A Month of Math Software – March 2012

April 2nd, 2012 | Categories: math software, Month of Math Software | Tags:

Welcome to this month’s MMS which includes the usual mix of commercial and open source software spanning across multiple disciplines.  Last month’s edition is here and the archive of all previous editions is at http://www.walkingrandomly.com/?cat=47.  Thanks so much for all of the contributors this month without whom these articles would be significantly more difficult to write.  As always, if you have some mathematical software news then feel free to contact me.

General purpose commercial packages

  • Maple 16 was released in March and according to Maplesoft it has over 4500 additions and improvements compared to the previous version.  Maple is very strong in polynomial arithmetic and Maplesoft have released benchmarks showing how Maple 16 is hundreds of times faster than Mathematica 8 in this area.  For example, multiplication of two dense polynomials in 3 variables, each of degree 30 takes 110 seconds in Mathematica 8 but only 0.52 seconds in Maple 16 according to these new benchmarks.
  • MATLAB version 2012a was also released in March with the usual batch of improvements and updates.  One of the highlights for me is the fact that The Mathworks now offer the MATLAB Compiler Runtime for free download, significantly simplifying the deployment of compiled applications.
  • Version 2.18-5 of Magma, the commerical computer algebra system specializing in number theory, has been released.  Click here for the v2.18-5 changelog

Mathematical Open Source and Freeware

3D Bar Plot created using Euler Math ToolboxAn interactive shell for the GNU Scientific Library

Python takes on R with pandas

  • The Python Data Analysis library, pandas, is designed to help Python programmers perform in depth data analysis projects without having to resort to R.  Version 0.7.2 was released in March and you can see what’s new at http://pandas.pydata.org/pandas-docs/dev/whatsnew.html.  Thanks to Tom Brander for the heads up on this one.

Vital statistics

Finite Differences and Elements

  • “The Chombo software package provides a set of tools for implementing finite difference methods for the solution of partial differential equations on block-structured adaptively refined rectangular grids with embedded boundaries. Both elliptic and time-dependent modules are included. Support for parallel platforms and standardized self-describing file formats are included.”  Version 3.1 was released in March…get it at https://commons.lbl.gov/display/chombo/Chombo+Download+Page
  • The FEniCS book has been published and is available online and in print. The online version is available at http://dx.doi.org/10.1007/978-3-642-23099-8 and hard copies can be ordered from Springer (http://tinyurl.com/3ueq9hk) or book sellers.  The FEniCS Project is a collection of free software with an extensive list of features for automated, efficient solution of differential equations.

Eigenvalues everywhere

The following two packages were recently announced on the Numerical Analysis Digest.

  • “The FEAST solver package is a free high-performance numerical library for solving the standard or generalized eigenvalue problem, and obtaining all the eigenvalues and eigenvectors within a given search interval.  The FEAST algorithm takes its inspiration from the density-matrix representation and contour integration technique in quantum mechanics.”  Download version 2.0 from http://www.ecs.umass.edu/~polizzi/feast/download.htm
  • “ELPA” is a new direct eigensolver library that addresses scalability and performance, especially for parallel applications. ELPA builds on the ScaLAPACK type interfaces that are often used in existing implementations, but key parts of the eigenvalue solution are then replaced with ELPA’s own routines in an easy-to-use way. The library is particularly useful when a substantial part of all eigenvalue / eigenvector pairs is needed. Released under an LGPL-like license, ELPA has been successfully tested for matrix sizes up to 680,000 and with up to 294,000 CPU cores on a BlueGene/P system.”  A hybrid version (OpemMP and MPI) was released in March. http://elpa.rzg.mpg.de/

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