Polynomials in arbitrary basis

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Polynomials in arbitrary basis

Vladislav Malyshkin
Octave currently has polynomials manipulation functionality
https://octave.org/doc/v4.0.3/Polynomial-Manipulations.html
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 & B.
Let me know if you have any interest.
Vladislav
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 goals.

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Re: Polynomials in arbitrary basis

Juan Pablo Carbajal-2
Hi,

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 <[hidden email]> wrote:

> Octave currently has polynomials manipulation functionality
> https://octave.org/doc/v4.0.3/Polynomial-Manipulations.html
> 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 &
> B.
> Let me know if you have any interest.
> Vladislav
> 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
> goals.
>

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Re: Polynomials in arbitrary basis

Vladislav Malyshkin
Juan,
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  AMuseOfCashFlowAndLiquidityDeficit.20_Sept_2017.zip
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  com/polytechnik/utils/BasisPolynomials.java
  • Gauss--type quadratures calculation in generalized basis com/polytechnik/utils/OrthogonalPolynomialsABasis.java
These API are implemented for Chebyshev, Legendre, HermiteE, Laguerre, Shifted Legendre, Monomials  bases.
Polynomials operations are implemented in com/polytechnik/utils/{Chebyshev,Legendre,HermiteE,Laguerre,LegendreShifted,Monomials}.java
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.

Vladislav

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:
Hi,

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 [hidden email] wrote:
Octave currently has polynomials manipulation functionality
https://octave.org/doc/v4.0.3/Polynomial-Manipulations.html
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 &
B.
Let me know if you have any interest.
Vladislav
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
goals.



polynomial_code.zip (623K) Download Attachment
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Re: Polynomials in arbitrary basis

Juan Pablo Carbajal-2
Hi,

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!

Regards,


On Sun, Jun 17, 2018 at 10:06 PM, Vladislav Malyshkin <[hidden email]> wrote:

> Juan,
> 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
> AMuseOfCashFlowAndLiquidityDeficit.20_Sept_2017.zip
> 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
> com/polytechnik/utils/BasisPolynomials.java
> Gauss--type quadratures calculation in generalized basis
> com/polytechnik/utils/OrthogonalPolynomialsABasis.java
>
> These API are implemented for Chebyshev, Legendre, HermiteE, Laguerre,
> Shifted Legendre, Monomials  bases.
> Polynomials operations are implemented in
> com/polytechnik/utils/{Chebyshev,Legendre,HermiteE,Laguerre,LegendreShifted,Monomials}.java
> 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.
>
> Vladislav
>
> 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:
>
> Hi,
>
> 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 <[hidden email]> wrote:
>
> Octave currently has polynomials manipulation functionality
> https://octave.org/doc/v4.0.3/Polynomial-Manipulations.html
> 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 &
> B.
> Let me know if you have any interest.
> Vladislav
> 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
> goals.
>
>

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Re: Polynomials in arbitrary basis

Vladislav Malyshkin
Juan,
it is now available from https://yadi.sk/d/AtPJ4a8copmZJ?locale=en
the file  polynomial_code.June_17_2018.zip
Vladislav

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

> Hi,
>
> 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!
>
> Regards,
>
>
> On Sun, Jun 17, 2018 at 10:06 PM, Vladislav Malyshkin <[hidden email]> wrote:
>> Juan,
>> 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
>> AMuseOfCashFlowAndLiquidityDeficit.20_Sept_2017.zip
>> 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
>> com/polytechnik/utils/BasisPolynomials.java
>> Gauss--type quadratures calculation in generalized basis
>> com/polytechnik/utils/OrthogonalPolynomialsABasis.java
>>
>> These API are implemented for Chebyshev, Legendre, HermiteE, Laguerre,
>> Shifted Legendre, Monomials  bases.
>> Polynomials operations are implemented in
>> com/polytechnik/utils/{Chebyshev,Legendre,HermiteE,Laguerre,LegendreShifted,Monomials}.java
>> 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.
>>
>> Vladislav
>>
>> 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:
>>
>> Hi,
>>
>> 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 <[hidden email]> wrote:
>>
>> Octave currently has polynomials manipulation functionality
>> https://octave.org/doc/v4.0.3/Polynomial-Manipulations.html
>> 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 &
>> B.
>> Let me know if you have any interest.
>> Vladislav
>> 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
>> goals.
>>
>>


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Re: Polynomials in arbitrary basis

Vladislav Malyshkin
Juan,
generalized basis polynomial code is now also available from two places:
Vladislav

#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:
Juan,
it is now available from https://yadi.sk/d/AtPJ4a8copmZJ?locale=en
the file  polynomial_code.June_17_2018.zip
Vladislav

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

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!

Regards,


On Sun, Jun 17, 2018 at 10:06 PM, Vladislav Malyshkin [hidden email] wrote:
Juan,
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
AMuseOfCashFlowAndLiquidityDeficit.20_Sept_2017.zip
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
com/polytechnik/utils/BasisPolynomials.java
Gauss--type quadratures calculation in generalized basis
com/polytechnik/utils/OrthogonalPolynomialsABasis.java

These API are implemented for Chebyshev, Legendre, HermiteE, Laguerre,
Shifted Legendre, Monomials  bases.
Polynomials operations are implemented in
com/polytechnik/utils/{Chebyshev,Legendre,HermiteE,Laguerre,LegendreShifted,Monomials}.java
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.

Vladislav

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:

Hi,

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 [hidden email] wrote:

Octave currently has polynomials manipulation functionality
https://octave.org/doc/v4.0.3/Polynomial-Manipulations.html
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 &
B.
Let me know if you have any interest.
Vladislav
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
goals.




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Re: Polynomials in arbitrary basis

Juan Pablo Carbajal-2
Hi Vlad,

I suggest the next following steps:

A. If you have time to do it yourself:
1.A Read about linking java and the octave interpreter
https://octave.org/doc/v4.4.0/Java-Interface.html
2.A Prepare a package so we can help with the
testing.https://wiki.octave.org/Creating_packages, you can find some
slides and simple examples here
https://sites.google.com/site/octavecole/my-forms/OctaveHSR_2018.zip?attredirects=0&d=1
Also check other packages with java code, e.g. LTFAT
https://github.com/ltfat/ltfat/tree/master/blockproc

I have never interfaced with Java myself so I have no clue how much
work that is. It seems like it shouldn't be too much.

B. If you do not have time:
1.B Prepare a description of the project
https://wiki.octave.org/Summer_of_Code_Project_Ideas



On Wed, Jun 20, 2018 at 9:01 AM, Vladislav Malyshkin <[hidden email]> wrote:

> Juan,
> generalized basis polynomial code is now also available from two places:
>
> http://www.ioffe.ru/LNEPS/malyshkin/code_polynomials_quadratures.zip
> (referenced from my https://arxiv.org/pdf/1510.05510 paper, page 30)
> https://yadi.sk/d/AtPJ4a8copmZJ?locale=en , the file
> polynomial_code.June_17_2018.zip
>
> Vladislav
>
> #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:
>
> Juan,
> it is now available from https://yadi.sk/d/AtPJ4a8copmZJ?locale=en
> the file  polynomial_code.June_17_2018.zip
> Vladislav
>
> On 06/17/2018 04:21 PM, Juan Pablo Carbajal wrote:
>
> Hi,
>
> 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!
>
> Regards,
>
>
> On Sun, Jun 17, 2018 at 10:06 PM, Vladislav Malyshkin <[hidden email]>
> wrote:
>
> Juan,
> 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
> AMuseOfCashFlowAndLiquidityDeficit.20_Sept_2017.zip
> 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
> com/polytechnik/utils/BasisPolynomials.java
> Gauss--type quadratures calculation in generalized basis
> com/polytechnik/utils/OrthogonalPolynomialsABasis.java
>
> These API are implemented for Chebyshev, Legendre, HermiteE, Laguerre,
> Shifted Legendre, Monomials  bases.
> Polynomials operations are implemented in
> com/polytechnik/utils/{Chebyshev,Legendre,HermiteE,Laguerre,LegendreShifted,Monomials}.java
> 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.
>
> Vladislav
>
> 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:
>
> Hi,
>
> 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 <[hidden email]> wrote:
>
> Octave currently has polynomials manipulation functionality
> https://octave.org/doc/v4.0.3/Polynomial-Manipulations.html
> 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 &
> B.
> Let me know if you have any interest.
> Vladislav
> 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
> goals.
>
>
>
>

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Re: Polynomials in arbitrary basis

Vladislav Malyshkin
Juan,
Right now I have to finish some other things, but in any case regardless of whether the final implementation will be done by me or by somebody else the "Summer_of_Code_Project" need to be written anyway, for the reason it requires an API to be be introduced, and as you know, API selection is a very "political" issue. Below I will try to write my first draft of Generalized Polynomials API proposal, the extended version of which will be added to the "Summer_of_Code_Project".
What do you think if I write API like below? With java-implementation available it will not be of much work either to integrate my existing java code, or re-implement it natively in octave (the code is simple, the most difficult part there - is unit tests, but my java code does have all the unit tests needed).
Vladislav

P.S. proposal example:
Currenty https://octave.org/doc/v4.0.3/Polynomial-Manipulations.html perform polynomial manipulation only in monomial (xk) basis. This proposal to introduce octave class API with the goal to manipulate polynomials in arbitrary basis.

1. In arbitrary Qk(x) basis (e.g. Chebyshev, Hermite, etc), a polynomial is represented as array coefficients
P(x)= a0*Q0(x) + a1*Q1(x) + a2*Q2(x) +a3*Q3(x) + ...
The coefficients a0, a1, a2 are represented as vector elements a = [a0, a1, a2, …, an]; vector (see https://octave.org/doc/v4.2.1/Creating-a-Class.html#Creating-a-Class example, note the order is different from https://octave.org/doc/v4.0.3/Polynomial-Manipulations.html where it is [an, ....,a2,a1,a0]  example)
An instance of GeneralizedPolynomial class to implement the following methods (like com/polytechnik/utils/BasisPolynomials.java)

(return types: s- scalar, [] - vector)
  • [] convertToMonomialFromBasis(a) convert a polynomial in T-basis to the polynomial in monomial basis
  • [] convertToBasisFromMonomial(a) convert a polynomial in monomial basis to the polynomial in T-basis
  • s calculateSum(p,x) calculate sum p[k-1]Qk(x)
  • s calculateSumD1(p,x) calculate sum p[k-1] d/dx Qk(x)
  • s calculateSumD2(p,x) calculate sum p[k-1] d2/dx2 Qk(x)
  • [] differentiate(p) differentiate a polynomial
  • [] Integrate(p) integrate
  • [] getQjQkLinearization(j,k) expand QjQk product as a sum cmQm
  • [] multiplyPQ(p,q) multiplies P*Q
  • [] multiplyAxB(p,a,b) multiplies p*(ax+b)
  • [[],s] sdiv1(p,x0) synthetic division p/(x-x0), returns quotient and remainder
  • [[],[]] sdiv(p,q) synthetic division p/q, returns quotient and remainder
  • [[]] expandNewtonBinomialLike(m,a,b) expand Qm(a(x+b))  as sum ckQk(x)
  • [] getXQmoments(Qmoments) given <Qk(x)> moments calculates <xQk(x)>
  • [] getPQmoments(p,Qmoments) given <Qk(x)> moments and polynomial P(x) calculates <P(x)Qk(x)>
  • [][] getConfederateMatrix(p) given a polynomial, calculate its confederate matrix (used to find polynomial roots)

2. The class GaussQuadratures calculates Gauss --type quadratures working in polynomial basis of GeneralizedPolynomial type.
This way input moments can be of <Qk(x)> type, not necessary <xk>. The methods
  • .... about 10 methods from OrthogonalPolynomialsABasis.java ...



 

On 06/20/2018 03:11 AM, Juan Pablo Carbajal wrote:
Hi Vlad,

I suggest the next following steps:

A. If you have time to do it yourself:
1.A Read about linking java and the octave interpreter
https://octave.org/doc/v4.4.0/Java-Interface.html
2.A Prepare a package so we can help with the
testing.https://wiki.octave.org/Creating_packages, you can find some
slides and simple examples here
https://sites.google.com/site/octavecole/my-forms/OctaveHSR_2018.zip?attredirects=0&d=1
Also check other packages with java code, e.g. LTFAT
https://github.com/ltfat/ltfat/tree/master/blockproc

I have never interfaced with Java myself so I have no clue how much
work that is. It seems like it shouldn't be too much.

B. If you do not have time:
1.B Prepare a description of the project
https://wiki.octave.org/Summer_of_Code_Project_Ideas



On Wed, Jun 20, 2018 at 9:01 AM, Vladislav Malyshkin [hidden email] wrote:
Juan,
generalized basis polynomial code is now also available from two places:

http://www.ioffe.ru/LNEPS/malyshkin/code_polynomials_quadratures.zip
(referenced from my https://arxiv.org/pdf/1510.05510 paper, page 30)
https://yadi.sk/d/AtPJ4a8copmZJ?locale=en , the file
polynomial_code.June_17_2018.zip

Vladislav

#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:

Juan,
it is now available from https://yadi.sk/d/AtPJ4a8copmZJ?locale=en
the file  polynomial_code.June_17_2018.zip
Vladislav

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

Hi,

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!

Regards,


On Sun, Jun 17, 2018 at 10:06 PM, Vladislav Malyshkin [hidden email]
wrote:

Juan,
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
AMuseOfCashFlowAndLiquidityDeficit.20_Sept_2017.zip
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
com/polytechnik/utils/BasisPolynomials.java
Gauss--type quadratures calculation in generalized basis
com/polytechnik/utils/OrthogonalPolynomialsABasis.java

These API are implemented for Chebyshev, Legendre, HermiteE, Laguerre,
Shifted Legendre, Monomials  bases.
Polynomials operations are implemented in
com/polytechnik/utils/{Chebyshev,Legendre,HermiteE,Laguerre,LegendreShifted,Monomials}.java
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.

Vladislav

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:

Hi,

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 [hidden email] wrote:

Octave currently has polynomials manipulation functionality
https://octave.org/doc/v4.0.3/Polynomial-Manipulations.html
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 &
B.
Let me know if you have any interest.
Vladislav
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
goals.





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Re: Polynomials in arbitrary basis

Vladislav Malyshkin
Juan,

I have made a first working octave-integrated version, it is available at https://yadi.sk/d/AtPJ4a8copmZJ?locale=en file polynomial_code.July_05_2018.zip ("official" link http://www.ioffe.ru/LNEPS/malyshkin/code_polynomials_quadratures.zip currently outdated and will be updated to last version soon).
#sha1sum polynomial_code.July_05_2018.zip # last version
161af5c8f718590bf040a26435d18df633bb3eaa  polynomial_code.July_05_2018.zip

Java API was cleaned up/simplified for an easy octave access. Recent versions of octave/matlab have a good java integration functionality.
Once the polynomials_abasis.jar library is added to octave classpath: javaaddpath (["/path/to/dir/FIXME", "/polynomials_abasis.jar"]);
Polynomials manipulation in Chebyshev/Legendre/ShiftedLegendre/Laguerre/HermiteE/Monomials (implemented as
com/polytechnik/utils/BasisPolynomials.java interface) is easily accessible from octave, for usage example see com/polytechnik/utils/LebesgueQuadratures_call_java_example.m, (do in octave):
run LebesgueQuadratures_call_java_example.m
The API has all regular operations (multiplication/synthetic division/differentiation/integration/etc.), which are are implemented for all 6 bases: e.g. to multiply P and Q just do PmulQ=M.B.mult2Pol(P,Q); see polynomials_readme.txt file for short description.

Second available API is com/polytechnik/utils/OrthogonalPolynomialsABasis.java which calculates Gauss/Lebesgue quadratures, Orthogonal polynomials/Christoffel function/etc. uses aforementioned polynomial basis interface. This allows to perform all the calculations not from typical <xk> moments, but from <Qk(x)> moments, where Qk(x) is one 6 polynomial bases implemented. This greatly increase numerical stability and increase range of options available. Besides standard functionality there is an original Lebesgue quadrature functionality (see my paper https://arxiv.org/abs/1807.08197 ) implemented.

There is also pure octave, without java, (a small subset of functionality, very slow, but simple and useful) implementation of Lebesgue quadrature (Gaussian quadrature is special case f(x)=x of Lebesgue quadrature) in com/polytechnik/utils/LebesgueQuadraturesWithEVData.m (do in octave):
run LebesgueQuadratures.m
for demonstration. This octave-class implementation has only Gauss/Lebesgue quadratures implemented, no polynomials of general basis.

Vladislav


On 06/20/2018 04:22 AM, Vladislav Malyshkin wrote:
Juan,
Right now I have to finish some other things, but in any case regardless of whether the final implementation will be done by me or by somebody else the "Summer_of_Code_Project" need to be written anyway, for the reason it requires an API to be be introduced, and as you know, API selection is a very "political" issue. Below I will try to write my first draft of Generalized Polynomials API proposal, the extended version of which will be added to the "Summer_of_Code_Project".
What do you think if I write API like below? With java-implementation available it will not be of much work either to integrate my existing java code, or re-implement it natively in octave (the code is simple, the most difficult part there - is unit tests, but my java code does have all the unit tests needed).
Vladislav

P.S. proposal example:
Currenty https://octave.org/doc/v4.0.3/Polynomial-Manipulations.html perform polynomial manipulation only in monomial (xk) basis. This proposal to introduce octave class API with the goal to manipulate polynomials in arbitrary basis.

1. In arbitrary Qk(x) basis (e.g. Chebyshev, Hermite, etc), a polynomial is represented as array coefficients
P(x)= a0*Q0(x) + a1*Q1(x) + a2*Q2(x) +a3*Q3(x) + ...
The coefficients a0, a1, a2 are represented as vector elements a = [a0, a1, a2, …, an]; vector (see https://octave.org/doc/v4.2.1/Creating-a-Class.html#Creating-a-Class example, note the order is different from https://octave.org/doc/v4.0.3/Polynomial-Manipulations.html where it is [an, ....,a2,a1,a0]  example)
An instance of GeneralizedPolynomial class to implement the following methods (like com/polytechnik/utils/BasisPolynomials.java)

(return types: s- scalar, [] - vector)
  • [] convertToMonomialFromBasis(a) convert a polynomial in T-basis to the polynomial in monomial basis
  • [] convertToBasisFromMonomial(a) convert a polynomial in monomial basis to the polynomial in T-basis
  • s calculateSum(p,x) calculate sum p[k-1]Qk(x)
  • s calculateSumD1(p,x) calculate sum p[k-1] d/dx Qk(x)
  • s calculateSumD2(p,x) calculate sum p[k-1] d2/dx2 Qk(x)
  • [] differentiate(p) differentiate a polynomial
  • [] Integrate(p) integrate
  • [] getQjQkLinearization(j,k) expand QjQk product as a sum cmQm
  • [] multiplyPQ(p,q) multiplies P*Q
  • [] multiplyAxB(p,a,b) multiplies p*(ax+b)
  • [[],s] sdiv1(p,x0) synthetic division p/(x-x0), returns quotient and remainder
  • [[],[]] sdiv(p,q) synthetic division p/q, returns quotient and remainder
  • [[]] expandNewtonBinomialLike(m,a,b) expand Qm(a(x+b))  as sum ckQk(x)
  • [] getXQmoments(Qmoments) given <Qk(x)> moments calculates <xQk(x)>
  • [] getPQmoments(p,Qmoments) given <Qk(x)> moments and polynomial P(x) calculates <P(x)Qk(x)>
  • [][] getConfederateMatrix(p) given a polynomial, calculate its confederate matrix (used to find polynomial roots)

2. The class GaussQuadratures calculates Gauss --type quadratures working in polynomial basis of GeneralizedPolynomial type.
This way input moments can be of <Qk(x)> type, not necessary <xk>. The methods
  • .... about 10 methods from OrthogonalPolynomialsABasis.java ...



 

On 06/20/2018 03:11 AM, Juan Pablo Carbajal wrote:
Hi Vlad,

I suggest the next following steps:

A. If you have time to do it yourself:
1.A Read about linking java and the octave interpreter
https://octave.org/doc/v4.4.0/Java-Interface.html
2.A Prepare a package so we can help with the
testing.https://wiki.octave.org/Creating_packages, you can find some
slides and simple examples here
https://sites.google.com/site/octavecole/my-forms/OctaveHSR_2018.zip?attredirects=0&d=1
Also check other packages with java code, e.g. LTFAT
https://github.com/ltfat/ltfat/tree/master/blockproc

I have never interfaced with Java myself so I have no clue how much
work that is. It seems like it shouldn't be too much.

B. If you do not have time:
1.B Prepare a description of the project
https://wiki.octave.org/Summer_of_Code_Project_Ideas



On Wed, Jun 20, 2018 at 9:01 AM, Vladislav Malyshkin [hidden email] wrote:
Juan,
generalized basis polynomial code is now also available from two places:

http://www.ioffe.ru/LNEPS/malyshkin/code_polynomials_quadratures.zip
(referenced from my https://arxiv.org/pdf/1510.05510 paper, page 30)
https://yadi.sk/d/AtPJ4a8copmZJ?locale=en , the file
polynomial_code.June_17_2018.zip

Vladislav

#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:

Juan,
it is now available from https://yadi.sk/d/AtPJ4a8copmZJ?locale=en
the file  polynomial_code.June_17_2018.zip
Vladislav

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

Hi,

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!

Regards,


On Sun, Jun 17, 2018 at 10:06 PM, Vladislav Malyshkin [hidden email]
wrote:

Juan,
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
AMuseOfCashFlowAndLiquidityDeficit.20_Sept_2017.zip
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
com/polytechnik/utils/BasisPolynomials.java
Gauss--type quadratures calculation in generalized basis
com/polytechnik/utils/OrthogonalPolynomialsABasis.java

These API are implemented for Chebyshev, Legendre, HermiteE, Laguerre,
Shifted Legendre, Monomials  bases.
Polynomials operations are implemented in
com/polytechnik/utils/{Chebyshev,Legendre,HermiteE,Laguerre,LegendreShifted,Monomials}.java
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.

Vladislav

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:

Hi,

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 [hidden email] wrote:

Octave currently has polynomials manipulation functionality
https://octave.org/doc/v4.0.3/Polynomial-Manipulations.html
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 &
B.
Let me know if you have any interest.
Vladislav
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
goals.






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Re: Polynomials in arbitrary basis

Juan Pablo Carbajal-2
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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Re: Polynomials in arbitrary basis

Vladislav Malyshkin
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,