derivatives.hpp

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// -------------------------------------------------------//
//
// SHAMROCK code for hydrodynamics
// Copyright (c) 2021-2026 Timothée David--Cléris <tim.shamrock@proton.me>
// SPDX-License-Identifier: CeCILL Free Software License Agreement v2.1
// Shamrock is licensed under the CeCILL 2.1 License, see LICENSE for more information
//
// -------------------------------------------------------//
 
#pragma once
 
#include "shambase/numeric_limits.hpp"
#include "shambackends/sycl.hpp"
#include <functional>
 
namespace shammath {
 
    template<class T>
    inline T derivative_upwind(T x, T dx, std::function<T(T)> &&fct) {
        return (fct(x + dx) - fct(x)) / dx;
    }
 
    template<class T>
    inline T derivative_centered(T x, T dx, std::function<T(T)> &&fct) {
        return (fct(x + dx) - fct(x - dx)) / (2 * dx);
    }
 
    template<class T>
    inline T derivative_3point_forward(T x, T dx, std::function<T(T)> &&fct) {
        return (-3 * fct(x) + 4 * fct(x + dx) - fct(x + 2 * dx)) / (2 * dx);
    }
 
    template<class T>
    inline T derivative_3point_backward(T x, T dx, std::function<T(T)> &&fct) {
        return (3 * fct(x) - 4 * fct(x - dx) + fct(x - 2 * dx)) / (2 * dx);
    }
 
    template<class T>
    inline T derivative_5point_midpoint(T x, T dx, std::function<T(T)> &&fct) {
        return (-fct(x + 2 * dx) + 8 * fct(x + dx) - 8 * fct(x - dx) + fct(x - 2 * dx)) / (12 * dx);
    }
 
    template<class T>
    inline T estim_deriv_step(u32 order) {
        return sycl::powr(shambase::get_epsilon<T>(), 1.0 / (order + 1));
    }
 
} // namespace shammath