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|
// 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/lexical_cast.hpp>
#include <boost/math/differentiation/autodiff.hpp>
#include <boost/mp11/tuple.hpp>
#include <boost/mp11/utility.hpp>
#include <boost/multiprecision/cpp_bin_float.hpp>
#include <iostream>
using namespace boost::math::differentiation;
struct f {
template <typename W, typename X, typename Y, typename Z>
promote<W, X, Y, Z> operator()(W const& w, X const& x, Y const& y, Z const& z) const {
return exp(w * sin(x * log(y) / z) + sqrt(w * z / (x * y))) + w * w / tan(z);
}
};
// Derivatives calculated from symbolic differentiation by Mathematica for comparison. Script:
// mixed_partials.nb
static constexpr std::array<char const*, 240> answers{
{"19878.40628980434922342465374997798674242532797789489",
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"1840.559936449813118734351750381849294157477519107602",
"-9219.318005237072129605008516120710807803827373819700",
"-7272.300634012811783845589472196110804386170683300081",
"-2135.296370062283924160196772166043360841114107521292",
"3095.081027251846799545897828297310835169325417217168",
"4249.026762908615627428402369471953790564918480025345",
"2063.989061062734416582172072883742097425754355167541",
"-885.5284114876496084068555333811894392182458751895290",
"-1962.133420441743158021558423645064067562765178375508",
"-1846.899830787084518564013512948598850243350915531775",
"-160.9590127603295755195950112199107484483554942817846",
"1091.039412341633994110997652976585409621806446647794",
"452.4395574345229946707651998323417632800605985181691",
"666.4013922727704990031159406121675703174518834914461",
"-415.6464114333629107803309520898363153301435468382605",
"-625.1464179039986361267627631122900331946746137220517",
"369.9491669772617110087494756677334192842413470837587",
"-24330.89613849389343130420303653062335840497802221681",
"-18810.41605175626752065686192937776868736029049989926",
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"8833.005054768976417065486877649473665597894570245307",
"8484.350739681613747819854384228795938450532463850094",
"3097.204151240398893507362023543393154680147349049848",
"-3255.045136783440612110181337652522080890693968833148",
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"861.1173916470300084261504495377425043024739914571554",
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"484.9208133389233959103861107714757012185008046446372",
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"-15939.98056417465751946455567789306872745912255628512",
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"194.9972545980371127390142753318206783334452047502143",
"-402.8156857682688265622049800462325595907987257153782",
"-3518.871908683063371167722463713374376552181380727802",
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"4640.927509426080087451995953783429589632369803588940",
"1585.757705203227141964561144798400703219894640413562",
"1565.169992404407137888592924342582799362959736185298",
"-1513.259809733540018859089666188672238777297615451800",
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"-918.9310546317296090214320737728927500362088478158839",
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"2837.903194613938414496183429129769829434890424213252",
"1976.319600747797717779881875290418720908121189218755"}};
int main() {
using float50 = boost::multiprecision::cpp_bin_float_50;
constexpr std::size_t Nw = 3; // Max order of derivative to calculate for w
constexpr std::size_t Nx = 2; // Max order of derivative to calculate for x
constexpr std::size_t Ny = 4; // Max order of derivative to calculate for y
constexpr std::size_t Nz = 3; // Max order of derivative to calculate for z
auto const variables = make_ftuple<float50, Nw, Nx, Ny, Nz>(11, 12, 13, 14);
auto const v = boost::mp11::tuple_apply(f{}, variables);
std::size_t ia = 0;
double max_relative_error = 0;
for (std::size_t iw = 0; iw <= Nw; ++iw)
for (std::size_t ix = 0; ix <= Nx; ++ix)
for (std::size_t iy = 0; iy <= Ny; ++iy)
for (std::size_t iz = 0; iz <= Nz; ++iz) {
float50 const value = v.derivative(iw, ix, iy, iz);
float50 const answer = boost::lexical_cast<float50>(answers[ia++]);
double const error = static_cast<double>(fabs(value / answer - 1));
max_relative_error = (std::max)(error, max_relative_error);
}
std::cout << "max_relative_error = " << std::setprecision(3) << max_relative_error << " out of " << ia
<< " calculated values." << std::endl;
return 0;
}
/*
Output:
max_relative_error = 6.82e-13 out of 240 calculated values. (for double)
max_relative_error = 3.36e-47 out of 240 calculated values. (for cpp_bin_float_50)
**/
|
