Python

Point and interval estimation in Python

Heiko BaukeLeave a comment

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

Uncategorized

Some Math

Heiko BaukeLeave a comment

Math in WordPress has become as easy as $1,2,3,\dots$ thanks to MathJax. Some trigonometric identities: \begin{gather} \sin\alpha^2 +\cos\alpha^2 = 1 \\ \sqrt{2}\left|\cos(\alpha/2)\right| = \sqrt{\cos(\alpha) +1} \end{gather} The Dirac equation for a relativistic electron: \begin{equation} \mathrm{i}\hbar\frac{\partial\Psi(\vec{r}, t)}{\partial t} = \left(c\vec{\alpha}\cdot\left(\hat{\vec{p}}- q \vec{A}(\vec{r}, t) \right) + q \phi(\vec{r}, t) + mc^2\beta \right)\Psi(\vec{r}, t) \end{equation}

GPU computing

Accelerating the Fourier split operator method

Heiko BaukeLeave a comment

In past postings I wrote on fast Fourier transform (FFT) performance and on GPU computing. In a new project both topics meet. We evaluated the FFT performance on GPUs. We found performance gains of more than one order of magnitude as compared to traditional (non-parallel) CPU codes. The FFT is a core algorithm that finds… Continue reading Accelerating the Fourier split operator method