NonlinearModelFit::cvmit: Failed to converge to the requested accuracy or precision within 100 iterations

Question

I have got a problem in my program with NonlinearModelFit:

datan = Take[data, {1, 350}, {1, 1}];
mn =  939.565;

hbarc = 2*(197.33)^2;

datak = Sqrt[mn*datan/hbarc];

datadephasage = Take[data, {1, 350}, {2, 2}];

datanew = Join[datak, datadephasage, 2]

nlm1 = NonlinearModelFit[datanew, ((-ArcTan[x/a]*180/Pi) - (ArcTan[x/b]*180/Pi) -(ArcTan[x/c]*180/Pi) - (ArcTan[x/d]*180/Pi) - (ArcTan[x/e]*180/Pi)), {a, b, c, d, e}, x];

I get the error in the title of my post.

If you wan to test my values,

datanew = {{0., 0.}, {0.0109839, 14.551}, {0.0155335, 20.5526}, {0.0190246, 
  23.7734}, {0.0219677, 26.9133}, {0.0245607, 29.7561}, {0.0269049, 
  32.0505}, {0.0290606, 33.9131}, {0.0310671, 35.5476}, {0.0329516, 
  37.0554}, {0.034734, 38.4352}, {0.0364294, 39.6848}, {0.0380492, 
  40.8166}, {0.0396029, 41.8463}, {0.0410979, 42.7896}, {0.0425403, 
  43.6624}, {0.0439355, 44.4783}, {0.0452876, 45.2432}, {0.0466006, 
  45.9605}, {0.0478776, 46.6338}, {0.0491214, 47.2669}, {0.0503344, 
  47.8631}, {0.0515189, 48.4255}, {0.0526768, 48.9567}, {0.0538097, 
  49.4595}, {0.0549193, 49.9368}, {0.056007, 50.3911}, {0.0570739, 
  50.8239}, {0.0581212, 51.2366}, {0.0591499, 51.6305}, {0.0601611, 
  52.0069}, {0.0611556, 52.3671}, {0.0621341, 52.712}, {0.0630975, 
  53.0425}, {0.0640464, 53.3596}, {0.0649814, 53.6641}, {0.0659032, 
  53.9569}, {0.0668123, 54.2386}, {0.0677091, 54.5098}, {0.0685942, 
  54.771}, {0.0694681, 55.0228}, {0.0703311, 55.2658}, {0.0711836, 
  55.5003}, {0.072026, 55.7268}, {0.0728587, 55.9457}, {0.073682, 
  56.1574}, {0.0744962, 56.3622}, {0.0753016, 56.5605}, {0.0760985, 
  56.7525}, {0.0768871, 56.9385}, {0.0776677, 57.1188}, {0.0784405, 
  57.2937}, {0.0792058, 57.4634}, {0.0799638, 57.6281}, {0.0807146, 
  57.788}, {0.0814585, 57.9434}, {0.0821957, 58.0943}, {0.0829264, 
  58.241}, {0.0836506, 58.3837}, {0.0843687, 58.5225}, {0.0850807, 
  58.6575}, {0.0857868, 58.7889}, {0.0864871, 58.9168}, {0.0871817, 
  59.0414}, {0.0878709, 59.1628}, {0.0885548, 59.2811}, {0.0892334, 
  59.3964}, {0.0899068, 59.5088}, {0.0905753, 59.6183}, {0.0912389, 
  59.7252}, {0.0918976, 59.8295}, {0.0925517, 59.9313}, {0.0932012, 
  60.0306}, {0.0938462, 60.1276}, {0.0944868, 60.2222}, {0.0951231, 
  60.3147}, {0.0957551, 60.405}, {0.096383, 60.4933}, {0.0970069, 
  60.5795}, {0.0976268, 60.6638}, {0.0982427, 60.7462}, {0.0988548, 
  60.8267}, {0.0994632, 60.9055}, {0.100068, 60.9825}, {0.100669, 
  61.0579}, {0.101266, 61.1316}, {0.10186, 61.2037}, {0.102451, 
  61.2743}, {0.103038, 61.3434}, {0.103622, 61.411}, {0.104202, 
  61.4772}, {0.104779, 61.542}, {0.105354, 61.6054}, {0.105925, 
  61.6676}, {0.106493, 61.7285}, {0.107058, 61.7881}, {0.107619, 
  61.8465}, {0.108179, 61.9037}, {0.108735, 61.9598}, {0.109288, 
  62.0148}, {0.109839, 62.0686}, {0.110387, 62.1214}, {0.110932, 
  62.1732}, {0.111474, 62.2239}, {0.112014, 62.2737}, {0.112551, 
  62.3224}, {0.113086, 62.3703}, {0.113618, 62.4171}, {0.114148, 
  62.4631}, {0.114675, 62.5082}, {0.1152, 62.5525}, {0.115722, 
  62.5959}, {0.116242, 62.6384}, {0.11676, 62.6802}, {0.117276, 
  62.7212}, {0.117789, 62.7614}, {0.1183, 62.8008}, {0.118809, 
  62.8395}, {0.119315, 62.8775}, {0.11982, 62.9148}, {0.120322, 
  62.9514}, {0.120823, 62.9873}, {0.121321, 63.0226}, {0.121817, 
  63.0572}, {0.122311, 63.0911}, {0.122803, 63.1245}, {0.123294, 
  63.1572}, {0.123782, 63.1893}, {0.124268, 63.2209}, {0.124753, 
  63.2518}, {0.125235, 63.2822}, {0.125716, 63.3121}, {0.126195, 
  63.3414}, {0.126672, 63.3702}, {0.127147, 63.3984}, {0.127621, 
  63.4262}, {0.128093, 63.4534}, {0.128563, 63.4802}, {0.129031, 
  63.5064}, {0.129498, 63.5322}, {0.129963, 63.5575}, {0.130426, 
  63.5824}, {0.130888, 63.6068}, {0.131348, 63.6308}, {0.131806, 
  63.6544}, {0.132263, 63.6775}, {0.132719, 63.7002}, {0.133172, 
  63.7225}, {0.133625, 63.7444}, {0.134075, 63.7659}, {0.134524, 
  63.787}, {0.134972, 63.8078}, {0.135418, 63.8281}, {0.135863, 
  63.8481}, {0.136306, 63.8677}, {0.136748, 63.887}, {0.137188, 
  63.9059}, {0.137627, 63.9245}, {0.138065, 63.9428}, {0.138501, 
  63.9607}, {0.138936, 63.9783}, {0.13937, 63.9955}, {0.139802, 
  64.0125}, {0.140233, 64.0291}, {0.140662, 64.0454}, {0.14109, 
  64.0615}, {0.141517, 64.0772}, {0.141943, 64.0926}, {0.142367, 
  64.1078}, {0.14279, 64.1227}, {0.143212, 64.1372}, {0.143633, 
  64.1516}, {0.144052, 64.1656}, {0.14447, 64.1794}, {0.144887, 
  64.1929}, {0.145303, 64.2062}, {0.145717, 64.2192}, {0.146131, 
  64.232}, {0.146543, 64.2445}, {0.146954, 64.2568}, {0.147364, 
  64.2688}, {0.147773, 64.2806}, {0.14818, 64.2922}, {0.148587, 
  64.3036}, {0.148992, 64.3147}, {0.149397, 64.3256}, {0.1498, 
  64.3363}, {0.150202, 64.3468}, {0.150603, 64.357}, {0.151003, 
  64.3671}, {0.151402, 64.3769}, {0.1518, 64.3866}, {0.152197, 
  64.396}, {0.152593, 64.4053}, {0.152988, 64.4143}, {0.153381, 
  64.4232}, {0.153774, 64.4319}, {0.154166, 64.4404}, {0.154557, 
  64.4487}, {0.154947, 64.4568}, {0.155335, 64.4648}, {0.155723, 
  64.4725}, {0.15611, 64.4801}, {0.156496, 64.4876}, {0.156881, 
  64.4948}, {0.157265, 64.5019}, {0.157648, 64.5089}, {0.15803, 
  64.5157}, {0.158412, 64.5223}, {0.158792, 64.5287}, {0.159171, 
  64.535}, {0.15955, 64.5412}, {0.159928, 64.5472}, {0.160304, 
  64.553}, {0.16068, 64.5587}, {0.161055, 64.5643}, {0.161429, 
  64.5697}, {0.161802, 64.575}, {0.162175, 64.5801}, {0.162546, 
  64.5851}, {0.162917, 64.59}, {0.163287, 64.5947}, {0.163656, 
  64.5993}, {0.164024, 64.6038}, {0.164391, 64.6081}, {0.164758, 
  64.6123}, {0.165124, 64.6164}, {0.165489, 64.6203}, {0.165853, 
  64.6242}, {0.166216, 64.6279}, {0.166579, 64.6315}, {0.16694, 
  64.635}, {0.167301, 64.6383}, {0.167661, 64.6416}, {0.168021, 
  64.6447}, {0.16838, 64.6477}, {0.168737, 64.6506}, {0.169094, 
  64.6534}, {0.169451, 64.6561}, {0.169806, 64.6587}, {0.170161, 
  64.6612}, {0.170515, 64.6635}, {0.170869, 64.6658}, {0.171222, 
  64.668}, {0.171574, 64.67}, {0.171925, 64.672}, {0.172275, 
  64.6739}, {0.172625, 64.6756}, {0.172974, 64.6773}, {0.173323, 
  64.6789}, {0.17367, 64.6804}, {0.174017, 64.6818}, {0.174363, 
  64.6831}, {0.174709, 64.6843}, {0.175054, 64.6854}, {0.175398, 
  64.6864}, {0.175742, 64.6874}, {0.176085, 64.6883}, {0.176427, 
  64.689}, {0.176769, 64.6897}, {0.17711, 64.6903}, {0.17745, 
  64.6908}, {0.177789, 64.6913}, {0.178128, 64.6916}, {0.178467, 
  64.6919}, {0.178804, 64.6921}, {0.179141, 64.6923}, {0.179478, 
  64.6923}, {0.179814, 64.6923}, {0.180149, 64.6922}, {0.180483, 
  64.692}, {0.180817, 64.6917}, {0.181151, 64.6914}, {0.181483, 
  64.691}, {0.181815, 64.6906}, {0.182147, 64.69}, {0.182478, 
  64.6894}, {0.182808, 64.6887}, {0.183138, 64.688}, {0.183467, 
  64.6872}, {0.183795, 64.6863}, {0.184123, 64.6854}, {0.184451, 
  64.6844}, {0.184777, 64.6833}, {0.185103, 64.6821}, {0.185429, 
  64.6809}, {0.185754, 64.6797}, {0.186079, 64.6783}, {0.186402, 
  64.677}, {0.186726, 64.6755}, {0.187049, 64.674}, {0.187371, 
  64.6724}, {0.187692, 64.6708}, {0.188014, 64.6691}, {0.188334, 
  64.6674}, {0.188654, 64.6656}, {0.188974, 64.6637}, {0.189293, 
  64.6618}, {0.189611, 64.6599}, {0.189929, 64.6579}, {0.190246, 
  64.6558}, {0.190563, 64.6537}, {0.190879, 64.6515}, {0.191195, 
  64.6492}, {0.19151, 64.647}, {0.191825, 64.6446}, {0.192139, 
  64.6423}, {0.192453, 64.6398}, {0.192766, 64.6373}, {0.193079, 
  64.6348}, {0.193391, 64.6322}, {0.193703, 64.6296}, {0.194014, 
  64.6269}, {0.194324, 64.6242}, {0.194635, 64.6214}, {0.194944, 
  64.6186}, {0.195254, 64.6158}, {0.195562, 64.6128}, {0.19587, 
  64.6099}, {0.196178, 64.6069}, {0.196485, 64.6039}, {0.196792, 
  64.6008}, {0.197098, 64.5977}, {0.197404, 64.5945}, {0.19771, 
  64.5913}, {0.198014, 64.588}, {0.198319, 64.5847}, {0.198623, 
  64.5814}, {0.198926, 64.578}, {0.199229, 64.5746}, {0.199532, 
  64.5712}, {0.199834, 64.5677}, {0.200136, 64.5641}, {0.200437, 
  64.5606}, {0.200738, 64.557}, {0.201038, 64.5533}, {0.201338, 
  64.5496}, {0.201637, 64.5459}, {0.201936, 64.5421}, {0.202234, 
  64.5384}, {0.202533, 64.5345}, {0.20283, 64.5307}, {0.203127, 
  64.5268}, {0.203424, 64.5228}, {0.20372, 64.5189}, {0.204016, 
  64.5149}, {0.204312, 64.5108}, {0.204607, 64.5067}, {0.204901, 
  64.5026}, {0.205196, 64.4985}}

I know from Matlab (another program) that some good parameter {a, b, c, d, e} I search with the "NonlinearModelFit tool" are {-0.04,-0.75,4.16,0.61,2.04}.

But can you please tell me why I cannot find something in Mathematica?

Thank you for your time and sorry for my bad english :)

Like this

nlm2 = NonlinearModelFit[
datanew, -(ArcTan[x/a] + ArcTan[x/b] + ArcTan[x/c] + ArcTan[x/d] + 
ArcTan[x/e]) 180/Pi, {a, {b, 2.04}, {c, -0.043717}, d, e}, x]

And then like this

nlm2[{ "BestFit", "BestFitParameters", "ParameterTable", "RSquared", 
"AdjustedRSquared", "AIC", "BIC"}]

the section BestFitParameters of the output give me good results.

but it is because I knew some values (2.04 and -0.04) before from MATLAB so how can I do this with only Mathematica?

Answer 1

Perhaps you have too many parameters:

model = -(ArcTan[x/c] + ArcTan[x/d] + ArcTan[x/e]) 180/Pi; 
nlm1 = FindFit[datanew, {model}, {c, d, e}, x];
Show[ListPlot[datanew, PlotStyle -> Red], Plot[model /. nlm1, {x, 0, .2}], PlotRange -> All]

{c -> 0.704089, d -> -0.0400201, e -> -6.58175}

Edit

With your full dataset post at ideone:

nlm1 = FindFit[datanew, {model}, {a, b, c, d, e}, x];
Show[ListPlot[datanew, PlotStyle -> {Red, PointSize[.001]}], 
     Plot[model /. nlm1, {x, 0, 2}], PlotRange -> All]

Edit

Run this command to load the evaluating notebook, including the data

 NotebookPut@ImportString[Uncompress@FromCharacterCode@Flatten@ImageData[Import@
             "http://i.stack.imgur.com/XR9A2.png","Byte"],"NB"]