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