GSoC 2023 Fortran-lang resources for prospective contributors

If you’re interested in applying for the Google Summer of Code 2023 program with Fortran-lang, please visit this page:

From that page, you can navigate to our Contributor Instructions and Project Ideas pages.

Please review these pages and let us know in this thread if you have any questions.

We also encourage you to join our upcoming monthly call on March 2 at 1800 UTC and discuss what you would like to work on. See Fortran Monthly Call: February 2023 for more info. We’ll post the Zoom link in that thread ahead of time.

The application window for contributors opens on March 20 at 1800 UTC and closes on April 4 at 1800 UTC.

We look forward to all your interest and ideas!


@milancurcic : Thank you so much for sharing this information about the Google Summer of Code 2023 program with Fortran-lang. I’m excited to explore the opportunity and contribute to the open source software development community.



Looks like I lost touch with you guys for a while due to my college exams but nvm congratulations on getting selected in GSOC’23 and thank you so much sharing all these resources. Also, I’m really looking forward to interacting with you all on 2nd March.

Thank you so much again for providing this opportunity.


Thanks for the post and resources. I wasn’t sure if anyone would be interested in mentoring the following, but it’s a project I’m interested in working on related to my research. I’ll leave the details below, but will try and go to the Fortran meeting tomorrow.

Something I am interested in doing is creating a multidimensional integration routine, for the below form of integrals. If there were an interested mentor, perhaps this could be something to contribute as a Fortran project?


In general, the denominator may approach 0 when f does not; depending on the number of dimensions, this is in fact an integrable singularity. However, traditional integration methods take a large number of points to be able to resolve this region accurately. In addition, these functions f and g may only be known numerically on a given set of points (due to being difficult to compute), so adaptive mesh refinement may not be possible, or if it’s being used, it’s at a higher-level. This is the use case I’ve been thinking of.

In condensed matter physics, these are typically 2D or 3D integrals over a convex domain, and the closest thing they have to this is the so-called Tetrahedron Method, which is only able to compute the imaginary part of the above integrals, for z = i\epsilon; additionally, the tetrahedra meshes must be uniform. Additionally, they rely on f(x) = 1. Despite these restrictions, this so-called Tetrahedron method is amazing because of the massive reduction in sampling points needed.

Scuffed Example
As an example, here is an early comparison I made a few months ago of computing the above integrals in 3D with f=1, g(x) ~ cos(ax) + cos(by) + cos(cz), plotting I(w+i eps) for small epsilon.:

The naive method essentially is the rectangle method. We get basically equivalent accuracy between the two methods, although one mesh is 4^3 as small. [The asymmetry in the tetrahedron method result came from an accidental shift of the mesh that produced a systematic error] Additionally, in the limit epsilon → 0, the rectangle method becomes super noisy, whereas the tetrahedron does not.

Improvement/Project Idea
However, Kaprzyk in this set of papers:
3D algebraic (generalized) tetrahedron method
N-D algebraic (generalized) simplex method
outlines a procedure for an integration routine that works for non-uniform meshes of simplices, works for arbitrary f(x) and g(x) (including numerically generated ones), and generalized to N-dimensions. In the 3D case, he has hardcoded his idea for a given set of functions, and there is no code for the N-D case.

The idea is as such: you subdivide the domain into simplices, linearly interpolate f(x) and g(x) in each simplex, and use analytic integration formulae to evaluate the integrals. Each point in the domain gets a weight, and the most difficult part of the computation becomes evaluating these parts of the weights:

The above are the formulae for 3-D integrals, but there is a similar form (with bigger determinants and higher powers of z) for N-dimensions.

Pros/Advantages of the Method

  • From the simple experiment above, getting the same accuracy for a 4^N smaller mesh seems great
  • The BIGGEST strength is that the integrals w.r.t. z of I(z) above are also analytically obtained with a simple change to the weights computed above. What this means is you can also compute integrals of I(z) without needing to repeat the above for N_z mesh points.
    • In other words, computing \int I(z) dz (and further integrals) is the same cost as computing I(z). This will be very useful for many-body condensed matter applications (the GW method, electron-phonon calculations, etc) and I’m sure would be generally applicable.
  • The formalism is agnostic to the chosen mesh (uniform vs nonuniform, etc)

Cons of the Method

  • The user has to have the numerator f(x) and denominator g(x) known separately.
  • If the denominator doesn’t approach 0, then in general other integration schemes will be faster or more accurate.

Issues to solve for the project:

  • Obtaining simplified formulae for when the quantities z_j → z_k, which may occur in some simplices, for high dimensions will require a fair amount of algebra. However, I believe I can simplify the process better than Kaprzyk did.
  • Evaluating the above quickly. They in general simplify to (N-th recursive) finite differences [if all z_i are distinct) which ends up being fairly slow. A clever lookup table/memoization could massively speed up this part of the calculation.
  • Interfacing with an N-dim Delaunay generator; Qhull appears to be the only library that does this for N-dimensions. Up to 8-D integrals might be the max that’s realistic however.