294 lines
17 KiB
C++
294 lines
17 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/lexical_cast.hpp>
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#include <boost/math/differentiation/autodiff.hpp>
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#include <boost/mp11/tuple.hpp>
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#include <boost/mp11/utility.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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struct f {
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template <typename W, typename X, typename Y, typename Z>
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promote<W, X, Y, Z> operator()(W const& w, X const& x, Y const& y, Z const& z) const {
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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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};
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// Derivatives calculated from symbolic differentiation by Mathematica for comparison. Script:
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// mixed_partials.nb
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static constexpr std::array<char const*, 240> answers{
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{"19878.40628980434922342465374997798674242532797789489",
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"20731.74838274939517275508122761443159515217855975002",
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"14667.60767623939014840117674691707821648144188283774",
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"1840.559936449813118734351750381849294157477519107602",
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"-9219.318005237072129605008516120710807803827373819700",
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"-7272.300634012811783845589472196110804386170683300081",
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"-2135.296370062283924160196772166043360841114107521292",
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"3095.081027251846799545897828297310835169325417217168",
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"4249.026762908615627428402369471953790564918480025345",
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"2063.989061062734416582172072883742097425754355167541",
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"-885.5284114876496084068555333811894392182458751895290",
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"-1962.133420441743158021558423645064067562765178375508",
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"-1846.899830787084518564013512948598850243350915531775",
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"-160.9590127603295755195950112199107484483554942817846",
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"1091.039412341633994110997652976585409621806446647794",
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"452.4395574345229946707651998323417632800605985181691",
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"666.4013922727704990031159406121675703174518834914461",
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"-415.6464114333629107803309520898363153301435468382605",
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"369.9491669772617110087494756677334192842413470837587",
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"-24330.89613849389343130420303653062335840497802221681",
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"2861.155651116567526208762405651011317435252198548496",
|
|
"-918.9310546317296090214320737728927500362088478158839",
|
|
"-5803.211323646092019259074499814222806376618363553826",
|
|
"-1767.541897994477314401145980308432268207111761980100",
|
|
"-663.0646207520075726320417301262932382663072876188661",
|
|
"2837.903194613938414496183429129769829434890424213252",
|
|
"1976.319600747797717779881875290418720908121189218755"}};
|
|
|
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int main() {
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using float50 = boost::multiprecision::cpp_bin_float_50;
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constexpr std::size_t Nw = 3; // Max order of derivative to calculate for w
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constexpr std::size_t Nx = 2; // Max order of derivative to calculate for x
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constexpr std::size_t Ny = 4; // Max order of derivative to calculate for y
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constexpr std::size_t Nz = 3; // Max order of derivative to calculate for z
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auto const variables = make_ftuple<float50, Nw, Nx, Ny, Nz>(11, 12, 13, 14);
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auto const v = boost::mp11::tuple_apply(f{}, variables);
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std::size_t ia = 0;
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double max_relative_error = 0;
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for (std::size_t iw = 0; iw <= Nw; ++iw)
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for (std::size_t ix = 0; ix <= Nx; ++ix)
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for (std::size_t iy = 0; iy <= Ny; ++iy)
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for (std::size_t iz = 0; iz <= Nz; ++iz) {
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float50 const value = v.derivative(iw, ix, iy, iz);
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float50 const answer = boost::lexical_cast<float50>(answers[ia++]);
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double const error = static_cast<double>(fabs(value / answer - 1));
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max_relative_error = (std::max)(error, max_relative_error);
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}
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std::cout << "max_relative_error = " << std::setprecision(3) << max_relative_error << " out of " << ia
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<< " calculated values." << std::endl;
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return 0;
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}
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/*
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Output:
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max_relative_error = 6.82e-13 out of 240 calculated values. (for double)
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max_relative_error = 3.36e-47 out of 240 calculated values. (for cpp_bin_float_50)
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**/
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