MISC
Educational
PHP Matrix Decompositions
This library implements common matrix decompositions in PHP. Based on the library, a demonstration application provides the theoretical background and may be used to compute these matrix decompositions. The following table provides an overview:
| Decomposition | Factorization | Applicable for | Runtime |
|---|---|---|---|
| LU | $A = LU$ | $A \in \mathbb{R}^{n \times n}$, $A$ regular | $\mathcal{O}(\frac{1}{3}n^3)$ |
| Cholesky | $A = LDL^T$ | $A \in \mathbb{R}^{n \times n}$, $A$ symmetric and positive definite | $\mathcal{O}(\frac{1}{6}n^3)$ |
| QR: Givens Rotations | $A = QR$ | $A \in \mathbb{R}^{m \times n}$ | $\mathcal{O}(\frac{4}{3}n^3)$ |
| QR: Householder Transformations | $A = QR$ | $A \in \mathbb{R}^{m \times n}$ | $\mathcal{O}(\frac{2}{3}n^3)$ |
The demonstration application is available on GitHub as well, however, as separate repository.
PHP Matrix Decompositions on GitHub Demonstration Application Demonstration Application on GitHubPHP Simplex
This library implements the Simplex algorithm in PHP as discussed in [1] and the course Linear and Integer Programming on Coursera.
PHP Simplex on GitHub- [1] R. J. Vanderbei. Linear Programming: Foundations and Extensions. Springer, 2001.
MatLab Two-Layer Perceptron
This is a MatLab implementation of a two-layer perceptron, that is a neural network with one input, one hidden and one output layer. The implementation was assessed using the MNIST dataset.
Further details on neural networks can be found in my seminar paper: Seminar Paper "Introduction to Neural Networks".
MatLab Two-Layer Perceptron on GitHubKohana Demo
A simple application demonstrating the use of several of my Kohana modules together with Kohana 3.1, 3.2 and 3.3.6 (see the corresponding branches in the below GitHub repository). Figure 1 shows some screenshots of the application. The following modules are included in the applications:
Kohana Demo on GitHub