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Re: Polynomials in arbitrary basis


From: Vladislav Malyshkin
Subject: Re: Polynomials in arbitrary basis
Date: Tue, 24 Jul 2018 16:34:51 -0400
User-agent: Mozilla/5.0 (X11; Linux x86_64; rv:52.0) Gecko/20100101 Thunderbird/52.8.0

Juan,
Yes, I now I do have a working implementation. For a task for Summer of code project - it can be, say to write a proper package documentation.
Currently there are (mostly independent) three piece of code:
  • Polynomial calculations in generalized basis API and implementation. Look at BasisPolynomials.java API, do you see any issues (a couple of internal methods are not pretty, but these few were written for extremely fast execution in mind and are not supposed to be called from octave). In recent octave it is really easy to call java method, octave calls it directly, no wrapper is needed, and typical multiplication/differentiation/integration/f(x)/Df(x)/etc. can be called clean and simple from octave, see my mult2Pol example.
  • Orthogonal polynomials/quadratures/Christoffel function/etc. relatively an arbitrary measure using one of 6 implemented polynomial bases, the file OrthogonalPolynomialsABasis.java
  • Gauss/Lebesgue quadratures LebesgueQuadraturesWithEVData.m (a small subset of OrthogonalPolynomialsABasis functionality, e.g. there is no multiplication operator, <QjQk> is calculated directly as n2 complexity instead on 2n if multiplication is used. But this LebesgueQuadraturesWithEVData.m code is so small, so simple, octave-native, and works good enough, that many people found it very useful despite all its deficiencies.
I think it is more of "political" issue now: what API to chose and what to include into the package. Look at what I sent you, may be you like/do not like some things. Especially run/look at octave examples LebesgueQuadratures.m and ,LebesgueQuadratures_call_java_example.m  to decide what you like/do not like.

Vladislav


 
On 07/24/2018 03:58 PM, Juan Pablo Carbajal wrote:
Hi Vladislav,

This is pretty cool. Shall I understand then that the Summer of code
project is not necessary anymore?
Give me some time to test you code. The enxt step, I guess, is to put
it into the shape of a package so it can be installed with "pkg
install"

Regards,


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