Brent's Method - Example Code

Example Code

The above algorithm can be translated to c-like code as follows:

public static double BrentsMethodSolve(Func function, double lowerLimit, double upperLimit, double errorTol) { double a = lowerLimit; double b = upperLimit; double c = 0; double d = double.MaxValue; double fa = function(a); double fb = function(b); double fc = 0; double s = 0; double fs = 0; // if f(a) f(b) >= 0 then error-exit if (fa * fb >= 0) { if (fa < fb) return a; else return b; } // if |f(a)| < |f(b)| then swap (a,b) end if if (Math.Abs(fa) < Math.Abs(fb)) { double tmp = a; a = b; b = tmp; tmp = fa; fa = fb; fb = tmp; } c = a; fc = fa; bool mflag = true; int i = 0; while (!(fb==0) && (Math.Abs(a-b) > errorTol)) { if ((fa != fc) && (fb != fc)) // Inverse quadratic interpolation s = a * fb * fc / (fa - fb) / (fa - fc) + b * fa * fc / (fb - fa) / (fb - fc) + c * fa * fb / (fc - fa) / (fc - fb); else // Secant Rule s = b - fb * (b - a) / (fb - fa); double tmp2 = (3 * a + b) / 4; if ((!(((s > tmp2) && (s < b)) || ((s < tmp2) && (s > b)))) || (mflag && (Math.Abs(s - b) >= (Math.Abs(b - c) / 2))) || (!mflag && (Math.Abs(s - b) >= (Math.Abs(c - d) / 2)))) { s = (a + b) / 2; mflag = true; } else { if ((mflag && (Math.Abs(b - c) < errorTol)) || (!mflag && (Math.Abs(c - d) < errorTol))) { s = (a + b) / 2; mflag = true; } else mflag = false; } fs = function(s); d = c; c = b; fc = fb; if (fa * fs < 0) { b = s; fb = fs; } else { a = s; fa = fs; } // if |f(a)| < |f(b)| then swap (a,b) end if if (Math.Abs(fa) < Math.Abs(fb)) { double tmp = a; a = b; b = tmp; tmp = fa; fa = fb; fb = tmp; } i++; if (i > 1000) throw new Exception(String.Format("Error is {0}", fb)); } return b; }

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