47 lines
2.1 KiB
C++
47 lines
2.1 KiB
C++
// Copyright Matthew Pulver 2018 - 2019.
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// Distributed under the Boost Software License, Version 1.0.
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// (See accompanying file LICENSE_1_0.txt or copy at
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// https://www.boost.org/LICENSE_1_0.txt)
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#include <boost/math/differentiation/autodiff.hpp>
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#include <boost/multiprecision/cpp_bin_float.hpp>
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#include <iostream>
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using namespace boost::math::differentiation;
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template <typename W, typename X, typename Y, typename Z>
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promote<W, X, Y, Z> f(const W& w, const X& x, const Y& y, const Z& z) {
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using namespace std;
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return exp(w * sin(x * log(y) / z) + sqrt(w * z / (x * y))) + w * w / tan(z);
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}
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int main() {
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using float50 = boost::multiprecision::cpp_bin_float_50;
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constexpr unsigned Nw = 3; // Max order of derivative to calculate for w
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constexpr unsigned Nx = 2; // Max order of derivative to calculate for x
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constexpr unsigned Ny = 4; // Max order of derivative to calculate for y
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constexpr unsigned Nz = 3; // Max order of derivative to calculate for z
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// Declare 4 independent variables together into a std::tuple.
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auto const variables = make_ftuple<float50, Nw, Nx, Ny, Nz>(11, 12, 13, 14);
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auto const& w = std::get<0>(variables); // Up to Nw derivatives at w=11
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auto const& x = std::get<1>(variables); // Up to Nx derivatives at x=12
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auto const& y = std::get<2>(variables); // Up to Ny derivatives at y=13
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auto const& z = std::get<3>(variables); // Up to Nz derivatives at z=14
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auto const v = f(w, x, y, z);
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// Calculated from Mathematica symbolic differentiation.
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float50 const answer("1976.319600747797717779881875290418720908121189218755");
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std::cout << std::setprecision(std::numeric_limits<float50>::digits10)
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<< "mathematica : " << answer << '\n'
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<< "autodiff : " << v.derivative(Nw, Nx, Ny, Nz) << '\n'
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<< std::setprecision(3)
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<< "relative error: " << (v.derivative(Nw, Nx, Ny, Nz) / answer - 1) << '\n';
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return 0;
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}
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/*
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Output:
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mathematica : 1976.3196007477977177798818752904187209081211892188
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autodiff : 1976.3196007477977177798818752904187209081211892188
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relative error: 2.67e-50
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**/
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