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• Training as a Numerical Analyst
• Seeking a Master of Engineering degree in Applied Mathematics and Computer Science
• Interested in the development of scientific libraries

HPC model of planet earth using a 3-d spherical harmonics decomposition and using a scalable parallel implentation that's been tested with up to 248 MPI processes.

In short, we approximate a function (in this case the altitude of the earth at a given location) by a sum of spherical harmonics.

This is exactly analagous with a Fourier series for functions defined on the sphere. Our function f(longitude, latitude) is defined on the sphere and can be written as an infinite sum of the basis functions, in this case the spherical harmonics. The models were built using NASA's ETOP01 data set and parallel programming techniques using both OpenMP and OpenMPI.

Caption: Model of planet Earth using increasingly precise Laplace series approximations. As we increase the number of terms in our discrete Laplace series, we can better approximate the true altitude function.

Numerical routines spanning a broad range of topics in scientific computing from quadrature to linear least squares. libejovo is build around a foundational Matrix_<type>, where <type> can be be d, f, or i, representing two dimensional matrices of type double, float, and int.

An exploration of Monte Carlo methods and how a deterministic computer generates pseudo-random numbers. Using R we create a shiny app that simulates samples taken from a multivariable guassian distribution to estimate the length of an underwater cable laid between two modern cities separated by a large body of water. We experience R's approach to the functional programming paradigm and also learned how to compile C++ code using the R package Rcpp to speed up mission-critical segments of code.

col 1	col 2	--

Study of the spherical harmonic decomposition of virus normal modes

A collection of MATLAB functions wrapped up in the +ejovo package that was written while a SIP student and Research Assistant under the advisement of Dr. David Wilson at Kalamazoo College, MI. This package contains the code that I wrote for my senior undergraduate thesis and an extension that permits the automatic fetching and downloading of viral capsids from the VIPERdb to be instantiated as one of many user-defined virus classes in MATLAB. The software decomposed normal vibrational modes into icosahedrally symmetric versions of the Spherical Harmonics - which represent a symmetric analogue of a Discrete Fourier Series for functions in spherical coordinates.

Linear Combination	SAF6

Foreng is a series of solutions to exercises for the book Fortran for Scientists and Engineers written to practice and learn the revered Fortran programming language. This project taught me how to write numeric programs in Fortran like calculating finite difference derivates, steady-state diffusion problems, computations of orbits, etc. There is even a chapter of exercices dedicated to using Coarrays and the OpenMP protocol. Formath is a continuation of my interest in Fortran and is a library written to practice modern fortran and fundamental linear algebra routines like Gaussian elimination, Gram-Schmidt orthogonalization, Householder Reflections, and many more.

A complete synthesis of the numeric methods and theoretical concepts learned while pursuing a masters in scientific computing. Written in C++20 with heavy utilisation of lambdas and adaptation to modern C++ practices (smart-pointers, concepts, template programming), this library concretizes the core concepts of my diploma. With a robust 2-dimensional Matrix library at its heart (with implementations of Matrix decompositions, direct and iterative methods, eigenvalue algorithms), this library provides numerous core modules needed invaluable for a scientific library:

• discretization routines like linspace and seq
• quadrature routines using both Newton-Cotes and Gaussian methods
• polynomial interpolation
• resolution of differential equations
• RNG functions (using a xoroshiro shift-register generator) in the style of R's runif, rexp, rbinom
• Monte Carlo integration routines
• Markov Chain Monte Carlo methods implementing Metropolis, Metropolis-Hastings, and Gibbs-Sampling
• Plotting interface that generates R ggplot code to visualize contour plots, scatter plots, and simple functions of a single variable.
• First-order gradient methods, Second-order Newton/Quasi-Newton methods for optimization and machine learning.

This library implements industry standard practices using CMake as a build system, unit testing with CTest, and continuous integration using GitHub Actions. Heavily inspired by MATLAB, numpy, Julia, and R, this project is not an attempt to reinvent the wheel - it is a reenforcement of the fundamental aspects of Numerical Methods studied while at Sorbonne Université. After writing libejovo, this project has been an absolute breathe of fresh air and a great leap forward 20 years into the feature. Generic programming, standard containers, namespaces, operator overloading, support for functional programming paradigms, abstract base classes, and many more are language features that have helped me break free of C's structured constraints. Maximizing readibility and minimizing redundancy of code allows for simple instances of user-facing code like

auto x = ejovo::linspace(0, trig::two_pi);
ejovo::plot(x, x.map(cos));

Which generates the following ggplot2 plot via a call to Rscript:

Or

auto f = [&] (double x) { return x * x; };
ejovo::integrate(f, 0, 3) // use 5 point Gauss-Legendre quadrature rule as default

A watered down version of libejovo++ that was written in C and naturally spawned from the code I was writing for our general C programming, DSA, and systems programming classes. There is also an implementation of a solid matrix library that taught me how to appreciate Fortran's simplistic A(:,3) = B + 3 type indexing compared to a C function that would require a monstrosity like: Matrix_set_col_mat(A, Matrix_add_scalar(B, 3)). This syntax is implicitly implemented in modern languages like Python and C++ by operator overloading but in C simple indexing must be explicitly called via descriptive and namespaced functions prefixed with Matrix_.