/// This bisection method returns the best double approximation
/// to a root of F.f. Returns double.NaN if the F.f(a)*F.f(b) > 0.
public static double Bisection(Function F, double a, double b)
{
if (F.f(a) == 0) {
return a;
}
if (F.f(b) == 0) {
return b;
}
if (Math.Sign(F.f (b)) == Math.Sign (F.f (a))) { //or F.f(a)*F.f(b)>0
return double.NaN;
}
double c = (a + b) / 2;
// If no f(c) is exactly 0, iterate until the smallest possible
// double interval, when there is no distinct double midpoint.
while (c != a && c != b) {
Console.WriteLine ("a = {0} b= {1}", a, b);
if (F.f(c) == 0) {
return c;
}
if (Math.Sign(F.f (c)) == Math.Sign (F.f (a)))
a = c;
else
b = c;
c = (a + b) / 2;
}
return c;
}
/// This is the basic bisection method.
/// Ported straight from http://en.wikipedia.org/wiki/Bisection_method.
/// Source: Burden, Richard L.; Faires, J. Douglas (1985),
/// "2.1 The Bisection Algorithm",
/// Numerical Analysis (3rd ed.), PWS Publishers
public static double Bisection(Function F, double a, double b,
double tolerance, int iterations)
{
// check the preconditions for the method to work
// a must be greater than b so we can do the interval search
if (a >= b)
return double.NaN;
Console.WriteLine ("a >= b ok");
bool ok = false;
// The function must cross the x-axis between the endpoints,
// meaning its sign changes.
if ((F.f(a) < 0 && F.f (b) > 0)) {
Console.WriteLine ("Test 1 passed");
ok = true;
}
if ((F.f(a) > 0 && F.f (b) < 0)) {
Console.WriteLine ("Test 2 passed");
ok = true;
}
if (!ok)
return double.NaN;
int n=0;
while (n < iterations) {
double c = (a + b) / 2;
Console.WriteLine ("a = {0} b={1}", a, b);
if (F.f(c) == 0 || (b - a)/2 < tolerance)
return c;
if (Math.Sign(F.f (c)) == Math.Sign (F.f (a)))
a = c;
else
b = c;
n = n+1;
}
return double.NaN;
}
