/// <summary>
/// Finds minimum via gold section search. x1 must be between x0 and x2
/// </summary>
/// <param name="f"></param>
/// <param name="x0"></param>
/// <param name="x1"></param>
/// <param name="x2"></param>
/// <param name="maxIter"></param>
/// <param name="eps"></param>
/// <param name="xmin"></param>
/// <returns></returns>
public int FindMinimumViaGoldenSection(IOneDFunction f, double x0, double x1, double x2,
int maxIter, double eps, ref double xmin)
{
double x3, f1, f2;
x3 = x2;
if (System.Math.Abs(x3 - x1) > System.Math.Abs(x1 - x0))
//x0-x1 is the smaller segment
{
x2 = x1 + Constants.CGOLDEN_SECTION_VAL * (x3 - x1);
}
else
{
x2 = x1;
x1 = x2 - Constants.CGOLDEN_SECTION_VAL * (x2 - x0);
}
f1 = f.GetVal(x1);
f2 = f.GetVal(x2);
int i = 0;
while (System.Math.Abs(x3 - x0) > eps * (System.Math.Abs(x1) + System.Math.Abs(x2)) &&
i < maxIter)
{
if (f2 < f1)
{
x0 = x1;
x1 = x2;
//moving the bracket
x2 = Constants.RGOLDEN_SECTION_VAL * x1 + Constants.CGOLDEN_SECTION_VAL * x3;
f1 = f2;
f2 = f.GetVal(x2);
}
else
{
x3 = x2;
x2 = x1;
x1 = Constants.RGOLDEN_SECTION_VAL * x2 + Constants.CGOLDEN_SECTION_VAL * x0;
f2 = f1;
f1 = f.GetVal(x1);
}
i++;
}
xmin = (f1 < f2)?x1:x2;
return(i);
} //end golden section search
/// <summary>
///
/// </summary>
/// <param name="f"></param>
/// <param name="x0"></param>
/// <param name="step"></param>
/// <param name="maxIter"></param>
/// <param name="xfin"></param>
/// <returns></returns>
public int FindMinInterval(IOneDFunction f, double x0, double step, int maxIter, ref double[] xfin)
{
double x1, ax, bx, cx;
double fa, fb, fc;
int i;
int counter;
counter = 0;
//by convention x1>x0
x1 = x0 + System.Math.Abs(step);
fa = f.GetVal(x0);
fb = f.GetVal(x1);
if (fa > fb)
{
ax = x0;
bx = x1;
}
else
{
ax = x1;
bx = x0;
fb = fa;
}
double [] x = new double[Constants.DIV + 1];
double [] fx = new double[Constants.DIV + 1];
//searching inside the xo + step interval
for (i = 0; i <= Constants.DIV; i++)
{
x[i] = ax + i * (bx - ax) / ((double)Constants.DIV);
fx[i] = f.GetVal(x[i]);
}
for (i = 1; i < Constants.DIV; i++)
{
if (fx[i] < fx[i - 1] && fx[i] < fx[i + 1])
{ /* the minimum has been found in the interval */
xfin[0] = x[i - 1];
xfin[1] = x[i];
xfin[2] = x[i + 1];
return(counter);
}
}
//since no minimum has been found in the interval,
//use Golden Section value to search for interval
cx = bx + Constants.GOLDEN_SECTION_VAL * (bx - ax);
fc = f.GetVal(cx);
while (fb >= fc && counter < maxIter)
{
ax = bx;
bx = cx;
cx = bx + Constants.GOLDEN_SECTION_VAL * (bx - ax);
fb = fc;
fc = f.GetVal(cx);
counter++;
}
xfin[0] = ax;
xfin[1] = bx;
xfin[2] = cx;
return(counter);
}
} //end golden section search
/// <summary>
/// Finds minimum of the 1-dimensional function via a Brent Method:
/// http://mathworld.wolfram.com/BrentsMethod.html
/// </summary>
/// <param name="f"></param>
/// <param name="x0"></param>
/// <param name="x1"></param>
/// <param name="x2"></param>
/// <param name="maxIter"></param>
/// <param name="eps"></param>
/// <param name="xmin"></param>
/// <returns></returns>
public int FindMinimumViaBrent(IOneDFunction f, double x0, double x1, double x2,
int maxIter, double eps, ref double xmin)
{
double a, b, d, e, u, v, w, x;
double p, q, r;
double fx, fu, fv, fw;
double xm, tol1, tol2;
double temp;
int i, flag;
// a and b must be in ascending order
a = System.Math.Min(x0, x2);
b = System.Math.Max(x0, x2);
x = w = v = x1;
d = e = 0.0;
fv = fw = fx = f.GetVal(x);
i = 0;
for (i = 0; i < maxIter; i++)
{
xm = (a + b) / 2.0;
// this avoids searching for 0
tol1 = eps * System.Math.Abs(x) + Constants.TINY;
tol2 = 2 * tol1;
if (System.Math.Abs(x - xm) <= (tol2 - (b - a) / 2.0))
{
xmin = x;
return(i);
}
flag = 0;
//parabolic fit
if (System.Math.Abs(e) > tol1)
{
r = (x - w) * (fx - fv);
q = (x - v) * (fx - fw);
p = (x - v) * q - (x - w) * r;
q = 2 * (q - r);
if (q > 0.0)
{
p = -p;
}
q = System.Math.Abs(q);
temp = e;
e = d;
// now check if parabolic fit is ok
if (System.Math.Abs(p) < System.Math.Abs(.5 * q * temp) || (p > q * (a - x) && p < q * (b - x)))
{
d = p / q;
u = x + d;
if (u - a < tol2 || b - u < tol2)
{
d = tol1 * System.Math.Sign(xm - x);
}
flag = 1;
}
}
if (flag == 0)
{
if (x >= xm)
{
e = a - x;
}
else
{
e = b - x;
}
d = Constants.CGOLDEN_SECTION_VAL * e;
}
if (System.Math.Abs(d) >= tol1)
{
u = x + d;
}
else
{
u = x + tol1 * System.Math.Sign(d);
}
fu = f.GetVal(u);
if (fu <= fx)
{
if (u >= x)
{
a = x;
}
else
{
b = x;
}
v = w;
fv = fw;
w = x;
fw = fx;
x = u;
fx = fu;
}
else
{
if (u < x)
{
a = u;
}
else
{
b = u;
}
if (fu <= fw || w == x)
{
v = w;
fv = fw;
w = u;
fw = fu;
}
else if (fu <= fv || v == x || v == w)
{
v = u;
fv = fu;
}
} //end of else
} //end of the loop
xmin = x;
return(i);
} //end of Brent