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


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bug #34361: gsl_bspline_knots_greville needs inequality constrained linear least squares

Submitter:  Rhys Ulerich <rhysu>
Submitted:  Thu 22 Sep 2011 08:12:00 PM UTC
Category:  Runtime error Severity:  3 - Normal
Operating System:  All Status:  Need Info
Assigned to:  rhysu Open/Closed:  Open

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>
Group administrator
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

** Added gsl_bspline_knots_greville to allow initializing a B-spline
   workspace so that it best approximates a target set of Greville
   abscissae.  The function facilitates projecting data from fixed
   collocation points onto a B-spline basis.

I apologize for the partial-but-incomplete feature,

Rhys Ulerich <rhysu>
Group administrator


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