Re: leasqr with bounds

[Francesco Potortì]

>I am new to the use of octave and I have tried to use the leasqr function
>for the adjustment of some experimental data. Given the characteristics of
>the adjustment function, some of the parameters to be adjusted must be
>within certain limits (since they have a certain physical meaning). I wanted
>to use the "bounds" option to limit the possible values that these
>parameters can have.
>
>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 =
>
>   10.8900
>    7.2773
>    4.5502
>    2.7086
>    1.7527
>    1.6824
>    2.4977
>    4.1986
>    6.7852
>   10.2573
>
>pfit =
>
>    0.44280
>   -4.94114
>   15.38833
>
>kvg = 1
>iter =  6
>
>Assuming I want parameter 3 to be within the limit -1 and 1
>
>bounds =[-5,5; -5,5; -1,1 ]
>
>it gives me 
>
>[f, pfit, kvg, iter, corp, covp, stdresid, Z, r2] = leasqr (x, y, p, F,tol,
>iter,wt, dp, dFdp, bounds)
> CONVERGENCE NOT ACHIEVED!
>f =
>
>   10.8516
>    7.2616
>    4.5519
>    2.7225
>    1.7732
>    1.7041
>    2.5153
>    4.2067
>    6.7783
>   10.2302
>
>pfit =
>
>    0.44011
>   -4.91026
>   15.32171
>
>kvg = 0
>iter =  6
>
>As I said, this is a function invented to test the operation.
>I have tried with my experimental data and it does not work either.
>
>I expected that by limiting the possible values of parameter 3, the
>iterations would give a function that may not be the best, but that has the
>parameter 3 with values within the allowed ones

I have used leasqr in the past, but never with bounds.  Leasqr is a
complicated beast.  I would try with a more gradual approach.  As far as
I understand, when unbounded you obtain p3=15.3.  Then instead of
forcing [-1,1] bounds try something easier, for example [-15,15] and see
what happens.

Also, try playing with the convergence options, maybe there is a
possibility of increasing the number of iterations, or you should change
the fractional precision or step change?

As a last suggestion, maybe you can sqp, described in Octave's manual at
"Nonlinear programming", or have a look at the many alternatives offered
by the optim package at
<https://octave.sourceforge.io/optim/package_doc/index.html>.  I haev no
experience with any of these alternatives.

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