# DAVIDSTUTZ

## Educational

This page presents some educational projects corresponding. These mostly correspond to course or seminar projects from my bachelor and master studies.

### 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.

#### Latest Commits

[github-commits repositories="davidstutz/php-matrix-decompositions,davidstutz/php-matrix-decompositions-demonstration" limit="3" template="bootstrap"]

### PHP Simplex

This library implements the Simplex algorithm in PHP as discussed in [1] and the course Linear and Integer Programming on Coursera.

#### Latest Commits

[github-commits repositories="davidstutz/php-simplex" limit="3" template="bootstrap"]
• [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".

#### Latest Commits

[github-commits repositories="davidstutz/matlab-mnist-two-layer-perceptron" limit="3" template="bootstrap"]

### Kohana 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:

#### Latest Commits

[github-commits repositories="davidstutz/matlab-mnist-two-layer-perceptron" limit="3" template="bootstrap"]