A Random Blog About Math and Life
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In this post I would like to reflect a bit on the Julia programming language. These are my personal views and I have had more than a year developing a lot of packages for the Julia programming language. After roaming around many different languages including R, MATLAB, C, and Python; Julia is finally a language I am…
To understand the differences between automatic differentiation libraries, let’s talk about the engineering trade-offs that were made. I would personally say that none of these libraries are “better” than another, they simply all make engineering trade-offs based on the domains and use cases they were aiming to…
In some previous blog posts we described in details how one can generalize automatic differentiation to give automatically stability enhancements and all sorts of other niceties by incorporating graph transformations into code generation. However, one of the things which we didn’t go into too much is the limitation of…
Many times a scientist is choosing a programming language or a software for a specific purpose. For the field of scientific computing, the methods for solving differential equations are one of the important areas. What I would like to do is take the time to compare and contrast between the most popular offerings. This…
I get it, you’re too good to vibe code. You’re a senior developer who has been doing this for 20 years and knows the system like the back of your hand. Or maybe you’re the star individual contributor who is the only person who can ever figure out how to solve the hard problems. Or maybe you’re the professor who…
A very common adage in ODE solvers is that if you run into trouble with an explicit method, usually some explicit Runge-Kutta method like RK4, then you should try an implicit method. Implicit methods, because they are doing more work, solving an implicit system via a Newton method having “better” stability, should be…