cftool and fit function returns different results

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]

[dpb]

Apparently those aren't identically the same options as cftool used...

>> fit(x',y','power1')
ans = 
     General model Power1:
     ans(x) = a*x^b
     Coefficients (with 95% confidence bounds):
       a =   3.239e+10  (-6.089e+10, 1.257e+11)
       b =      -1.573  (-1.747, -1.399)
>>

Default options result in same result it appears.

[yonatan s]

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]

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