SearchMin.hpp

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/**
 * @file Seach.hpp
 *
 * - Binary Search (ToDo)
 * - Golden Section Search
 */

#pragma once

namespace math
{
static constexpr double GOLDEN_RATIO = 1.6180339887; //(sqrt(5)+1)/2

// Type-safe abs
template<typename _Tp>
_Tp abs_t(_Tp val)
{
    return ((val > (_Tp)0) ? val : -val);
}

// golden section search to find extremeum for function with minimum
template<typename _Tp>
inline const _Tp goldensection(const _Tp &arg1, const _Tp &arg2, _Tp(*fun)(_Tp), const _Tp &tol)
{
    _Tp a = arg1;
    _Tp b = arg2;
    _Tp c = b - (b - a) / GOLDEN_RATIO;
    _Tp d = a + (b - a) / GOLDEN_RATIO;

    while (abs_t(c - d) > tol) {

        if (fun(c) < fun(d)) {
            b = d;

        } else {
            a = c;
        }

        c = b - (b - a) / GOLDEN_RATIO;
        d = a + (b - a) / GOLDEN_RATIO;

    }

    return ((b + a) / (_Tp)2);
}
}