What's New in IMSL C Numerical Library

data_read:

• Reads a delimited ascii flat file. Accepts numeric, string (char), and date/time fields and converts the data to a double matrix suitable for input into IMSL data mining algorithms.  See a full example of using this new functionality in our data ingestion blog.

Math/Library

Eigensystem Analysis:

• arpack_svd - Function arpack_svd computes some of the singular values and left and right singular vectors of a real rectangular matrix. The SVD is a very important factorization technique that has many applications in engineering, science and statistics. Example application fields are image processing (e.g. image compressing and reconstruction), signal processing (e.g. noise reduction in signals), applied mathematics (e.g. least squares and matrix approximation problems), control theory, pattern recognition, time series analysis and bioinformatics (e.g. SVD Analysis or Principal Component Analysis of gene expression data).
• arpack_general (complex) Function arpack_general (complex) uses an iterative method, called the implicitly restarted Arnoldi method, to compute a few eigenvalues and eigenvectors of a complex general matrix. It is mainly used on large sparse matrices. Typical application areas of sparse complex eigenvalue solvers like arpack_general are quantum physics, plasma physics, quantum chemistry, optics, electromagnetic simulations, frequency estimation in signal processing and eigenfrequency analysis in structural mechanics.

Data Mining:

• multiclass_auc - Computes the Area Under the Curve (AUC) for two-class classification problems, or a multiclass generalization to AUC for problems having more than two classes. The AUC is a popular and useful measure of accuracy for classification methods. The curve referenced in AUC is the Receiver Operating Characteristic (ROC) curve. For a two-class problem, the ROC is a plot of the false positive rate vs the true positive rate for a range of cutoff probability values.

Probability Distribution Functions and Inverses:

• Evaluation of the generalized Gaussian distribution (GGD). The GGD generalizes the normal (Gaussian) distribution by adding an additional shape parameter. Allowing for a variety of shapes different from the familiar bell-shape of the normal distribution, the GGD is a better fit for many processes. The GGD is widely used in signal and image processing applications.

Random Number Generation:

• random_generalized_gaussian Generates pseudorandom variates from the generalized Gaussian distribution.

zeros_poly function:

• Added companion matrix and Aberth's method according to D. A. Bini's implementation as root finding methods. The new methods can be called via optional arguments IMSL_COMPANION_METHOD and IMSL_ABERTH_METHOD, respectively.

zeros_poly (complex) function:

• Added companion matrix and Aberth's method according to D. A. Bini's implementation as root finding methods. The new methods can be called via optional arguments IMSL_COMPANION_METHOD and IMSL_ABERTH_METHOD, respectively.

min_uncon_polytope function:

• Fixed bugs in the computation of the shrinking step and the computation of the second worst point.

min_con_polytope function:

• Fixed bugs in the computation of the second worst and final best point.

pls_regression function:

• Added new optional arguments: IMSLS_OPT_N_COMPONENTS for the optimal component number, IMSLS_STANDARD_COEF(_USER) for the standard PLS regression coefficients, IMSLS_INTERCEPT_TERMS(_USER) for the intercept terms and IMSLS_PCT_VAR(_USER) for the percentage of variance of predictor and response variables explained by the components. 
• Improved the performance of the cross-validation section of the code that determines the optimal number of PLS components, and we've fixed a few defects.  More details can be found in the change log.

categorical_glm function:

• Refined computation of complementary log-log function and simplified computation of some internal constants.

arma function:

• Extended applicability of the method of moments from the standard ARMA model to general ARMA models.

support_vector_trainer function:

• Fixed an issue in the radial basis function kernel that significantly improving performance.

A number of bug fixes and performance improvements were implemented in the following chapters of the CMATH library:

• Linear Systems
• Interpolation and Approximation
• Quadrature
• Differential Equations
• Optimization
• Special Functions
• Utilities

A number of bug fixes and performance improvements were implemented in the following chapters of the CSTAT library:

• Regression
• Categorical and Discrete Data Analysis
• Time Series and Forecasting
• Probability Distribution Functions and Inverses
• Random Number Generation

Math and Stat User Guide now includes information about:

• OpenMP "schedule(runtime)" clause.
• OpenMP OMP_NUM_THREADS and OMP_NESTED environment.