why get different values when matlab also use maple for calculation?. Maple vs Matlab??

Question

gourav pandey 2021-12-24

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链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1616910-why-get-different-values-when-matlab-also-use-maple-for-calculation-maple-vs-matlab

编辑： Walter Roberson 2021-12-24

Hi, I have this problem where the maple show very small result but matlab show very large value. I have written the code in Maple and Matlab. I'm working on this from last 4 days and didn't find any result, why this is happening.

Thank you in advance and please share if you know the reason behind this difference.

n,m,omega1 are real numbers n>m, n and m are integer, omega>0, n=m+2, and m is any odd no.s greater then 2.

%%%%%%  MATLAB CODE
clc; clear; close;
n=5;m=3;omega1=500;
fun_matlab=(omega1*gamma(n/2)*gamma(m/2 + 1)*hypergeom(m/2 + 1, [3/2, 1 - n/2], omega1^2/4))/(2*gamma(m/2 + n/2 + 1)) + (omega1*omega1^n*pi^(1/2)*gamma(-n/2)*hypergeom(m/2 + n/2 + 1, [n/2 + 1, n/2 + 3/2], omega1^2/4))/(4*2^n*gamma(n/2 + 3/2));

fun_matlab = 6.575169876935467e+209

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%% MAPLE CODE

restart; Digits:=500: n:=5: m:=3: omega1:=500:
Fun_maple:=evalf((omega1*GAMMA(n/2)*GAMMA(m/2 + 1)*hypergeom([m/2 + 1], [3/2, 1 - n/2], omega1^2/4))/(2*GAMMA(m/2 + n/2 + 1)) + (omega1*omega1^n*Pi^(1/2)*GAMMA(-n/2)*hypergeom([m/2 + n/2 + 1], [n/2 + 1, n/2 + 3/2], omega1^2/4))/(4*2^n*GAMMA(n/2 + 3/2)));

Fun_maple := -1.81414220781335980673653067232748014592172464361706594606931258364*10^(-209)

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Walter Roberson 2021-12-24

n=m+1? But 5 is not 3+1

gourav pandey 2021-12-24

编辑：gourav pandey 2021-12-24

thank you for correcting me. but Will you please suggest any idea/reason behind this

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Answer 1

Walter Roberson 2021-12-24

1
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1616910-why-get-different-values-when-matlab-also-use-maple-for-calculation-maple-vs-matlab#answer_861405

在 MATLAB Online 中打开

fun_matlab=(omega1*gamma(n/2)*gamma(m/2 + 1)*hypergeom(m/2 + 1, [3/2, 1 - n/2], omega1^2/4))/(2*gamma(m/2 + n/2 + 1)) + (omega1*omega1^n*pi^(1/2)*gamma(-n/2)*hypergeom(m/2 + n/2 + 1, [n/2 + 1, n/2 + 3/2], omega1^2/4))/(4*2^n*gamma(n/2 + 3/2));

n and m are double precision. omega is double precision. The gamma() calls are being evaluated at double precision, and your hypergeom() calls are being evaluated at double precision. Double precision is not accurate enough for your purposes.

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Walter Roberson 2021-12-24

编辑：Walter Roberson 2021-12-24

在 MATLAB Online 中打开

sqrt(pi) was also a problem.

n = sym(5); m = sym(3); omega1 = sym(500);
Pi = sym(pi);
fun_matlab = (omega1*gamma(n/2)*gamma(m/2 + 1)*hypergeom(m/2 + 1, [3/2, 1 - n/2], omega1^2/4))/(2*gamma(m/2 + n/2 + 1)) + (omega1*omega1^n*Pi^(1/2)*gamma(-n/2)*hypergeom(m/2 + n/2 + 1, [n/2 + 1, n/2 + 3/2], omega1^2/4))/(4*2^n*gamma(n/2 + 3/2));
string(fun_matlab)
ans = "(375*pi*((500009*cosh(500))/9 + (124995500*sinh(500))/9))/64 - (97656250000000*pi*((749973*cosh(500))/100000000000 + (1500027*sinh(500))/50000000000000))/9"
double(vpa(fun_matlab,500))
ans = -1.8141e-209

But if your question is whether it can be done in double precision in MATLAB, then I doubt it. The calculation involves cosh(500) and sinh(500) which are about 10^216 and differ by about 10^-218 so you would need more than 434 digits of precision.

John D'Errico 2021-12-24

编辑：John D'Errico 2021-12-24

在 MATLAB Online 中打开

Even if you use the symbolic toolbox, with everything in sym form, a large value is still produced, not the infinitessimally small one apparently produced from Maple.

n=sym(5);m=sym(3);omega1=sym(500);
digits 5000
fun_matlab=(omega1*gamma(n/2)*gamma(m/2 + 1)*hypergeom(m/2 + 1, [3/2, 1 - n/2], omega1^2/4))/(2*gamma(m/2 + n/2 + 1)) + (omega1*omega1^n*pi^(1/2)*gamma(-n/2)*hypergeom(m/2 + n/2 + 1, [n/2 + 1, n/2 + 3/2], omega1^2/4))/(4*2^n*gamma(n/2 + 3/2));
vpa(fun_matlab)
ans = 147748731616237577931448363241910368283180484634000496100665387387718411349283956852373300175539197760922694640142292157562340440898059897980298202574649566231171561333775852154622445545528768308520930015426487.0863498830823765232823480627139222936503715438799464412851830768478983831036296973344755151435098437067437752391294062011452385312004303314656598808096311285145864980219749132556964600592390223455372953776512924490749958419751683873694385571230866979076302422525604930389533068747876362921891153760519734949338592654764531423925140806092090149888536227492888000923032296131366435507730103786420120218859203547085762997974107915729496756974053271088704728638187898053487675232852417616027618083087504497866163187415356170127322059067782083699563325588706621591438750039928022806285962578490840905063417687646547749245326945723557137978260046735238027396283720984590429674805556644098317669576443124441670981410255367029949936182153808843774660839144590472058384441299247528947675139797955621415394375443849053717899771742184755822787852276136646671933818125855174241072254334632780328000036308553314885060950269856196498793393606666552973537267376390169904344484764843074139018715753581572343010303661897945659915499169913394200232588627633151116060080364895158479676748781610745396475483288454825580865090714158662308657557433605382767136806246862020578700099946196284159964726339698164147107673911838790682145013229594511047285781270968596256827862215822470685106782190984432702702292103678892731665019125506501067388591399205113889796260660103182613672477681436818186904010621555251288714279518544719787238937443236444105316445645580057487554891642882034380970041760733794513864168932707249169175791210195487602121674578387737364790653948362659062583097934072705877077753099910766064973233982921766408718971002389585572756382046531800026450420915996862092472014366665093128625844683884456327441995359995094755671454333741849675350716427590968111383719035406523526415695911834748274184820516867436953945826232909105715965078570915320502259126290512818913313877420704218572682678098013431891997814279297049106299858615695633000718423647223430191779836456826387399561401197603771489170131208829096174783189739125052199788092496926022160823952450783800167193276370726798734156072774937990743894401684344358349257183707299693962663094234407332871408932652239299831546036033569381647972573178943603603285044062345759733792302999355908523925112609920030222973338108400713851144586222851232544397308448104164094072898506510345180658593016074656825742076505200914491294932930515431757156180763724847372060149750838118403882740191715431899502315068505631366944030641643501690121612806246148737459079019011461697588684682304825024137240423228904568075148244863590488435547668930028683371712401215740667223044574375329086967484218365017648256496067858651787089022986708050914547128166673766890605616055113216980565492628120034707174699532421909430708906231270732558284176077211389470684737860304877621036480815416371821478981860388735867663688907482445886586092645434987955091586685479870079176675897949627074893006506049330923746770069948742165934949685361114106958051913446978613546980111760801166847989843696233620120806975788957685588627466301934429219151026838394165412383233195831897070116715071389233427085379364706867446529026010399745019822441891854161740931421751154201056135119466746664416844750071721139563638949860033018976611483134988781174161132655870332572971927942261442618504455856570424862372485153118612960613012160427992763177647028380651116798426446740489748995135739230578478850241074209199523193415574664534042638953307613218296751960291588989029302363830433384692526139047220174111234476563765807338907716224456931764504072247961906469436135647032620539821264393670688905897395214825872724945098035540504290787265393716141527743157416854665405241789282709262811613272563251545741502230733996411735405260618237971351153845760880686980364183509484338435610898547857679708341225081738202345854205843954850929323088578413558590272973311256739597131596535276489770634966198619636676421873016780309617942694385009052020922459238733120162841517521185131785617099175720739231119080001279130653248127283004524937165292086986161642139457748796826109422507865015341473582193312793687111771056851880485571822320134311356877918646112101585224167647956238830825405527821711038516391336115291663519502823405367600864820713030936994800507233538386118970758530570795772045625738917259556602078618155992916892902400874609976240131803835137431103875794095842773993781554114441585881767950113635740851107802556554132571379276185542922733305923364985915364089205031022265184845783271795869425922452632788370799186733586905958028872319984373021210084090813772664930277280795406721885484043943658932898059132166540358379662834952435864982834842361303218289109922349437428413854927786478680351267442158088638852896814753016845716837821160566014644165069585212571556756518111206068557838534894630596
double(fun_matlab)
ans = 1.4775e+209