Global and Target Analysis constitute a methodology to describe spectroscopic data that have been measured as a function of independent variables (van Stokkum et al. 2004; Mullen and van Stokkum 2009). The most important data are time-resolved spectra, where the dynamic response of a system after an excitatory input is measured in order to identify the system. The time resolution can range from femtoseconds to minutes. The spectra can be emission or difference absorption, in both the visible and infrared, and in stimulated Raman spectroscopy. In global analysis the dynamics of the system is described as a linear combination of exponential decays. In target analysis compartmental models are used to describe the system with the help of coupled ordinary differential equations. Each compartment has a spectrum, and can exchange with other compartments. The parameters of the model are the rate constants that describe the exchange and the spectra. The parameter estimation is based upon the variable projection algorithm (van Stokkum et al. 2004; Mullen and van Stokkum 2009; Golub and LeVeque 1979). Public domain software for Global and Target Analysis has been developed on the basis of R (TIMP) and using Java (Glotaran 1) (Mullen and van Stokkum 2007; Snellenburg et al. 2012). Glotaran 2.0 is a completely new implementation, based upon Python. We leverage the libraries NumPy, SciPy and LmFit to enable variable Projection in Python and created a powerful modelling language, which allows a non-programmer scientist to model time-resolved spectra with great flexibility in order to identify highly complex systems.
Golub GH, LeVeque RJ (1979) Extensions and uses of the variable projection algorithm for solving nonlinear least squares problems. Proc. of the 1979 Army Numerical Analysis and Comp. Conf., ARO Report 79-3. Mullen KM, van Stokkum IHM (2007) TIMP: An R package for modeling multi-way spectroscopic measurements. Journal of Statistical Software 18 (3). Mullen KM, van Stokkum IHM (2009) The variable projection algorithm in time-resolved spectroscopy, microscopy and mass spectrometry applications. Numerical Algorithms 51 (3):319-340. Snellenburg JJ, Laptenok SP, Seger R, Mullen KM, van Stokkum IHM (2012) Glotaran: a Java-based Graphical User Interface for the R-package TIMP. Journal of Statistical Software 49:1-22. van Stokkum IHM, Larsen DS, van Grondelle R (2004) Global and target analysis of time-resolved spectra. Biochimica Et Biophysica Acta 1657:82-104.