cftool and fit function returns different results

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I fit data using both methods and am getting different results.
The fitted function is: f(x)=a*x^(b).
The results are:
cftool: a=3.238e+10, b=-1.573.
fit function: a=1.516e+07, b=-1.111.
And of course, the goodness of fit parameters are different.
I set the options in the fit function to be the same as in cftool.
The script:
PowerEqn='a*x^(b)';
fo = fitoptions('Method','NonlinearLeastSquares',...
'Robust','off',...
'Algorithm','Trust-Region',...
'DiffMinChange',1e-8,...
'DiffMaxChange',.1,...
'MaxFunEvals',600,...
'MaxIter',400,...
'TolFun',1e-6,...
'TolX',1e-6,...
'StartPoint',[x(1),y(1)]);
ft=fittype(PowerEqn,'options',fo);
[f,stat]=fit(x',y',ft);
The Data:
x=[1.5804e+07,1.1580e+08,2.1580e+08,3.1580e+08,4.1580e+08,5.1580e+08,6.1580e+08,7.1580e+08,
8.1580e+08,9.1580e+08,1.0158e+09,1.1158e+09,1.2158e+09,1.3158e+09,1.4158e+09];
y=[1.5398e-01,4.7623e-03,6.6259e-03,1.7019e-03,1.4101e-03,0,5.8168e-06,
0,0,0,0,0,0,0,0]
  3 个评论
yonatan s
yonatan s 2018-9-27
编辑:yonatan s 2018-9-27
yeah you're right. but in cftool I pressed on FitOptions button (see image) and just entered those results. so what am I missing?
dpb
dpb 2018-9-27
编辑:dpb 2018-9-27
Your starting points aren't the same as in the cftool window -- if I use the builtin form of the equation I get the default result.
However using the text form for the equation and the [x(1) y(1)] startpoints then I get your same result. So, there's something going on behind the scenes...
>> fit(x',y','power1',fo)
ans =
General model Power1:
ans(x) = a*x^b
Coefficients (with 95% confidence bounds):
a = 3.231e+10 (-6.071e+10, 1.253e+11)
b = -1.573 (-1.746, -1.399)
>> fo.StartPoint=[x(1) y(1)];
>> fit(x',y','power1',fo)
ans =
General model Power1:
ans(x) = a*x^b
Coefficients (with 95% confidence bounds):
a = 3.276e+10 (-6.174e+10, 1.273e+11)
b = -1.574 (-1.748, -1.4)
>> eqn='a*x^b';
>> fit(x',y',eqn,fo)
ans =
General model:
ans(x) = a*x^b
Coefficients (with 95% confidence bounds):
a = 1.58e+07 (-2.917e+07, 6.077e+07)
b = -1.114 (-1.285, -0.9424)
>> fo.StartPoint=[8.2638E11 -1.7388];
>> fit(x',y',eqn,fo)
ans =
General model:
ans(x) = a*x^b
Coefficients (with 95% confidence bounds):
a = 8.264e+11 (-3.335e+12, 4.988e+12)
b = -1.768 (-2.072, -1.464)
>>
What, specifically, I've no klew

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