public static double[] Bracket(Func <double, double> function, double a, double b)
{
double xa;
double xb;
double xc;
double fa;
double fb;
double fc;
double GLIMIT = 100.0;
double TINY = 1.0e-20;
xa = a;
fa = function(xa);
xb = b;
fb = function(xb);
if (fb > fa)
{
swap(ref xa, ref xb);
swap(ref fa, ref fb);
}
xc = xb + MathTool.PHI * (xb - xa);
fc = function(xc);
double fu;
while (fb > fc)
{
double r = (xb - xa) * (fb - fc);
double q = (xb - xc) * (fb - fa);
double u = xb - ((xb - xc) * q - (xb - xa) * r) / (2.0 * MathTool.CopySign(Math.Max(Math.Abs(q - r), TINY), q - r));
double ulim = xb + GLIMIT * (xc - xb);
if ((xb - u) * (u - xc) > 0.0)
{
fu = function(u);
if (fu < fc)
{
xa = xb;
fa = fb;
xb = u;
fb = fu;
return(new double[] { xa, fa, xb, fb, xc, fc });
}
if (fu > fb)
{
xc = u;
fc = fu;
return(new double[] { xa, fa, xb, fb, xc, fc });
}
u = xc + MathTool.PHI * (xc - xb);
fu = function(u);
}
else
{
if ((xc - u) * (u - ulim) > 0.0)
{
fu = function(u);
if (fu < fc)
{
shift(ref xb, ref xc, ref u, u + MathTool.PHI * (u - xc));
shift(ref fb, ref fc, ref fu, function(u));
}
}
else
{
if ((u - ulim) * (ulim - xc) >= 0.0)
{
u = ulim;
fu = function(u);
}
else
{
u = xc + MathTool.PHI * (xc - xb);
fu = function(u);
}
}
}
shift(ref xa, ref xb, ref xc, u);
shift(ref fa, ref fb, ref fc, fu);
}
return(new double[] { xa, fa, xb, fb, xc, fc });
}
public Brent(Func <double, double> function, double xa, double xb, double xc, double tolerance)
{
const int ITMAX = 100;
const double CGOLD = 0.3819660;
const double ZEPS = 0.00001;// Double.Epsilon;// *1.0e-3;
double a = (xa < xc ? xa : xc);
double b = (xa > xc ? xa : xc);
double d = 0.0;
double e = 0.0;
double u;
double fu;
double v = xb;
double fv = function(v);
double w = v;
double fw = fv;
double x = v;
double fx = fv;
for (int i = 0; i < ITMAX; ++i)
{
double xm = 0.5 * (a + b);
double tol1 = tolerance * Math.Abs(x) + ZEPS;
double tol2 = 2.0 * tol1;
if (Math.Abs(x - xm) <= (tol2 - 0.5 * (b - a)))
{
xmin = x;
fmin = fx;
return;
}
if (Math.Abs(e) > tol1)
{
double r = (x - w) * (fx - fv);
double q = (x - v) * (fx - fw);
double p = (x - v) * q - (x - w) * r;
q = 2.0 * (q - r);
if (q > 0.0)
{
p = -p;
}
q = Math.Abs(q);
double etemp = e;
e = d;
if (Math.Abs(p) >= Math.Abs(0.5 * q * etemp) || p <= q * (a - x) || p >= q * (b - x))
{
d = CGOLD * (e = (x >= xm ? a - x : b - x));
}
else
{
d = p / q;
u = x + d;
if (u - a < tol2 || b - u < tol2)
{
d = MathTool.CopySign(tol1, xm - x);
}
}
}
else
{
d = CGOLD * (e = (x >= xm ? a - x : b - x));
}
u = (Math.Abs(d) >= tol1 ? x + d : x + MathTool.CopySign(tol1, d));
fu = function(u);
if (fu <= fx)
{
if (u >= x)
{
a = x;
}
else
{
b = x;
}
shift(ref v, ref w, ref x, u);
shift(ref fv, ref fw, ref fx, fu);
}
else
{
if (u < x)
{
a = u;
}
else
{
b = u;
}
if (fu <= fw || w == x)
{
v = w;
w = u;
fv = fw;
fw = fu;
}
else
{
if (fu <= fv || v == x || v == w)
{
v = u;
fv = fu;
}
}
}
}
//throw("Too many iterations in brent");
xmin = double.NaN;
fmin = double.NaN;
}