I switched to git from mercurial about two years ago. See here why I switched and here my experience after 4 months. Back then I was unsure, whether git will win, but I thought it has a bigger momentum. Well, I think that now it's quite clear that git has already won. Pretty much everybody that I collaborate with is using git now.
I use github everyday, and now thanks to github pull requests, I think it's the best collaboration platform out there (compared to Google Code, Sourceforge, Bitbucket or Launchpad).
I think it's partly because the github guys have a clear vision of what has to be done in order to make collaboration more easier and they do it, but more importantly that git branches is the way to go, as well as other git features, that are "right" from the beginning (branches, interactive rebase, and so on), while other VCS like bzr and mercurial simply either don't have them, or are getting them, but it's hard to get used to it (for example mercurial uses the "mercurial queues", and I think that is the totally wrong approach to things).
Anyway, this is just my own personal opinion. I'll be happy to discuss it in the comments, if you disagree.
Sunday, October 31, 2010
Friday, August 13, 2010
Week Aug 9 - 13
On Monday I learned fwrap (excellent piece of software btw), there were a few minor technical issues, that I communicated with Kurt on the fwrap mailinglist and I also send him a simple patch, so that it works fine for my fortran code (functions returning the value itself, instead of a tuple of length 1).
Then I took my old fortran based shooting method solvers that I wrote couple years ago and wrapped them using fwrap and run couple simulations against my FE solver.
On Tuesday we had a lunch with all the advisors and students and the llnl director and a little presentation about what we did.
On Wednesday I run shooting method calculations for 50 states of silver, both for selfconsistent DFT potential and Z/r potential. I then also run the FE solver for the same DFT potential and compared results. There are lots of small technical issues, for example I had to use cubic splines to interpolate the potential, play with the mesh for the shooting method and so on.
However, the shooting method and FE agrees to every single printed digit, after making sure that the mesh is ok for both methods. For all potentials that I tried. That's very cool.
In the process of it, I also wrote a patch to SymPy to calculate exact energies for the Hydrogen atom, both from Schroedinger and Dirac equations. I still need to polish it a bit.
On Thursday I run couple more calculations and setup a poster and had a poster session, it was two hours, and I think around 7 people (not counting other students and people from our group) stopped by and talked with me about it, so I was very happy. Being able to solve radial Schroedinger and especially Dirac equations robustly is something that several people in the lab would really need.
Today I talked little bit (finally) about some Green functions in QM and QFT with a postdoc in the Quantum Simulations group, that I always wanted to, but didn't have time before, then packed my things and went back to Reno.
My plan for the next week(s) is to wrap up what I did and put it into articles. I already have enough material for some articles, so it has to be done. In parallel, I'd like to finish the FE Dirac solver, the coding is done, but now I need to play with adaptivity and also investigate if we are getting the spurious states, that other people are getting when using b-splines.
Then I took my old fortran based shooting method solvers that I wrote couple years ago and wrapped them using fwrap and run couple simulations against my FE solver.
On Tuesday we had a lunch with all the advisors and students and the llnl director and a little presentation about what we did.
On Wednesday I run shooting method calculations for 50 states of silver, both for selfconsistent DFT potential and Z/r potential. I then also run the FE solver for the same DFT potential and compared results. There are lots of small technical issues, for example I had to use cubic splines to interpolate the potential, play with the mesh for the shooting method and so on.
However, the shooting method and FE agrees to every single printed digit, after making sure that the mesh is ok for both methods. For all potentials that I tried. That's very cool.
In the process of it, I also wrote a patch to SymPy to calculate exact energies for the Hydrogen atom, both from Schroedinger and Dirac equations. I still need to polish it a bit.
On Thursday I run couple more calculations and setup a poster and had a poster session, it was two hours, and I think around 7 people (not counting other students and people from our group) stopped by and talked with me about it, so I was very happy. Being able to solve radial Schroedinger and especially Dirac equations robustly is something that several people in the lab would really need.
Today I talked little bit (finally) about some Green functions in QM and QFT with a postdoc in the Quantum Simulations group, that I always wanted to, but didn't have time before, then packed my things and went back to Reno.
My plan for the next week(s) is to wrap up what I did and put it into articles. I already have enough material for some articles, so it has to be done. In parallel, I'd like to finish the FE Dirac solver, the coding is done, but now I need to play with adaptivity and also investigate if we are getting the spurious states, that other people are getting when using b-splines.
Friday, August 6, 2010
Week Aug 2 - 6
This week I essentially only worked on my LLNL poster, which I finally finished about two hours ago. I have created a web page for it:
http://certik.github.com/ccms-10-poster/
where you can download pdf, sources, I also put there some relevant info and links.
It turned out to be a lot more work than I expected (well, as usual), but we were very thorough with John and in the process I discovered several bugs in my program, so I am glad we did it. I used to generate all the plots by hand, by manually adjusting all the parameters in the Python script (like atomic number, mesh parameters, element orders, adaptivity parameters, error tolerance and so on). Essentially I had to remember all these parameters for each of the plots (about 10 of them). Then I settled to have a Python dictionary, that holds all the parameters, and then I just pass them to a radial_schroedinger_equation_adapt(params, error_tol=1e-8) function.
Here are example of the parameters:
I mean, this is kind of obvious if you think about it, but for some reason I didn't do that at all at the beginning, because I thought --- I'll just run this once and I am done with it. But I had to run it like 20x, e.g. regenerating he plots, then creating a table about meshes, then redoing the table after changing the error tolerance, and so on.
Besides that I also got permission to release my code, so I'll go over it in the coming days and generate nice patches against Hermes1D.
Also in the process of creating the poster, I played a lot with p-FEM, uniform-p-FEM, hp-FEM and h-FEM and I will keep playing with that. It's clear to me now, that our current Hermes1D is not optimal. Especially the convergence of hp-FEM and p-FEM (as it is implemented right now) greatly depends on the initial mesh.
Nevertheless, even with the above limitations, hp-FEM seems to be really good if you don't a-priori know anything about the problem/mesh. One should not make any deep conclusions in 1D (it might be a bit different in 2D and 3D, and also I only did couple test problems), but from my experience so far, hp-FEM is a really good choice, if you just want to solve the problem and get a decent convergence (way better than h-FEM, and in general about the same as uniform-p-FEM with optimized mesh).
Another conclusion is that uniform-p-FEM (also called spectral element method), if you optimize the mesh for the problem, is very fast. All you have to do is increase the polynomial order and it goes very straight on the convergence graphs, it's very hard to beat. Also, and that I would like to write in the coming days, the algorithm for optimizing the mesh is really simple: just solve it with high "p", then play with the mesh parameters (for logarithmic mesh, there are only 2 parameters --- number of elements, and a ratio of first vs. last element), so that the eigenvalues (that one is interested in) are converged (with given accuracy) and optimize it wrt DOFs. The algorithm can also "look" at the convergence graphs and make sure it's steep enough. For atomic problems, my experience shows that the logarithmic mesh is good enough (as long as you optimize it). The advantage is that you do this once, and then (for close enough potentials in the Schroedinger equation), you just increase "p", and it's very robust and fast (no need for reference mesh, or trial refinements and so on).
When I get back to Reno, we'll do more research on hp-FEM with Pavel and I think this is not the last word to say. We need to review how we choose the candidates for eigenvectors, especially "p" vs "hp" and make it more robust. We'll see.
http://certik.github.com/ccms-10-poster/
where you can download pdf, sources, I also put there some relevant info and links.
It turned out to be a lot more work than I expected (well, as usual), but we were very thorough with John and in the process I discovered several bugs in my program, so I am glad we did it. I used to generate all the plots by hand, by manually adjusting all the parameters in the Python script (like atomic number, mesh parameters, element orders, adaptivity parameters, error tolerance and so on). Essentially I had to remember all these parameters for each of the plots (about 10 of them). Then I settled to have a Python dictionary, that holds all the parameters, and then I just pass them to a radial_schroedinger_equation_adapt(params, error_tol=1e-8) function.
Here are example of the parameters:
params_hydrogen_p_L = dict(l=0, Z=1, a=0, b=100, el_num=4, el_order=1,
eig_num=3, mesh_uniform=False, mesh_par1=20, adapt_type="p",
eqn_type="R")
params_hydrogen_p_U = dict(l=0, Z=1, a=0, b=100, el_num=4, el_order=2,
eig_num=3, mesh_uniform=True, adapt_type="p", eqn_type="R")
params_hydrogen_hp_U = dict(l=0, Z=1, a=0, b=100, el_num=4, el_order=2,
eig_num=3, mesh_uniform=True, adapt_type="hp", eqn_type="R")
params_hydrogen_h_U = dict(l=0, Z=1, a=0, b=100, el_num=4, el_order=6,
eig_num=3, mesh_uniform=True, adapt_type="romanowski",
eqn_type="rR")
params_silver_p_L = dict(l=0, Z=47, a=0, b=150, el_num=4, el_order=13,
eig_num=50, mesh_uniform=False, mesh_par1=35, adapt_type="p",
eqn_type="R")
params_silver_hp_L = dict(l=0, Z=47, a=0, b=150, el_num=4, el_order=13,
eig_num=50, mesh_uniform=False, mesh_par1=35, adapt_type="hp",
eqn_type="R")
I mean, this is kind of obvious if you think about it, but for some reason I didn't do that at all at the beginning, because I thought --- I'll just run this once and I am done with it. But I had to run it like 20x, e.g. regenerating he plots, then creating a table about meshes, then redoing the table after changing the error tolerance, and so on.
Besides that I also got permission to release my code, so I'll go over it in the coming days and generate nice patches against Hermes1D.
Also in the process of creating the poster, I played a lot with p-FEM, uniform-p-FEM, hp-FEM and h-FEM and I will keep playing with that. It's clear to me now, that our current Hermes1D is not optimal. Especially the convergence of hp-FEM and p-FEM (as it is implemented right now) greatly depends on the initial mesh.
Nevertheless, even with the above limitations, hp-FEM seems to be really good if you don't a-priori know anything about the problem/mesh. One should not make any deep conclusions in 1D (it might be a bit different in 2D and 3D, and also I only did couple test problems), but from my experience so far, hp-FEM is a really good choice, if you just want to solve the problem and get a decent convergence (way better than h-FEM, and in general about the same as uniform-p-FEM with optimized mesh).
Another conclusion is that uniform-p-FEM (also called spectral element method), if you optimize the mesh for the problem, is very fast. All you have to do is increase the polynomial order and it goes very straight on the convergence graphs, it's very hard to beat. Also, and that I would like to write in the coming days, the algorithm for optimizing the mesh is really simple: just solve it with high "p", then play with the mesh parameters (for logarithmic mesh, there are only 2 parameters --- number of elements, and a ratio of first vs. last element), so that the eigenvalues (that one is interested in) are converged (with given accuracy) and optimize it wrt DOFs. The algorithm can also "look" at the convergence graphs and make sure it's steep enough. For atomic problems, my experience shows that the logarithmic mesh is good enough (as long as you optimize it). The advantage is that you do this once, and then (for close enough potentials in the Schroedinger equation), you just increase "p", and it's very robust and fast (no need for reference mesh, or trial refinements and so on).
When I get back to Reno, we'll do more research on hp-FEM with Pavel and I think this is not the last word to say. We need to review how we choose the candidates for eigenvectors, especially "p" vs "hp" and make it more robust. We'll see.
Saturday, July 31, 2010
Week July 26 - 30
This week I have been wrapping up my work at LLNL and trying to generate some comparisons between different approaches to adapt to multiple eigenvectors at once.
It turns out that most of the issues are in the way we create the new mesh for the next adaptivity iteration, in particular, how do we choose which candidates to refine. I have tried to converge to the lowest eigenvector (as well as to any other eigenvector too), to the sum of the eigenvectors, to each eigenvector individually and taking the union of the meshes and so on. I have also implemented the uniform p-FEM as well as tried p-FEM and hp-FEM using the approaches I mentioned above.
It seems to be crucial to have a good initial mesh, at least for p-FEM. If I use a good mesh and p-adaptivity, I am able to get the best results so far. In principle hp adaptivity should be at least as good, but our current approach doesn't show it yet. Hopefully we'll manage to make it work.
Besides that I have also implemented H1 norms for the Function class (based on Fekete points) by calculating coefficients with regards to a FE basis and some other little things.
It turns out that most of the issues are in the way we create the new mesh for the next adaptivity iteration, in particular, how do we choose which candidates to refine. I have tried to converge to the lowest eigenvector (as well as to any other eigenvector too), to the sum of the eigenvectors, to each eigenvector individually and taking the union of the meshes and so on. I have also implemented the uniform p-FEM as well as tried p-FEM and hp-FEM using the approaches I mentioned above.
It seems to be crucial to have a good initial mesh, at least for p-FEM. If I use a good mesh and p-adaptivity, I am able to get the best results so far. In principle hp adaptivity should be at least as good, but our current approach doesn't show it yet. Hopefully we'll manage to make it work.
Besides that I have also implemented H1 norms for the Function class (based on Fekete points) by calculating coefficients with regards to a FE basis and some other little things.
Friday, July 23, 2010
Week July 19 - 23
This week I have learned how projections work in detail and wrote it up here:
http://theoretical-physics.net/dev/src/math/la.html
including all proofs (that orthogonal projection finds the closest vector and so on). At the end of the notes I have calculated some examples in 1D, so that one can see that indeed it doesn't depend on the basis and that the basis doesn't even have to be orthogonal. Then one has to use this approach to calculate the coefficients:
http://theoretical-physics.net/dev/src/math/la.html#nonorthogonal-basis
I have then implemented it in h1d. Due to the lack of time, I am now developing everything in my private branch. I'll obtain the permission in about 2 or 3 weeks, so then I'll push it into the master.
Besides that I have implemented Chebyshev points for orders greater than 48, for which I don't have exact Fekete points anymore (it'd be just a matter of running my sympy script longer, but I was hitting some accuracy issues when solving those large polynomials numerically -- one needs to obtain all roots, so Chebyshev points are ok for now). So I can now represent arbitrary polynomials in 1D.
I have implemented powering of the discrete function, it automatically determines which polynomial order it has to use and creates a new discrete function (the power) on the new mesh. I wrote lots of tests for that, and I hit an interesting bug, that my naive comparison code:
was not good enough anymore for larger numbers and I had to read some documentation, and implement the following function:
Then I implemented the global H1 and L2 projections, so far the projected function is hardwired, I still need to allow the user to specify any discrete function to be projected. I need to precalculate it and so on.
I wrote bunch of tests for the projections and powers and I always discovered some bugs by writing more tests, so the progress is slow, but at least I can trust the code that is tested.
I also helped Pavel to fix couple segfaults, as well as some other things.
http://theoretical-physics.net/dev/src/math/la.html
including all proofs (that orthogonal projection finds the closest vector and so on). At the end of the notes I have calculated some examples in 1D, so that one can see that indeed it doesn't depend on the basis and that the basis doesn't even have to be orthogonal. Then one has to use this approach to calculate the coefficients:
http://theoretical-physics.net/dev/src/math/la.html#nonorthogonal-basis
I have then implemented it in h1d. Due to the lack of time, I am now developing everything in my private branch. I'll obtain the permission in about 2 or 3 weeks, so then I'll push it into the master.
Besides that I have implemented Chebyshev points for orders greater than 48, for which I don't have exact Fekete points anymore (it'd be just a matter of running my sympy script longer, but I was hitting some accuracy issues when solving those large polynomials numerically -- one needs to obtain all roots, so Chebyshev points are ok for now). So I can now represent arbitrary polynomials in 1D.
I have implemented powering of the discrete function, it automatically determines which polynomial order it has to use and creates a new discrete function (the power) on the new mesh. I wrote lots of tests for that, and I hit an interesting bug, that my naive comparison code:
assert abs(x-y) < eps
was not good enough anymore for larger numbers and I had to read some documentation, and implement the following function:
@vectorize(0, 1)
def feq(a, b, max_relative_error=1e-12, max_absolute_error=1e-12):
a = float(a)
b = float(b)
# if the numbers are close enough (absolutely), then they are equal
if abs(a-b) < max_absolute_error:
return True
# if not, they can still be equal if their relative error is small
if abs(b) > abs(a):
relative_error = abs((a-b)/b)
else:
relative_error = abs((a-b)/a)
return relative_error <= max_relative_error
Then I implemented the global H1 and L2 projections, so far the projected function is hardwired, I still need to allow the user to specify any discrete function to be projected. I need to precalculate it and so on.
I wrote bunch of tests for the projections and powers and I always discovered some bugs by writing more tests, so the progress is slow, but at least I can trust the code that is tested.
I also helped Pavel to fix couple segfaults, as well as some other things.
Monday, July 19, 2010
Theoretical Physics Reference Book
Today I fulfilled my old dream --- I just created my first book! Here is how it looks like:
More images
here.
Here is the source code of the book: http://github.com/certik/theoretical-physics, the repository contains a branch 'master' with the code and 'gh-pages' with the generated html pages, that are hosted at github, at the url theoretical-physics.net.
Then I published the book at Lulu: http://www.lulu.com/product/hardcover/theoretical-physics-reference/11612144, I wanted a hardcover book, so I setup a project at Lulu, used some Lulu templates for the cover and that was it. Lulu's price for the book is $19.20 (166 black & white pages, hardcover), then I can set my own price and the rest of the money probably goes to me. I set the price to $20, because Lulu has free shipping for orders $20 or more. You can also download the pdf (for free) at the above link (or just use my git repository). So far this didn't cost me anything.
I have then ordered the book myself (just like anybody else would, at the above address) and it arrived today. It's a regular hardcover book. Beautiful, you can browse the pictures above. It smells deliciously (that you have to believe me). And all that it cost me was $19.20.
As for the contents itself, you can browse it online at theoretical-physics.net, essentially it's most of my physics notes, that I collected over the years. I'd like to treat books like software --- release early release often. This is my first release and I would call it beta. The main purpose of it was to see if everything goes through, how long it takes (the date inside the book is July 4, 2010, I created and ordered it on July 5, got the physical book on July 19) and what the quality is (excellent). I also wanted to see how the pages correspond to the pdf (you can see for yourself on the photos, click on the picasa link above).
Now I need to improve the first pages a bit, as well as the last pages, improve the index, write some foreword and so on. I also need to think how to better organize the contents itself and generally improve it. I also need to figure out some versioning scheme, so far this is version 0.1. I think I'll do edition 1, edition 2, edition 3, and so on. And whenever I feel that I have added enough new content, I'll just publish it as a new edition. So if you want to buy it, I suggest to wait for my 1.0 version, that will have the mentioned improvements.
It'd be also cool to have all the editions online somehow and create nice webpages for it (currently theoretical-physics.net points directly to the book html itself).
So far the book is just text. I still need to figure out how to handle pictures and also whether or not to use program examples (in Python, using sympy, scipy, etc.). So far I am inclining not to put there any program codes, as then I don't need to maintain them.
Overall I am very pleased with the quality, up to some minor issues that I mentioned above, everything else end up just fine. I think we have come a long way from the discovery of the printing press. Anybody can now create a book for free, and if you want to hold the hardcopy in your hands, it costs around $20. You don't need to order certain amounts of books, nor partner with some publisher etc. I think that's just awesome.
More images
here.
Here is the source code of the book: http://github.com/certik/theoretical-physics, the repository contains a branch 'master' with the code and 'gh-pages' with the generated html pages, that are hosted at github, at the url theoretical-physics.net.
Then I published the book at Lulu: http://www.lulu.com/product/hardcover/theoretical-physics-reference/11612144, I wanted a hardcover book, so I setup a project at Lulu, used some Lulu templates for the cover and that was it. Lulu's price for the book is $19.20 (166 black & white pages, hardcover), then I can set my own price and the rest of the money probably goes to me. I set the price to $20, because Lulu has free shipping for orders $20 or more. You can also download the pdf (for free) at the above link (or just use my git repository). So far this didn't cost me anything.
I have then ordered the book myself (just like anybody else would, at the above address) and it arrived today. It's a regular hardcover book. Beautiful, you can browse the pictures above. It smells deliciously (that you have to believe me). And all that it cost me was $19.20.
As for the contents itself, you can browse it online at theoretical-physics.net, essentially it's most of my physics notes, that I collected over the years. I'd like to treat books like software --- release early release often. This is my first release and I would call it beta. The main purpose of it was to see if everything goes through, how long it takes (the date inside the book is July 4, 2010, I created and ordered it on July 5, got the physical book on July 19) and what the quality is (excellent). I also wanted to see how the pages correspond to the pdf (you can see for yourself on the photos, click on the picasa link above).
Now I need to improve the first pages a bit, as well as the last pages, improve the index, write some foreword and so on. I also need to think how to better organize the contents itself and generally improve it. I also need to figure out some versioning scheme, so far this is version 0.1. I think I'll do edition 1, edition 2, edition 3, and so on. And whenever I feel that I have added enough new content, I'll just publish it as a new edition. So if you want to buy it, I suggest to wait for my 1.0 version, that will have the mentioned improvements.
It'd be also cool to have all the editions online somehow and create nice webpages for it (currently theoretical-physics.net points directly to the book html itself).
So far the book is just text. I still need to figure out how to handle pictures and also whether or not to use program examples (in Python, using sympy, scipy, etc.). So far I am inclining not to put there any program codes, as then I don't need to maintain them.
Overall I am very pleased with the quality, up to some minor issues that I mentioned above, everything else end up just fine. I think we have come a long way from the discovery of the printing press. Anybody can now create a book for free, and if you want to hold the hardcopy in your hands, it costs around $20. You don't need to order certain amounts of books, nor partner with some publisher etc. I think that's just awesome.
Friday, July 16, 2010
Week June 12 -- July 16
This week I was implementing hp-adaptivity based on H1 projections first for the ground state and later for other states.
It took me the whole week to debug things and I am still not done. There were issues with normalizing vectors and other problems. I am now able to converge any individual vector and that seems to work fine, but I am still not able to converge multiple vectors somehow.
I spent also some time with speeding up my implementation of fekete points, and I have implemented the fast evaluation based on Lagrange interpolation polynomials. In general, I made for example the l2_norm() method about 10x faster. I think it's about as fast now as if it was written in C++ directly. The main loops are now optimized C without any Python C/API calls.
My plan is now to implement taking squares of the solutions (exactly), and so on, and projecting it back to the original mesh. I'll try converging to that. At the same time, I'll try to converge to multiple eigenvalues. Hermes1d needs some improvements, that take me quite some time to implement.
It took me the whole week to debug things and I am still not done. There were issues with normalizing vectors and other problems. I am now able to converge any individual vector and that seems to work fine, but I am still not able to converge multiple vectors somehow.
I spent also some time with speeding up my implementation of fekete points, and I have implemented the fast evaluation based on Lagrange interpolation polynomials. In general, I made for example the l2_norm() method about 10x faster. I think it's about as fast now as if it was written in C++ directly. The main loops are now optimized C without any Python C/API calls.
My plan is now to implement taking squares of the solutions (exactly), and so on, and projecting it back to the original mesh. I'll try converging to that. At the same time, I'll try to converge to multiple eigenvalues. Hermes1d needs some improvements, that take me quite some time to implement.
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