public static double Brent(
FunctionOfTwoVariables f,
double left,
double right,
double tolerance = 1e-6,
double target = 0.0,
double[] y = null
)
{
// extra info that callers may not always want
int iterationsUsed;
double errorEstimate;
return Brent(f, left, right, tolerance, target, out iterationsUsed, out errorEstimate, y);
}
public static double Brent(
FunctionOfTwoVariables g,
double left,
double right,
double tolerance,
double target,
out int iterationsUsed,
out double errorEstimate,
double[] y
)
{
if (tolerance <= 0.0)
{
string msg = string.Format("Tolerance must be positive. Received {0}.", tolerance);
throw new ArgumentOutOfRangeException(msg);
}
errorEstimate = double.MaxValue;
// Standardize the problem. To solve g(x) = target,
// solve f(x) = 0 where f(x) = g(x) - target.
FunctionOfTwoVariables f = (x, y2) => g(x, y2) - target;
// Implementation and notation based on Chapter 4 in
// "Algorithms for Minimization without Derivatives"
// by Richard Brent.
double c, d, e, fa, fb, fc, tol, m, p, q, r, s;
// set up aliases to match Brent's notation
double a = left;
double b = right;
double t = tolerance;
iterationsUsed = 0;
fa = f(a, y);
fb = f(b, y);
// *************************************************
// This is the where the exception is being raised
if (fa * fb > 0.0)
{
string str = "Invalid starting bracket. Function must be above target on one end and below target on other end.";
string msg = string.Format("{0} Target: {1}. f(left) = {2}. f(right) = {3}", str, target, fa + target, fb + target);
throw new ArgumentException(msg);
}
// *************************************************
label_int:
c = a;
fc = fa;
d = e = b - a;
label_ext:
if (Math.Abs(fc) < Math.Abs(fb))
{
a = b;
b = c;
c = a;
fa = fb;
fb = fc;
fc = fa;
}
iterationsUsed++;
double machine_epsilon = Math.Pow(2.0, -53);
tol = 2.0 * machine_epsilon * Math.Abs(b) + t;
errorEstimate = m = 0.5 * (c - b);
if (Math.Abs(m) > tol && fb != 0.0) // exact comparison with 0 is OK here
{
// See if bisection is forced
if (Math.Abs(e) < tol || Math.Abs(fa) <= Math.Abs(fb))
{
d = e = m;
}
else
{
s = fb / fa;
if (a == c)
{
// linear interpolation
p = 2.0 * m * s;
q = 1.0 - s;
}
else
{
// Inverse quadratic interpolation
q = fa / fc;
r = fb / fc;
p = s * (2.0 * m * q * (q - r) - (b - a) * (r - 1.0));
q = (q - 1.0) * (r - 1.0) * (s - 1.0);
}
if (p > 0.0)
q = -q;
else
p = -p;
s = e;
e = d;
if (2.0 * p < 3.0 * m * q - Math.Abs(tol * q) && p < Math.Abs(0.5 * s * q))
d = p / q;
else
d = e = m;
}
a = b;
fa = fb;
if (Math.Abs(d) > tol)
b += d;
else if (m > 0.0)
b += tol;
else
b -= tol;
if (iterationsUsed == maxIterations)
return b;
fb = f(b, y);
if ((fb > 0.0 && fc > 0.0) || (fb <= 0.0 && fc <= 0.0))
goto label_int;
else
goto label_ext;
}
else
return b;
}
