Genetic algorithms (GA) are one of the standard optimization methods. They work by evolving a population of trial solutions towards better solutions using biological inspired genetic operators. The trial solutions are also called individuums. The above graphics shows the evolution of a particular genetic algorithm – genetic programming – solving a problem of symbolic regression. It shows beautifully how the GA optimizes the problem. The above graphic can be used for visual debugging. Furthermore, it uncovers the beauty of a complex algorithm.
The full visualization with additional explanation can be found here.
In the previous post I wrote some words about VexCL, a library for OpenCL. This library can easily be used within odeint. I only needed to create an adapter for the odeint resizing mechanism and then it was done. VexCL supports expression template and therefore, it can be used with odeints vector_space_algebra and default_operations. Continue reading →
Some days ago I found a very nice library for building OpenCL applications: VexCL. It is really high level such that you must not care about things like memory management. It uses expression templates, such that you can write very compact and readable code. It is also possible to use VexCL with odeint, I will show in the next days some examples here.
Last december I gave a talk about the Taylor series method for ordinary differential equations. See here and here for more informations. I put the slides for this talk online, as well as the source files which can be found here.
Mario Mulansky and me will visit this years C++Now! conference formerly known as BoostCon, held on May 13-18, 2012, in Aspen Colorado. It is one of the largest conferences devoted to C++ and we will present an overview talk on odeint. Furthermore, we will introduce some techniques used in odeint. We would be happy to meet and discuss with anyone who has interest in odeint there, of course.
I use bjam and Boost.Build since a while and they are really great. You can easily use them to build multi-platform applications and they automatically resolve the C++ header dependencies, which is difficult to realize with make and makefiles. Writing Jamfiles is in principle easy, but in the beginning it is hard to figure out how it works, especially if you are following the official documentation. Today, I found an easy way to link the boost libraries and how easy the boost headers can be included: Continue reading →
We have worked for one year on a new version of odeint – a highly flexible library for solving ordinary differential equations. It was hidden in some branch of the boost sandbox. Today, we put this version into the github:
It is not compatible with the old version such that we call the library odeint v2. Some nice and new features are:
Algebras and operations which can be adapted for nearly all container types. For example, a specialized algebra for thrust exists, such that you can use the power of modern graphics cards and CUDA for solving ODEs.
A generic implementation of the Runge-Kutta solvers. Any Butcher tableau can now be used without any performance loss.
Methods with dense output for example the Dopri5 solver.
I have created a github project for the Taylor series method of ordinary differential equations. It is an addon to odeint and will be one day a part of it.
The Taylor series methods determines the solution of an ODE by its Taylor coefficients. The theory is extremely simple but the difficulty is to determine these coefficients numerically and in an unique way. To do so automatic differentiation is used where the formulas defining the ODE are given as expression trees and are then sequentially evaluated to obtain the n-the derivative or the n-th Taylor coefficient. Continue reading →