NAG's numerical libraries instrumental in development of new software application
October 2007. The Numerical Algorithms Group (NAG), the world's leading provider of mathematical and statistical software components, announces that its numerical components play an integral part in new analytical software developed by a Professor at the University of Oxford.
The original impetus for developing the new analytical software application came from the availability of new experimental probes for studying magnetism. Neutron spectroscopy, in particular, has become a very powerful probe of the magnetic state of atoms thanks largely to advances in instrumentation at spallation neutron sources like the ISIS Facility at the Rutherford Appleton Laboratory. This technique makes it possible to obtain accurate measurements of level splittings in atoms caused by interactions with the crystalline environment. Detailed information on the many-electron states of atoms can be obtained from these level splittings and the corresponding spectral intensities.
Experiments that determine the electronic state of atoms in magnetic substances are extremely valuable for understanding the origin of magnetic behaviour and for engineering materials with new or improved magnetic properties. Armed with extensive experimental data, Professor Andrew Boothroyd, at the University of Oxford Physics Department, needed the analytical tools to work out the state of the electrons and hence understand their magnetic behaviour.
The creation of SPECTRE - the system designed to undertake the data analysis - and its subsequent evolution took place over many years as specific problems arose during the course of the research. Having used numerical routines from NAG in previous projects, Professor Boothroyd turned to NAG once again to provide the mathematical code required by SPECTRE. SPECTRE uses the most up-to-date atomic models, which makes the results very accurate and quantitative. In brief, SPECTRE calculates the neutron spectra in terms of a small number of unknown parameters, and determines these parameters by least-squares fitting to the data. The core of the calculation is a series of matrix diagonalizations carried out by NAG routines designed to handle Hermitian matrices. The least-squares fitting is also performed by NAG routines. The lowest energy eigenfunctions found by the program are used to calculate other experimentally accessible physical properties such as the magnetic susceptibility and specific heat capacity.
SPECTRE will be made freely available to other magnetic materials groups in the hope that it will make it easier for scientists to interpret neutron spectroscopy data and thereby contribute towards the improvement of magnet materials.
Professor Andrew Boothroyd said “NAG's reputation for accuracy, flexibility and robustness made it the first choice for the calculations in SPECTRE. I am delighted to be working with NAG to make the fruits of one person's labour freely available to the whole scientific community.”
Mick Pont, Principal Technical Consultant at NAG added “Software such as that developed by Professor Boothroyd is of fundamental importance in advancing human knowledge in the field of magnetism. We at NAG are very proud that our numerical components have proved useful in this endeavour. Since NAG was founded on collaborative principles we are particularly pleased that SPECTRE will be available for the use of others.”
The Numerical Algorithms Group (NAG) is dedicated to making world-class cross-platform mathematical, statistical, data mining components and tools for developers as well as 3D visualization application development environments. NAG serves it customers from offices in Oxford, Chicago and Tokyo supporting over 10,000 customer sites worldwide in finance, engineering, and scientific research. NAG software is the choice of over 25 independent software vendors including Oracle, IBM, DemandTec and many others.