Curve fitting exponential data

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Jordan Mertes
Jordan Mertes 2011-9-6
Hi all,
Hopefully someone can help me to solve this problem. It's beginning to drive me nutts.
I have an array of data and i am trying to fit a curve to the data from each column. I started firstly by looking at just a few of the curves and they appear to be of the exponential form, increasing with x to an asymptote where y goes to infinity.
you can see a jpeg here http://www.flickr.com/photos/jordanmertes/6120910460/in/photostream
the problem is that i cannot get the fit to bend correctly. i've tried using different equations but nothing gets there. this fit was done using a*exp(b*x)+c*exp(d*x).
At first i was plotting this backwards, and then the curve was fitting very well. Then i realized i needed it this way and haven't been able to get a decent fit.
I know that all of the curves from the data set have asymptotes at a values that i know.
I've also tried adjusting some of the fitting options but in all honesty i'm not sure that's helped. Nothing seems to follow the sloow increase up to the curve and then sharp turn upwards.
Any help with this or suggestions would be most greatfully appreciated.
Cheers
  2 个评论
bym
bym 2011-9-6
how about posting your data?
Jordan Mertes
Jordan Mertes 2011-9-8
0 0
0.0500000000000000 4.27232580968402
0.100000000000000 7.33012531877430
0.150000000000000 9.26733553281253
0.200000000000000 10.4884642048611
0.250000000000000 11.3252619444444
0.300000000000000 11.9369098958333
0.350000000000000 12.3890363541667
0.400000000000000 12.7232681597222
0.450000000000000 12.9760964236111
0.500000000000000 13.1767785416667
0.550000000000000 13.3448810069444
0.600000000000000 13.4914273611111
0.650000000000000 13.6216759027778
0.700000000000000 13.7378076736111
0.750000000000000 13.8408662152778
0.800000000000000 13.9316885763889
0.850000000000000 14.0112569097222
0.900000000000000 14.0807263888889
0.950000000000000 14.1413769444444
1 14.1944065277778
1.05000000000000 14.2409873263889
1.10000000000000 14.2821199652778
1.15000000000000 14.3186536805556
1.20000000000000 14.3512460763889
1.25000000000000 14.3804235069445
1.30000000000000 14.4065932291667
1.35000000000000 14.4300906250000
1.40000000000000 14.4511681250000
1.45000000000000 14.4700337152778
1.50000000000000 14.4868598263889
1.55000000000000 14.5017887152778
1.60000000000000 14.5149857986111
1.65000000000000 14.5265671527778
1.70000000000000 14.5366812847222
1.75000000000000 14.5454557291667
1.80000000000000 14.5529785069445
1.85000000000000 14.5594046527778
1.90000000000000 14.5648257986111
1.95000000000000 14.5693260416666
2 14.5730389583333
2.05000000000000 14.5760411805556
2.10000000000000 14.5784046527778
2.15000000000000 14.5802209027778
2.20000000000000 14.5815407638889
2.25000000000000 14.5824436111111
2.30000000000000 14.5829714583333
2.35000000000000 14.5831906250000
2.40000000000000 14.5831222222222
2.45000000000000 14.5828108680555
2.50000000000000 14.5823066319444
2.55000000000000 14.5816237500000
2.60000000000000 14.5807869444444
2.65000000000000 14.5798264930556
2.70000000000000 14.5787653819444
2.75000000000000 14.5775764930555
2.80000000000000 14.5763302430555
2.85000000000000 14.5750176388889
2.90000000000000 14.5736318055556
2.95000000000000 14.5721863888889
3 14.5707084722222
3.05000000000000 14.5691877083333
3.10000000000000 14.5676252083334
3.15000000000000 14.5660226388889
3.20000000000000 14.5643981250000
3.25000000000000 14.5627595486112
3.30000000000000 14.5610847916666
3.35000000000000 14.5593791666667
3.40000000000000 14.5576788194444
3.45000000000000 14.5559236458333
3.50000000000000 14.5541662847222
3.55000000000000 14.5524002083333
3.60000000000000 14.5506187152778
3.65000000000000 14.5487996527778
3.70000000000000 14.5469857291666
3.75000000000000 14.5451417361112
3.80000000000000 14.5433044444444
3.85000000000000 14.5414396875000
3.90000000000000 14.5395756944444
3.95000000000000 14.5376785763889
4 14.5357784375000

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回答（1 个）

the cyclist
the cyclist 2011-9-6
I suggest you try plotting the log of your data. That might help you infer a better fitting function.
  2 个评论
Jordan Mertes
Jordan Mertes 2011-9-7
Hi cyclist. I did that, but it still doesn't come out linear to make for an easier fit. I tried semilogx, semilogy, loglog all to see if it appeared to become more linear. While part of it does get close, there is still the section that goes asymptotic.
Jordan Mertes
Jordan Mertes 2011-9-7
Just incase my picture wasn't enough. Here is the data. Maybe someone might have the time to try this and see if they can come up with the right form. I'm not sure I totally understand the different options in the cftool gui. I know the equation needs to have more coeff than 1 or 2. otherwise the curve doesn't snug close enough. I'll keep at it.
0 0
0.0500000000000000 4.27232580968402
0.100000000000000 7.33012531877430
0.150000000000000 9.26733553281253
0.200000000000000 10.4884642048611
0.250000000000000 11.3252619444444
0.300000000000000 11.9369098958333
0.350000000000000 12.3890363541667
0.400000000000000 12.7232681597222
0.450000000000000 12.9760964236111
0.500000000000000 13.1767785416667
0.550000000000000 13.3448810069444
0.600000000000000 13.4914273611111
0.650000000000000 13.6216759027778
0.700000000000000 13.7378076736111
0.750000000000000 13.8408662152778
0.800000000000000 13.9316885763889
0.850000000000000 14.0112569097222
0.900000000000000 14.0807263888889
0.950000000000000 14.1413769444444
1 14.1944065277778
1.05000000000000 14.2409873263889
1.10000000000000 14.2821199652778
1.15000000000000 14.3186536805556
1.20000000000000 14.3512460763889
1.25000000000000 14.3804235069445
1.30000000000000 14.4065932291667
1.35000000000000 14.4300906250000
1.40000000000000 14.4511681250000
1.45000000000000 14.4700337152778
1.50000000000000 14.4868598263889
1.55000000000000 14.5017887152778
1.60000000000000 14.5149857986111
1.65000000000000 14.5265671527778
1.70000000000000 14.5366812847222
1.75000000000000 14.5454557291667
1.80000000000000 14.5529785069445
1.85000000000000 14.5594046527778
1.90000000000000 14.5648257986111
1.95000000000000 14.5693260416666
2 14.5730389583333
2.05000000000000 14.5760411805556
2.10000000000000 14.5784046527778
2.15000000000000 14.5802209027778
2.20000000000000 14.5815407638889
2.25000000000000 14.5824436111111
2.30000000000000 14.5829714583333
2.35000000000000 14.5831906250000
2.40000000000000 14.5831222222222
2.45000000000000 14.5828108680555
2.50000000000000 14.5823066319444
2.55000000000000 14.5816237500000
2.60000000000000 14.5807869444444
2.65000000000000 14.5798264930556
2.70000000000000 14.5787653819444
2.75000000000000 14.5775764930555
2.80000000000000 14.5763302430555
2.85000000000000 14.5750176388889
2.90000000000000 14.5736318055556
2.95000000000000 14.5721863888889
3 14.5707084722222
3.05000000000000 14.5691877083333
3.10000000000000 14.5676252083334
3.15000000000000 14.5660226388889
3.20000000000000 14.5643981250000
3.25000000000000 14.5627595486112
3.30000000000000 14.5610847916666
3.35000000000000 14.5593791666667
3.40000000000000 14.5576788194444
3.45000000000000 14.5559236458333
3.50000000000000 14.5541662847222
3.55000000000000 14.5524002083333
3.60000000000000 14.5506187152778
3.65000000000000 14.5487996527778
3.70000000000000 14.5469857291666
3.75000000000000 14.5451417361112
3.80000000000000 14.5433044444444
3.85000000000000 14.5414396875000
3.90000000000000 14.5395756944444
3.95000000000000 14.5376785763889
4 14.5357784375000

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