Editor’s Note: We have two students working on numerical minimization and integration this summer, Rajat and Lahiru. Lahiru will be writing a separate post about his work.
Introduction to the Minimization and Integration Project
Hi. My name is Rajat Kapoor and I have been selected to work with SciRuby for Google Summer of Code 2014.
Minimization and Integration are two of the many available gems in the SciRuby suite. My project this year aims to improve these gems to replicate the functionality provided by GNU’s GSL. I will be trying to implement all the minimization and integration algorithms present in GSL in pure Ruby, with improvements as needed, so that these functions are easily accesible to all Ruby users, while the users which have GSL already installed will have an advantage in terms of speedy computations.
What Minimization and Integration actually mean
Minimization refers to the process of finding out the minimum of a mathematical function whose values might depend on multiple variables. Unidimensional minimization restricts these problems to functions of one single variable. Integration is the same as the very widely used concept in calculus which basically boils down to finding the summation of the value of a function at small intervals, when the width of the intervals in infinitesimally small. I can bet that you knowingly or unknowingly use both these things on a daily basis.
The project can be broken into two major parts: Minimization and Integration, as these are two seperate gems.
The Minimization gem can be broken in two parts: unidimensional (or univariate) and multidimensional (multivariate). With respect to coding, these two can again be broken down into sub-parts: pure Ruby implementations and GSL support. The Integration gem will include the pure Ruby implementations as well as GSL support. Along with this, some support for symbolic integration will be added for JRuby users by way of the JScience library.
The pure Ruby implementations of the unidimensional minimization part are almost finished. I am also working on the GSL support for the same along with it. I plan to finish up any unidimensional minimization work by the end of this week and start the work with multidimensional minimization methods.
Keep watching this blog for more updates regarding my project.