About

General description of software

FACPACK is a numerical software for the computation of multi-component factorizations for spectroscopic data matrices. For a time series of spectra taken from a chemical reaction system the software helps to recover the spectra and concentration profiles of the underlying pure components. The chemical reaction system can consist of two, three or four chemical components. In cases of more components, spectral windows that represent a maximum of four components can be used to start the decomposition analysis.

Usually, no unique nonnegative factorisation exists for these decomposition problems. However, FACPACK can compute the set of all nonnegative factorizations and can display the results in a certain low-dimensional form, the so-called Area of Feasible Solutions (AFS). It is also possible to present the feasible factors in the form of feasible bands. FACPACK supports the user in reducing the sets of feasible factors to the chemically and physically meaningful decompositions by means of adding proper constraints on the solution.

The software needs as input a mat-file that contains the spectral data matrix whose rows are formed by the series of spectra. FACPACK comes with a user-friendly graphical interface. The program output can be accessed in graphical and numerical form for a user-defined postprocessing.

FACPACK is optimized for numerical efficiency and robustness with respect to noise. The core of the software is a C-program, which is called for any time-consuming numerical computations. The C-core uses the LAPACK library and the ACM routine NL2SOL from netlib.org. Executable code is available for the following architectures: Windows 32/64 bit, Unix 32/64 bit and Mac 64 bit.

Modules of FACPACK

The following modules are included in FACPACK, Rev. 1.3:

  1. Baseline correction module:
    • Interactive window selection for the baseline correction,
    • Fast baseline correction for each spectrum controlled by "zero-intervals",
    • Baseline models by polynomials, Gauss curves or Lorentz curves.
  2. AFS computation module (2,3 and 4 components):
    • Computation of an initial singular value decomposition (SVD) and of an initial nonnegative matrix factorisation (NMF),
    • Computation of the AFS for the spectral factor A (or for concentration factor C after transposing D),
    • Representation of the factors with respect to a certain grid,
    • Live-view mode allows an interactive representation of the factors while moving the mouse pointer through the AFS,
    • Reduction of the AFS: computation of the restricted AFS after detecting and locking known spectra (or concentration profiles).
  3. Generalized Borgen plots module:
    • Computation of classical Borgen plots (Borgen, Kowalski [2] and Rajkó, István [6]),
    • Computation of generalized Borgen plots for perturbed data [5],
    • Factor representation and live-view mode for interactive representation,
    • Reduction of the AFS by factor locking.
  4. Complementarity & AFS module (2, 3 and 4 components):
    • Computation of FIRPOL and/or of the AFS for the factors C and A,
    • Interactive construction of feasible factorisations in a live-view mode,
    • Reduction of the rotational ambiguity in the AFS by the complementarity theorem,
    • Import of pure concentration profiles or spectra from MATLAB files,
    • Contour plot of various soft constraint functions in the AFS.
  5. Peak Group Analysis:
    • Computation of single pure component spectra,
    • Selection of frequency windows for Peak Group Analysis,
    • Interactive modification of weight factors,
    • Combination of single pure component spectra for a complete pure component decomposition.
  6. FACPACK library:
    • Organizing computed single component spectra,
    • Interactive applications to various modules.

Video tutorial

This video can also be found in downloads.

Users Guide

This file can also be found in downloads.