RE: FW: roots of quartic equation (fwd)

RE: FW: roots of quartic equation (fwd)

[Matthias Winkler]

Dear Andrew,

for what concerns our needs at the moment, we need it for real 
coefficients only.

Cheers,
Matthias

-- 

---------- Forwarded message ----------
Date: Wed, 24 Sep 2003 16:34:41 +0200
From: Marco Cattaneo <Marco.Cattaneo@cern.ch>
To: Matthias Winkler <Matthias.Winkler@cern.ch>
Subject: RE: FW: roots of quartic equation (fwd)

For what it's worth, our application uses only real coefficients

> -----Original Message-----
> From: Matthias Winkler 
> Sent: Wednesday, September 24, 2003 09:08
> To: Marco Cattaneo
> Subject: Re: FW: roots of quartic equation (fwd)
> 
> 
> Hello Marco!
> 
> Fyi, I got this mail today.
> 
> Cheers,
> Matthias
> 
> -- 
> 
> ---------- Forwarded message ----------
> Date: Tue, 23 Sep 2003 15:46:58 -0500 (CDT)
> From: Andrew Steiner <stein@physics.umn.edu>
> To: gsl-discuss@sources.redhat.com
> Cc: Matthias.Winkler@cern.ch
> Subject: Re: FW: roots of quartic equation (fwd)
> 
> Hello all!
> 
> 	Depending on the type of quartic you would like to solve
> (coefficients real or complex?), there are a couple options. For real
> coefficients, the C'ification of rrteq4.F would be pretty 
> straightforward,
> but for complex coefficients you need something more. On the topic of
> cubics, I have found that the GSL implementation of solutions to cubic
> equations tends to be a little more accurate (for random coefficients)
> than CERNLIB.
> 	It is also important to know what kind of quartics you have.
> Most of these routines fail miserably for sufficiently pathological
> choices of coefficients (i.e. small odd-powered coefficients).
> 
> Later,
> Andrew
> 
> ----------------------------------------------------------------------
>  Andrew W. Steiner                   Post-doctoral Research Associate
>  Nuclear Theory Group                University of Minnesota
>  Phone: 612-624-7872                 Fax: 612-624-4875
>  Email: stein@physics.umn.edu        URL: http://umn.edu/~stein178
> ----------------------------------------------------------------------
> 
> Brian Gough writes:
> > Matthias Winkler writes:
> >  > Dear GSL developers!
> >  >
> >  > May I forward you this question about the root of 
> quartic polynomial
> >  > equations in GSL. Will there be a dedicated 
> gsl_poly_solve_quartic
> >  > function?
> >
> > There is an empty space for it -- if someone writes a good
> > implementation it would certainly be added.
> >
> > I wasn't planning to write it myself though.
> >
> > If you specifically want the function within a fixed timescale, my
> > company can offer a GSL maintenance contract that would cover it.
> >
> > --
> > Brian
> 
> 
> 
> 

Re: FW: roots of quartic equation (fwd)

[Andrew Steiner]

Hello all!

	Depending on the type of quartic you would like to solve
(coefficients real or complex?), there are a couple options. For real
coefficients, the C'ification of rrteq4.F would be pretty straightforward,
but for complex coefficients you need something more. On the topic of
cubics, I have found that the GSL implementation of solutions to cubic
equations tends to be a little more accurate (for random coefficients)
than CERNLIB.
	It is also important to know what kind of quartics you have.
Most of these routines fail miserably for sufficiently pathological
choices of coefficients (i.e. small odd-powered coefficients).

Later,
Andrew

----------------------------------------------------------------------
 Andrew W. Steiner                   Post-doctoral Research Associate
 Nuclear Theory Group                University of Minnesota
 Phone: 612-624-7872                 Fax: 612-624-4875
 Email: stein@physics.umn.edu        URL: http://umn.edu/~stein178
----------------------------------------------------------------------

Brian Gough writes:
> Matthias Winkler writes:
>  > Dear GSL developers!
>  >
>  > May I forward you this question about the root of quartic polynomial
>  > equations in GSL. Will there be a dedicated gsl_poly_solve_quartic
>  > function?
>
> There is an empty space for it -- if someone writes a good
> implementation it would certainly be added.
>
> I wasn't planning to write it myself though.
>
> If you specifically want the function within a fixed timescale, my
> company can offer a GSL maintenance contract that would cover it.
>
> --
> Brian

Re: FW: roots of quartic equation (fwd)

[Brian Gough]

Matthias Winkler writes:
 > Dear GSL developers!
 > 
 > May I forward you this question about the root of quartic polynomial 
 > equations in GSL. Will there be a dedicated gsl_poly_solve_quartic 
 > function?

There is an empty space for it -- if someone writes a good
implementation it would certainly be added.

I wasn't planning to write it myself though.

If you specifically want the function within a fixed timescale, my
company can offer a GSL maintenance contract that would cover it.

-- 
Brian

Network Theory Ltd
15 Royal Park
Bristol BS8 3AL
United Kingdom

Tel: +44 (0)117 3179309
Fax: +44 (0)117 9048108
Web: http://www.network-theory.co.uk/

FW: roots of quartic equation (fwd)

[Matthias Winkler]

Dear GSL developers!

May I forward you this question about the root of quartic polynomial 
equations in GSL. Will there be a dedicated gsl_poly_solve_quartic 
function?

Cheers,
Matthias 

-- 

---------- Forwarded message ----------

-----Original Message-----


Hi Antonis,

I have already replaced the two CERNlib calls in the global and local 
algorithms with GSL equivalents. In the RICH we have one remaining, 
which is drteq4 (roots of quartic equation 
http://consult.cern.ch/shortwrups/c208/top.html) in the RichDetTools 
packages. I think this call might be slightly tricky to change to GSL 
since I couldn't find a direct replacement in GSL. The nearest I could 
get was (http://sources.redhat.com/gsl/ref/gsl-ref_6.html#SEC52) 
gsl_poly_complex_solve which solves general n-degree polynominals. The 
funny thing is that, as GSL themselves quote in the manual "The roots of

polynomial equations cannot be found analytically beyond the special 
cases of the quadratic, cubic and quartic equation" but as far as I can 
tell they only provide analytic functions for quadratic and cubic 
equations.

May be we should try the general equation ? - but I am slightly worried 
that since it uses an iterative approach it may not work as well as the 
CERNLIB call. Another (less tidy) possible solution would be to 
transplant the CERNLIB routines into the package, and effectively use a 
private version of the CERNLIB call. What do you think ?

cheers  Chris