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- To: eigen@xxxxxxxxxxxxxxxxxxx
- Subject: Re: [eigen] Module for orth. Polynomials
- From: Manuel Yguel <manuel.yguel@xxxxxxxxx>
- Date: Mon, 25 Aug 2014 15:05:38 +0200
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On 08/25/2014 10:59 AM, Christoph Hertzberg wrote:
Definitely sounds interesting.
Independent of that, the polynomial module could need some (very
basic) functionality, like polynomial multiplication/division and even
addition (of polynomials with different degree):
I definitely agree and it is on my todo list since a long time.
http://eigen.tuxfamily.org/bz/show_bug.cgi?id=700
Having that, could simplify writing unit tests.
Christoph
On 25.08.2014 10:16, 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