Re: [eigen] Numerical Integration module

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Yes, I am happy to (try to) implement the computation of the Gauss-Konrad weights on the fly for a give precision based methods Pavel pointed out earlier in this conversation. Let me do some research and some coding. Any requirements / suggestions are most welcome. I Will update you guys very soon. 


On 3 Aug 2014, at 00:28, Jeff J <complexzeros@xxxxxxxxx> wrote:

Hey Sree (or anyone else),

I have some code written that implements the QAG routine from QUADPACK. It's not ready for distribution, yet, but it's on its way. One of the main issues is that it uses hard-coded weights and abscissae (as in QUADPACK). Would you be interested in implementing the Gauss-Kronrod rules for calculating the weights and abscissae? We need that functionality to make the module precision-independent.

On Wed, Jul 16, 2014 at 10:03 PM, Jeff J <complexzeros@xxxxxxxxx> wrote:
Excellent, thank you! I'll probably be a little slow to get started, but I certainly welcome the help. It will be nice to have input from someone who uses Quadpack for different purposes than myself. I only have immediate technical need (read: funding) for the QAG routine but I'd like to lay the groundwork for more to be implemented by either myself at a later time or others. What is your opinion of Quadpack++? Is there anything particular that you'd change or that you like about the implementation and interface?

Also, if this chatter is not appropriate for this mailing list, I hope someone will let me know.

On Wed, Jul 16, 2014 at 7:24 AM, Sreekumar Thaithara Balan <tbs1980@xxxxxxxxx> wrote:
Hi Jeff,

I am very much interested in this module as I use both Eigen and Quadpack++ in my code.  I am happy to provide help in coding / documenting this module if I get some guidance. 


On Mon, Jul 14, 2014 at 12:32 AM, Jeff J <complexzeros@xxxxxxxxx> wrote:
I am planning on making it precision-independent. I hadn't really looked into it though. It is good to know about mpreal. That will be convenient. Thanks for reaching out!

On Sat, Jul 12, 2014 at 10:32 PM, Pavel Holoborodko <pavel@xxxxxxxxxxxxxxx> wrote:
Hi Jeff, 

I am interested in such extension.

Do you plan to make it precision-independent, so that it can compute with any desired precision using multiple-precision scalar types (e.g. "mpreal")?
(most of the code in Eigen is precision-independent and "mpreal" is included in distribution).

The main obstacle for this is that QUADPACK uses pre-computed coefficients in "double" precision only.

So that we have to implement additional algorithms to compute Gauss-Kronrod nodes & weights for (any) required precision on the fly.

The are several algorithms to generate GK:

D. Laurie (1997). Calculation of Gauss-Kronrod Quadrature Rules. Mathematics of Computation, 66(219).
G. Monegato (1978). Some remarks on the construction of extended Gaussian quadrature rules. Mathematics of Computation, 32(141).

Here is one of the (unfinished) attempts to implement Monegato method:

I am ready to help with any "mpreal"-related questions (as I am its author).

Thank you,

On Sat, Jul 12, 2014 at 2:38 AM, Jeff J <complexzeros@xxxxxxxxx> wrote:
I'm planning on converting some QUADPACK code to the Eigen paradigm for my own purposes. Is there interest for this in the Eigen community? If so, I'm interested in hearing thoughts/requests on implementation and API.

Sreekumar Thaithara Balan
Research Associate in Cosmology
University College London

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