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55 lines
16 KiB
C++
55 lines
16 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/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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{
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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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// Derivatives calculated from symbolic differentiation by Mathematica for comparison. Script: mixed_partials.nb
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const char* const answers[] = {"19878.40628980434922342465374997798674242532797789489","20731.74838274939517275508122761443159515217855975002","14667.60767623939014840117674691707821648144188283774","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","-4890.406122702359099863022925593448420259414896197252","8833.005054768976417065486877649473665597894570245307","8484.350739681613747819854384228795938450532463850094","3097.204151240398893507362023543393154680147349049848","-3255.045136783440612110181337652522080890693968833148","-4342.778553332193097878812792875447018366988006584840","-2407.987237906523486012534085031032446996713414362131","861.1173916470300084261504495377425043024739914571554","2436.743725763308619092960749816106318692933687303014","-19.24649610733827783846392798978023489104363382129689","187.7855148870511714395275130898958731897480766620821","-1259.466063335212195169531010871023748854744563232277","-709.6860523972158261343923419671629587637051060458295","1423.000558608604536932163648918899935569543711292466","484.9208133389233959103861107714757012185008046446372","763.9746885074453180462508029718247316712990115789154","-327.4162918228055568224139277603073169658358026440432","-1122.337707248494521123614369562896901904418640152220","23973.06007192346989337502250398494874845408708506720","8840.543151778796869949670401421984604862699128880003","-9082.571033221549378277312292526023838132689941236879","-12270.27378289258717737657881957466807305650429436397","-4320.434071420599854743576892819691675331049612545664","3281.351967707280898543984556670710235259118405463698","5880.336263083418767219493592767818708317492833223933","-1288.482785219706549809211085113790275109642879331959","-803.9713537626580526627976840414468844364935388365037","-2986.387245331698390346145949708414455858834967096376","-586.7316859822658306283656047992829723003491823675739","3929.073189280739356198769778905960586080418779863615","1453.728280983826630077825553258703050898056317382483","1037.878071685953829685046234106860743366780050925514","-1482.745805277401336553926171580259185140208053329753","-1877.134792933828810602377451370316364621357891989679","-931.7138710369298207131581126980851620513905805624544","254.6565590420322632851077818917210811815919344882311","1391.248064745611663849820246430123214796614030838600","-431.4820563154137955051720207563800896297257103310465","16975.34005365179555009050533000516107937041784876054","19662.60356303341709846238790020024593550984564081068","15765.85130704020004301064240357947656083104783442825","3972.155036195937013764185795634749937308876197976202","-8681.748539789720512499473840242996096730194203989543","-7703.183042460387656743498394861780784700076575106134","-3049.708696569518774040135942468704911634779352213044","2971.469685992270876159892302788930292108129670398058","4370.196499857550025657084783894747734031876677385611","2524.632473357435670756946837415389227139966527203701","-656.6080000236679071742450437463693211275208125750923","-2423.452917325258132591368397957959217829861665178601","-2074.987664204263204162199830716851483704870169031179","-381.2253794988132984501358802316138392247470857452486","1219.507245791997351017860252538035146744682380716428","805.3802239840836877339667281819652171888443003165988","838.4004190058912380470543219448821914235443115661655","-390.6125197108983831575656956558201636111305409512701","-828.2085489298235758253219930356006757081473789845849","293.8999854454994790079171865082094494146506490533363","-22965.85985843951977785883587223006628792405076928067","-20026.69101529929621743747554537576887048069629325374","-7316.092745063355996548975300169565482331369744607021","8632.466133972614659252310985982644793465043032940318","8987.046882870452266200748127338744248816756004290490","4199.925399536137541108783465785304128965582292174062","-2958.429850896062893179851696175634522187021390095560","-5665.563891218624062243686482808197054863235184904433","-2945.4045522503416158831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int main()
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{
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using type = boost::multiprecision::cpp_bin_float_50;
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constexpr int Nw=3; // Max order of derivative to calculate for w
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constexpr int Nx=2; // Max order of derivative to calculate for x
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constexpr int Ny=4; // Max order of derivative to calculate for y
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constexpr int Nz=3; // Max order of derivative to calculate for z
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const auto w = make_fvar<type,Nw>(11);
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const auto x = make_fvar<type,0,Nx>(12);
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const auto y = make_fvar<type,0,0,Ny>(13);
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const auto z = make_fvar<type,0,0,0,Nz>(14);
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const auto v = f(w,x,y,z); // auto = autodiff_fvar<type,Nw,Nx,Ny,Nz>
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int ia=0;
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double max_relative_error=0;
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for (int iw=0 ; iw<=Nw ; ++iw)
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for (int ix=0 ; ix<=Nx ; ++ix)
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for (int iy=0 ; iy<=Ny ; ++iy)
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for (int iz=0 ; iz<=Nz ; ++iz)
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{
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const type value = v.derivative(iw,ix,iy,iz);
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const type answer = boost::lexical_cast<type>(answers[ia++]);
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const double 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
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<< " out of " << ia << " 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 type=double)
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max_relative_error = 3.3e-47 out of 240 calculated values. (for type=cpp_bin_float_50)
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**/
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