XPFit performs advanced analysis of superposition of exponentially decaying curves with positive and negative amplitudes. XPFit effectively combines a user friendly, graphical interface with sophisticated mathematical algorithms for solving the associated ill-posed optimization problems.
XPFit software is based on Alango proprietary and well proven computational algorithms providing fast and reliable automatic fitting. The two main algorithms are: Global Least Squares Analysis (GLSA) algorithm and Non-negative Truncated Singular Value Decomposition (NTSVD) algorithm.
GLSA minimization algorithm and software library
were developed for treatment of unstable, non-linear least squares optimisation
problems with multiple local minima. Performance of traditional Marquardt-Levenberg
algorithm is generally inadequate for these types of problems that are typical
for multiset/multimodel fitting tasks.
Exceptional robustness of GLSA approach is achieved
by:
- Ensuring that only reliable directions are considered on each iteration step. Singular value decomposition of the corresponding Jacobian matrix provides the necessary information
- Adaptive step length strategy used for numerical differentiation while computing the Jacobian matrix
NTSVD algorithm and the corresponding software library were developed for the treatment of severe ill-posed mathematical problems where the condition of non-negativity may be applied to the solution due to physical nature of the problem. Such condition may provided significant stabilization of the problem allowing to recover multidimensional information from otherwise untreatable problem. NTSVD algorithm is the only approach that combines:
- Singular Value Decomposition - the most effective way for stabilization of ill-posed mathematical problems
- Non Negative Least Squares (NNLS) algorithm
Discrete Components Analysis
Discrete Components Analysis provides robust multi-exponential analysis (up to four components) with automatic choice of initial conditions. Robust convergence in ensured by using GLSA algorithm. Background is estimated automatically or fixed to predefined value. The fitting channel range is easily changed if the full range is inadequate.Decay Times Distribution Analysis
Robust, easy to use Distribution Analysis allows recovering of lifetime distribution function with up to 200 logarithmically or linear scaled distribution columns and simultaneous (optional) estimation of background parameter. The functionality is based on NTSVD software library. The fitting channels range is easily changed. The optimal level or "regularization" is set automatically. A priori information about the distribution may be utilized by using a "resolution slider" that allows making other than default trade-off between the smoothness and fitting quality.Global Decay Times Analysis
The Global Analysis allows simultaneous analysis of several sets of experimental data where some (or all) decay times are linked together (e.i. must have the same values). This functionality is achieved by using GLSA software library.Additional functionality
XPFit includes many other new features that make it unique software for decay curves analysis:- Simultaneous plot of decay curves, residuals, computed graphical representation of multi-exponential analysis and numerical results
- Simultaneous analysis and overlapping presentation of results for several decay curves greatly simplifies comparison without using any external software
- Simultaneous analysis and results presentation of experimental data by different processing methods provides additional confidence in the results
- Export of results in text format or in one of popular image formats
- Export of results into file or clipboard for easy import into documents and presentations
XPFit screenshot example
