trjhtr

Numerical differentiation is known to be ill-conditioned unless using a Chebyshev series, but this requires global information about the function and a priori knowledge of a compact domain on which the function will be evaluated. For this reason, simple finite differences are often useful. The unit roundoff gives a natural choice of step-see here and here for more details. I felt that this technique is better than the technique used in the GSL which requires specifying the stepsize, so I felt it should be given life in Boost.Math, esp. since spectral element methods are getting so popular. Regrettably, the pull-request was panned because the implementation is awkward, requiring a bunch of if checks on the order of accuracy and quite a bit of code duplication. Can it be cleaned up?

#ifndef BOOST_MATH_TOOLS_NUMERICAL_DIFFERENTIATION_HPP
#define BOOST_MATH_TOOLS_NUMERICAL_DIFFERENTIATION_HPP
#include <boost/math/constants/constants.hpp>

namespace boost namespace math namespace tools 
template<class F, class Real, size_t order=6>
Real finite_difference_derivative(const F f, Real x, Real* error = nullptr)
 order == 2 


#endif