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ridin2
Brazil
2 Posts |
 Posted - 12/08/2009 : 12:20:12 PM
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Hi:
I have two data sets statistically identical (95% confidence level), but the results of a non linear curve fitting are totally different for each data set. The non linear equation is of the form:
y = A/((2*pi*x)^2+B^2)+C, where A, B and C are the fitting parameters and pi = 3.141592654....
Bellow are the two data sets. The first column is the independent variable, x. Also, the error bars in each experiental point y are 0.045 (4.5%) of the y value. The non linear fitting of the second data set, shown in the third column, gives a negative value for the C parameter. This is totally wrong, and does not occur with the data set of the second column.
1.5 1.0653E-4 1.10291E-4
1.75 1.02682E-4 1.06542E-4
2 1.05668E-4 1.08566E-4
2.25 1.06872E-4 1.05761E-4
2.5 1.05639E-4 1.00336E-4
2.75 9.74293E-5 1.00582E-4
3 1.00689E-4 1.01019E-4
3.25 1.07909E-4 1.0273E-4
3.5 1.0448E-4 9.71016E-5
3.75 1.02578E-4 9.52014E-5
4 1.09042E-4 1.05171E-4
4.25 1.06515E-4 1.10169E-4
4.5 9.74016E-5 1.08222E-4
4.75 9.74826E-5 9.62112E-5
5 9.78642E-5 9.63402E-5
5.25 1.01521E-4 1.03969E-4
5.5 1.06522E-4 1.01263E-4
5.75 1.1201E-4 1.02887E-4
6 1.17538E-4 1.001E-4
6.25 1.09338E-4 1.0031E-4
6.5 1.08243E-4 1.03702E-4
6.75 9.92558E-5 1.03948E-4
7 9.75339E-5 9.68444E-5
7.25 1.03687E-4 9.90675E-5
7.5 1.06519E-4 1.03288E-4
7.75 1.07903E-4 9.87396E-5
8 1.00245E-4 9.92659E-5
8.25 1.04995E-4 9.77134E-5
8.5 1.1204E-4 9.84788E-5
8.75 1.06987E-4 1.0059E-4
9 9.99121E-5 1.00993E-4
9.25 9.82022E-5 9.89934E-5
9.5 1.04284E-4 9.93085E-5
9.75 1.07676E-4 1.01536E-4
10 9.97823E-5 1.03602E-4
10.25 9.48966E-5 1.04061E-4
10.5 9.73184E-5 1.01944E-4
10.75 9.42404E-5 1.0216E-4
11 9.93224E-5 9.48546E-5
11.25 9.6329E-5 9.12127E-5
11.5 9.44757E-5 9.29212E-5
11.75 9.83107E-5 9.23806E-5
12 9.45693E-5 8.827E-5
12.25 9.90622E-5 8.97724E-5
12.5 9.37491E-5 9.48513E-5
12.75 9.53892E-5 9.31173E-5
13 1.00716E-4 9.29687E-5
13.25 9.69386E-5 9.71641E-5
13.5 9.32703E-5 1.0091E-4
13.75 9.62695E-5 1.02893E-4
14 9.54011E-5 1.01666E-4
14.25 9.6283E-5 1.04613E-4
14.5 9.16098E-5 9.92583E-5
14.75 8.85173E-5 9.15122E-5
15 8.45982E-5 9.20526E-5
15.25 9.30705E-5 8.75113E-5
15.5 8.74084E-5 8.41368E-5
15.75 8.7587E-5 9.1589E-5
16 8.74814E-5 8.95427E-5
16.25 8.73537E-5 9.02543E-5
16.5 8.78064E-5 9.21876E-5
16.75 8.68047E-5 9.25322E-5
17 9.12191E-5 9.29717E-5
17.25 9.19184E-5 9.02421E-5
17.5 8.80657E-5 9.10153E-5
17.75 8.12411E-5 9.05213E-5
18 8.60052E-5 8.31883E-5
18.25 8.91659E-5 8.15171E-5
18.5 8.22129E-5 8.87371E-5
18.75 8.31635E-5 8.56407E-5
19 8.11928E-5 8.79865E-5
19.25 8.01945E-5 8.11675E-5
19.5 8.19013E-5 8.25628E-5
19.75 8.5627E-5 9.18881E-5
20 8.5459E-5 8.40444E-5
20.25 8.21669E-5 8.53132E-5
20.5 7.73091E-5 7.94772E-5
20.75 8.03101E-5 7.65493E-5
21 8.47817E-5 8.16415E-5
21.25 8.67083E-5 8.64493E-5
21.5 8.91754E-5 8.4889E-5
21.75 8.41978E-5 7.99565E-5
22 8.36209E-5 7.65701E-5
22.25 8.31339E-5 7.79849E-5
22.5 7.72813E-5 7.89085E-5
22.75 8.14227E-5 7.9356E-5
23 7.79059E-5 8.58887E-5
23.25 7.48421E-5 8.4979E-5
23.5 7.54918E-5 8.11602E-5
23.75 7.35763E-5 7.94127E-5
24 6.96814E-5 7.62286E-5
24.25 7.5253E-5 7.39849E-5
24.5 7.62946E-5 7.2088E-5
24.75 7.10933E-5 7.57467E-5
25 7.39441E-5 7.75477E-5
25.25 7.756E-5 7.43446E-5
25.5 7.74868E-5 7.38288E-5
25.75 7.29484E-5 7.69571E-5
26 7.28524E-5 7.71558E-5
26.25 7.09045E-5 7.94869E-5
26.5 6.91889E-5 7.89319E-5
26.75 7.01754E-5 7.50101E-5
27 7.25628E-5 7.02355E-5
27.25 7.29024E-5 7.31806E-5
27.5 7.0369E-5 7.31949E-5
27.75 6.95861E-5 7.14599E-5
28 6.56988E-5 6.94912E-5
28.25 6.81082E-5 7.44602E-5
28.5 7.40562E-5 7.0172E-5
28.75 7.07426E-5 6.75793E-5
29 6.87213E-5 6.94727E-5
29.25 7.04413E-5 7.22295E-5
29.5 7.53788E-5 6.83911E-5
29.75 6.96946E-5 6.60147E-5
30 6.55538E-5 7.26341E-5
30.25 6.60846E-5 7.14241E-5
30.5 6.3164E-5 6.40399E-5
30.75 6.41086E-5 6.25811E-5
31 6.7919E-5 6.61704E-5
31.25 7.02884E-5 6.21281E-5
31.5 6.71883E-5 6.64794E-5
31.75 6.37479E-5 6.802E-5
32 6.32261E-5 6.26867E-5
32.25 6.12864E-5 6.30708E-5
32.5 6.0269E-5 6.88997E-5
32.75 6.90859E-5 6.58483E-5
33 6.7158E-5 6.70259E-5
33.25 6.4268E-5 6.63964E-5
33.5 6.33888E-5 6.69362E-5
33.75 6.49419E-5 6.30609E-5
34 6.56043E-5 6.46479E-5
34.25 5.99896E-5 6.48418E-5
34.5 6.26777E-5 6.00743E-5
34.75 6.17671E-5 5.76962E-5
35 5.89451E-5 6.47288E-5
35.25 6.05034E-5 5.78204E-5
35.5 6.27943E-5 5.80827E-5
35.75 6.08366E-5 5.69355E-5
36 5.90751E-5 5.63016E-5
36.25 5.58264E-5 6.32785E-5
36.5 5.81278E-5 6.02256E-5
36.75 5.78896E-5 5.47692E-5
37 5.49033E-5 5.22995E-5
37.25 5.8519E-5 5.40423E-5
37.5 5.89598E-5 5.87863E-5
37.75 5.73655E-5 6.10026E-5
38 5.57381E-5 6.13701E-5
38.25 5.44153E-5 5.81001E-5
38.5 5.34399E-5 5.38845E-5
38.75 5.32216E-5 5.56372E-5
39 5.70246E-5 5.33559E-5
39.25 5.51766E-5 5.32465E-5
39.5 5.75951E-5 5.19337E-5
39.75 5.71521E-5 5.029E-5
40 5.29463E-5 5.05833E-5
40.25 5.06527E-5 5.68852E-5
40.5 5.25654E-5 5.18715E-5
40.75 5.04523E-5 5.13699E-5
41 5.20925E-5 5.23309E-5
41.25 5.16187E-5 4.83992E-5
41.5 5.04968E-5 5.19935E-5
41.75 4.81808E-5 5.19258E-5
42 4.78313E-5 4.66117E-5
Any suggestion will be very apreciated.
Thanks in advance
Ricardo |
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easwar
USA
1965 Posts |
Posted - 12/08/2009 : 12:33:56 PM
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Hi Ricardo,
The minimization routine has no knowledge of what values are appropriate for what parameters, so it is quite possible that a negative value of C gives a better fit result mathematically even though it may not make any sense for your particular data and model.
So what you can do is specify lower and/or upper bounds on the parameters so as to constrain their values within what may be physically meaningful values.
If bounds do not work, I suggest you send your FDF fitting function, your OPJ, and the initial values you use, to tech support.
Easwar
OriginLab |
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ridin2
Brazil
2 Posts |
Posted - 12/09/2009 : 10:45:49 AM
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Thanks Mr. Easwar, but I have a question: How can I send to you an entire Origin projetc? By e-mail with the project attached?
Regards,
Ricardo.
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easwar
USA
1965 Posts |
Posted - 12/09/2009 : 12:31:24 PM
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Hi Ricardo,
Please see instructions here on how to send files:
http://originlab.com/index.aspx?s=1&lm=123&pid=752
this instructions page is accessible by clicking the "Sending files to technical support" link on our main support page.
Easwar
OriginLab
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Problems with non-linear curve fitting