TRNG

New TRNG release

A new version of TRNG (Tina’s Random Number Generator Library) has been released. TRNG may be utilized in sequential as well as in parallel Monte Carlo simulations. It does not depend on a specific parallelization technique, e.g., POSIX threads, MPI and others. The new version 4.17 is a bug fix and maintenance release.

Software

Lost in translation

Recently I found myself unexpectedly lost in translation.  As a “native speaker” of several languages of the C family I was facing the problem of calling various functions of a FORTRAN library from my C/C++ program. Although, I had done such kind of mixed-language programming in the past this time something went seriously wrong.  To… Continue reading Lost in translation

TRNG

New TRNG release

A new version of TRNG (Tina’s Random Number Generator Library) has been released. TRNG may be utilized in sequential as well as in parallel Monte Carlo simulations. It does not depend on a specific parallelization technique, e.g., POSIX threads, MPI and others. The new version 4.16 is a bug fix and maintenance release. A class… Continue reading New TRNG release

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

TRNG

New TRNG release

A new version of TRNG (Tina’s Random Number Generator Library) has been released. TRNG may be utilized in sequential as well as in parallel Monte Carlo simulations. It does not depend on a specific parallelization technique, e.g., POSIX threads, MPI and others. The new version 4.15 is a bug fix and maintenance release. Classes for… Continue reading New TRNG release

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 $$E\psi(x) = H\psi(x) = -\frac{1}{2}\frac{\mathrm{d}^2\psi(x)}{\mathrm{d} x^2} + V(x)\psi(x)$$for some given potential $V(x)$. Analytical solutions, however, are scare goods. Thus, one has to rely on approximations… Continue reading Eigenvalues and eigenfunctions

Python

Visualizing streamlines

In Visualizing vector fields I showed how to plot vector fields using Python and Matplotlib. Streamlines are a concept that is closely related to vector fields. Mathematically speaking streamlines are continuous lines whose tangent at each point is given by a vector field. Each line, and therefore also streamlines, can be parametrized by some parameter $t$.… Continue reading Visualizing streamlines

Python

Visualizing vector fields

A vector field assigns to every point in space some vector. Vector fields are used in many branches of physics, e.g., to describe force fields, electromagnetic fields or velocity fields. Two-dimensional vector fields can be easily visualized using Python and the popular matplotlib package. As an example let us visualize the vector field \vec… Continue reading Visualizing vector fields

TRNG

New TRNG release

A new version of TRNG (Tina’s Random Number Generator Library) has been released. TRNG may be utilized in sequential as well as in parallel Monte Carlo simulations. It does not depend on a specific parallelization technique, e.g., POSIX threads, MPI and others. The new version 4.14 is a bug fix and maintenance release introcucing compatibility… Continue reading New TRNG release

Python

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$$\hat\mu = \frac{1}{N}\sum_{i=1}^{N} x_i$$ and the sample variance $$\hat\sigma^2 = \frac{1}{N-1}\sum_{i=1}^{N} (x_i-\hat\mu)^2\,,$$ respectively. The sample mean… Continue reading Point and interval estimation in Python