Re: [eigen] Module for orth. Polynomials

[Sreekumar Thaithara Balan <tbs1980@xxxxxxxxx>]

Hi all,

This is excellent news. I am very excited about this (and watching your work in bitbucket).

Me, Mark Sauder and  Matt Beal took over excellent work done by Jeff Jenkins on Numerical Integration and I believe we have made good progress. We haven’t made our code public yet. It will be done so on 10th of December. We have very good implementations of Laurie-Gautschi and Piessens methods for computing the Kronrod nodes and weights.  We have also implemented the QAG method from QUADPACK with multi precision support (including on the fly computation of nodes/weights). We have some issues with mpfr types at high precision and we are working with Pavel Holoborodko to sort out these issues. 

I believe there is a lot overlap between our projects and that the codes are complementary. It will be good to have a chat with your development group about possible collaboration on making our codes compatible. Thanks very much.

Best regards,
Sree



> On 3 Dec 2014, at 13:54, <romanus@xxxxxxxxxx> <romanus@xxxxxxxxxx> wrote:
> 
> Hello,
> 
> we've made some progress on our module for orthogonal polynomials in the mean time. If you want to have a look at the current development status you can access the code from here: https://bitbucket.org/xenon/opq
> 
> We've only partly implemented support for high-precision data types, so this part certainly needs quite some more work. Also there's definitely potential for further optimization, e.g. using faster algorithms for the root computations as Claas suggests, combining it with numerical integration modules that Jeff and Sree are working on and much more.
> 
> Best,
> Roman
> 
> On 26 Aug 2014, at 17:14, Sreekumar Thaithara Balan <tbs1980@xxxxxxxxx> wrote:
> 
> I am interested in the orthogonal polynomials modules very much. 
> 
> As Pavel noted below, Jeff and me are involved in developing a numerical integration module (Please see Jeff’s emails into this list for more details). 
> 
> I have already implemented Laurie’s method for calculating Gauss-Kronrad nodes and weights with multi-precision support (https://github.com/tbs1980/GaussKronrod). I am now implementing the Monegato 1978. It will be ready very soon.
> 
> 
> Best,
> Sree
> 
> On 25 Aug 2014, at 11:40, Claas H. Köhler <claas.koehler@xxxxxx> wrote:
> 
> As a side note:
> 
> Some time ago I also implemented a Gauss integration with Legendre Polynomials and found that the
> Goloub-Welsh method is not very effective for the calculaton of the roots. I implemented another
> method (first guess based on heuristic formula followed by Newton like iteration), which usually
> outperformed the Goloub method. If this is of interest, I could submit the code, which is template
> based and should allow for arbitrary precision (I tested up to Quad precision only, though)
> 
> Regards
> Claas
> 
> On 25/08/14 10:38, Pavel Holoborodko wrote:
> This module would be of high value indeed. 
> Especially in combination with multi-precision support.
> 
> Then Eigen would have full spectrum of classic numerical integration methods (and in arbitrary
> precision!).
> (As far as I know, adaptive Guass-Kronrod is being developed as another module for Eigen as well)
> 
> Pavel. 
> 
> 
> On Mon, Aug 25, 2014 at 5:19 PM, Manuel Yguel <manuel.yguel@xxxxxxxxx
> <mailto:manuel.yguel@xxxxxxxxx>> wrote:
> 
>   Great !
>   I think it is a nice thing to have, I am interested to take a look at it.
> 
> 
>   Dr. Ing. Manuel Yguel
>   Porteur du projet StraTagGem
>   36, rue de l'Université
>   67000, Strasbourg.
>   FRANCE
> 
>   Tel:       +33 9 73 52 86 75 <tel:%2B33%20%209%2073%2052%2086%2075>
>   Mobile: +33 6 59 59 17 30 <tel:%2B33%20%206%2059%2059%2017%2030>
> 
> 
>   On 08/25/2014 10:16 AM, Roman Pascal Schärer wrote:
> 
>       Dear Eigen developers and users,
> 
>       we developed a small C++ package  for the computation of orthogonal polynomials (OPQ++) as an
>       unsupported module inside Eigen for our own needs.
> 
>       The main goal of this package is to provide methods to compute an orthogonal set of
>       polynomials for a given weight function. This has been realised with the modified Chebyshev
>       algorithm, which computes the recurrence coefficients of the polynomials. This algorithm
>       makes use of the moments of the weight function, which in general need to be computed using
>       some numerical integration method. For now we provide our own implementations of quadrature
>       formulas (e.q. Gaussian quadratures). With the obtained recurrence coefficients the nodes and
>       weights of a Gaussian quadrature formula for the weight function can be easily computed using
>       e.g. the Golub-Welsch algorithm.
> 
>       Since this package could be easily integrated in the Eigen library, I’d like to ask if there
>       is interest for such a module to be made public. Since it is a rather small module, it could
>       e.g. also be integrated in the “Polynomials Module”..
> 
>       If such interest exists, we would be open for suggestions regarding the API and the
>       implementation of more features such as multi-precision floating point number support etc.
> 
>       Best,
>       Roman
> 
> 
> 
> 
> 
> 
> -- 
> Deutsches Zentrum für Luft- und Raumfahrt e.V. (DLR)
> Institut für Methodik der Fernerkundung | Experimentelle Verfahren | Münchener Str 20| 82234 Weßling
> 
> Dr. Claas H. Köhler
> Telefon 08153 28-1274 | Telefax 08153 28-1337 | claas.koehler@xxxxxx
> 
> www.DLR.de/EOC
> 
> 
> 
>