Best of
Matrix.java: An in-development matrix library intended to be used in tandem with Numerical.java to have a fairly complete set of matrix operations - eigenvalues, determinants, matrix norms, inverses, et cetera. The end result is a from-scratch numerical PDE solver and various scientific computing algorithms - conjugate gradients, finite elements, system of non-linear equations solver.
Divisor Functions: This Perl Module implements the Sieve of Atkin, as well as, several important number theoretic functions. The sieve, in particular, is a sophisticated algorithm that rapidly builds large lists of prime numbers.
Optimal Non-uniform Mesh: This work-in-progress searches for the optimal non-uniform, linear mesh for a given single-valued function. This program was mainly written to demonstrate techniques used in statistical programming to optimize function approximation. The actual optimization of non-uniform meshes is quite difficult, and produces large systems of equations based on the number of desired partitions. The majority of the code is devoted towards implementing piecewise functions and function norms in R. The code is largely unoptimized and written for clarity/practicality, as opposed to actual functionality. Look here for the set of results. Each pdf displays the original "best" approximation of y(x) = x^3 vs. the results approximation after 40 iterations of crossover using roulette selection.
select.py, Genetics.py: These python modules implement several important techniques important to developing genetic algorithms. Genetics.py houses the largely computationally intense functions, which in practice are not used, but are of theoretical significance. Select.py implements ranking algorithms and sampling algorithms - which have been tested with large sample sizes to prove accuracy - for use with the scoring and phase of a genetic algorithm. The ranking selection, in particular, implements a Gaussian numerical integration technique to score the fitness of particular chromosones.
Power Spectrum Analyzer: This program computes the power spectrum of wav files, and then outputs the result as both a png file and spreadsheet. The resulting data sets were then used to compare the 1-dimensional wave equation with empirical data gathered from a plucked guitar string.
Project Euler #27: This program finds the optimal quadratic function to produce consecutive prime numbers given a specific constraint on the coefficients. Due to the amount of time it takes to check primality, as well as, the large search space of quadratic functions, this problem requires a subtle approach to weeding out bad solutions. See the project euler problem specification for details.
