Hi all, I am Nicolas Del Piano, and currently studying the last year of computer science career. I was searching for a GSoC project that involves mathematical concepts, and I found one very interesting. I have experience on python programming and I studied calculus, so I have a background of the problem context. I am interested on the implementation and testing of Levenberg-Marquardt / trust region nonlinear least squares algorithm. Here are some useful links, that I have searched to having a reference about the problem: http://ananth.in/docs/lmtut.pdf (Introduction) www.cs.nyu.edu/~roweis/notes/lm.pdf (Optimization) http://scribblethink.org/Computer/Javanumeric/index.html (java implementation) I would be glad if there is an interested mentor to discuss the issues, talk about the problem and its possible implementations, and provide me some support and guide. Thanks! Regards.
scipy.optimize.leastsq uses a trust-region Levenberg-Marquardt solver from MINPACK. I think one that uses LAPACK subroutine DGELS could be made more efficient. MINPACK has an unoptimized QR factorization and is also not re-entrant (global variables). But the numerical quality and stability of the MINPACK version in undisputed. Sturla Nico Del Piano <ndel314@gmail.com> wrote:
Hi all,
I am Nicolas Del Piano, and currently studying the last year of computer science career. I was searching for a GSoC project that involves mathematical concepts, and I found one very interesting. I have experience on python programming and I studied calculus, so I have a background of the problem context.
I am interested on the implementation and testing of Levenberg-Marquardt / trust region nonlinear least squares algorithm.
Here are some useful links, that I have searched to having a reference about the problem:
<a href="http://ananth.in/docs/lmtut.pdf">http://ananth.in/docs/lmtut.pdf</a> (Introduction) www.cs.nyu.edu/~roweis/notes/lm.pdf (Optimization) <a href="http://scribblethink.org/Computer/Javanumeric/index.html">http://scribblethink.org/Computer/Javanumeric/index.html</a> (java implementation)
I would be glad if there is an interested mentor to discuss the issues, talk about the problem and its possible implementations, and provide me some support and guide.
Thanks!
Regards.
_______________________________________________ SciPy-Dev mailing list SciPy-Dev@scipy.org <a href="http://mail.scipy.org/mailman/listinfo/scipy-dev">http://mail.scipy.org/mailman/listinfo/scipy-dev</a>
This is present already, See http://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.leastsq.h... which wraps: http://www.math.utah.edu/software/minpack/minpack/lmder.html Benny 2014-02-25 16:16 GMT+01:00 Nico Del Piano <ndel314@gmail.com>:
Hi all,
I am Nicolas Del Piano, and currently studying the last year of computer science career. I was searching for a GSoC project that involves mathematical concepts, and I found one very interesting. I have experience on python programming and I studied calculus, so I have a background of the problem context.
I am interested on the implementation and testing of Levenberg-Marquardt / trust region nonlinear least squares algorithm.
Here are some useful links, that I have searched to having a reference about the problem:
http://ananth.in/docs/lmtut.pdf (Introduction) www.cs.nyu.edu/~roweis/notes/lm.pdf (Optimization) http://scribblethink.org/Computer/Javanumeric/index.html (java implementation)
I would be glad if there is an interested mentor to discuss the issues, talk about the problem and its possible implementations, and provide me some support and guide.
Thanks!
Regards.
_______________________________________________ SciPy-Dev mailing list SciPy-Dev@scipy.org http://mail.scipy.org/mailman/listinfo/scipy-dev
25.02.2014 17:45, Benny Malengier kirjoitti:
This is present already, See http://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.leastsq.h...
which wraps: http://www.math.utah.edu/software/minpack/minpack /lmder.html
The current leastsq implementation does not support sparse Jacobians or constraints. MINPACK does dense QR factorizations, and this approach doesn't work well for problems where the number of variables is too big. This was one of our the GSoC topic ideas [1] --- if you have suggestions on how to improve these, please speak up. [1] https://github.com/scipy/scipy/wiki/GSoC-project-ideas -- Pauli Virtanen
2014-02-25 19:25 GMT+01:00 Pauli Virtanen <pav@iki.fi>:
25.02.2014 17:45, Benny Malengier kirjoitti:
This is present already, See
http://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.leastsq.h...
which wraps: http://www.math.utah.edu/software/minpack/minpack /lmder.html
The current leastsq implementation does not support sparse Jacobians or constraints.
Problems with sparse Jacobians could be nice improvement, have not encountered such problems yet, my outputs being typically measurements depending on all parameters. As to constrainst, typically I use: 1. if contstrained on [c,inf], rescale the parameter to p=c+exp(q), with q new parameter 2. if constrained on an interval, rescale the parameter to p=arctan(q) with some offset and scaling for the interval size and start. Results of this are typically good.. One just has to keep in mind that the covariance is then on the transformed parameters. So doing on the optimized variables a run to determine the covariance of the original parameters is a good idea. Doing such transformation in your own code for full control is probably best, but allowing transformations in the python layer is a nice idea. One can alternatively just return a continuous penalty which scales with the distance from the required interval, going to error of 1e15 or so out of the requried interval, and then 1e15 + dist_to_interval e15. Also then, constraining will happen normally good. As to LM, it's actually a simple algorithm. I used to have a C implementation before using python on minpack. Adapting lmder.or a cython implemetation seems not too hard to add sparse. The problem would be a good sparse implementation in fortran, not the LM algorithm. No experience on that. Doing LM in cython should be fast too. Benny
MINPACK does dense QR factorizations, and this approach doesn't work well for problems where the number of variables is too big. This was one of our the GSoC topic ideas [1] --- if you have suggestions on how to improve these, please speak up.
[1] https://github.com/scipy/scipy/wiki/GSoC-project-ideas
-- Pauli Virtanen
_______________________________________________ SciPy-Dev mailing list SciPy-Dev@scipy.org http://mail.scipy.org/mailman/listinfo/scipy-dev
FWIW, One other possiblity for constrained minimization would be to wrap BOBYQA by Powell. (Disclaimer: All I know about it is from skimming this paper www.damtp.cam.ac.uk/user/na/NA_papers/NA2009_06.pdf and talking to people in PyData London last weekend.) As far as I understand, * it's a state of the art minimizer * the original Fortran code is in public domain * a wrapper is available in OpenOpt. Which might be usable for scipy as well (or we may just point users to it). As a side note, we may either want to look into NEWUOA / LINQOA as well: http://mat.uc.pt/~zhang/software.html#powell_software
From a brief reading of the author's comments, it seems that neither of these deals with sparse problems though.
FWIW, Evgeni On Tue, Feb 25, 2014 at 9:04 PM, Benny Malengier <benny.malengier@gmail.com> wrote:
2014-02-25 19:25 GMT+01:00 Pauli Virtanen <pav@iki.fi>:
25.02.2014 17:45, Benny Malengier kirjoitti:
This is present already, See
http://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.leastsq.h...
which wraps: http://www.math.utah.edu/software/minpack/minpack /lmder.html
The current leastsq implementation does not support sparse Jacobians or constraints.
Problems with sparse Jacobians could be nice improvement, have not encountered such problems yet, my outputs being typically measurements depending on all parameters.
As to constrainst, typically I use: 1. if contstrained on [c,inf], rescale the parameter to p=c+exp(q), with q new parameter 2. if constrained on an interval, rescale the parameter to p=arctan(q) with some offset and scaling for the interval size and start.
Results of this are typically good.. One just has to keep in mind that the covariance is then on the transformed parameters. So doing on the optimized variables a run to determine the covariance of the original parameters is a good idea. Doing such transformation in your own code for full control is probably best, but allowing transformations in the python layer is a nice idea.
One can alternatively just return a continuous penalty which scales with the distance from the required interval, going to error of 1e15 or so out of the requried interval, and then 1e15 + dist_to_interval e15. Also then, constraining will happen normally good.
As to LM, it's actually a simple algorithm. I used to have a C implementation before using python on minpack. Adapting lmder.or a cython implemetation seems not too hard to add sparse. The problem would be a good sparse implementation in fortran, not the LM algorithm. No experience on that. Doing LM in cython should be fast too.
Benny
MINPACK does dense QR factorizations, and this approach doesn't work well for problems where the number of variables is too big. This was one of our the GSoC topic ideas [1] --- if you have suggestions on how to improve these, please speak up.
[1] https://github.com/scipy/scipy/wiki/GSoC-project-ideas
-- Pauli Virtanen
_______________________________________________ SciPy-Dev mailing list SciPy-Dev@scipy.org http://mail.scipy.org/mailman/listinfo/scipy-dev
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On Tue, Feb 25, 2014 at 9:25 PM, Evgeni Burovski <evgeny.burovskiy@gmail.com> wrote:
FWIW, One other possiblity for constrained minimization would be to wrap BOBYQA by Powell.
(Disclaimer: All I know about it is from skimming this paper www.damtp.cam.ac.uk/user/na/NA_papers/NA2009_06.pdf and talking to people in PyData London last weekend.)
As far as I understand,
* it's a state of the art minimizer * the original Fortran code is in public domain
I see no indication of this. -- Robert Kern
On Tue, Feb 25, 2014 at 4:37 PM, Robert Kern <robert.kern@gmail.com> wrote:
On Tue, Feb 25, 2014 at 9:25 PM, Evgeni Burovski <evgeny.burovskiy@gmail.com> wrote:
FWIW, One other possiblity for constrained minimization would be to wrap BOBYQA by Powell.
(Disclaimer: All I know about it is from skimming this paper www.damtp.cam.ac.uk/user/na/NA_papers/NA2009_06.pdf and talking to people in PyData London last weekend.)
As far as I understand,
* it's a state of the art minimizer * the original Fortran code is in public domain
I see no indication of this.
The readme says "There are no restrictions on or charges for the use of the software." which may or may not be phrased using enough legal jargon to allow corporations to do whatever they want with it.
2014-02-25 22:37 GMT+01:00 Robert Kern <robert.kern@gmail.com>:
On Tue, Feb 25, 2014 at 9:25 PM, Evgeni Burovski <evgeny.burovskiy@gmail.com> wrote:
FWIW, One other possiblity for constrained minimization would be to wrap BOBYQA by Powell.
(Disclaimer: All I know about it is from skimming this paper www.damtp.cam.ac.uk/user/na/NA_papers/NA2009_06.pdf and talking to people in PyData London last weekend.)
As far as I understand,
* it's a state of the art minimizer * the original Fortran code is in public domain
I see no indication of this.
:-) Apart from that, they are not LM, so if added, should be an extra name in optimize. Looking at it fast, I don't expect the benefits to be that great to warrant moving there myself. Benny
-- Robert Kern _______________________________________________ SciPy-Dev mailing list SciPy-Dev@scipy.org http://mail.scipy.org/mailman/listinfo/scipy-dev
On Tue, Feb 25, 2014 at 9:37 PM, Robert Kern <robert.kern@gmail.com> wrote:
On Tue, Feb 25, 2014 at 9:25 PM, Evgeni Burovski <evgeny.burovskiy@gmail.com> wrote:
FWIW, One other possiblity for constrained minimization would be to wrap BOBYQA by Powell.
(Disclaimer: All I know about it is from skimming this paper www.damtp.cam.ac.uk/user/na/NA_papers/NA2009_06.pdf and talking to people in PyData London last weekend.)
As far as I understand,
* it's a state of the art minimizer * the original Fortran code is in public domain
I see no indication of this.
The very last paragraph of readme.txt in bobyqa.zip from http://mat.uc.pt/~zhang/software.html#bobyqa """ <snip> There are no restrictions on or charges for the use of the software. I hope that the time and effort I have spent on developing the package will be helpful to much research and to many applications. """ IANAL of course :-). At any rate, turns out there's a ticket in scipy tracker for this: https://github.com/scipy/scipy/issues/1477 Evgeni
-- Robert Kern _______________________________________________ SciPy-Dev mailing list SciPy-Dev@scipy.org http://mail.scipy.org/mailman/listinfo/scipy-dev
On Tue, Feb 25, 2014 at 9:48 PM, Evgeni Burovski <evgeny.burovskiy@gmail.com> wrote:
On Tue, Feb 25, 2014 at 9:37 PM, Robert Kern <robert.kern@gmail.com> wrote:
On Tue, Feb 25, 2014 at 9:25 PM, Evgeni Burovski <evgeny.burovskiy@gmail.com> wrote:
FWIW, One other possiblity for constrained minimization would be to wrap BOBYQA by Powell.
(Disclaimer: All I know about it is from skimming this paper www.damtp.cam.ac.uk/user/na/NA_papers/NA2009_06.pdf and talking to people in PyData London last weekend.)
As far as I understand,
* it's a state of the art minimizer * the original Fortran code is in public domain
I see no indication of this.
The very last paragraph of readme.txt in bobyqa.zip from http://mat.uc.pt/~zhang/software.html#bobyqa """ <snip> There are no restrictions on or charges for the use of the software. I hope that the time and effort I have spent on developing the package will be helpful to much research and to many applications. """
Well, that's certainly not public domain. It *might* be a license grant that is intended to be maximally free, but I wouldn't risk it. "use" is not really sufficient. It might refer to simply running the program unmodified, not the additional rights to modify and redistribute that scipy's BSD license explicitly calls for (in addition to, and thus separate and distinct from "use"). When in doubt, ask the original author. -- Robert Kern
As literature study is mentioned on the GSOC page, fort constrained optimization, for reference: http://www.ai7.uni-bayreuth.de/software.htm It is all non-free software (http://www.ai7.uni-bayreuth.de/SOFTWARE_A.pdf), but the papers of Prof Schittkowski are available. It's a pity professors write so much for profit software with tax payers money. Benny 2014-02-26 0:27 GMT+01:00 Robert Kern <robert.kern@gmail.com>:
On Tue, Feb 25, 2014 at 9:48 PM, Evgeni Burovski <evgeny.burovskiy@gmail.com> wrote:
On Tue, Feb 25, 2014 at 9:37 PM, Robert Kern <robert.kern@gmail.com> wrote:
On Tue, Feb 25, 2014 at 9:25 PM, Evgeni Burovski <evgeny.burovskiy@gmail.com> wrote:
FWIW, One other possiblity for constrained minimization would be to wrap BOBYQA by Powell.
(Disclaimer: All I know about it is from skimming this paper www.damtp.cam.ac.uk/user/na/NA_papers/NA2009_06.pdf and talking to people in PyData London last weekend.)
As far as I understand,
* it's a state of the art minimizer * the original Fortran code is in public domain
I see no indication of this.
The very last paragraph of readme.txt in bobyqa.zip from http://mat.uc.pt/~zhang/software.html#bobyqa """ <snip> There are no restrictions on or charges for the use of the software. I hope that the time and effort I have spent on developing the package will be helpful to much research and to many applications. """
Well, that's certainly not public domain. It *might* be a license grant that is intended to be maximally free, but I wouldn't risk it. "use" is not really sufficient. It might refer to simply running the program unmodified, not the additional rights to modify and redistribute that scipy's BSD license explicitly calls for (in addition to, and thus separate and distinct from "use"). When in doubt, ask the original author.
-- Robert Kern _______________________________________________ SciPy-Dev mailing list SciPy-Dev@scipy.org http://mail.scipy.org/mailman/listinfo/scipy-dev
In light of my remark, I see this type of constrained optimization is present in scipy via fmin_slsqp. I did a pull request to add example in the reference on the capabilities and use. Benny 2014-02-28 9:50 GMT+01:00 Benny Malengier <benny.malengier@gmail.com>:
As literature study is mentioned on the GSOC page, fort constrained optimization, for reference: http://www.ai7.uni-bayreuth.de/software.htm
It is all non-free software (http://www.ai7.uni-bayreuth.de/SOFTWARE_A.pdf), but the papers of Prof Schittkowski are available. It's a pity professors write so much for profit software with tax payers money.
Benny
2014-02-26 0:27 GMT+01:00 Robert Kern <robert.kern@gmail.com>:
On Tue, Feb 25, 2014 at 9:48 PM, Evgeni Burovski
<evgeny.burovskiy@gmail.com> wrote:
On Tue, Feb 25, 2014 at 9:37 PM, Robert Kern <robert.kern@gmail.com> wrote:
On Tue, Feb 25, 2014 at 9:25 PM, Evgeni Burovski <evgeny.burovskiy@gmail.com> wrote:
FWIW, One other possiblity for constrained minimization would be to wrap BOBYQA by Powell.
(Disclaimer: All I know about it is from skimming this paper www.damtp.cam.ac.uk/user/na/NA_papers/NA2009_06.pdf and talking to people in PyData London last weekend.)
As far as I understand,
* it's a state of the art minimizer * the original Fortran code is in public domain
I see no indication of this.
The very last paragraph of readme.txt in bobyqa.zip from http://mat.uc.pt/~zhang/software.html#bobyqa """ <snip> There are no restrictions on or charges for the use of the software. I hope that the time and effort I have spent on developing the package will be helpful to much research and to many applications. """
Well, that's certainly not public domain. It *might* be a license grant that is intended to be maximally free, but I wouldn't risk it. "use" is not really sufficient. It might refer to simply running the program unmodified, not the additional rights to modify and redistribute that scipy's BSD license explicitly calls for (in addition to, and thus separate and distinct from "use"). When in doubt, ask the original author.
-- Robert Kern _______________________________________________ SciPy-Dev mailing list SciPy-Dev@scipy.org http://mail.scipy.org/mailman/listinfo/scipy-dev
28.02.2014 12:41, Benny Malengier kirjoitti:
In light of my remark, I see this type of constrained optimization is present in scipy via fmin_slsqp.
Yes, and also COBYLA does constrained optimization. But both are general scalar function minimization, rather than nonlinear least squares. You can of course express NLLSQ as a minimization problem, but there usually is a difference in efficiency. -- Pauli Virtanen
25.02.2014 23:04, Benny Malengier kirjoitti: [clip]
As to constrainst, typically I use: 1. if contstrained on [c,inf], rescale the parameter to p=c+exp(q), with q new parameter 2. if constrained on an interval, rescale the parameter to p=arctan(q) with some offset and scaling for the interval size and start.
Most optimization toolboxes I've seen use projection methods to deal with boundaries in LM. [clip]
As to LM, it's actually a simple algorithm. I used to have a C implementation before using python on minpack. Adapting lmder.or a cython implemetation seems not too hard to add sparse. The problem would be a good sparse implementation in fortran, not the LM algorithm. No experience on that. Doing LM in cython should be fast too.
There's likely no real need to write it in a low-level language, as most of the algorithm should decompose to some matrix algebra. If it doesn't, then writing a sparse version wouldn't be possible... Porting LMDER to Python has been done (a several times), but as such, it doesn't have so much advantage over MINPACK. -- Pauli Virtanen
On 25/02/14 23:13, Pauli Virtanen wrote:
Porting LMDER to Python has been done (a several times), but as such, it doesn't have so much advantage over MINPACK.
It would allow us to use optimized LAPACK for linear least squares, instead of the MINPACK supplied QR routines. Sturla
FWIW I came across a python LM implementation of the minpack LM routine in https://code.google.com/p/astrolibpy/source/browse/mpfit/mpfit.py The license is GPLv3 though. Johann On Tue, Feb 25, 2014 at 7:25 PM, Pauli Virtanen <pav@iki.fi> wrote:
25.02.2014 17:45, Benny Malengier kirjoitti:
This is present already, See
http://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.leastsq.h...
which wraps: http://www.math.utah.edu/software/minpack/minpack /lmder.html
The current leastsq implementation does not support sparse Jacobians or constraints.
MINPACK does dense QR factorizations, and this approach doesn't work well for problems where the number of variables is too big. This was one of our the GSoC topic ideas [1] --- if you have suggestions on how to improve these, please speak up.
[1] https://github.com/scipy/scipy/wiki/GSoC-project-ideas
-- Pauli Virtanen
_______________________________________________ SciPy-Dev mailing list SciPy-Dev@scipy.org http://mail.scipy.org/mailman/listinfo/scipy-dev
This issue does seem to come up regularly. There is a BSD licensed version: https://github.com/newville/lmfit-py For mpfit.py, at one point, I got license permissions for scipy from the original authors, but no one wanted to include it. Has that changed? I haven't followed the issue since 2012. Best, William On Tue, Apr 1, 2014 at 7:57 AM, Johann cohen-tanugi < johann.cohentanugi@gmail.com> wrote:
FWIW I came across a python LM implementation of the minpack LM routine in https://code.google.com/p/astrolibpy/source/browse/mpfit/mpfit.py The license is GPLv3 though. Johann
On Tue, Feb 25, 2014 at 7:25 PM, Pauli Virtanen <pav@iki.fi> wrote:
25.02.2014 17:45, Benny Malengier kirjoitti:
This is present already, See
http://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.leastsq.h...
which wraps: http://www.math.utah.edu/software/minpack/minpack /lmder.html
The current leastsq implementation does not support sparse Jacobians or constraints.
MINPACK does dense QR factorizations, and this approach doesn't work well for problems where the number of variables is too big. This was one of our the GSoC topic ideas [1] --- if you have suggestions on how to improve these, please speak up.
[1] https://github.com/scipy/scipy/wiki/GSoC-project-ideas
-- Pauli Virtanen
_______________________________________________ SciPy-Dev mailing list SciPy-Dev@scipy.org http://mail.scipy.org/mailman/listinfo/scipy-dev
_______________________________________________ SciPy-Dev mailing list SciPy-Dev@scipy.org http://mail.scipy.org/mailman/listinfo/scipy-dev
william ratcliff <william.ratcliff@gmail.com> wrote:
This issue does seem to come up regularly. There is a BSD licensed version: <a href="https://github.com/newville/lmfit-py">https://github.com/newville/lmfit-py</a>
For mpfit.py, at one point, I got license permissions for scipy from the original authors, but no one wanted to include it. Has that changed? I haven't followed the issue since 2012.
I just looked briefly at the code. It seems to use scipy.optimize.leastsq for Levenberg-Marquardt, so what is the extra benefit? Sturla
Sturla Molden <sturla.molden@gmail.com> wrote:
william ratcliff <william.ratcliff@gmail.com> wrote:
This issue does seem to come up regularly. There is a BSD licensed version: <a href="https://github.com/newville/lmfit-py">https://github.com/newville/lmfit-py</a>
For mpfit.py, at one point, I got license permissions for scipy from the original authors, but no one wanted to include it. Has that changed? I haven't followed the issue since 2012.
I just looked briefly at the code. It seems to use scipy.optimize.leastsq for Levenberg-Marquardt, so what is the extra benefit?
For the record: scipy.optimize.leastsq and scipy.optimize.curve_fit are Levenberg-Marquardt solvers. Sturla
On Tue, Jun 17, 2014 at 10:32 AM, Sturla Molden <sturla.molden@gmail.com> wrote:
Sturla Molden <sturla.molden@gmail.com> wrote:
william ratcliff <william.ratcliff@gmail.com> wrote:
This issue does seem to come up regularly. There is a BSD licensed version: <a href="https://github.com/newville/lmfit-py">https://github.com/newville/lmfit-py</a>
For mpfit.py, at one point, I got license permissions for scipy from the original authors, but no one wanted to include it. Has that changed? I haven't followed the issue since 2012.
I just looked briefly at the code. It seems to use scipy.optimize.leastsq for Levenberg-Marquardt, so what is the extra benefit?
For the record: scipy.optimize.leastsq and scipy.optimize.curve_fit are Levenberg-Marquardt solvers.
curve_fit and lmfit are wrappers for Levenberg-Marquardt. What scipy needs, among other things, are more pure optimizers. lmfit allows fancier parameter definitions, imposes constraints through reparameterization and produces more results statistics. The optimizer that it uses is just Levenberg-Marquardt, although IIRC it also wraps other optimizers. Josef
Sturla
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<josef.pktd@gmail.com> wrote:
lmfit allows fancier parameter definitions, imposes constraints through reparameterization and produces more results statistics. The optimizer that it uses is just Levenberg-Marquardt, although IIRC it also wraps other optimizers.
Yes, and since we were talking about Levenberg-Marquardt, trust-region optimizers are among the ones I miss... Among the one-dimensional minimizers Newton-Raphson is a basic method which is missing, though we have it for root-finding. While it is possible to search for the root of the first derivative, but it would be better to have a convergence check for function minimization instead. Multidimensional Newton-Raphson is also missing. Though multidimensional root-finding is dubious business, it is sometimes useful as a minimizer when the Hessian is known. We could probably also use some form of the EM algorithm in scipy.optimize. (Yes I know what to do with it, just post a PR...) Sturla
participants (10)
-
alex -
Benny Malengier -
Evgeni Burovski -
Johann cohen-tanugi -
josef.pktd＠gmail.com -
Nico Del Piano -
Pauli Virtanen -
Robert Kern -
Sturla Molden -
william ratcliff