Update of Catalogue of Software for Matrix Functions


Edvin Hopkins and I have updated to version 3.0 the catalogue of software for matrix functions that we originally produced in 2014 and updated in 2016. It covers what is available in various languages (C++, Fortran, Java, Julia, Python, Rust), problem solving environments (GNU Octave, Maple, Mathematica, MATLAB and associated toolboxes, R, Scilab), and libraries (Armadillo, GNU Scientific Library, NAG Library, SLEPc, SLICOT).

Here are some highlights of changes in the last four years that are reflected in the new version.

  • Several new MATLAB third-party functions have been written, by various authors, notably for f(A)b and for arbitrary precision evaluation of the exponential and logarithm.
  • Matrix function support in Julia has been expanded.
  • Armadillo, Rust, SLEPc, and Tensorflow are included in new entries.

In addition, all URLs and references have been updated.

Suggestions for inclusion in a future revision are welcome.

Updated Catalogue of Software for Matrix Functions

From “help matfun” in MATLAB.

Edvin Deadman and I have updated the catalogue of software for matrix functions that we produced in 2014 (and which was discussed in this post). The new version, which has undergone some minor reorganization, is available here. It covers what is available in languages (C++, Fortran, Java, Julia, Python), problem solving environments (GNU Octave, Maple, Mathematica, MATLAB, R, Scilab), and libraries (GNU Scientific Library, NAG Library, SLICOT).

From NAG LIbrary Mark 25 News.

Here are some highlights of changes in the last two years that are reflected in the new version.

Other changes to the catalogue include these.

  • SLICOT has been added.
  • Two more R packages are included.

Suggestions for inclusion in a future revision are welcome.

Cataloguing Software for Matrix Functions

I began working on functions of matrices just over thirty years ago, when I was an MSc student, my original interest being in the matrix square root. In those days relatively little research had been done on the topic and no software for evaluating matrix functions was generally available. Since then interest in matrix functions has grown greatly.

Functions of interest include the exponential, the logarithm, and real powers, along with all kinds of trigonometric functions and some less generally known functions such as the sign function and the unwinding function.

Gil Strang at the Advances in Matrix Functions and Matrix Equations Workshop in Manchester, April 2013.

A large amount of software for evaluating matrix functions now exists, covering many languages (C++, Fortran, Julia, Python, …) and problem solving environments (GNU Octave, Maple, Mathematica, MATLAB, R, Scilab, …). Some of it is part of a core product or package, while other codes are available individually on researchers’ web sites. It is hard to keep up with what is available.

Edvin Deadman and I therefore decided to produce a catalogue of matrix function software, which is available in the form of MIMS EPrint 2014.8. We have organized the catalogue by language/package and documented the algorithms that are implemented. The EPrint also contains a summary of the rapidly growing number of applications in which matrix functions are used, including some that we discovered only recently, and a list of what we regard as the best current algorithms.

Producing the catalogue took more work than I expected. Many packages are rather poorly documented and we sometimes had to delve deep into documentation or source code in order to find out which algorithms had been implemented.

One thing our survey shows is that the most complete and up to date collection of codes for matrix functions currently available is that in the NAG Library, which contains over 40 codes all implementing state of the art algorithms. This is no accident. We recently completed a three year Knowledge Transfer Partnership (KTP) funded by the Technology Strategy Board, the University of Manchester, and EPSRC, whose purpose was to translate matrix function algorithms into software for the NAG Engine (the underlying code base from which all NAG products are built) and to embed processes and expertise in developing matrix functions software into the company. Edvin was the Associate employed on the project and wrote all the codes, which are in Fortran.

A video about the KTP project been made by the University of Manchester and more information about the project can be obtained from Edvin’s posts at the NAG blog:

We intend to update the catalogue from time to time and welcome notification of errors and omissions.

SIAM Conference on Computational Science and Engineering 2013

As predicted in my my preview post, this conference, held on the Boston waterfront, proved to be SIAM’s largest ever, with 1378 attendees. Over 1000 presentations were given in up to 20 parallel minisymposia at a time, but this did mean that there was at least one talk (and usually several) of interest to me in almost every time slot.

One thing I learned from the conference is how widely Python is being used in computational science, especially for solving real world problems involving large amounts of data. This is partly due to its ability to act as the glue between codes written in other languages and web applications. The IPython environment, with its notebook interface, was featured in a number of talks, in some of which the slides were displayed using the notebook.

The following highly selective photos will give a flavour of the conference.

file://d:/dropbox/org/images/130225-0726-35-1605.jpg The conference venue. Note the residual snow, which fortunately did not fall in any serious amounts during the conference.

file://d:/dropbox/org/images/130226-2124-20-1630.jpg The poster session of about 65 posters was preceded by a poster blitz (1 minute presentations) and was accompanied by an excellent dessert. This photo shows Edvin Deadman (University of Manchester and NAG Ltd.) discussing his poster on Matrix Functions and the NAG Library with Cleve Moler and Charlie Van Loan (authors of the classic Nineteen Dubious Ways to Compute the Exponential of a Matrix paper). For some thoughts on poster sessions by one of the conference attendees see Please, no posters! by David Gleich.

file://d:/dropbox/org/images/130227-1327-55-1690.jpg Josh Bloom’s (UC Berkeley) invited presentation Automated Astrophysics in the Big Data Era contained a fascinating mix of observational astronomy, machine learning, robotic telescopes, numerical linear algebra, and Python, with a focus on classifying stars.

file://d:/dropbox/org/images/130228-1629-26-1706.jpg It was interesting to see MapReduce being used to implement numerical algorithms, notably in the minisymposium Is MapReduce Good for Science and Simulation Data? organized by Paul Constantine (Stanford; standing) and David Gleich (Purdue; sitting, with pointer).

file://d:/dropbox/org/images/130227-1157-03-1678.jpg Here is the lunchtime panel Big Data Meets Big Models being videod. Highlights from this panel and some of the invited plenary talks will be available in due course on the SIAM Presents YouTube channel.

If you weren’t at the conference perhaps you can make it to the next one in two year’s time (date and location to be announced). In the meantime a good way to keep up with events is to join the SIAM Activity Group on Computational Science and Engineering, which organizes the conference.