bugGNU Scientific Library - Bugs: bug #34361, gsl_bspline_knots_greville needs...

 
 

You are not allowed to post comments on this tracker with your current authentification level.

bug #34361: gsl_bspline_knots_greville needs inequality constrained linear least squares

Submitted by:  Rhys Ulerich <rhysu>
Submitted on:  Thu 22 Sep 2011 08:12:00 PM UTC  
 
Category: Runtime errorSeverity: 3 - Normal
Operating System: AllStatus: Need Info
Assigned to: Rhys Ulerich <rhysu>Open/Closed: Open
Release: 

Fri 23 Sep 2011 03:01:39 PM UTC, comment #1:

Having done some more legwork...

It appears that the nonnegative least squares (NNLS), least distance programming (LDP), and linear least squares with inequality constraints (LSI in PROG6) source from Lawson and Hanson appears on Netlib at http://www.netlib.org/lawson-hanson/ and is public domain (see Appendix C's introduction in their text). Others have f2c-ed this code, removed the libf2c build-and-link prereqs by hand, and successfully employed it. For example, the LGPLed old APPSPACK 3.0.1 available at https://software.sandia.gov/appspack/version3/ did so.

I intend to perform the same f2c-then-cleanup task starting directly from the Netlib sources to ensure the license pedigree remains firmly public domain. According to http://www.gnu.org/licenses/gpl-faq.html#CombinePublicDomainWithGPL and http://www.gnu.org/s/gsl/design/gsl-design.html#SEC40, the resulting code can be distributed with the GSL provided that it remains separated from GPL code.

That should give me the LSI solver I need to correctly finish gsl_bspline_knots_greville.

Rhys Ulerich <rhysu>
Project AdministratorIn charge of this item.
Thu 22 Sep 2011 08:12:00 PM UTC, original submission:

A working note...

The new B-spline routine gsl_bspline_knots_greville was added in
r4750, r4751, r4752, r4753, r4754, and r4755. It aims to provide the best B-spline basis to best approximate a given target set of Greville abscissae. The crux of the implementation is minimizing ||Ax-b||_2 for A describing the mapping from breakpoints to the Greville abscissae. It's just least squares.

Having worked with code a bit, I goofed and failed to include the constraint that breakpoints be strictly increasing. As of r4755 the implementation works for "benign" breakpoint requests but produces broken knot vectors for more challenging ones.

The correct implementation would minimize ||Ax-b||_2 subject to Cx>=d where C describes the difference between adjacent breakpoints and d is strictly positive (and likely double-precision epsilon). That falls into the classical "linear least squares with linear inequality constraints" camp and is covered by Lawson and Hanson in Chapter 23 of "Solving least squares problems" published by SIAM.

I need to spend some time investigating the right way to solve such a problem in the context of the GSL (either by implementing classical techniques or reformulating the problem for another constrained solve approach).

In the meantime, I do not wish to release a partially working implementation. I am removing gsl_bspline_knots_greville from the NEWS file and commenting out its mention in the documentation. I will add a link to this bug in the source code.
Once this bug is fixed, the NEWS entry should again be

I apologize for the partial-but-incomplete feature,
Rhys

Rhys Ulerich <rhysu>
Project AdministratorIn charge of this item.

 

No files currently attached

 

Depends on the following items: None found

Items that depend on this one: None found

 

Carbon-Copy List
  • -unavailable- added by rhysu (Submitted the item)
  •  

    Please enter the title of George Orwell's famous dystopian book (it's a date):

     

     

    No Changes Have Been Made to This Item

    Back to the top


    Powered by Savane 3.1-cleanup