1 // Copyright Matthew Pulver 2018 - 2019.
2 // Distributed under the Boost Software License, Version 1.0.
3 // (See accompanying file LICENSE_1_0.txt or copy at
4 // https://www.boost.org/LICENSE_1_0.txt)
5
6 #include <boost/math/differentiation/autodiff.hpp>
7 #include <boost/multiprecision/cpp_bin_float.hpp>
8 #include <iostream>
9
10 using namespace boost::math::differentiation;
11
12 template <typename W, typename X, typename Y, typename Z>
f(const W & w,const X & x,const Y & y,const Z & z)13 promote<W, X, Y, Z> f(const W& w, const X& x, const Y& y, const Z& z) {
14 using namespace std;
15 return exp(w * sin(x * log(y) / z) + sqrt(w * z / (x * y))) + w * w / tan(z);
16 }
17
main()18 int main() {
19 using float50 = boost::multiprecision::cpp_bin_float_50;
20
21 constexpr unsigned Nw = 3; // Max order of derivative to calculate for w
22 constexpr unsigned Nx = 2; // Max order of derivative to calculate for x
23 constexpr unsigned Ny = 4; // Max order of derivative to calculate for y
24 constexpr unsigned Nz = 3; // Max order of derivative to calculate for z
25 // Declare 4 independent variables together into a std::tuple.
26 auto const variables = make_ftuple<float50, Nw, Nx, Ny, Nz>(11, 12, 13, 14);
27 auto const& w = std::get<0>(variables); // Up to Nw derivatives at w=11
28 auto const& x = std::get<1>(variables); // Up to Nx derivatives at x=12
29 auto const& y = std::get<2>(variables); // Up to Ny derivatives at y=13
30 auto const& z = std::get<3>(variables); // Up to Nz derivatives at z=14
31 auto const v = f(w, x, y, z);
32 // Calculated from Mathematica symbolic differentiation.
33 float50 const answer("1976.319600747797717779881875290418720908121189218755");
34 std::cout << std::setprecision(std::numeric_limits<float50>::digits10)
35 << "mathematica : " << answer << '\n'
36 << "autodiff : " << v.derivative(Nw, Nx, Ny, Nz) << '\n'
37 << std::setprecision(3)
38 << "relative error: " << (v.derivative(Nw, Nx, Ny, Nz) / answer - 1) << '\n';
39 return 0;
40 }
41 /*
42 Output:
43 mathematica : 1976.3196007477977177798818752904187209081211892188
44 autodiff : 1976.3196007477977177798818752904187209081211892188
45 relative error: 2.67e-50
46 **/
47