public static Polynomial Newtonsecond(double [] Y ,double h ,int n ,double x0)
{
Double[] DalthY = new double[3];
Double[] Dalth2Y = new double[2];
double Dalth3Y = 0;
for (int i = 0; i < 3; i++)
{
DalthY[i] = Y[i + 1] - Y[i];
}
for (int i = 0; i < 2; i++)
{
Dalth2Y[i] = DalthY[i + 1] - DalthY[i];
}
Dalth3Y = Dalth2Y[1] - Dalth2Y[0];
Polynomial p = new Polynomial();
Polynomial temp = new Polynomial();
Polynomial temp1 = new Polynomial();
Polynomial temp2 = new Polynomial();
temp = Polynomial.insert(Dalth2Y[0], 0, temp);
p = Polynomial.insert(1 / h, 1, p);
p = Polynomial.insert(-1 * (x0 / h), 0, p);
temp1 = Polynomial.insert(Dalth3Y, 0, temp1);
temp1 = Polynomial.multi(temp1, p);
temp1 = Polynomial.insert(-1*Dalth3Y, 0, temp1);
temp1 = Polynomial.add(temp1, temp);
h = h * h;
temp2 = Polynomial.insert((1 / h), 0, temp2);
temp1 = Polynomial.multi(temp1, temp2);
return temp1;
}
public static Polynomial Derive(Polynomial temp)
{
Polynomial l=temp ;
while((l != null)&&(l.power != 0))
{
l.amthal = l.power*l.amthal;
l.power = l.power - 1;
l=l.next;
}
return temp;
}
public static Polynomial insert(double x, double y, Polynomial l)
{
Polynomial temp = new Polynomial();
temp.amthal = x;
temp.power = y;
temp.next = null;
if ((l.next == null) && (l.power == 0) && (l.amthal == 0))
l = temp;
else
{
Polynomial prv = l;
if (prv.power < temp.power)
{
temp.next = prv;
l = temp;
}
else
{
while ((prv.next != null) && (prv.next.power > temp.power))
prv = prv.next;
if (prv.next == null)
{
if (prv.power == temp.power)
prv.amthal = prv.amthal + temp.amthal;
else
prv.next = temp;
}
else
{
if ((prv.next.power == temp.power))
prv.next.amthal = prv.next.amthal + temp.amthal;
else if (prv.power == temp.power)
prv.amthal = prv.amthal + temp.amthal;
else
{
temp.next = prv.next;
prv.next = temp;
}
}
}
}
return l;
}
public static Polynomial Newton(double [] Y ,double h ,int n ,double x0)
{
Double[] DalthY =new double[3];
Double[] Dalth2Y = new double[2];
double Dalth3Y = 0;
for (int i = 0; i < 3; i++)
{
DalthY[i] = Y[i + 1] - Y[i];
}
for (int i = 0; i < 2; i++)
{
Dalth2Y[i] = DalthY[i + 1] - DalthY[i];
}
Dalth3Y = Dalth2Y[1] - Dalth2Y[0];
Polynomial first = new Polynomial();
Polynomial second = new Polynomial();
Polynomial third= new Polynomial();
Polynomial p= new Polynomial();
Polynomial p2= new Polynomial();
Polynomial temp = new Polynomial();
Polynomial temp1 = new Polynomial();
Polynomial temp2 = new Polynomial();
p = Polynomial.insert(1/h, 1, p);
p = Polynomial.insert(-1*(x0/h), 0, p);
p2 = Polynomial.multi(p, p);
second=Polynomial.insert((2*Dalth2Y[0])/2, 0,second );
second = Polynomial.multi(second, p);
second = Polynomial.insert(-1*(Dalth2Y[0]/h), 0, second);
first = Polynomial.insert(DalthY[0], 0, first);
third = Polynomial.insert((3*Dalth3Y)/6, 0, third);
third = Polynomial.multi(p2, third);
temp = Polynomial.insert(-1*(Dalth3Y), 0, temp);
temp = Polynomial.multi(temp, p);
third = Polynomial.add(third, temp);
temp1 = Polynomial.insert((2*Dalth3Y)/6,0,temp1);
third = Polynomial.add(third, temp1);
third = Polynomial.add(third,first);
third = Polynomial.add(third, second);
temp2 = Polynomial.insert((1/h), 0, temp2);
third = Polynomial.multi(third, temp2);
return third;
}
public static Polynomial add(Polynomial n, Polynomial m)
{
Polynomial temp = n;
Polynomial z = new Polynomial();
while (temp != null)
{
double frst = temp.amthal;
double frstpw = temp.power;
z = insert(frst, frstpw, z);
temp = temp.next;
}
temp = m;
while (temp != null)
{
double frst = temp.amthal;
double frstpw = temp.power;
z = insert(frst, frstpw, z);
temp = temp.next;
}
return z;
}
private void Calculate_Click(object sender, EventArgs e)
{
string Method = comboBox1.Text;
string[] allMethod = {"newton"};
string AnyOfMethod = Array.Find(allMethod, s => s.Equals(Method));
if ((Method != AnyOfMethod))
{
MessageBox.Show("This Is Not Method", "Error", MessageBoxButtons.OK, MessageBoxIcon.Error);
}
else
{
bool XarrayZero = false;
bool YarrayZero = false;
xcolum = CreatXarray(ref ThereIsErrorX);
ycolum = CreatYarray(ref ThereIsErrorY);
XarrayZero = Share.IfallZero(xcolum);
YarrayZero = Share.IfallZero(ycolum);
if ((ThereIsErrorX != true) && (ThereIsErrorY != true) && (XarrayZero != true) && (YarrayZero != true))
{
switch (Method)
{
case "newton":
{
textBox2.Visible = true;
textBox3.Visible = true;
Polynomial newton = new Polynomial();
newton = deriveationclass.Newton(ycolum, xcolum[1] - xcolum[0], NumOfNode, xcolum[0]);
textBox2.Text = Polynomial.tostring(newton);
newton = deriveationclass.Newtonsecond(ycolum, xcolum[1] - xcolum[0], NumOfNode,
xcolum[0]);
textBox3.Text = Polynomial.tostring(newton);
}
break;
}
}
}
}
public static string lagrang(double[] x, int node, double[] y)
{
Polynomial temp = new Polynomial();
Polynomial onepoly = new Polynomial();
bool loop = false;
for (int i = 0; i < node; i++)
{
for (int j = 0; j < node; j++)
{
loop = false;
if (i != j)
{
loop = true;
temp = new Polynomial();
double amthallagrang = x[i] - x[j];
temp = Polynomial.insert(y[i] * amthallagrang, 1, temp);
temp = Polynomial.insert(y[i] * amthallagrang * -x[j], 0, temp);
}
if (loop)
onepoly = Polynomial.add(temp, onepoly);
}
}
return Polynomial.tostring(onepoly);
}
public static Polynomial Splin(double []x,double []y,int node,double point)
{
Polynomial temp=new Polynomial();
int c = 0;
for (int i = 0; i < node - 1; i++)
{
if ((x[i] <= point) && (x[i + 1] >= point))
{
c = i;
break;
}
}
double constant = (y[c + 1] - y[c])/(x[c + 1] - x[c]);
temp = Polynomial.insert(constant, 1, temp);
temp = Polynomial.insert(-1*constant*x[c], 0, temp);
temp = Polynomial.insert(y[c], 0, temp);
return temp;
}
public static Polynomial newtonemethod(double[] x, double[] y, double[,] tab, int n)
{
Polynomial temp = new Polynomial();
Polynomial temp1 = new Polynomial();
Polynomial temp2 = new Polynomial();
Polynomial temp3 = new Polynomial();
temp = Polynomial.insert(y[0], .0, temp);
for (int i = 1; i < n; i++)
{
temp1 = new Polynomial();
temp1 = Polynomial.insert(1.0, .0, temp1);
temp3 = new Polynomial();
temp3 = Polynomial.insert(tab[0, i], .0, temp3);
for (int j = 0; j < i; j++)
{
temp2 = new Polynomial();
temp2 = Polynomial.insert(1.0, 1.0, temp2);
temp2 = Polynomial.insert(-1.0 * x[j], .0, temp2);
temp1 = Polynomial.multi(temp2, temp1);
}
temp3 = Polynomial.multi(temp1, temp3);
temp = Polynomial.add(temp, temp3);
}
return temp;
}
private void Send_Click(object sender, EventArgs e)
{
bool XarrayZero = false;
bool YarrayZero = false;
string Method = comboBox1.Text;
string[] allMethod = { "General Methode", "Spline", "Lagrange", "Newton", "Least Square Method" };
if (Method != ".......")
{
xcolum = CreatXarray(ref ThereIsErrorX);
XarrayZero = Share.IfallZero(xcolum);
if (XarrayZero != true)
ycolum = CreatYarray(ref ThereIsErrorY);
YarrayZero = Share.IfallZero(ycolum);
string AnyOfMethod = Array.Find(allMethod, s => s.Equals(Method));
if ((XarrayZero != true) && (YarrayZero != true) && (ThereIsErrorX != true) && (ThereIsErrorY != true))
if ((Method == AnyOfMethod))
comboBox1.Enabled = false;
else
MessageBox.Show("This Is Not Method", "Error", MessageBoxButtons.OK, MessageBoxIcon.Error);
}
XarrayZero = Share.IfallZero(xcolum);
YarrayZero = Share.IfallZero(ycolum);
switch (Method)
{
case "General Methode":
{
if ((XarrayZero != true) && (YarrayZero != true) && (ThereIsErrorX != true) && (ThereIsErrorY != true))
{
#region General Methode
double[,] matrx;
matrx = new double[NumOfNode, NumOfNode];
matrx = InterpolationClass.CreatVandrmondmatrix(NumOfNode, xcolum);
double determatrx = InterpolationClass.determine(matrx);
double[,] another = new double[NumOfNode, NumOfNode];
Polynomial temp = new Polynomial();
double[] Constant;
Constant = new double[NumOfNode];
for (int j = 0; j < NumOfNode; j++)
{
another = InterpolationClass.creatanothermatrix(j, xcolum, ycolum, NumOfNode);
double deternother = InterpolationClass.determine(another);
Constant[j] = deternother / determatrx;
}
for (int i = 0; i < Constant.Length; i++)
{
temp = Polynomial.insert(Constant[i], i, temp);
}
string result = Polynomial.tostring(temp);
if (MessageBox.Show("If You Have An Internet Connection Click Yes To Show The Function On Net Or Click No To See It Here", "Internet Connection",
MessageBoxButtons.YesNo, MessageBoxIcon.Question) ==
DialogResult.Yes)
{
string url = "http://texify.com/?" + result;
Process.Start(url);
}
else
{
label3.Visible = true;
richTextBox1.Visible = true;
richTextBox1.Text = result;
}
Send.Enabled = false;
Refresh.Visible = true;
#endregion
}
}
break;
case "Least Square Method":
{
if ((XarrayZero != true) && (YarrayZero != true) && (ThereIsErrorX != true) && (ThereIsErrorY != true))
{
#region Least Square Method
int exp = NumOfNode - 1;
double sum;
double[] tableX = new double[2 * exp];
double[] tableY = new double[NumOfNode];
for (int j = 0; j < (2 * exp); j++)
{
sum = 0;
for (int i = 0; i < NumOfNode; i++)
{
sum = sum + Math.Pow(xcolum[i], j + 1);
tableX[j] = sum;
}
}
for (int j = 0; j < NumOfNode; j++)
{
sum = 0;
for (int i = 0; i < NumOfNode; i++)
{
if (j == 0)
{
sum = sum + ycolum[i];
}
else
{
sum = sum + (Math.Pow(xcolum[i], j) * ycolum[i]);
}
tableY[j] = sum;
}
}
double[,] squer = new double[NumOfNode, NumOfNode];
squer[0, 0] = NumOfNode;
for (int i = 1; i < NumOfNode; i++)
{
squer[0, i] = tableX[i - 1];
}
for (int i = 1; i < NumOfNode; i++)
{
for (int j = 0; j < NumOfNode; j++)
squer[i, j] = tableX[i + j - 1];
}
double[] A = new double[NumOfNode];
double d = InterpolationClass.determine((double[,])squer.Clone());
for (int j = 0; j < NumOfNode; j++)
A[j] = InterpolationClass.ChangeXY((double[,])squer.Clone(), tableY, j, NumOfNode) / d;
Send.Enabled = false;
Refresh.Visible = true;
#endregion
}
}
break;
case "Lagrange":
{
if ((XarrayZero != true) && (YarrayZero != true) && (ThereIsErrorX != true) && (ThereIsErrorY != true))
{
#region Lagrange
{
string result = InterpolationClass.lagrang(xcolum, NumOfNode, ycolum);
if (MessageBox.Show("If You Have An Internet Connection Click Yes To Show The Function On Net Or Click No To See It Here", "Internet Connection",
MessageBoxButtons.YesNo, MessageBoxIcon.Question) ==
DialogResult.Yes)
{
string url = "http://texify.com/?" + result;
Process.Start(url);
}
else
{
label3.Visible = true;
richTextBox1.Visible = true;
richTextBox1.Text = result;
}
}
#endregion
}
}
break;
case "Spline":
{
if ((XarrayZero != true) && (YarrayZero != true) && (ThereIsErrorX != true) && (ThereIsErrorY != true))
{
#region Splin
{
double point = 0;
if ((textBox2.Text != null) && (Share.Isnumber(textBox2.Text)))
{
point = double.Parse(textBox2.Text);
string result = Polynomial.tostring(InterpolationClass.Splin(xcolum, ycolum, NumOfNode, point));
if (MessageBox.Show("If You Have An Internet Connection Click Yes To Show The Function On Net Or Click No To See It Here", "Internet Connection",
MessageBoxButtons.YesNo, MessageBoxIcon.Question) ==
DialogResult.Yes)
{
string url = "http://texify.com/?" + result;
Process.Start(url);
}
else
{
label3.Visible = true;
richTextBox1.Visible = true;
richTextBox1.Text = result;
}
}
else
MessageBox.Show("Error Entry", "Error", MessageBoxButtons.OK, MessageBoxIcon.Error);
}
#endregion
}
}
break;
case "Newton":
{
if ((XarrayZero != true) && (YarrayZero != true) && (ThereIsErrorX != true) && (ThereIsErrorY != true))
{
#region Newton
double[,] Temp = InterpolationClass.newtonftab(xcolum, ycolum, NumOfNode);
Polynomial Newton = InterpolationClass.newtonemethod(xcolum, ycolum, Temp, NumOfNode);
string result = Polynomial.tostring(Newton);
if (MessageBox.Show("If You Have An Internet Connection Click Yes To Show The Function On Net Or Click No To See It Here", "Internet Connection",
MessageBoxButtons.YesNo, MessageBoxIcon.Question) ==
DialogResult.Yes)
{
string url = "http://texify.com/?" + result;
Process.Start(url);
}
else
{
label3.Visible = true;
richTextBox1.Visible = true;
richTextBox1.Text = result;
}
#endregion
}
}
break;
default:
{
if (Method == ".......")
MessageBox.Show("No Method Is Selceted ", "Error", MessageBoxButtons.OK, MessageBoxIcon.Error);
}
break;
}
}
public static Polynomial multi(Polynomial n, Polynomial m)
{
Polynomial temp1 = n;
Polynomial temp2 = m;
Polynomial q = new Polynomial();
while (temp1 != null)
{
temp2 = m;
while (temp2 != null)
{
double a = temp1.amthal * temp2.amthal;
double wn = temp1.power + temp2.power;
q = insert(a, wn, q);
temp2 = temp2.next;
}
temp1 = temp1.next;
}
return q;
}
public static string tostring(Polynomial l)
{
Polynomial p = l;
string temp = "";
while (p != null)
{
if (p.power == 0)
if (p.amthal > 0)
temp += "+" + p.amthal.ToString();
else if (p.amthal == 0)
temp += "";
else
temp += p.amthal.ToString();
else if ((p.amthal > 0) && (p.power > 0))
temp += "+" + p.amthal.ToString() + "X^" + p.power.ToString();
else if ((p.amthal > 0) && (p.power < 0))
temp += "+" + p.amthal.ToString() + "X^" + p.power.ToString();
else if ((p.amthal < 0) && (p.power != 0))
temp += p.amthal.ToString() + "X^" + p.power.ToString();
p = p.next;
}
return temp;
}
