Getting Selected and First Two Weeks
The Summer of Code results came out April 23rd, 9:30pm, and I vividly rememeber the moment. I was elated and was surrounded by friends, who seemed equally elated about the results. I got selected for Google Summer of Code 2018 under the umbrella organisation NumFOCUS, for a project under the Julia programming language under the mentorship of David P. Sanders.
Julia is a new, up-and-coming programming language, which launched back in 2012 and is undergoing a lot of development on a variety of topics, ranging from the core of the language to its packages for almost everything.
I got selected for a project under JuliaIntervals, the project title being Guaranteed Root Finding and Global Optimization with Intervals.
About The Project
Interval arithmetic provides a way to perform computations with continuous sets of real numbers or vectors, for example to bound the range of a function over a given set.
This can be used to find roots (zeros) of functions in a guaranteed way, by excluding regions where there are no roots and zooming in on roots, but always within a given interval.
It can also be used to do global optimization of functions in a deterministic way, that is, find the global minimum of a non-convex, nonlinear function. Interval methods for global optimization provide a guaranteed bound for the global optimum, and sets that contain the optimizers.
This project proposes to significantly improve these methods using techniques found in the interval arithmetic literature.
Community Bonding Period
I spent the first two weeks of May, after my final examinations learning more about writing idiomatic Julia code, reading the docs, reading the books and research papers to build a better base about interval analysis and interacting with the Julia community.
The Julia community is delightful. The slack workspace is really active and there are a lot of channels for all purposes. Everyone is really helpful and fun to talk to. It has been a truly amazing experience being a part of this thriving community.
Coding Period
Two weeks of the coding period have elapsed, and I am happy to say that I am definitely well on track according to the timeline I proposed as a part of my application.
In the first week, I implemented the methods for solving a system of linear equations (Gauss-Seidel method and Gaussian Elimination) along with the testing and the benchmarking of the same PR #67. I also implemented methods for solving quadratic equations with interval coefficients PR #68.
In the second week, I implemented algorithms for automatically evaluating the slope of a function expanding about a point with respect to a given interval. Slopes tend to give better and tighter intervals as compared to derivatives, and this was an essential step to make the interval root-finding and optimisation methods more efficient PR #69.