GoldenRatioMinima.cpp

#define _USE_MATH_DEFINES
#include <float.h>
#include <math.h>
#include <stdio.h>
#include <assert.h>

double f(double x)
{
	return sin(x);
}

double GoldenRatioMinima(double a, double b, double tol)
{
	const double k = (sqrt(5) - 1) / 2;
	double c = b - k * (b - a);
	double fc = f(c);
	double d = a + k * (b - a);
	double fd = f(d);
	
	double eps = tol + fabs(b)*DBL_EPSILON;
	while ((b - a) > eps)
	{
		if (fc < fd)
		{
			// choose interval [a, d]
			b = d;
			d = c;
			fd = fc;
			c = b - k * (b - a);
			fc = f(c);
		}
		else
		{
			// choose interval [c, b]
			a = c;
			c = d;
			fc = fd;
			d = a + k * (b - a);
			fd = f(d);
		}
		eps = tol + fabs(b)*DBL_EPSILON;
	}
	return (a + b) / 2;
}

int main()
{
	double res = GoldenRatioMinima(4.7, 4.8, 1e-16);
	printf("min in %.16f\n", res);
	return 0;
}