1 // Copyright Matthew Pulver 2018 - 2019.
2 // Distributed under the Boost Software License, Version 1.0.
3 // (See accompanying file LICENSE_1_0.txt or copy at
4 // https://www.boost.org/LICENSE_1_0.txt)
5
6 #include <boost/lexical_cast.hpp>
7 #include <boost/math/differentiation/autodiff.hpp>
8 #include <boost/mp11/tuple.hpp>
9 #include <boost/mp11/utility.hpp>
10 #include <boost/multiprecision/cpp_bin_float.hpp>
11 #include <iostream>
12
13 using namespace boost::math::differentiation;
14
15 struct f {
16 template <typename W, typename X, typename Y, typename Z>
operator ()f17 promote<W, X, Y, Z> operator()(W const& w, X const& x, Y const& y, Z const& z) const {
18 return exp(w * sin(x * log(y) / z) + sqrt(w * z / (x * y))) + w * w / tan(z);
19 }
20 };
21
22 // Derivatives calculated from symbolic differentiation by Mathematica for comparison. Script:
23 // mixed_partials.nb
24 static constexpr std::array<char const*, 240> answers{
25 {"19878.40628980434922342465374997798674242532797789489",
26 "20731.74838274939517275508122761443159515217855975002",
27 "14667.60767623939014840117674691707821648144188283774",
28 "1840.559936449813118734351750381849294157477519107602",
29 "-9219.318005237072129605008516120710807803827373819700",
30 "-7272.300634012811783845589472196110804386170683300081",
31 "-2135.296370062283924160196772166043360841114107521292",
32 "3095.081027251846799545897828297310835169325417217168",
33 "4249.026762908615627428402369471953790564918480025345",
34 "2063.989061062734416582172072883742097425754355167541",
35 "-885.5284114876496084068555333811894392182458751895290",
36 "-1962.133420441743158021558423645064067562765178375508",
37 "-1846.899830787084518564013512948598850243350915531775",
38 "-160.9590127603295755195950112199107484483554942817846",
39 "1091.039412341633994110997652976585409621806446647794",
40 "452.4395574345229946707651998323417632800605985181691",
41 "666.4013922727704990031159406121675703174518834914461",
42 "-415.6464114333629107803309520898363153301435468382605",
43 "-625.1464179039986361267627631122900331946746137220517",
44 "369.9491669772617110087494756677334192842413470837587",
45 "-24330.89613849389343130420303653062335840497802221681",
46 "-18810.41605175626752065686192937776868736029049989926",
47 "-4890.406122702359099863022925593448420259414896197252",
48 "8833.005054768976417065486877649473665597894570245307",
49 "8484.350739681613747819854384228795938450532463850094",
50 "3097.204151240398893507362023543393154680147349049848",
51 "-3255.045136783440612110181337652522080890693968833148",
52 "-4342.778553332193097878812792875447018366988006584840",
53 "-2407.987237906523486012534085031032446996713414362131",
54 "861.1173916470300084261504495377425043024739914571554",
55 "2436.743725763308619092960749816106318692933687303014",
56 "-19.24649610733827783846392798978023489104363382129689",
57 "187.7855148870511714395275130898958731897480766620821",
58 "-1259.466063335212195169531010871023748854744563232277",
59 "-709.6860523972158261343923419671629587637051060458295",
60 "1423.000558608604536932163648918899935569543711292466",
61 "484.9208133389233959103861107714757012185008046446372",
62 "763.9746885074453180462508029718247316712990115789154",
63 "-327.4162918228055568224139277603073169658358026440432",
64 "-1122.337707248494521123614369562896901904418640152220",
65 "23973.06007192346989337502250398494874845408708506720",
66 "8840.543151778796869949670401421984604862699128880003",
67 "-9082.571033221549378277312292526023838132689941236879",
68 "-12270.27378289258717737657881957466807305650429436397",
69 "-4320.434071420599854743576892819691675331049612545664",
70 "3281.351967707280898543984556670710235259118405463698",
71 "5880.336263083418767219493592767818708317492833223933",
72 "-1288.482785219706549809211085113790275109642879331959",
73 "-803.9713537626580526627976840414468844364935388365037",
74 "-2986.387245331698390346145949708414455858834967096376",
75 "-586.7316859822658306283656047992829723003491823675739",
76 "3929.073189280739356198769778905960586080418779863615",
77 "1453.728280983826630077825553258703050898056317382483",
78 "1037.878071685953829685046234106860743366780050925514",
79 "-1482.745805277401336553926171580259185140208053329753",
80 "-1877.134792933828810602377451370316364621357891989679",
81 "-931.7138710369298207131581126980851620513905805624544",
82 "254.6565590420322632851077818917210811815919344882311",
83 "1391.248064745611663849820246430123214796614030838600",
84 "-431.4820563154137955051720207563800896297257103310465",
85 "16975.34005365179555009050533000516107937041784876054",
86 "19662.60356303341709846238790020024593550984564081068",
87 "15765.85130704020004301064240357947656083104783442825",
88 "3972.155036195937013764185795634749937308876197976202",
89 "-8681.748539789720512499473840242996096730194203989543",
90 "-7703.183042460387656743498394861780784700076575106134",
91 "-3049.708696569518774040135942468704911634779352213044",
92 "2971.469685992270876159892302788930292108129670398058",
93 "4370.196499857550025657084783894747734031876677385611",
94 "2524.632473357435670756946837415389227139966527203701",
95 "-656.6080000236679071742450437463693211275208125750923",
96 "-2423.452917325258132591368397957959217829861665178601",
97 "-2074.987664204263204162199830716851483704870169031179",
98 "-381.2253794988132984501358802316138392247470857452486",
99 "1219.507245791997351017860252538035146744682380716428",
100 "805.3802239840836877339667281819652171888443003165988",
101 "838.4004190058912380470543219448821914235443115661655",
102 "-390.6125197108983831575656956558201636111305409512701",
103 "-828.2085489298235758253219930356006757081473789845849",
104 "293.8999854454994790079171865082094494146506490533363",
105 "-22965.85985843951977785883587223006628792405076928067",
106 "-20026.69101529929621743747554537576887048069629325374",
107 "-7316.092745063355996548975300169565482331369744607021",
108 "8632.466133972614659252310985982644793465043032940318",
109 "8987.046882870452266200748127338744248816756004290490",
110 "4199.925399536137541108783465785304128965582292174062",
111 "-2958.429850896062893179851696175634522187021390095560",
112 "-5665.563891218624062243686482808197054863235184904433",
113 "-2945.404552250341615883104643651287431663294281737652",
114 "555.6566272478262524735403145861484390537770707372992",
115 "2936.796403550079139218970638242013974322758744804216",
116 "651.5191650747110008135060635556227666232180743487328",
117 "444.7629427486155148584918602702161457622049333694568",
118 "-1390.989671799095801316658971275073184600067187023729",
119 "-1142.861468946763860859271224968631944511098747155437",
120 "1541.978723117340843491920690654997335632919116206279",
121 "455.7146063293814470171599782651235242129856311098151",
122 "998.7943503940357037260061331795191352937661538946216",
123 "-204.8485581981121295383497187536442450324011940647949",
124 "-1560.354115460478786113711476250386112014306509906244",
125 "25278.29450605247223516529112562423587288781657290275",
126 "11873.22337179046469888005044109378787446671408425048",
127 "-8242.187303368878103323785658604027555126374435611949",
128 "-15939.98056417465751946455567789306872745912255628512",
129 "-5648.833539698031486810309720694416837861242341227280",
130 "2751.513926122717118525029734574022921057261239749143",
131 "7349.432002479077129245930487320138527887196396579062",
132 "194.9972545980371127390142753318206783334452047502143",
133 "-402.8156857682688265622049800462325595907987257153782",
134 "-3518.871908683063371167722463713374376552181380727802",
135 "-1494.304793474682619087166400375396721307777439607909",
136 "4640.927509426080087451995953783429589632369803588940",
137 "1585.757705203227141964561144798400703219894640413562",
138 "1565.169992404407137888592924342582799362959736185298",
139 "-1513.259809733540018859089666188672238777297615451800",
140 "-2974.437872674680092826212901753475972242208819679978",
141 "-1203.236292653823441598437153564865951527142648802876",
142 "72.52425949879153384040698301599842998884036742649047",
143 "1871.625274253419949517250818647194858608124560073483",
144 "-2.489984337379681666361341362948045621969765070197429",
145 "14462.74423518633102580192225823524237502860825596609",
146 "18367.74740916432711689913219912502810575714860430297",
147 "16565.76324499673961400925630526921000337443450249297",
148 "6054.315252651102952034254100792777051580892954459740",
149 "-8084.981271982030146065497115893934803061545998433631",
150 "-7988.314359128201297240919364015959817416101519999194",
151 "-3989.319346941492698525859335371231602272119870228687",
152 "2616.721186534649016680934493970036169897788778926434",
153 "4420.859270970486562095630193355634655337290952862363",
154 "2973.033519764547909146474824627687039969488363657908",
155 "-324.1453016982713707989332262410969595194473127209825",
156 "-2843.242039958969221918101261762794653424879358390111",
157 "-2281.461806143289517702658392470195144560150025832652",
158 "-642.9353229582055924928927665183236308235598082837497",
159 "1299.287274176955358490409470855361289523321919337117",
160 "1238.597083372069762230817383681570828675426312803376",
161 "1021.334042770848165110529668635291528449691525937968",
162 "-329.0529345069271079573348500899329811170455711610811",
163 "-1046.254301544052075124857362060924818517694048905299",
164 "134.7343039554480655186788228552325941588620079791654",
165 "-21431.41643507661192392650726158493697457993678274754",
166 "-20856.88281479015784660571401663659059349708627445067",
167 "-9829.261970591930907585958999196966814861251125275804",
168 "7806.858647077811827981774785577363365546600234846335",
169 "9319.700085649568180114405924685286453652118439999060",
170 "5319.898768025758256383579171601100187435481641933401",
171 "-2387.954826466841736373447020403170264502066930376059",
172 "-6958.298525165359760665355886221309296550746152109847",
173 "-3468.539106391972560670887295398968213297736424267559",
174 "130.4167253342709401698825285623058661085645012029873",
175 "3371.139930235175987370940343096776588915600470241960",
176 "1569.232678004908105313880673484968847566948896728142",
177 "750.0912101179065245750415609380442359608197763310413",
178 "-1462.257209626597452197736652121394535208578921869658",
179 "-1661.577809630240615684355192771059515041884351493459",
180 "1509.628528603869133250456671040505284128185908768108",
181 "383.8950902580816259502239917715884779698864996879279",
182 "1248.051096343638013308778159911906703363730187986273",
183 "17.18569564265260274901760034571610990094333217519021",
184 "-2038.024598002604853054532645991188063394308018947374",
185 "26118.98132017823514803387529120810044029492871875474",
186 "14943.61943482227903328457116850255971625430735856355",
187 "-6650.686262276131072415580833374348889422387492668440",
188 "-19519.81529547404067945704333355155941895199228108631",
189 "-6983.190236500848647457042860591724089812405118922223",
190 "1899.297502873688983038424995203515277346497811783168",
191 "8715.003652642963488202943622358986745434720576722170",
192 "2368.150690681864301926962120618658083737878227231428",
193 "136.8920793093482831910443246272238406481527839521448",
194 "-3954.732706163417141961077488373290331419627965482785",
195 "-2673.556440231186786375595871506657802723673830409989",
196 "5078.483935249043594670125721926702845818403229980691",
197 "1643.459143721204817182772630730123271413273760820347",
198 "2182.216979506380293664703833586468523416961563720645",
199 "-1345.838830963620501537777318021157952722412472356094",
200 "-4309.285350629108413525304135326225818270616857298235",
201 "-1488.050869922417817689426519211523527088509094291312",
202 "-228.0584943070343720919835603886532454450555855354340",
203 "2373.398940425709177876367020236623713151456855728138",
204 "773.8481328103928058186643458500631723389600248582833",
205 "12294.40387737855548614823173849184004455244840062464",
206 "16977.34966571858301862913845572077593071467784570724",
207 "17057.17475622503175013658695220988017704387344177727",
208 "8121.189758511830935868344768490586007624092305459885",
209 "-7458.443541406284389918808653948439156033975014107187",
210 "-8134.131160882738058651976911725365291142418949378248",
211 "-4912.881158613784419581465435995807691111897279859302",
212 "2030.653136098933717888434825960516061206391833398177",
213 "4407.490527709412730881592594976776779312299897714205",
214 "3392.434568825892752350943548729559313328141534290860",
215 "104.0372355841506198680609232049783930050635078746762",
216 "-3180.817620484463214391157460812371170723810181051096",
217 "-2460.523987075069437321629265332968914260047631079537",
218 "-938.2209314069133432825590545267820890922150850657831",
219 "1315.246905571876456706320919211807375254975062430487",
220 "1735.862392405992188189147617586418269768276241147998",
221 "1209.759657223166954850207025399731503326968841680649",
222 "-227.3320054566642297128407910803774238020746116287390",
223 "-1266.126209991929259396966729664100401813091860201682",
224 "-123.0794572338149156803989321165094334755661021559442",
225 "-19806.90794333834685506732819834090525250045748665845",
226 "-21314.81635440575229337844631555492486744407550254908",
227 "-12317.58384430130805020250005527399703840208659666608",
228 "6349.418659888281474363154227419204673663621492760982",
229 "9489.819687696527735093973063679592839666155440941289",
230 "6409.538948456309994399374417972222747225748405617373",
231 "-1550.281799013125267606263057621300789555474258987989",
232 "-8109.711199785217512061886243157800006692908759687186",
233 "-3957.840330296874877742767473517819198882831790006004",
234 "-404.0796555836667858753163727999380679499192203780272",
235 "3693.614351301181980145006883746936633676934626580499",
236 "2716.146658322790064799415509615557123789406209068981",
237 "1094.591086641398900496318896947912437274250932576747",
238 "-1456.269645549946420883827817869876763706452982413420",
239 "-2244.380608735636962338392373719455877272151458411079",
240 "1268.593891556261871090883000459505759446497182073132",
241 "265.2206730327749346649809229271069944357537135668622",
242 "1496.091578778639488439197917198148587432113387871024",
243 "354.6137351047722781932932090799444060236757625488818",
244 "-2508.477110048684129181005769771219369377836598443263",
245 "26517.86140875157324686379805134248778305979287686214",
246 "17922.98387741915144079932445041215068937644694653527",
247 "-4328.259142127668040873054918170572859673703425721293",
248 "-22704.70245940080949074466622805971940616027152354999",
249 "-8268.613747173738971390434576274225941735552759965376",
250 "740.4056074392611464740778308961471299437619012164253",
251 "9848.900182836035080973766381422758538530595451048714",
252 "5213.598341476210337710365441072904970861063876340963",
253 "801.2462923723508233330997243930793458484750729415321",
254 "-4241.870133920767845856621968904769727964770527614244",
255 "-4092.241355868550570635569815488217469506874233892269",
256 "5074.435909206083943809967780457349942315503368249477",
257 "1607.765329254820915989772546102530187884674235100928",
258 "2861.155651116567526208762405651011317435252198548496",
259 "-918.9310546317296090214320737728927500362088478158839",
260 "-5803.211323646092019259074499814222806376618363553826",
261 "-1767.541897994477314401145980308432268207111761980100",
262 "-663.0646207520075726320417301262932382663072876188661",
263 "2837.903194613938414496183429129769829434890424213252",
264 "1976.319600747797717779881875290418720908121189218755"}};
265
main()266 int main() {
267 using float50 = boost::multiprecision::cpp_bin_float_50;
268 constexpr std::size_t Nw = 3; // Max order of derivative to calculate for w
269 constexpr std::size_t Nx = 2; // Max order of derivative to calculate for x
270 constexpr std::size_t Ny = 4; // Max order of derivative to calculate for y
271 constexpr std::size_t Nz = 3; // Max order of derivative to calculate for z
272 auto const variables = make_ftuple<float50, Nw, Nx, Ny, Nz>(11, 12, 13, 14);
273 auto const v = boost::mp11::tuple_apply(f{}, variables);
274 std::size_t ia = 0;
275 double max_relative_error = 0;
276 for (std::size_t iw = 0; iw <= Nw; ++iw)
277 for (std::size_t ix = 0; ix <= Nx; ++ix)
278 for (std::size_t iy = 0; iy <= Ny; ++iy)
279 for (std::size_t iz = 0; iz <= Nz; ++iz) {
280 float50 const value = v.derivative(iw, ix, iy, iz);
281 float50 const answer = boost::lexical_cast<float50>(answers[ia++]);
282 double const error = static_cast<double>(fabs(value / answer - 1));
283 max_relative_error = (std::max)(error, max_relative_error);
284 }
285 std::cout << "max_relative_error = " << std::setprecision(3) << max_relative_error << " out of " << ia
286 << " calculated values." << std::endl;
287 return 0;
288 }
289 /*
290 Output:
291 max_relative_error = 6.82e-13 out of 240 calculated values. (for double)
292 max_relative_error = 3.36e-47 out of 240 calculated values. (for cpp_bin_float_50)
293 **/
294