Re: [eigen] Module for orth. Polynomials

[<romanus@xxxxxxxxxx>]

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






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