
From:  Przemek Klosowski 
Subject:  Re: leasqr with bounds 
Date:  Fri, 26 Jan 2018 10:31:24 0500 
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On 01/25/2018 10:09 PM, mrodrig wrote:
I did a lot of data fitting and so I'd like to help you on this. Thank you for providing the sample code you are working withit makes it easy to engage. I think you mean to use x,y instead of what I assume are your original fitting data tables Temp_bkg and Int_Prom_bkg:In order to test the operation of the leasqr function I tried with the following x=[1:10] y= [10,8,5.5,3.5,0,1.2,2.5,4.6,7.5,9.8] F=@(x, p) (p (1) * x .^ 2 + p (2) * x + p (3)) a=1 b=1 c=1 p = [a,b,c]; wt=ones(size(x)); iter=400; tol=0.000000001; dFdp="dfdp"; dp=0.001*ones(size(p)); [f, pfit, kvg, iter, corp, covp, stdresid, Z, r2] = leasqr (Temp_bkg, Int_Prom_bkg, par, F,tol, iter,wt, dp, dFdp); and gives this results;
[f, pfit, kvg, iter, corp, covp, stdresid, Z, r2] = leasqr (x,y, par, F,tol, iter,wt, dp, dFdp)
because this gives the results you quote. Next, it seems, you need to do something like
options.bounds=[5,5; 5,5; 1,1] par=[1,1,1] # avoid exceeding the bounds in initial parameters[f, pfit, kvg, iter, corp, covp, stdresid, Z, r2] = leasqr (x,y, par, F,tol, iter,wt, dp, dFdp, options)
and indeed we get no convergence.I think that's because your function, with the parameter bounds you propose, will not fit the data. I concluded that by plotting your function with some values of parameters in your proposed range:
plot(x,y,'o',x,F(x,[3,15,1]))Perhaps I missed something, but I ran out of time I could spend on it because I had to start by figuring out the small problems with running the code from the problem as you posed it: that's why it's important to crosscheck and test the code you are about to publish, so that others don't have to.
I think that you need to play with the function F and the parameter limits by plotting and inspecting it, to find the reasonable values of initial parameters, in the way I showed above. Good luck and please come back with more questions as you gain experience with this problem.
Greetings p
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