CentralDifferencePartial2D.h

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#pragma once
 
#include <cmath>
 
namespace math::differentiation::numeric_3D::central_difference {
  inline auto partialX(auto f, const auto x, const auto y, const auto t) {
    const auto h = std::sqrt(std::numeric_limits<decltype(x)>::epsilon()) * std::max(1.0, std::abs(x));
    return (f(x + h, y, t) - f(x - h, y, t)) / (2.0 * h);
  };

  inline auto partialY(auto f, const auto x, const auto y, const auto t) {
    const auto h = std::sqrt(std::numeric_limits<decltype(y)>::epsilon()) * std::max(1.0, std::abs(y));
    return (f(x, y + h, t) - f(x, y - h, t)) / (2.0 * h);
  };

  inline auto partialT(auto f, const auto x, const auto y, const auto t) {
    const auto h = std::sqrt(std::numeric_limits<decltype(t)>::epsilon()) * std::max(1.0, std::abs(t));
    return (f(x, y, t + h) - f(x, y, t - h)) / (2.0 * h);
  };
} // namespace math::differentiation::numeric_3D::central_difference