/// <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>
/// Get the McLaurien series based off already given values for derivatives
/// </summary>
/// <param name="mcLaurienRoot">Where the McLaurien series will be outputted</param>
/// <param name="order">Order of the McLaurien</param>
public void CreateMcLaurienSeriesByLimits(out BaseNode mcLaurienRoot, int order)
{
List <double> values = new List <double> ();
for (int i = 0; i <= order; i++)
{
var value = ProcessNthDerivative_Quotient(0, i, root);
values.Add(value);
}
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.Count; 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;
}
public BaseNode CreatePolynomialThroughPoints(DataPoint[] points)
{
/* Let X be the number of points user has selected
* Then the polynomial is going to be of the degree (X - 1)
*
* Example: X = 5 => ax^4 + bx^3 + cx^2 + dx + e
*/
SumNode polynomial = new SumNode(null, null, null);
var firstDivision = ProduceLagrange(points, 0);
var firstMultiplication = new MultiplicationNode(firstDivision, new NumberNode(null, points[0].Y), null);
polynomial.left = firstMultiplication;
for (int j = 1; j < points.Length; j++)
{
var division = ProduceLagrange(points, j);
MultiplicationNode node = new MultiplicationNode(division, new NumberNode(null, points[j].Y), null);
polynomial.PutToRightNode(node);
}
return(polynomial);
}