a previously built binary tree. To be called only after ProcessString() func
/// </summary>
/// <param name="input"></param>
/// <returns></returns>
public double ProcessTree(double input, BaseNode root)
{
BaseNode @base = root;
return(@base.Calculate(input));
}
