  First-order reversal curves (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, light-induced and pressure hysteresis 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 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.
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 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.
