GPU computing · MPI · parallel computing · Performance

CUDA-aware MPI

CUDA and MPI provide two different APIs for parallel programming that target very different parallel architectures. While CUDA allows to utilize parallel graphics hardware for general purpose computing, MPI is usually employed to write parallel programs that run on large SMP systems or on cluster computers. In order to improve a cluster’s overall computational capabilities… Continue reading CUDA-aware MPI

numerical methods · Python

Eigenvalues and eigenfunctions

Computing the eigenvectors $\psi(x)$ and eigenvalues $E$ of some Hamiltonian $H$ belongs to the key problems of quantum mechanics. For the one-dimensional Schrödinger equation we have to solve \begin{equation} E\psi(x) = H\psi(x) = -\frac{1}{2}\frac{\mathrm{d}^2\psi(x)}{\mathrm{d} x^2} + V(x)\psi(x) \end{equation}for some given potential $V(x)$. Analytical solutions, however, are scare goods. Thus, one has to rely on approximations… Continue reading Eigenvalues and eigenfunctions


Point and interval estimation in Python

Let us consider a random sample $x_1,x_2,\dots,x_N$ drawn from a normal distribution with unknown mean $\mu$ and unknown variance $\sigma^2$. The best point estimates for the mean and the variance are given by the sample mean\begin{equation} \hat\mu = \frac{1}{N}\sum_{i=1}^{N} x_i \end{equation} and the sample variance \begin{equation} \hat\sigma^2 = \frac{1}{N-1}\sum_{i=1}^{N} (x_i-\hat\mu)^2\,, \end{equation} respectively. The sample mean… Continue reading Point and interval estimation in Python