lsqnonneg is not benchmarked against other code. I’m unaware of any results comparisons with TSNNLS or other software, although I’m sure they exist somewhere.

You might want to look for comparisons of accuracy as well, if it is a concern. From the short description, it says that it uses a Cholesky factorization, which leads me to believe that the normal equations (including

A'*A

) are explicitly formed. This can be bad if A is ill-conditioned.

I’m also sure you can make a MEX wrapper to call this code as well.

Regards,
+Steve

The code TSNNLS claims to be substantially faster than the matlab implementation (as of the 2009 writing presumably) with comparable solutions.
http://www.jasoncantarella.com/webpage/index.php?title=Tsnnls
Have you compared the most recent matlab lsqnonneg with the speed and results of this code, or any others, or is the matlab implementation developed without reference to other codes? If these comparisons have been done, do you know where we can find a report about them, and is it possible to run these codes through a mex wrapper from within matlab?

Thanks!

In MATLAB I can think of some workarounds that may help you.

(1) If your energy constraint is linear (this is not likely but may be you can linearize it) you can append it to the pair C,d in lsqnonneg(C,d). Note that at the end lsqnonneg will reduce NORM(d-C*X): your linear constraint may be satisfied at this point (no guarantees, though). Another note: if you have a linear inequality, don’t forget to add a slack variable to make your constraint an equality.

(2) If you cannot (don’t want to) linearize your energy constraint, you can use fminsearch by creating your own objective function and adding your energy constraint with a penalty parameter in front, i.e. something like
min NORM(d-C*X) + aPenParameter * g(X)
where g(X) = 0.

I hope this helps.
Best Regards,
Derya

Thanks for your contribution on the lsqnonneg. It does help me a lot. I am currently looking into some problem invovled with minimizing the standard non-negative least squares and an extra constraint, e.g. the energy constraint to smooth the spikes provided by the nnls and the misfit derived from the modified minimization equation would be a bit larger than the standard nnls. Is there any function built-in matlab could do this?

Thank you,
Jing

lsqnonneg was upgraded in version R2008b; it now uses sparse linear algebra if the
matrix is sparse (it uses “\”, backslash).

R2008b Release notes:
http://www.mathworks.com/access/helpdesk/help/techdoc/rn/brqyzsl-1.html
(See “Upgrades to lsqnonneg”.)

-Marcelo

I’m not aware of one. We’d love to have your contribution on MATLAB Central File Exchange if/when you have one!

–Loren

Do you happen to know if there is an alternative version of lsqnonneg which will handle large, sparse matrices?

The current version generates a full matrix at line 159, so is causing me memory issues.

I’ll work on one if there’s not an algorithm floating around… in that event, I’ll send it to you once I finish (IF I finish!).

Kind regards

Tom Clark

I don’t have anything. You can check our documentation and the book I cite above.

–Loren