MISC
PHP Matrix Decompositions
This library implements common matrix decompositions in PHP. An interactive demo application provides the theoretical background and can 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 on GitHub