Dear ROOT experts,
I’m trying to fit a custom function:
f(x) = c0 + c2.x + c1.exp(c3.x)
from a binned histogram with weights (errors).
I’ve tried using TGraphError, but the fit fails.
(As a new user, I’m unable to post pictures or files, so I copied the code below test1.c and test2.c).
Then I tried to do the fit with the functions that I had been successfully using to perform weighted affine fitting, but here again I fail to find what I have to modify. My initial set of parameters is quite close to data.
Using ROOT::Math::MinimizerOptions::SetStrategy(0), the fit result says it has converged, however the result doesn’t seem fine to me.
Would someone please point out what I’m missing ?
Thanks for your help.
_ROOT Version: 6.26.10
_Platform: win64
_Compiler: MSVC 19.32.31332.0
- test1.c:
#include "TH1.h"
#include "TF1.h"
#include "Fit/BinData.h"
#include "Fit/Fitter.h"
#include "Math/WrappedMultiTF1.h"
#include "TGraph.h"
double X[329] = {
-9.1100, -9.0900, -9.0700, -9.0500, -9.0300, -9.0100, -8.9900
, -8.9700, -8.9500, -8.9300, -8.9100, -8.8900, -8.8700, -8.8500
, -8.8300, -8.8100, -8.7900, -8.7700, -8.7500, -8.7300, -8.7100
, -8.6900, -8.6700, -8.6500, -8.6300, -8.6100, -8.5900, -8.5700
, -8.5500, -8.5300, -8.5100, -8.4900, -8.4700, -8.4500, -8.4300
, -8.4100, -8.3900, -8.3700, -8.3500, -8.3300, -8.3100, -8.2900
, -8.2700, -8.2500, -8.2300, -8.2100, -8.1900, -8.1700, -8.1500
, -8.1300, -8.1100, -8.0900, -8.0700, -8.0500, -8.0300, -8.0100
, -7.9900, -7.9700, -7.9500, -7.9300, -7.9100, -7.8900, -7.8700
, -7.8500, -7.8300, -7.8100, -7.7900, -7.7700, -7.7500, -7.7300
, -7.7100, -7.6900, -7.6700, -7.6500, -7.6300, -7.6100, -7.5900
, -7.5700, -7.5500, -7.5300, -7.5100, -7.4900, -7.4700, -7.4500
, -7.4300, -7.4100, -7.3900, -7.3700, -7.3500, -7.3300, -7.3100
, -7.2900, -7.2700, -7.2500, -7.2300, -7.2100, -7.1900, -7.1700
, -7.1500, -7.1300, -7.1100, -7.0900, -7.0700, -7.0500, -7.0300
, -7.0100, -6.9900, -6.9700, -6.9500, -6.9300, -6.9100, -6.8900
, -6.8700, -6.8500, -6.8300, -6.8100, -6.7900, -6.7700, -6.7500
, -6.7300, -6.7100, -6.6900, -6.6700, -6.6500, -6.6300, -6.6100
, -6.5900, -6.5700, -6.5500, -6.5300, -6.5100, -6.4900, -6.4700
, -6.4500, -6.4300, -6.4100, -6.3900, -6.3700, -6.3500, -6.3300
, -6.3100, -6.2900, -6.2700, -6.2500, -6.2300, -6.2100, -6.1900
, -6.1700, -6.1500, -6.1300, -6.1100, -6.0900, -6.0700, -6.0500
, -6.0300, -6.0100, -5.9900, -5.9700, -5.9500, -5.9300, -5.9100
, -5.8900, -5.8700, -5.8500, -5.8300, -5.8100, -5.7900, -5.7700
, -5.7500, -5.7300, -5.7100, -5.6900, -5.6700, -5.6500, -5.6300
, -5.6100, -5.5900, -5.5700, -5.5500, -5.5300, -5.5100, -5.4900
, -5.4700, -5.4500, -5.4300, -5.4100, -5.3900, -5.3700, -5.3500
, -5.3300, -5.3100, -5.2900, -5.2700, -5.2500, -5.2300, -5.2100
, -5.1900, -5.1700, -5.1500, -5.1300, -5.1100, -5.0900, -5.0700
, -5.0500, -5.0300, -5.0100, -4.9900, -4.9700, -4.9500, -4.9300
, -4.9100, -4.8900, -4.8700, -4.8500, -4.8300, -4.8100, -4.7900
, -4.7700, -4.7500, -4.7300, -4.7100, -4.6900, -4.6700, -4.6500
, -4.6300, -4.6100, -4.5900, -4.5700, -4.5500, -4.5300, -4.5100
, -4.4900, -4.4700, -4.4500, -4.4300, -4.4100, -4.3900, -4.3700
, -4.3500, -4.3300, -4.3100, -4.2900, -4.2700, -4.2500, -4.2300
, -4.2100, -4.1900, -4.1700, -4.1500, -4.1300, -4.1100, -4.0900
, -4.0700, -4.0500, -4.0300, -4.0100, -3.9900, -3.9700, -3.9500
, -3.9300, -3.9100, -3.8900, -3.8700, -3.8500, -3.8300, -3.8100
, -3.7900, -3.7700, -3.7500, -3.7300, -3.7100, -3.6900, -3.6700
, -3.6500, -3.6300, -3.6100, -3.5900, -3.5700, -3.5500, -3.5300
, -3.5100, -3.4900, -3.4700, -3.4500, -3.4300, -3.4100, -3.3900
, -3.3700, -3.3500, -3.3300, -3.3100, -3.2900, -3.2700, -3.2500
, -3.2300, -3.2100, -3.1900, -3.1700, -3.1500, -3.1300, -3.1100
, -3.0900, -3.0700, -3.0500, -3.0300, -3.0100, -2.9900, -2.9700
, -2.9500, -2.9300, -2.9100, -2.8900, -2.8700, -2.8500, -2.8300
, -2.8100, -2.7900, -2.7700, -2.7500, -2.7300, -2.7100, -2.6900
, -2.6700, -2.6500, -2.6300, -2.6100, -2.5900, -2.5700, -2.5500
};
double Y[329] = {
-10.313923144440531, -9.861938020697474, -9.551783092393634, -9.620775963880586, -9.369461535599680,
-9.774926643707845, -8.892537463509370, -9.264101019941855, -9.369461535599680, -9.124339077566695,
-9.369461535599680, -9.369461535599680, -9.369461535599680, -9.001736755474363, -9.215310855772422,
-8.927628783320641, -8.892537463509370, -9.264101019941855, -9.315394314329405, -8.794097390696118,
-8.825846089010700, -8.763325732029365, -8.892537463509370, -9.426619949439630, -8.825846089010700,
-8.622247133769459, -8.570953839381909, -8.596271647366200, -8.704485232006432, -8.388632282587954,
-8.676314355039736, -8.409685691785786, -8.388632282587954, -8.388632282587954, -8.546261226791538,
-8.199390282949425, -8.216782025661296, -8.085446023600207, -8.199390282949425, -8.270849246931570,
-7.997153416454529, -8.040325588319739, -8.085446023600207, -7.853114046231592, -8.216782025661296,
-7.969373852347454, -8.070178551469420, -7.929099953209514, -7.782496479017639, -7.587004459033939,
-7.840992685699248, -7.903124466806253, -7.793925174841261, -7.771196923763705, -7.674865814825274,
-7.455812248762589, -7.439551727890808, -7.369484165274091, -7.400020889134173, -7.384635970294694,
-7.296988663235938, -7.262621019731730, -7.384635970294694, -7.283099551075271, -7.283099551075271,
-7.255886987550386, -7.159966865671647, -7.269400706717109, -6.946627314454058, -7.129934578572771,
-6.917499041531034, -6.936823314357437, -6.903247018823833, -6.966528468771353, -6.986833734932098,
-6.706873708574228, -6.796001488470235, -6.839298294223560, -6.610859055334640, -6.657714472616144,
-6.610859055334640, -6.691488789734748, -6.589952370515325, -6.513630102955692, -6.646705187107775,
-6.542805592089623, -6.365430459230994, -6.324939097876258, -6.338254873852030, -6.327588106047834,
-6.226747071697043, -6.280947528594723, -6.196048084808237, -6.115647659370199, -6.137340483981459,
-6.025422567777474, -5.986956286949678, -5.983189804154200, -5.983189804154200, -5.912444083839835,
-5.874638894498120, -5.874638894498120, -5.851304502436347, -5.779788731569192, -5.697389199802125,
-5.721693469728176, -5.654535372547643, -5.659962794283008, -5.688950331156261, -5.581491178841513,
-5.483326301123662, -5.513421164922471, -5.473116342890764, -5.438725821239380, -5.363138961873133,
-5.323490557661795, -5.343118273142236, -5.283485223048096, -5.269576793001964, -5.176445445870550,
-5.173931829130234, -5.159806126866585, -5.085874973739052, -5.066899072280045, -5.088176470727331,
-4.985353734721974, -4.929428081651443, -4.913178130319307, -4.907392193252262, -4.838057499851198,
-4.809753723688346, -4.790179120563717, -4.742856068891524, -4.696113625081479, -4.672016073502419,
-4.677604099219384, -4.588472370305201, -4.575049349973060, -4.569547272819078, -4.538484680877896,
-4.467484369382808, -4.409340112624704, -4.393877879562344, -4.406228480398009, -4.326394905868356,
-4.274008627076928, -4.290129710217190, -4.240549500579052, -4.178976873854859, -4.164234592117656,
-4.171578566373414, -4.103323067415879, -4.053249679175093, -3.988029262341137, -3.986241495296214,
-3.938411706597967, -3.925601863760986, -3.893462991814191, -3.841797673612826, -3.842460437361819,
-3.805366931987913, -3.768778759689302, -3.729921329671833, -3.676852361541605, -3.665308759143284,
-3.600793377851371, -3.574079460535690, -3.561819671411920, -3.520136755652821, -3.484592834757517,
-3.452810337570368, -3.420701540949736, -3.397491329979498, -3.382451338841079, -3.343461378614151,
-3.305030540644876, -3.286608630400755, -3.246968726085294, -3.216610644571344, -3.154853437177489,
-3.144793101373987, -3.102577292612118, -3.074093038387895, -3.057121948684153, -3.007295872819874,
-2.991884608899349, -2.952729253087354, -2.925683635793376, -2.910078865736984, -2.873440977739303,
-2.843210727280864, -2.805214297675494, -2.771785430215086, -2.742890964215371, -2.704344149419553,
-2.681868146394678, -2.665115265741983, -2.612077052179671, -2.602566023603904, -2.563246916728062,
-2.536369938704988, -2.500447084933974, -2.465546956003481, -2.447693780419022, -2.428755156477858,
-2.380177474213063, -2.351159214272417, -2.341210853375447, -2.299587407141108, -2.272464256979015,
-2.262036061488975, -2.218760078007154, -2.182770656614001, -2.148965784824985, -2.130007298748988,
-2.095636691759366, -2.074367403924615, -2.042959372719680, -2.015419153989124, -1.998881108906736,
-1.969961520664345, -1.944666646385085, -1.918897586998502, -1.878559971271927, -1.843791611920057,
-1.829932241852074, -1.803898442502907, -1.777487706801899, -1.748402480914340, -1.713308344885222,
-1.702381274275035, -1.670172824137108, -1.645702512783021, -1.618344704766146, -1.591389657653339,
-1.569913156343789, -1.541799846969211, -1.518968354728540, -1.491011518086415, -1.475205616368585,
-1.444223685957782, -1.421409914216723, -1.399220214647226, -1.373705628544028, -1.340263974232605,
-1.319803910492577, -1.294795164432434, -1.274659221714550, -1.249054556432170, -1.230491247147874,
-1.205837006503105, -1.181513426380198, -1.156998618623875, -1.132893891096297, -1.126412834964249,
-1.094538084962830, -1.068160472950146, -1.049838911740137, -1.036257958078095, -1.007441769058385,
-0.992118068189074, -0.967803907299347, -0.951941360667509, -0.930854705437012, -0.916202603479534,
-0.897149491856160, -0.882956672988893, -0.856532980386833, -0.847126033002528, -0.836329380381941,
-0.808676854923248, -0.796413248429456, -0.785378423088207, -0.776068909868604, -0.758251930226274,
-0.741273729908524, -0.735424020584331, -0.725802129028279, -0.712332503885926, -0.703120634557674,
-0.691766447529414, -0.689412804678507, -0.678044298736275, -0.674010589012952, -0.672069408927882,
-0.667514562462868, -0.667228263703542, -0.656464015756072, -0.655249764129009, -0.659180874289131,
-0.655003441856125, -0.656427475397242, -0.659886451585986, -0.661087994474738, -0.671067785843910,
-0.668956537108436, -0.678539151807693, -0.684195974729453, -0.696129166538607, -0.702756980790329,
-0.720840551463452, -0.726869934789109, -0.738701591978517, -0.749501188378216, -0.761311058836361,
-0.774782749291670, -0.798832901390536, -0.814020326166952, -0.833588351162675, -0.847900120999691,
-0.865387356676596, -0.886273349486128, -0.904041285747054, -0.928129989876270, -0.951732696180833,
-0.974661992397510, -1.002161433758060, -1.026053109955217, -1.060413819920218, -1.072859599821508,
-1.112075879869244, -1.136135480544120, -1.161802253238448, -1.193069938965885, -1.223026114237874,
-1.264472777279751, -1.289086529949630, -1.323143464178061, -1.349318910824085
};
double W[329] = {
0.000033168061621, 0.000052121239689, 0.000071074417758, 0.000066336123241, 0.000085289301310,
0.000056859534207, 0.000137410541000, 0.000094765890344, 0.000085289301310, 0.000108980773896,
0.000085289301310, 0.000085289301310, 0.000085289301310, 0.000123195657448, 0.000099504184862,
0.000132672246482, 0.000137410541000, 0.000094765890344, 0.000090027595827, 0.000151625424551,
0.000146887130034, 0.000156363719068, 0.000137410541000, 0.000080551006793, 0.000146887130034,
0.000180055191655, 0.000189531780689, 0.000184793486172, 0.000165840308103, 0.000227438136827,
0.000170578602620, 0.000222699842310, 0.000227438136827, 0.000227438136827, 0.000194270075206,
0.000274821081999, 0.000270082787482, 0.000307989143620, 0.000274821081999, 0.000255867903930,
0.000336418910723, 0.000322204027171, 0.000307989143620, 0.000388540150412, 0.000270082787482,
0.000345895499757, 0.000312727438137, 0.000360110383309, 0.000416969917516, 0.000506997513343,
0.000393278444930, 0.000369586972344, 0.000412231622999, 0.000421708212033, 0.000464352862688,
0.000578071931101, 0.000587548520136, 0.000630193170791, 0.000611239992722, 0.000620716581756,
0.000677576115963, 0.000701267588549, 0.000620716581756, 0.000687052704998, 0.000687052704998,
0.000706005883066, 0.000777080300825, 0.000696529294032, 0.000961873786997, 0.000800771773411,
0.000990303554100, 0.000971350376031, 0.001004518437652, 0.000942920608928, 0.000923967430859,
0.001222479985444, 0.001118237506065, 0.001070854560893, 0.001345675642892, 0.001284077814168,
0.001345675642892, 0.001241433163513, 0.001374105409995, 0.001483086183891, 0.001298292697720,
0.001440441533236, 0.001720000909753, 0.001791075327511, 0.001767383854925, 0.001786337032994,
0.001975868813683, 0.001871626334304, 0.002037466642407, 0.002208045245027, 0.002160662299854,
0.002416530203785, 0.002511296094129, 0.002520772683164, 0.002520772683164, 0.002705566169335,
0.002809808648714, 0.002809808648714, 0.002876144771955, 0.003089368025231, 0.003354712518195,
0.003274161511402, 0.003501599648229, 0.003482646470160, 0.003383142285298, 0.003766944141194,
0.004155484291606, 0.004032288634158, 0.004198128942261, 0.004345016072295, 0.004686173277535,
0.004875705058224, 0.004780939167880, 0.005074713427948, 0.005145787845706, 0.005648047064532,
0.005662261948084, 0.005742812954876, 0.006183474344978, 0.006301931707909, 0.006169259461427,
0.006837358988355, 0.007230637433285, 0.007349094796216, 0.007391739446871, 0.007922428432800,
0.008149866569627, 0.008310968583212, 0.008713723617176, 0.009130693534692, 0.009353393377002,
0.009301272137312, 0.010168380033964, 0.010305790574964, 0.010362650109171, 0.010689592430859,
0.011476149320718, 0.012163202025716, 0.012352733806405, 0.012201108381854, 0.013215103408540,
0.013925847586124, 0.013703147743814, 0.014399677037846, 0.015314167879670, 0.015541606016497,
0.015427886948084, 0.016517694687045, 0.017365849405629, 0.018536208151383, 0.018569376213004,
0.019479128760311, 0.019730258369724, 0.020374666424066, 0.021454997573994, 0.021440782690442,
0.022251031052887, 0.023080232593402, 0.023994723435226, 0.025302492721980, 0.025596266982048,
0.027302053008249, 0.028041226952936, 0.028387122452693, 0.029595387554586, 0.030666242115479,
0.031656545669579, 0.032689493874334, 0.033457097586124, 0.033964095099467, 0.035314509036876,
0.036698091035906, 0.037380405446386, 0.038891921397381, 0.040090709910239, 0.042644650655023,
0.043075835456090, 0.044933246906842, 0.046231539604562, 0.047022834788938, 0.049425150109171,
0.050192753820962, 0.052197052401748, 0.053628017345950, 0.054471433770016, 0.056504162117905,
0.058238377911209, 0.060493806101408, 0.062550225921884, 0.064383945900050, 0.066914195172248,
0.068435187712277, 0.069591331574480, 0.073381967188260, 0.074083234776809, 0.077054145439109,
0.079153209910239, 0.082048307860264, 0.084962358988357, 0.086492828117421, 0.088146492903932,
0.092534153626882, 0.095258672974286, 0.096211070172249, 0.100300218340613, 0.103057905749638,
0.104138236899566, 0.108743859170308, 0.112728764859294, 0.116604689774384, 0.118836426491997,
0.122991910783603, 0.125635879124214, 0.129644476285786, 0.133264533296946, 0.135486793425524,
0.139462222525476, 0.143034896591464, 0.146768672671037, 0.152809998180498, 0.158216392224652,
0.160424437469678, 0.164655734473560, 0.169062348374579, 0.174051772501217, 0.180268414907816,
0.182249022016016, 0.188214534813201, 0.192877016618151, 0.198226551128097, 0.203642421761285,
0.208063250545856, 0.213995595281421, 0.218937636462887, 0.225144802280451, 0.228731691229990,
0.235929160601655, 0.241373461001946, 0.246789331635134, 0.253167076055318, 0.261776557193116,
0.267187689531786, 0.273953974102383, 0.279526208454640, 0.286775799065993, 0.292149025048526,
0.299441260310535, 0.306814046579337, 0.314428485868517, 0.322099784691904, 0.324194110868517,
0.334694171518687, 0.343640071567208, 0.349994124514806, 0.354779801977203, 0.365151928675408,
0.370790499150906, 0.379916454391080, 0.385990947962163, 0.394216627244065, 0.400035252911217,
0.407730243207190, 0.413558345463376, 0.424631739750130, 0.428645075206220, 0.433298080422134,
0.445447067564299, 0.450943489204279, 0.455947128214469, 0.460211593279971, 0.468484655507045,
0.476506588124707, 0.479302181889870, 0.483936233927715, 0.490498771834072, 0.495038057981573,
0.500690843340622, 0.501870678675411, 0.507608753335770, 0.509660434861729, 0.510650738415828,
0.512981979318303, 0.513128866448337, 0.518682147622524, 0.519312340793315, 0.517274874150909,
0.519440274745280, 0.518701100800593, 0.516910025473082, 0.516289308891326, 0.511162474223689,
0.512242805373616, 0.507357623726357, 0.504495693837954, 0.498511227862699, 0.495218113173227,
0.486343287542466, 0.483419759825338, 0.477733806404668, 0.472602233442514, 0.467053690562844,
0.460803880094624, 0.449853681465318, 0.443073182011169, 0.434487392345958, 0.428313394590014,
0.420888487081523, 0.412188978347898, 0.404929911147510, 0.395292220099475, 0.386071498968955,
0.377319868995641, 0.367085152838436, 0.358418812166432, 0.346312469674922, 0.342029051431351,
0.328875545851535, 0.321057359898115, 0.312921708212040, 0.303288755458522, 0.294338117115484,
0.282388138343043, 0.275522349587585, 0.266296890162548, 0.259416886523538
};
Double_t myfunc(Double_t *x, Double_t* params) {
Double_t arg = params[0] + params[2]*(*x) - params[1]*exp(params[3]*(*x));
return TMath::Exp(arg);
}
void test1() {
double yErr[329];
for (unsigned int i = 0; i < 329; ++i) {
yErr[i] = 0.01 / sqrt(W[i]);
}
TF1 *f1 = new TF1("f1", myfunc, X[0], X[328], 4);
double initParams[4] = { 6.781854336702532, 187.5966283934926, 1.846531711713894 , 1.495547402571554 };
f1->SetParameters(initParams);
TCanvas *c1 = new TCanvas();
TGraphErrors *grr = new TGraphErrors(329, X, Y, 0, yErr);
grr->Fit(f1, "WQRN"); // "initial pre-fit"
grr->Fit(f1, "RM+rob");
grr->Draw("ALP");
}
- test2.c
#include "TH1.h"
#include "TF1.h"
#include "Fit/BinData.h"
#include "Fit/Fitter.h"
#include "Math/WrappedMultiTF1.h"
#include "TGraph.h"
[Same data as in test1.c, removed because of post size limitation]
Double_t myfunc(Double_t *x, Double_t* params) {
Double_t arg = params[0] + params[2]*(*x) - params[1]*exp(params[3]*(*x));
return TMath::Exp(arg);
}
void test2() {
double yErr[329];
for (unsigned int i = 0; i < 329; ++i) {
yErr[i] = 0.01 / sqrt(W[i]);
}
TF1 *f1 = new TF1("f1", myfunc, X[0], X[328], 4);
double initParams[4] = { 6.781854336702532, 187.5966283934926, 1.846531711713894 , 1.495547402571554 };
f1->SetParameters(initParams);
double initFunc[329];
for (unsigned int i = 0; i < 329; ++i) {
initFunc[i] = initParams[0] + initParams[2]*X[i] - exp(initParams[3]*X[i])*initParams[1];
}
ROOT::Fit::BinData hdata(329, X, Y, NULL, yErr);
ROOT::Math::WrappedMultiTF1 fitFunction(*f1, f1->GetNdim());
ROOT::Math::MinimizerOptions::SetDefaultPrintLevel(1);
//ROOT::Math::MinimizerOptions::SetDefaultTolerance(0.1);
//ROOT::Math::MinimizerOptions::SetDefaultPrecision(1E-8);
//ROOT::Math::MinimizerOptions::SetDefaultMaxFunctionCalls(1000);
ROOT::Math::MinimizerOptions opts;
//opts.SetMinimizerAlgorithm("least_squares");
opts.SetStrategy(0);
ROOT::Fit::Fitter fitter;
fitter.SetFunction(fitFunction, f1->IsLinear());
fitter.Config().SetMinimizerOptions(opts);
fitter.Config().ParSettings(0).SetStepSize(1e-6);
fitter.Config().ParSettings(1).SetStepSize(1e-6);
fitter.Config().ParSettings(2).SetStepSize(1e-6);
fitter.Config().ParSettings(3).SetStepSize(1e-7);
fitter.Fit(hdata);
fitter.Result().Print(std::cout);
double outfit[329];
for (unsigned int i=0; i < 329; ++i) {
outfit[i] = fitter.Result().GetParams()[0] + fitter.Result().GetParams()[2]*X[i] - exp(fitter.Result().GetParams()[3]*X[i])*fitter.Result().GetParams()[1];
}
TCanvas *c1 = new TCanvas();
TMultiGraph *mg = new TMultiGraph();
TGraph *gr1 = new TGraph (329, X, Y);
mg->Add(gr1);
TGraph *gr2 = new TGraph (329, X, initFunc);
gr2->SetLineColor(2);
mg->Add(gr2);
TGraph *gr3 = new TGraph (329, X, outfit);
gr3->SetLineColor(3);
mg->Add(gr3);
mg->Draw("a");
}
