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golden.h

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#ifndef NR_GOLDEN_H
#define NR_GOLDEN_H

#include <math.h>

namespace nr {

template< class Real, class Func >
Real golden (
    Real ax, Real bx, Real cx, 
    Func (*f),
    Real tol,
    Real *xmin)
{
    const Real R = 0.61803399;
    const Real C = (1.0-R);
    #define SHFT2(a,b,c) (a)=(b);(b)=(c);
    #define SHFT3(a,b,c,d) (a)=(b);(b)=(c);(c)=(d);
    Real f1,f2,x0,x1,x2,x3;

    x0=ax;
    x3=cx;
    if (fabs(cx-bx) > fabs(bx-ax)) {
        x1=bx;
        x2=bx+C*(cx-bx);
    } else {
        x2=bx;
        x1=bx-C*(bx-ax);
    }
    f1=(*f)(x1);
    f2=(*f)(x2);
    while (fabs(x3-x0) > tol*(fabs(x1)+fabs(x2))) {
        if (f2 < f1) {
            SHFT3(x0,x1,x2,R*x1+C*x3)
            SHFT2(f1,f2,(*f)(x2))
        } else {
            SHFT3(x3,x2,x1,R*x2+C*x0)
            SHFT2(f2,f1,(*f)(x1))
        }
    }
    if (f1 < f2) {
        *xmin=x1;
        return f1;
    } else {
        *xmin=x2;
        return f2;
    }
    #undef SHFT2
    #undef SHFT3
}



} // end namespace nr
#endif

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