Dr. Anders Markvardsen (ISIS neutron & muon source, STFC)
Fitting is the process of trying to fit a mathematical model or function to some data, where the data may originate from measurements at beamlines or simulations. A simple example could be the problem of fitting a polynomial background function plus a set of peak functions to a spectrum. Fitting is commonly a core functionality in neutron, muon and x-ray data reduction and analysis software packages. It is required in tasks such as instrument calibration, refinement of structures, and various data analysis tasks specific to different scientific techniques. The [Mantid software project](http://www.mantidproject.org) provides an extensible framework that supports high-performance computing for data manipulation, analysis and visualisation of scientific data. It is primarily used for neutron and muon data at several facilities worldwide. One of the core sub-systems of Mantid is the curve fitting system. Mantid also includes generic and technique-specific fitting graphical user interfaces. The Mantid fitting system offers a great deal of flexibility in that it is possible to add and combine different functions, minimizers, types of constraints, and cost functions as plug-ins. Users can apply different combinations of these elements through the same user interface either via scripting (commands and algorithms) or graphical user interfaces. In addition, some of these elements, such as functions, are easy to add as plug-ins via scripting in Python. Minimizers play a central role when fitting a function to experimental or simulated data. The minimizer is the method that adjusts the function parameters so that the model fits the data as closely as possible, whereas the cost function defines the concept of how close a fit is to the data. Local minimizers are widely used to fit neutron & muon data. Several local minimizers are supported in Mantid (as in other software packages used in the neutron, muon and x-rays community). However there is a lack of openly available comparisons. We have included in the latest release of Mantid (v3.7) [a comparison](http://docs.mantidproject.org/nightly/concepts/FittingMinimizers.html) of the performance of 8 different minimizers in terms of goodness of fit (chi-squared or similar statistics) and run time. The comparison has been done against the [NIST nonlinear regression problems](http://itl.nist.gov/div898/strd/general/dataarchive.html). This can inform users and developers as to: - What performance can be expected from different minimizers in relative terms and what alternatives might be more appropiate for different applications. - How modified minimizer methods or newly added ones perform as compared to already available alternatives. For the next releases of Mantid we plan to extend the comparison with test problems from neutron and muon data, considering different scientific areas, and also further visualization of fitting results. Furthermore, on the basis of our comparisons, we intend to incorporate a new, flexible minimizer, RAL-NLLS, whose aim is to improve the reliability and broaden the functionality of the Mantid fitting system.
Dr. Federico Montesino Pouzols (ISIS Facility, Science & Technology Facilities Council)
Dr. Anders Markvardsen (ISIS neutron & muon source, STFC) Dr. Jennifer Scott (Scientific Computing Department, STFC) Dr. Jonathan Hogg (Scientific Computing Department, STFC) Dr. Nicholas Draper (Tessella Ltd.) Prof. Nicholas Gould (Scientific Computing Department, STFC) Dr. Roman Tolchenov (Tessella Ltd.) Dr. Tyrone Rees (Scientific Computing Department, STFC)