MathDerivatives.cpph

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// This file is part of the ExaHyPE2 project. For conditions of distribution and
// use, please see the copyright notice at www.peano-framework.org
 
#include <cmath>
 
static inline auto numerics::_3D::partialX(auto f, const auto x, const auto y, const auto t) {
  const auto h = std::cbrt(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);
};
 
static inline auto numerics::_3D::partialY(auto f, const auto x, const auto y, const auto t) {
  const auto h = std::cbrt(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);
};
 
static inline auto numerics::_3D::partialT(auto f, const auto x, const auto y, const auto t) {
  const auto h = std::cbrt(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);
};