/// <summary>
/// Produces a Lagrange Item, which looks like this: (x-Xj)/(Xterm - Xj), where term != j
/// Example: ((x-X1)(x-X2)...(x-Xn)) / ((Xterm - x1)(Xterm - x2)...(Xterm - Xn))
///
/// </summary>
/// <param name="points">Given set of points</param>
/// <param name="term">For which term you want to create a so-called Lagrange item</param>
/// <returns>Lagrange item of the type MultiplicationNode</returns>
public static MultiplicationNode ProduceLagrange(DataPoint[] points, int term)
{
MultiplicationNode item = new MultiplicationNode(null, null, null);
item.left = new NumberNode(null, 1);
for (int i = 0; i < points.Length; i++)
{
if (i == term)
{
continue;
}
SubstractionNode enumerator = new SubstractionNode(
new BasicFunctionXNode(""), // left
new NumberNode(null, points[i].X), // right
null // parent
);
NumberNode denominator = new NumberNode(null, points[term].X - points[i].X);
DivisionNode division = new DivisionNode(enumerator, denominator, null);
item.LagrangePutToRightNode(division);
}
return(item);
}
public override void CreateDerivativeTree(BaseNode parent, bool isLeft = true)
{
NumberNode node = new NumberNode(parent, 1);
if (parent != null)
{
if (isLeft)
{
parent.left = node;
}
else
{
parent.right = node;
}
}
//Plotter.SetDerivativeRoot (node);
SetDerivativeRoot(node);
return;
}
/// <summary>
/// Clones a specified tree based on a given node 'root'
/// </summary>
/// <param name="root"></param>
/// <returns></returns>
public static BaseNode CloneTree(BaseNode root)
{
if (root == null)
{
return(null);
}
BaseNode newNode = null;
if (root is SubstractionNode)
{
newNode = new SubstractionNode(root.value);
}
else if (root is MultiplicationNode)
{
newNode = new MultiplicationNode(root.value);
}
else if (root is SumNode)
{
newNode = new SumNode(root.value);
}
else if (root is DivisionNode)
{
newNode = new DivisionNode(root.value);
}
else if (root is NumberNode)
{
newNode = new NumberNode(null, (root as NumberNode).RealValue);
}
else if (root is BasicFunctionXNode)
{
newNode = new BasicFunctionXNode(root.value);
}
else if (root is SinNode)
{
newNode = new SinNode(root.value);
}
else if (root is CosNode)
{
newNode = new CosNode(root.value);
}
else if (root is PowerNode)
{
newNode = new PowerNode(root.value);
}
else if (root is ExponentNode)
{
newNode = new ExponentNode(root.value);
}
else if (root is LnNode)
{
newNode = new LnNode(root.value);
}
else if (root is FactorialNode)
{
newNode = new FactorialNode(root.value);
}
newNode.left = CloneTree(root.left);
newNode.right = CloneTree(root.right);
return(newNode);
}
/// <summary>
/// Creates tree based on an input string and root node
/// </summary>
/// <param name="s"></param>
/// <param name="baseNode"></param>
public void CreateTree(string s, BaseNode baseNode)
{
// if the string is empty, we don't do anything. This is the base case to leave the recursion
if (s == string.Empty)
{
return;
}
// if it's 's', or '+', or whatever, we create a dedicated class (watch first case to see the logic)
if (s[0] == 's')
{
SinNode node = new SinNode(s, baseNode); // dedicated class
baseNode.Insert(node); // we insert it to the current head node
CreateTree(node.value, node); // we change the head node to the newly created one
}
else if (s[0] == 'c')
{
CosNode node = new CosNode(s, baseNode);
baseNode.Insert(node);
CreateTree(node.value, node);
}
else if (s[0] == '*')
{
// same as in the first 'if'
MultiplicationNode node = new MultiplicationNode(s, baseNode);
baseNode.Insert(node);
CreateTree(node.value, node);
}
else if (s[0] == '+')
{
// same as in the first 'if'
SumNode node = new SumNode(s, baseNode);
baseNode.Insert(node);
CreateTree(node.value, node);
}
else if (s[0] == '/')
{
DivisionNode node = new DivisionNode(s, baseNode);
baseNode.Insert(node);
CreateTree(node.value, node);
}
else if (s[0] == '-' && !(s[1] >= '0' && s[1] <= '9'))
{
SubstractionNode node = new SubstractionNode(s, baseNode);
baseNode.Insert(node);
CreateTree(node.value, node);
}
else if (s[0] == 'l')
{
LnNode node = new LnNode(s, baseNode);
baseNode.Insert(node);
CreateTree(node.value, node);
}
else if (s[0] == '^')
{
PowerNode node = new PowerNode(s, baseNode);
baseNode.Insert(node);
CreateTree(node.value, node);
}
else if (s[0] == 'e')
{
ExponentNode node = new ExponentNode(s, baseNode);
baseNode.Insert(node);
CreateTree(node.value, node);
}
else if (s[0] == '!')
{
FactorialNode node = new FactorialNode(s, baseNode);
baseNode.Insert(node);
CreateTree(node.value, node);
}
else if (s[0] == 'p' || (s[0] >= '0' && s[0] <= '9'))
{
// stuff below just parses number
string toParseIntoNumber = string.Empty;
int counter = 0;
if (s[0] == 'p')
{
toParseIntoNumber = "p";
}
else
{
while ((s[counter] >= '0' && s[counter] <= '9') || s[counter] == '.')
{
toParseIntoNumber += s[counter];
counter++;
}
}
if (toParseIntoNumber.Contains('.'))
{
toParseIntoNumber = toParseIntoNumber.Replace('.', ',');
}
string @newS = string.Empty;
for (int i = (s[0] == 'p' ? 1 : counter); i < s.Length; i++)
{
newS += s[i];
}
// same stuff as in the first 'if'
NumberNode node = new NumberNode(newS, baseNode, toParseIntoNumber);
baseNode.Insert(node);
CreateTree(node.value, node);
}
else if (s[0] == '-' && (s[1] >= '0' && s[1] <= '9'))
{
// negative number
s = Plotter.GetStringFromIndex(s, 1);
string toParseIntoNumber = string.Empty;
int counter = 0;
if (s[0] == 'p')
{
toParseIntoNumber = "p";
}
else
{
do
{
toParseIntoNumber += s[counter];
counter++;
} while (counter < s.Length && ((s[counter] >= '0' && s[counter] <= '9') || s[counter] == '.'));
}
if (toParseIntoNumber.Contains('.'))
{
toParseIntoNumber = toParseIntoNumber.Replace('.', ',');
}
string @newS = string.Empty;
for (int i = (s[0] == 'p' ? 1 : counter); i < s.Length; i++)
{
newS += s[i];
}
NumberNode node = new NumberNode(newS, baseNode, "-" + toParseIntoNumber);
baseNode.Insert(node);
CreateTree(node.value, node);
}
else if (s[0] == 'x')
{
// same as in the first 'if'
BasicFunctionXNode node = new BasicFunctionXNode(s, baseNode);
baseNode.Insert(node);
CreateTree(node.value, node);
}
else if (s[0] == '(' || s[0] == ' ')
{
s = GetStringFromIndex(s, 1); // practically delete that ( or ' '
CreateTree(s, baseNode);
}
else if (s[0] == ')')
{
// count how many times ')' appears, let this number be 'i', then our head node is gonna go 'i' levels up
int i = 0;
while (s[i] == ')' && (s[i] != ',' || s[i] != ' '))
{
i++;
if (i == s.Length)
{
break;
}
}
for (int j = 0; j < i; j++)
{
if (baseNode.parent != null)
{
baseNode = baseNode.parent;
}
else
{
throw new Exception("Eror in your input");
}
}
s = GetStringFromIndex(s, i);
CreateTree(s, baseNode);
}
else if (s[0] == ',')
{
if (baseNode.parent == null)
{
throw new Exception("Error in your input");
}
// go one level up
baseNode = baseNode.parent;
s = GetStringFromIndex(s, 1);
CreateTree(s, baseNode);
}
}
public override BaseNode Simplify()
{
if (!(left is NumberNode || right is NumberNode)) // if neither left nor right guy is a number
{
this.left = this.left.Simplify(); // tell the left guy to get simple
this.right = this.right.Simplify(); // right guy also has to get simple
if (left is NumberNode && right is NumberNode)
{
if ((right as NumberNode).RealValue != 0)
{
NumberNode division = new NumberNode(
null,
((left as NumberNode).RealValue / (right as NumberNode).RealValue)
);
return(division);
}
return(this);
}
else if (left is NumberNode && !(right is NumberNode))
{
var value = (left as NumberNode).RealValue;
if (value == 0)
{
return(new NumberNode(null, 0));
}
this.right = this.right.Simplify();
return(this);
}
else if (!(left is NumberNode) && right is NumberNode)
{
if ((right as NumberNode).RealValue == 1)
{
return(this.left.Simplify());
}
this.left = this.left.Simplify();
return(this);
}
else
{
return(this);
}
}
else // if one of them IS actually a number
{
if (left is NumberNode && right is NumberNode)
{
if ((right as NumberNode).RealValue != 0)
{
NumberNode division = new NumberNode(
null,
((left as NumberNode).RealValue / (right as NumberNode).RealValue)
);
return(division);
}
return(this);
}
else if (left is NumberNode && !(right is NumberNode))
{
var value = (left as NumberNode).RealValue;
if (value == 0)
{
return(new NumberNode(null, 0));
}
this.right = this.right.Simplify();
return(this);
}
else if (!(left is NumberNode) && right is NumberNode)
{
if ((right as NumberNode).RealValue == 1)
{
return(this.left.Simplify());
}
this.left = this.left.Simplify();
return(this);
}
else
{
return(null);
}
}
}
public override BaseNode Simplify()
{
if (!(left is NumberNode || right is NumberNode)) // if neither left nor right guy is a number
{
this.left = this.left.Simplify(); // tell the left guy to get simple
this.right = this.right.Simplify(); // right guy also has to get simple
if (left is NumberNode && right is NumberNode)
{
NumberNode substraction = new NumberNode(
null,
((left as NumberNode).RealValue - (right as NumberNode).RealValue)
);
return(substraction);
}
else if (left is NumberNode && !(right is NumberNode))
{
this.right = this.right.Simplify();
return(this);
}
else if (!(left is NumberNode) && right is NumberNode)
{
var value = (right as NumberNode).RealValue;
this.left = this.left.Simplify();
if (value == 0)
{
return(this.left);
}
return(this);
}
else
{
return(this);
}
}
else // if one of them IS actually a number
// we go over all the possibilities
{
if (left is NumberNode && right is NumberNode)
{
NumberNode substraction = new NumberNode(
null,
((left as NumberNode).RealValue - (right as NumberNode).RealValue)
);
return(substraction);
}
else if (left is NumberNode && !(right is NumberNode))
{
this.right = this.right.Simplify();
return(this);
}
else if (!(left is NumberNode) && right is NumberNode)
{
var value = (right as NumberNode).RealValue;
this.left = this.left.Simplify();
if (value == 0)
{
return(this.left);
}
return(this);
}
else
{
return(null);
}
}
}
public override BaseNode Simplify()
{
if (!(left is NumberNode || right is NumberNode)) // if neither left nor right guy is a number
{
this.left = this.left.Simplify(); // tell the left guy to get simple
this.right = this.right.Simplify(); // right guy also has to get simple
if (left is NumberNode && right is NumberNode)
{
NumberNode power = new NumberNode(
null,
Math.Pow((left as NumberNode).RealValue, (right as NumberNode).RealValue)
);
return(power);
}
else if (left is NumberNode && !(right is NumberNode))
{
var value = (left as NumberNode).RealValue;
if (value == 0)
{
return(new NumberNode(null, 0));
}
// MIGHT BE CAUSING PROBLEMS (CHECK IT LATER)
else if (value == 1)
{
return(new NumberNode(null, 1));
}
this.right = this.right.Simplify();
return(this);
}
else if (!(left is NumberNode) && right is NumberNode)
{
var value = (right as NumberNode).RealValue;
if (value == 0)
{
return(new NumberNode(null, 1));
}
else if (value == 1)
{
return(this.left.Simplify());
}
this.left = this.left.Simplify();
return(this);
}
else
{
return(this);
}
}
else // if one of them IS actually a number
{
if (left is NumberNode && right is NumberNode)
{
NumberNode power = new NumberNode(
null,
Math.Pow((left as NumberNode).RealValue, (right as NumberNode).RealValue)
);
return(power);
}
else if (left is NumberNode && !(right is NumberNode))
{
var value = (left as NumberNode).RealValue;
if (value == 0)
{
return(new NumberNode(null, 0));
}
else if (value == 1)
{
return(new NumberNode(null, 1));
}
this.right = this.right.Simplify();
return(this);
}
else if (!(left is NumberNode) && right is NumberNode)
{
var value = (right as NumberNode).RealValue;
if (value == 0)
{
return(new NumberNode(null, 1));
}
// MIGHT BE CAUSING PROBLEMS (CHECK IT LATER)
else if (value == 1)
{
return(this.left.Simplify());
}
this.left = this.left.Simplify();
return(this);
}
else
{
return(null);
}
}
}
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;
}
}
}