Issue 70, 27 March 2008

In this issue:


Top Story - New NAG routine for nearest correlation matrix

In the last issue of NAGNews we featured an article about the planned new functionality of fast extraction of quantile values in the next NAG Library. In today's issue we continue our focus on future developments with a look at the a new routine that will compute a nearest correlation matrix, measured in the Frobenius norm, to a given input matrix.

Such matrices have unit diagonal and are symmetric positive semi-definite. They are important in many application areas since they reflect how two random variables vary with one another. In particular, in the field of finance, investors are often keen to use the relative behaviour of stocks in order to determine optimal portfolios. For such applications it is usually necessary to recover a correlation matrix from a matrix which only approximately fulfils the necessary conditions.

At the University of Manchester, Professor Nick Higham did some ground-breaking research into this problem and published an algorithm using alternating projections. He described this elegant method at the NAG Quant Day London 2006 http://www.nag.co.uk/market/Nick_Higham_Presentation.pdf. The method is however only linearly convergent. Subsequently Qi and Sun published a quadratically convergent algorithm based upon a Newton algorithm applied to a dual formulation of the problem.

As reported in past issues of NAGNews, NAG sponsors two prizes at the University of Manchester. One of these was awarded to an outstanding student, Ruediger Borsdorf http://www.nag.co.uk/nagnews/NAGNews_Issue67.asp#General, for his fine performance in the MSc examinations. His project for this degree was to study the Qi Sun algorithm under the supervision of Professor Higham. It is the algorithmic improvements suggested by this work that form the basis of the new material to be included in the NAG Library.

We are looking to receive real data sets to test the routine ourselves as well as shipping early versions of the code to selected clients for them to use and give feedback. If you are interested in becoming a beta tester for this material or providing test data sets, please contact us at nagnews@nag.co.uk.


General Information - Oxford Financial Research Centre utilises NAG Components

NAG is delighted to announce a new partnership with the Oxford Financial Research Centre (OFRC) http://www.finance.ox.ac.uk/. Faculty and students working within the OFRC have access to NAG's numerical libraries and toolboxes, including the forthcoming NAG Toolbox for MATLAB® http://www.nag.co.uk/numeric/MB/start.asp.

The OFRC brings together finance researchers throughout the University of Oxford, including members from the departments of Economics, Mathematics, Law, Physics, Computing and the Sa'd Business School. The NAG software will be also be used in Oxford's MSc courses in Mathematical Finance, Mathematical & Computational Finance and Financial Economics.

This partnership between NAG and OFRC reinforces NAG's long standing commitment to the worlds of academia and commercial finance through the development of accurate and flexible, numerical code. NAG's existing numerical libraries are already embedded within applications used by some of the worlds most prestigious and prominent finance houses; the new NAG Toolbox for MATLAB, makes the use of NAG's components for finance even easier.

Professor Mike Giles, Mathematical Institute, University of Oxford, commented “NAG's high quality mathematical software libraries are a great help in rapidly developing financial applications. The new NAG Toolbox for MATLAB complements the libraries because MATLAB is used increasingly to prototype software before moving to C++ for production code. We're very keen to put both products in the hands of our students, as well as using them for our research.”


NAG User Story ' Understanding subsonic and supersonic nozzle flow using the NAG Library
Subsonic and supersonic flow of perfect gas through orifices is a topic which is well studied by a number of researchers. Orial Kryeziu, University College London is currently considering the steady, isentropic, two-dimensional compressible flow from a nozzle for fluid velocities in both the subsonic and supersonic ranges. However the larger goal of his research is to have a clear understanding of incompressible fluid flow through gaps or slits modelled using the shallow water equations. Working with compressible instead of incompressible fluid is possible because of well established links between the shallow water equations and gas dynamic equations. Gas equations and methods developed to solve them should be useful for studying the geophysical dynamics of incompressible fluid through gaps.

A widely used technique for analysing steady two-dimensional, irrotational, compressible, homentropic flow is the hodograph method. The hodograph method is based on the idea of regarding position {x}=(x,y) as a function of the velocity {u}=(u,v) and determining the partial differential equations (PDE) satisfied by {x}. This transformation between variables corresponds to a general type of transformation called the Legendre transformation. An advantage of the hodograph transformation is that hodograph equations are linear and have solutions readily available by analytical and numerical techniques.

To read the entire article by NAG user, Orial Kryeziu visit our website here Understanding Subsonic and supersonic nozzle flow using the NAG Library


General Information - Careers at NAG: Join a place where academia meets industry

Expand your capabilities - join the NAG team today!

By joining NAG and its team of dedicated staff you are setting foot into a unique organisation spanning both the academic and commercial worlds. Established as a collaborative inter-university venture, NAG has become synonymous with quality, flexibility and expertise.

Steeped in numerical history, including world firsts, NAG's present and future is equally as exciting as its past. Collaborative projects including HECToR ' the UK's largest and fastest supercomputer project, and the continual development of NAG's highly renowned numerical libraries create the need for attracting new experts from both the technical and commercial arenas to join its team.

Staff enjoy the following benefits: outstanding pension scheme, flexible working hours, enhanced maternity/paternity leave, respect of work/life balance, personal development training scheme, opportunity to become a company member, childcare voucher scheme initiative, free personal travel insurance.

For more information about Careers at NAG visit our website http://www.nag.co.uk/about/careers/overview.asp


NAG Event Calendar

April is another busy month in NAG's event calendar. NAG experts will be on hand at each event listed below. If you're interested in attending any of the events yourself, please follow the links to the organiser's websites.

GAMM 2008
http://www.zarm.uni-bremen.de/gamm2008/
1-2 April 2008, University of Bremen

50th British Applied Mathematics Colloquium
http://www.maths.manchester.ac.uk/bamc/
2 April 2008, University of Manchester

The Mathematical Association Annual Conference
http://www.m-a.org.uk/resources/conferences/annual_conference_2008/index.html
3 April 2008, University of Keele

Association of C/C++ Users Association Conference
http://www.accu.org/index.php/conferences
3-4 April 2008, Oxford

* NAG is delighted to be supporting the:

4th Annual CARISMA Seminar: Risk control strategies for hedge funds & program trading
http://www.optirisk-systems.com/newsandevents_events.asp#
30 June ' 3 July 2008 ' London

Following in the success of CARISMA's 3rd annual conference, the 2008 conference promises to be even more informative for finance professionals and academics. Key issues being covered at the conference include: Program trading, algorithmic trading, risk control strategies for hedge funds, long-short portfolios, derivatives trading and risk management and investment strategies for hedge funds.

For more information on this exiting event visit the organisers website - see above for link.


Tips & Hints - NAG's Licence Management System - Kusari

Some of our users may have noticed that we are gradually moving to a new licence management system, called Kusari.

As we move to this system we have with 3 different systems in the field:

a) Kusari
b) FLEXlm
c) A PC-specific system

Eventually all our products will use Kusari and licence key installation will become uniform once more. We are, in addition, developing an interface to make the installation of a licence key much simpler.

Because many of our users are single-user, PC-Windows based, this note gives an overview of the steps required to obtain and install a Kusari licence key on this system. Other machine ranges will follow the same general procedures, but will differ in detail. The more detailed information is, in all cases, found under the license subdirectory or from http://www.nag.co.uk/Kusari/download.asp or in the Installer's Note for the appropriate implementation. These are provided with the product but are also available on the web (see http://www.nag.co.uk/doc/inun.asp.

To read the entire article visit http://www.nag.co.uk/techtips/techtip034.asp

Previous Tips & Hints can be found on our website http://www.nag.co.uk/techtips/index.asp.


Product News - Latest Implementations

NAG is committed to offering new implementations of its broad range of numerical and statistical software components and compilers and tools. The following implementations for NAG products have become available since the last issue of our newsletter:

The NAG C Library (http://www.nag.co.uk/numeric/CL/CLdescription.asp, Mark 8 is now also available for the following platforms:

  • Apple Intel Mac OS X 64-bit using the Gnu C Compiler

For full details of these and all other available implementations, visit the NAG site. Comprehensive technical details of each implementation are given in the relevant Installation and User Notes at http://www.nag.co.uk/doc/inun.asp


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