[Pkg-octave-devel] Bug#348480: polyfit breaks down over "large" x values

[Drew Parsons]

Package: octave2.1
Version: 1:2.1.72-8
Severity: normal

There are reports [1-4] over the years on the octave mailing lists about
octave's polyfit function.  When the x-values are "large" (e.g. 1000s
instead of 1s) then the fit at higher orders (e.g. order 10) is completely
screwed up.

Some of the reports [1] suggest prescaling (e.g. divide x-values by 1000)
before fitting. This does work.

Others [2,3] provide a script to fix the problem. Unfortunately they do NOT
work successfully for me (same bad fitting is obtained).

Another [4] claims that the problem is fixed in wpolyfit from octave-forge.
Unfortunately this is in fact NOT the case. wpolyfit gives the same
incorrect result as polyfit.

So I'm filing this bug to document the problem, rather than letting
half-rumoured fixes float littered somewhere on mailing lists. I guess
you'll want to notify upstream if you agree the problem is really.

The misbehaviour can be seen from my attached sample data, scripting as
follows:

	inputData = load( "test.dat" );
    	x = inputData( : , 1 );
      	y = inputData( : , 2 );
      	P = polyfit(x,y,10);
	polyval(P,x);
	
The coefficients in P are strangely all close to zero (< 1E-25).

Rescaling x provides the desired non-zero coefficients and an "exact" fit of
the original data:

	inputData = load( "test.dat" );
    	x = inputData( : , 1 );
      	y = inputData( : , 2 );
	xscaled = x/1000;
      	P = polyfit(xscaled,y,10);
	for k=1:columns(P)
	      power = columns(P)-k;
	      P(k) = P(k) / (1000^power );
	endfor
	polyval(P,x);

It'd be nice if this were to be fixed in polyfit itself, or at least if
wpolyfit would fix it as it's claimed to in [4].


[1] http://www.octave.org/octave-lists/archive/help-octave.1999/msg01008.html
[2] http://www.octave.org/octave-lists/archive/help-octave.1999/msg01027.html
[3] http://www.octave.org/octave-lists/archive/help-octave.1999/msg01052.html
[4] http://www.octave.org/octave-lists/archive/bug-octave.2004/msg00807.html

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Versions of packages octave2.1 depends on:
ii  atlas3-base [liblapack.s 3.6.0-20        Automatically Tuned Linear Algebra
ii  fftw3                    3.0.1-14        library for computing Fast Fourier
ii  lapack3 [liblapack.so.3] 3.0.20000531a-6 library of linear algebra routines
ii  libc6                    2.3.5-11        GNU C Library: Shared libraries an
ii  libgcc1                  1:4.0.2-6       GCC support library
ii  libgfortran0             4.0.2-6         Runtime library for GNU Fortran ap
ii  libhdf5-serial-1.6.4-0c2 1.6.4-4         Hierarchical Data Format 5 (HDF5) 
ii  libncurses5              5.5-1           Shared libraries for terminal hand
ii  libreadline5             5.1-5           GNU readline and history libraries
ii  libstdc++6               4.0.2-6         The GNU Standard C++ Library v3
ii  refblas3 [libblas.so.3]  1.2-8           Basic Linear Algebra Subroutines 3
ii  texinfo                  4.8-4           Documentation system for on-line i
ii  zlib1g                   1:1.2.3-9       compression library - runtime

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