doFORC tool for calculating first-order reversal curve diagrams of noisy scattered data

摘要

The first-order reversal curve (FORC) diagram method is one of the most successful characterization techniques used to characterize complex hysteretic phenomena not only in magnetism but also in other areas of science like in ferroelectricity, geology, archeology, in spin-transition materials, etc. Because the definition of the FORC diagram involves a second-order derivative, the main problem in their numerical calculation is that the derivative of a function for which only discrete noise contaminated data values are available magnifies the noise that is inevitably present in measurements. In this paper, we present the doFORC tool for calculating FORC diagrams of noise scattered data. It can provide both a smooth approximation of the measured magnetization and all its partial derivatives. Even if doFORC is mainly dedicated to FORC diagrams' computation, it can process a general set of arbitrarily distributed two-dimensional points. doFORC is a free, portable application working on various operating systems, with an easy to use graphical interface, with four regression methods implemented to obtain a smooth approximation of the data which may then be differentiated to obtain approximations for derivatives. In order to perform the diagnostics and goodness of fit, doFORC computes residuals to characterize the difference between the observed and predicted values, generalized cross-validation to measure the predictive performance, two information criteria to quantify the information that is lost by using an approximate model, and three degrees of freedom to compare different amounts of smoothing being performed by different smoothing methods. Based on these, doFORC can perform automatic smoothing parameter selection. Published under license by AIP Publishing.