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Re: Polynomials in arbitrary basis

From: Vladislav Malyshkin
Subject: Re: Polynomials in arbitrary basis
Date: Wed, 20 Jun 2018 03:01:46 -0400
User-agent: Mozilla/5.0 (X11; Linux x86_64; rv:52.0) Gecko/20100101 Thunderbird/52.8.0

generalized basis polynomial code is now also available from two places:

#sha1sum polynomial_code.June_17_2018.zip code_polynomials_quadratures.zip
d8dacf0c0573f850c38978a9fc97d70298e1fa68  polynomial_code.June_17_2018.zip
d8dacf0c0573f850c38978a9fc97d70298e1fa68  code_polynomials_quadratures.zip

On 06/17/2018 04:29 PM, Vladislav Malyshkin wrote:
it is now available from https://yadi.sk/d/AtPJ4a8copmZJ?locale=en
the file  polynomial_code.June_17_2018.zip

On 06/17/2018 04:21 PM, Juan Pablo Carbajal wrote:

There is little use of static zip sent around. Better set up a public
repository (gitlab, bitbucket, etc...) and share that.
I never linked java code to Octave, but since Java is a dependency of
Octave I can imagine it is very simple. Maybe you want to ask around
before investing time in re.writing your code.

I would say that the functionality is very important so if you do noot
have time to make a package of it, then we put it for the next summer
of code... or a bachelor student somewhere!


On Sun, Jun 17, 2018 at 10:06 PM, Vladislav Malyshkin <address@hidden> wrote:
The code is java written, I do not have octave package. Only java.
Earlier version (bundled with other code) is available at
https://yadi.sk/d/AtPJ4a8copmZJ?locale=en file
latest code version (minor API changes & code structure) is attached to this
e-mail: polynomial_code.zip (this is preferred version to use, I did not
release it yet, but changes from Sept 20 1017 version are really minor (few
functions renamed))
There are basically two API of interest to you:

Generalized polynomial basis functionality
Gauss--type quadratures calculation in generalized basis

These API are implemented for Chebyshev, Legendre, HermiteE, Laguerre,
Shifted Legendre, Monomials  bases.
Polynomials operations are implemented in
with built-in selftest (e.g. run java com/polytechnik/utils/Chebyshev to
selftest the class).

There are not that much code there, it may be easier to re-implement that
code natively  in octave, rather than do any java-wrapper, especially
because my quadraures (not polynomial) code call few lapack subs converted
from fortran, it is probably better for octave to call Lapack subs
directly). All my code is under GPL.

Polynomials manipulation and Gauss--type quadratures calculation in
generalized basis is described in https://arxiv.org/pdf/1510.05510 ,
Appendix A & B, page 30.


P.S. To test the code
unzip polynomial_code.zip
javac -g com/polytechnik/*/*java
# then one can run selftest for, say, Legendre Basis & Quadratures
calculation in Legendre basis.
java  com/polytechnik/utils/Legendre
java  com/polytechnik/utils/OrthogonalPolynomialsLegendreBasis
# to run all selftests
java  com/polytechnik/utils/UnitTests

P.P.S. http://www.chebfun.org/docs/guide/chebfun_guide.pdf by Lloyd N.
Trefethen is good, but has different goals.

On 06/17/2018 02:49 PM, Juan Pablo Carbajal wrote:


Sounds interesting. Could you share the repository where you host your code?
Also, you can create a package, compress it and provide an url, this
way anybody can install it from within octave

pkg install http://your.url

needs Octave >= 4.4

On Sat, Jun 16, 2018 at 9:39 PM, Vladislav Malyshkin <address@hidden> wrote:

Octave currently has polynomials manipulation functionality
only in monomials basis: sum ckxk
In practice it is often very convenient to have polynomial represented in
other polynomials basis: sum ckQk(x)
where the basis  Qk(x) is orthogonal polynomials of some kind.
There is my implementation of polynomials manipulation functionality (and
Gauss-type quadratures calculation) in the basis of Chebyshev, Legendre,
Laguerre, Hermite bases.
The code is available under GPL and is java-written (however it will not be
much a problem to rewrite it in C/C++).
You can read about code at https://arxiv.org/pdf/1510.05510 see Appendix A &
Let me know if you have any interest.
P.S. From the other alternative basis software I know only matlab-written
http://www.chebfun.org/ by Alex Townsend, but his project has different

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