public static string BisectionConsoleWriteLine(theFunction1 fBisection, double x1, double x2, double eps)
{
System.IO.StringWriter s = new System.IO.StringWriter();
s.WriteLine("x1=({0}) x2=({1}) iterations=({2})", x1, x2, eps);
if (BisectionValid(fBisection, x1, x2) == true)
{
s.WriteLine("Bisection Valid = TRUE");
s.WriteLine("m=({0})", BisectionMethod(fBisection, x1, x2, eps));
}
else { s.WriteLine("Bisection Valid = FALSE"); }
return s.ToString();
}
public static double BisectionMethod(theFunction1 fBisection, double x1, double x2, double eps)
{
double a = x1; double b = x2;
//starting values for x1 and x2... only works if they are on opposite side of the equation. you also need an equation.
double m = 0, fm;
fm = 1000000;
while (fm > eps)
{
{
m = (a + b) / 2;
fm = fBisection(m);
if (fBisection(a) * fm < 0) { b = m; }
else if (fBisection(b) * fm < 0) { a = m; }
}
}
return m;
}
//DIFFERENTIALXXXXXXX
//BISECTION.......
static bool BisectionValid(theFunction1 fBisection, double a, double b)
{
if (fBisection(a) * fBisection(b) < 0) return true;
else return false;
}
//ITERATIONSXXXXXXXXXX
//SimpsonsRule
public static double SimpRule(theFunction1 fSimpRule , double a, double b, int m)
{
double h = (b - a) / (2 * m);
double[] x = new double[2 * m + 1];
x[0] = a;
for (int i = 1; i <= 2 * m; i++)
{ x[i] += x[i - 1] + h; }
double sumfx1 = 0;
for (int i = 1; i <= m; i++)
{ sumfx1 += fSimpRule(x[2 * i - 1]); }
double sumfx2 = 0;
for (int i = 1; i <= m - 1; i++)
{
sumfx2 += fSimpRule(x[2 * i]);
}
return (h / 3) * (fSimpRule(a) + 4 * sumfx1 + 2 * sumfx2 + fSimpRule(b));
}
//VOLUME ESTIMATION
/*
public static double VolEstSimpRule(theFunction2 fVol, double ax, double bx, double y, int m)
{
double h = (bx - ax) / (2 * m);
double[] x = new double[2 * m + 1];
x[0] = ax;
for (int i = 1; i <= 2 * m; i++)
{ x[i] += x[i - 1] + h; }
double sumfx1 = 0;
for (int i = 1; i <= m; i++)
{ sumfx1 += fVol(x[2 * i - 1], y); }
double sumfx2 = 0;
for (int i = 1; i <= m - 1; i++)
{
sumfx2 += fVol(x[2 * i], y);
}
return (h / 3) * (fVol(ax, y) + 4 * sumfx1 + 2 * sumfx2 + fVol(bx, y));
}
public static double VolEst(theFunction2 fVol, double ax, double bx, double ay, double by, int m)
{
double h = (by - ay) / (2 * m);
double[] y = new double[2 * m + 1];
y[0] = ay;
for (int i = 1; i <= 2 * m; i++)
{ y[i] += y[i - 1] + h; }
//y matrix
int j = 0;
double sumVol = 0;
foreach (double y1 in y)
{
sumVol += h * VolEstSimpRule(fVol, ax, bx, y1, m);
j++;
}
return sumVol;
}
public static double VolEstAv(theFunction2 fVol, double ax, double bx, double ay, double by, int m)
{
double run1 = VolEst(fVol, ax, bx, ay, by, m);
double run2 = VolEst(fVol, ay, by, ax, bx, m);
return (run1 + run2) / 2;
}
public static double VolEstTrapRule(List<Vector3D> aList)
{
//just consider x's and z's;
//each x needs to be distinct.
double[,] xys = new double[aList.Count, 2];
double[] xs = new double[aList.Count];
int i = 0;
foreach (Vector3D a in aList)
{ xs[i] = a.x; i++; }
Array.Sort(xs);
i = 0;
foreach (double x in xs)
{ xys[i, 0] = x; i++; }
for (i = 1; i < xs.Length; i++)
{
if (xs[i] == xs[i - 1])
{
Console.WriteLine("x's coordinates are not all unique");
return 0;
}
}
for (i = 0; i < aList.Count; i++)
{
for (int j = 0; j < aList.Count; j++)
{
if (xys[i, 0] == aList[j].x)
{ xys[i, 1] = aList[j].z; }
}
}
double sum = 0;
for (i = 0; i < xys.GetUpperBound(0); i++)
{ sum += (xys[i + 1, 0] - xys[i, 0]) * ((xys[i, 1] + xys[i + 1, 1]) / 2); }
return sum;
}
//VOLUME ESTIMATIONXXXX
*/
//DIFFERENTIAL
public static double Diff2Point(theFunction1 fDiff, double x, double h)
{
return (fDiff(x + h) - fDiff(x - h)) / (2 * h);
}
