public override void CreateDerivativeTree(BaseNode parent, bool isLeft = true)
{
MultiplicationNode multiplicationNode1 = new MultiplicationNode(Plotter.CloneTree(this.left), Plotter.CloneTree(this.right), null);
MultiplicationNode multiplicationNode2 = new MultiplicationNode(Plotter.CloneTree(this.left), Plotter.CloneTree(this.right), null);
SubstractionNode substraction = new SubstractionNode(multiplicationNode1, multiplicationNode2, null);
PowerNode power = new PowerNode(Plotter.CloneTree(this.right), new NumberNode(null, 2), null);
DivisionNode node = new DivisionNode(substraction, power, null);
if (parent != null)
{
if (isLeft)
{
parent.left = node;
}
else
{
parent.right = node;
}
}
node.left.left.left.CreateDerivativeTree(node.left.left);
node.left.right.right.CreateDerivativeTree(node.left.right, false);
//Plotter.SetDerivativeRoot (node);
SetDerivativeRoot(node);
}
/// <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;
}
public override void CreateDerivativeTree(BaseNode parent, bool isLeft = true)
{
SumNode node = new SumNode(Plotter.CloneTree(this.left), Plotter.CloneTree(this.right), parent);
if (parent != null)
{
if (isLeft)
{
parent.left = node;
}
else
{
parent.right = node;
}
}
node.left.CreateDerivativeTree(node);
node.right.CreateDerivativeTree(node, false);
//Plotter.SetDerivativeRoot (node);
SetDerivativeRoot(node);
}
public override void CreateDerivativeTree(BaseNode parent, bool isLeft = true)
{
CosNode cosNode = new CosNode(Plotter.CloneTree(this.left), null);
MultiplicationNode node = new MultiplicationNode(Plotter.CloneTree(this.left), cosNode, null);
if (parent != null)
{
if (isLeft)
{
parent.left = node;
}
else
{
parent.right = node;
}
}
node.left.CreateDerivativeTree(node);
//Plotter.SetDerivativeRoot (node);
SetDerivativeRoot(node);
}
public override void CreateDerivativeTree(BaseNode parent, bool isLeft = true)
{
SumNode sum = new SumNode(Plotter.CloneTree(this), Plotter.CloneTree(this), this.parent);
if (parent != null)
{
if (isLeft)
{
parent.left = sum;
}
else
{
parent.right = sum;
}
}
sum.left.left.CreateDerivativeTree(sum.left);
sum.right.right.CreateDerivativeTree(sum.right, false);
//Plotter.SetDerivativeRoot (sum);
SetDerivativeRoot(sum);
}
public override void CreateDerivativeTree(BaseNode parent, bool isLeft = true)
{
// derivative of ln(x) = 1/x
DivisionNode division = new DivisionNode(new NumberNode(null, 1), Plotter.CloneTree(this.left), null);
MultiplicationNode multiplication = new MultiplicationNode(division, Plotter.CloneTree(this.left), null);
if (parent != null)
{
if (isLeft)
{
parent.left = multiplication;
}
else
{
parent.right = multiplication;
}
}
multiplication.right.CreateDerivativeTree(multiplication, false);
//Plotter.SetDerivativeRoot (multiplication);
SetDerivativeRoot(multiplication);
}
public override void CreateDerivativeTree(BaseNode parent, bool isLeft = true)
{
if (this.right is NumberNode && this.left is BasicFunctionXNode)
{
var lesser = (right as NumberNode).RealValue - 1;
BasicFunctionXNode x = new BasicFunctionXNode("", null);
MultiplicationNode multiplication = new MultiplicationNode(new NumberNode(null, (right as NumberNode).RealValue),
new PowerNode(x, new NumberNode(null, lesser), null), null);
if (parent != null)
{
if (isLeft)
{
parent.left = multiplication;
}
else
{
parent.right = multiplication;
}
}
SetDerivativeRoot(multiplication);
return;
}
else
{
if (this.right is NumberNode && this.left is NumberNode)
{
// if both this.left and this.right are numbers, return 0 for its just a number and it's anyway gon be 0
NumberNode node = new NumberNode(parent, 0);
if (parent != null)
{
if (isLeft)
{
parent.left = node;
}
else
{
parent.right = node;
}
}
//Plotter.SetDerivativeRoot (node);
SetDerivativeRoot(node);
return;
}
else if (this.right is NumberNode && !(this.left is NumberNode))
{
// f(x) ^ (some number)
// if left one some function
double nMinus1 = ((NumberNode)this.right).RealValue - 1;
var value = ((NumberNode)this.right).RealValue;
if (value == 1)
{
var node = Plotter.CloneTree(this);
if (parent != null)
{
if (isLeft)
{
parent.left = node;
}
else
{
parent.right = node;
}
}
node.left.CreateDerivativeTree(node);
SetDerivativeRoot(node);
return;
}
PowerNode power = new PowerNode(Plotter.CloneTree(this.left), new NumberNode(null, nMinus1), null);
MultiplicationNode multiplication = new MultiplicationNode(new NumberNode(null, value), Plotter.CloneTree(this.left), null);
// if the f(x) is more complicated than just 'x', we do additional calculation
if (!(multiplication.right is BasicFunctionXNode))
{
MultiplicationNode node = new MultiplicationNode(multiplication, Plotter.CloneTree(this.left), parent);
node.right.CreateDerivativeTree(multiplication, false);
if (parent != null)
{
if (isLeft)
{
parent.left = node;
}
else
{
parent.right = node;
}
}
//Plotter.SetDerivativeRoot (node);
SetDerivativeRoot(node);
return;
}
multiplication.parent = parent;
if (parent != null)
{
if (isLeft)
{
parent.left = multiplication;
}
else
{
parent.right = multiplication;
}
}
//Plotter.SetDerivativeRoot (multiplication);
SetDerivativeRoot(multiplication);
return;
}
else if (!(this.right is NumberNode) && (this.left is NumberNode))
{
// (some number) ^ f(x)
var value = ((NumberNode)this.left).RealValue;
if (this.right is BasicFunctionXNode)
{
// simple function
PowerNode power = new PowerNode(new NumberNode(null, value), new BasicFunctionXNode(""), null);
LnNode ln = new LnNode(new NumberNode(null, value), null);
MultiplicationNode node = new MultiplicationNode(power, ln, parent);
if (parent != null)
{
if (isLeft)
{
parent.left = node;
}
else
{
parent.right = node;
}
}
//Plotter.SetDerivativeRoot (node);
SetDerivativeRoot(node);
return;
}
else
{
// function is more complicated
PowerNode power = new PowerNode(new NumberNode(null, value), this.right, null);
LnNode ln = new LnNode(new NumberNode(null, value), null);
MultiplicationNode multiplication = new MultiplicationNode(power, ln, parent);
MultiplicationNode node = new MultiplicationNode(multiplication, Plotter.CloneTree(this.right), parent);
node.right.CreateDerivativeTree(node, false);
if (parent != null)
{
if (isLeft)
{
parent.left = node;
}
else
{
parent.right = node;
}
}
//Plotter.SetDerivativeRoot (node);
SetDerivativeRoot(node);
return;
}
}
else if (!(this.right is NumberNode) && !(this.left is NumberNode))
{
// neither is a number
// CASE: f(x) ^ g(x)
// d(f(x) ^ g(x))/dx = e^(g(x)*ln(f(x)) * d((g(x)*f(x)))/dx )
// this.left = f(x), this.right = g(x)
LnNode lnFx = new LnNode(Plotter.CloneTree(this.left), null); // create ln(f(x))
MultiplicationNode multiplication = new MultiplicationNode(Plotter.CloneTree(this.right), lnFx, null); // create g(x)*ln(f(x))
PowerNode ePower = new PowerNode(new NumberNode(null, Math.E), multiplication, null); // create e^(g(x)*ln(f(x)))
MultiplicationNode derivativeOfMultiplication = new MultiplicationNode(Plotter.CloneTree(multiplication.left), Plotter.CloneTree(multiplication.right), null); // do the derivative of g(x)*ln(f(x))
MultiplicationNode node = new MultiplicationNode(ePower, derivativeOfMultiplication, parent); // put it all together
node.right.CreateDerivativeTree(node, false); // take a derivative
if (parent != null)
{
if (isLeft)
{
parent.left = node;
}
else
{
parent.right = node;
}
}
//Plotter.SetDerivativeRoot (node);
SetDerivativeRoot(node);
return;
}
}
}