Re: leasqr with bounds

[Przemek Klosowski]

On 01/25/2018 10:09 PM, mrodrig wrote:
> 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;
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 with---it 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:

[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 
cross-check 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