IMSL^® C Numerical Library Function Catalog

Version 2025.1

At the heart of the IMSL C Numerical Library is a comprehensive set of pre-built mathematical and statistical analysis functions that developers can embed directly into their applications. Available for a wide range of computing platforms, the robust, scalable, portable and high performing IMSL analytics allow developers to focus on their domain of expertise and reduce development time.

COST-EFFECTIVENESS AND VALUE

The IMSL C Numerical Library significantly shortens application time to market and promotes standardization. Descriptive function names and variable argument lists have been implemented to simplify calling sequences. Using the IMSL C Library reduces costs associated with the design, development, documentation, testing and maintenance of applications. Robust, scalable, portable, and high performing analytics with IMSL forms the foundation for inherently reliable applications.

A RICH SET OF PREDICTIVE ANALYTICS FUNCTIONS

The library includes a comprehensive set of functions for machine learning, data mining, prediction, and classification, including:

Time series models such as ARIMA, GARCH, and VARMA vector auto-regression.
Predictive models such as decision trees, random forest, stochastic gradient boosting, support vector machines, neural networks, linear and multinomial logistic regression, and Bayes classification.
Data mining algorithms such as K-means and hierarchical clustering, Apriori market basket analysis and much more.

The IMSL C Library also includes functions for analyzing streaming data and working with big or distributed data.

A SUITE OF OPTIMIZATION FUNCTIONS

The library includes a suite of optimization methods for different problems including multivariate, derivative free, constrained or unconstrained, dense or sparse, linear or general objective functions. The library provides numerous functions for solving linear systems and systems of differential equations and offers broad coverage for mathematical analysis, including transforms, convolutions, splines, quadrature, and more.

EMBEDDABILITY

Development is made easier because library code readily embeds into application code, with no additional infrastructure such as app/management consoles, servers, or programming environments needed.

Wrappers complicate development by requiring the developer to access external compilers and pass arrays or user-defined data types to ensure compatibility between the different languages. The IMSL C Library allows developers to write, build, compile and debug code in a single environment, and to easily embed analytic functions in applications and databases.

RELIABILITY

100% pure C code maximizes robustness. It allows faster and easier debugging, through superior error handling that not only conveys the error condition, but also suggests corrective action if appropriate. The result is reduced application support cost due to the minimization of user error and data issues.

The IMSL C Library has been rigorously tested by Rogue Wave and seasoned by all industry verticals for over 40 years. You can expect consistent results across all supported platforms and languages, which makes platform migration and upgrade easy and efficient.

HIGH PERFORMANCE

The IMSL C Library integrates third-party, high-performance vendor BLAS libraries. For many linear algebra functions, work can be offloaded to the vendor library for enhanced performance. The calling sequences for the IMSL functions are unchanged, so there is no learning curve and users can be productive immediately.

The library is also designed to take advantage of symmetric multiprocessor (SMP) systems, both multi-CPU and multi-core. Many algorithms leverage OpenMP directives on supported environments to distribute calculations across available resources. In areas such as linear algebra and Fast Fourier Transforms, third-party high-performance vendor libraries leverage SMP capabilities on a variety of systems.

SCALABILITY

The IMSL C Library supports scalability through:

An enhanced ability to analyze time-sequenced data, or streaming, real-time data that isn’t stored.
Improved algorithms that can analyze data sets too large to fit into memory or that exist on separate nodes.
Memory management that ensures applications will not crash when they encounter a low memory condition.

USER FRIENDLY NOMENCLATURE

The IMSL C Library uses descriptive, explanatory function names for intuitive programming that:

Are easy to identify and use, and prevent conflicts with other software.
Provide a common root name for numerical functions that offer the choice of multiple precisions.

PROGRAMMING INTERFACE FLEXIBILITY

The IMSL C Library takes full advantage of the intrinsic characteristics and desirable features of the C language.

The functions support variable-length argument lists, where the concise set of required arguments contains only information necessary for usage. Optional arguments provide added functionality and power to each function. Memory allocation can be handled by the library or by the developer. Finally, user-defined functions are implemented with interfaces C developers will find natural.

THREAD SAFETY

The IMSL C Library is thread-safe. Thread safety allows the C Library to be used in multi-threaded applications where performance benefits can be realized through concurrent and/or parallel execution.

COMPREHENSIVE DOCUMENTATION

Documentation for the IMSL C Numerical Library is comprehensive, clearly written and standardized. The documentation, in multiple formats:

Provides organized, easy-to-find information.
Documents, explains, and provides references for algorithms.
Gives at least one example of each function’s usage, with sample input and result.

UNMATCHED PRODUCT SUPPORT

Behind every Rogue Wave license is a team of professionals ready to provide expert answers to questions about the IMSL Numerical Libraries.

Product support:

Gives users direct access to Rogue Wave’s resident staff of expert product support specialists.
Provides prompt, two-way communication with solutions to a user’s programming needs.
Includes product maintenance updates.

PROFESSIONAL SERVICES

Rogue Wave offers expert consulting services for algorithm development as well as complete application development. Please contact Rogue Wave to learn more about its extensive experience in developing custom algorithms, building algorithms on scalable platforms, and full applications development.

Mathematical Functionality Overview

The IMSL C Numerical Library is a collection of the most commonly required numerical functions, tailored for a C programmer’s needs. The mathematical functionality is organized into 12 sections. These capabilities range from solving systems of linear equations to optimization.

Linear Systems - including real and complex, full and sparse matrices, linear least squares, matrix decompositions, generalized inverses and vector-matrix operations. The least squares solvers may include non-negative and general linear constraints. Matrix decompositions now include non-negative, low-rank factorizations.

Eigensystems Analysis - including eigenvalues and eigenvectors of complex, real symmetric and complex Hermitian matrices.

Interpolation and Approximation - including constrained curve-fitting splines, cubic splines, least-squares approximation and smoothing, and scattered data interpolation.

Integration and Differentiation - including univariate, multivariate, Gauss quadrature and quasi-Monte Carlo.

Differential Equations - using Adams-Gear and Runge-Kutta methods for stiff and non-stiff ordinary differential equations, with support for partial differential equations, including the Feynman-Kac solver. Also included are second-order ODE solvers, constrained DAE solvers, and a method of lines PDE solver.

Transforms- including real and complex, one- and two-dimensional Fast Fourier Transforms, as well as convolutions, correlations and Laplace transforms.

Nonlinear Equations - including zeros and root finding of polynomials, zeros of a function and root of a system of equations.

Optimization - including unconstrained linearly and nonlinearly constrained minimizations and linear and quadratic programming interior point algorithms.

Special Functions - including error and gamma functions, real order complex valued Bessel functions and statistical functions.

Financial Functions - including functions for Bond and cash-flow analysis.

Random Number Generation - including a generator for multivariate normal distributions and pseudorandom numbers from several distributions, including gamma, Poisson and beta. Also, support for low discrepancy series using a generalized Faure sequence.

Utilities - including CPU time used, machine, mathematical, physical constants, retrieval of machine constants and customizable error-handling.

Statistical Functionality Overview

The statistical functionality is organized into thirteen sections. These capabilities range from analysis of variance to random number generation.

Basic Statistics - including univariate summary statistics, frequency tables, and rank and order statistics.

Regression - including linear (multivariate), polynomial, and nonlinear regression models as well as robust alternatives such as Lpnorm and Partial Least Squares. This section also contains stepwise and all best variable selection methods.

Correlation and Covariance - including sample variance-covariance, partial correlation and covariances, pooled variance-covariance and robust estimates of a covariance matrix and mean factor.

Analysis of Variance and Designed Experiments - analysis of standard factorial experiments, randomized complete block designs, Latin-square, lattice, split-plot and strip-plot and related experiments; analysis of hierarchical data, computation of false discovery rates and standard tests for multiple comparisons and homogeneity of variance.

Categorical and Discrete Data Analysis - including chi-squared analysis of a two-way contingency table, exact probabilities in a two-way contingency table, logistic regression for binomial or multinomial responses, and the analysis of categorical data using general linear models.

Nonparametric Statistics - including sign tests, Wilcoxon sum tests and Cochran Q test for related observations.

Tests of Goodness-of-Fit - including the chi-squared goodness-of-fit test, the Kolmogorov/Smirnov one-and two-sample tests for continuous distributions, the Shapiro-Wilk, Lilliefors, chi-squared, Anderson-Darling, and Cramer-Von Mises tests for normality, Mardia’s test for multivariate normality, and the runs, pairs-serial, d2, and triplets tests for randomness.

Time Series Analysis and Forecasting - analysis and forecasting of time series using a nonseasonal ARMA model, ARIMA with regression, Holt-Winters exponential smoothing, GARCH, Kalman filtering; various fitting and diagnostic utilities including portmanteau lack of fit test and difference of a seasonal or nonseasonal time series.

Multivariate Analysis - including principal component analysis, discriminant analysis, K-means and hierarchical cluster analysis, and factor analysis. Methods of factor analysis include principal factor, image analysis, unweighted least squares, generalized least squares, maximum likelihood, and various factor rotations.

Survival Analysis - including analysis of data using the Cox linear survival model, Kaplan-Meier survival estimates, actuarial survival tables, and non-parametric survival estimates.

Probability Distribution Functions and Inverses - including the cumulative distribution function (CDF), inverse CDF, and probability density function (PDF) for many common discrete and continuous distributions, as well as multivariate normal, non-central F, Chi-square, Beta, Students t, and others. This section also includes parameter estimation by maximum likelihood.

Random Number Generation - including generators for many univariate discrete and continuous distributions, as well as multivariate Normal, multinomial, Gaussian or Student’s t copula, an ARMA or nonhomogeneous Poisson process, order statistics, permutations, and more. This section also allows a choice of pseudorandom number generators, including the Mersenne Twister.

Data Mining - including decision trees, vector auto-regression, Apriori analysis, cluster analysis, Kohonen self-organizing maps, support vector machine, ensemble models, genetic algorithms, PCA, factor analysis, feed-forward neural networks, neural network data pre- and post-processing algorithms, and much more.

IMSL® Libraries Also Available for Fortran and Java

IMSL Fortran Numerical Library

The IMSL® Fortran Numerical Library is the gold standard mathematical and statistical code library for Fortran programmers developing high performance computing applications. The IMSL Fortran Library contains highly accurate and reliable Fortran algorithms with full coverage of mathematics and statistics and complete backward compatibility.

The IMSL Fortran Library is a comprehensive library of mathematical and statistical algorithms available in one cohesive package. It combines the powerful and flexible interface features of the Fortran language with the performance benefits of both distributed memory and shared memory multiprocessing architectures.

JMSL™ Numerical Library for Java Applications

The JMSL Numerical Library for Java applications is the broadest collection of mathematical, statistical, financial, data mining and charting classes available in 100% Java. It is the only Java programming solution that combines integrated charting with the reliable mathematical and statistical functionality of the industry-leading IMSL Numerical Library algorithms. This blend of advanced numerical analysis and visualization on the Java platform allows organizations to gain insight into valuable data and share analysis results across the enterprise quickly. The JMSL Library continues to be the leader, providing robust and portable data analysis and visualization technology for the Java platform, and a fast, scalable framework for tailored analytical applications.

Access from Python

The IMSL® C Library functions is also available within Python for rapid prototyping, and a collection of Python wrappers to the algorithms in the IMSL C Numerical Library are available on request. By using the same IMSL algorithms in the prototype as in the production code, developers can deliver accurate and consistent results in production application sooner rather than later. For more information, please contact info@roguewave.com.

IMSL C MATH LIBRARY

CHAPTER 1: LINEAR SYSTEMS

LINEAR EQUATIONS WITH FULL MATRICES
FUNCTION	DESCRIPTION
lin_sol_gen	Solves a real general system of linear equations `Ax = b`.
lin_sol_gen (complex)	Solves a complex general system of linear equations `Ax = b`.
lin_sol_posdef	Solves a real symmetric positive definite system of linear equations `Ax = b`.
lin_sol_posdef (complex)	Solves a complex Hermitian positive definite system of linear equations `Ax = b`.

LINEAR EQUATIONS WITH BAND MATRICES
FUNCTION	DESCRIPTION
lin_sol_gen_band	Solves a real general band system of linear equations `Ax = b`.
lin_sol_gen_band (complex)	Solves a complex general band system of linear equations `Ax = b`.
lin_sol_posdef_band	Solves a real symmetric positive definite system of linear equations `Ax = b` in band symmetric storage mode.
lin_sol_posdef_band (complex)	Solves a complex Hermitian positive definite system of linear equations `Ax = b` in band symmetric storage mode.

LINEAR EQUATIONS WITH GENERAL SPARSE MATRICES
FUNCTION	DESCRIPTION
lin_sol_gen_coordinate	Solves a sparse system of linear equations Ax = b.
lin_sol_gen_coordinate (complex)	Solves a system of linear equations Ax = b, with sparse complex coefficient matrix A.
superlu	Computes the LU factorization of a general sparse matrix by a column method and solves the real sparse linear system of equations Ax = b.
superlu (complex)	Computes the LU factorization of a general complex sparse matrix by a column method and solves the complex sparse linear system of equations Ax = b.
superlu_smp	Computes the `LU` factorization of a general sparse matrix by a left-looking column method using OpenMP parallelism, and solves the real sparse linear system of equations `Ax =b`.
superlu_smp (complex)	Computes the LU factorization of a general complex sparse matrix by a left-looking column method using OpenMP parallelism and solves the complex sparse linear system of equations Ax = b.
lin_sol_posdef_coordinate	Solves a sparse real symmetric positive definite system of linear equations Ax = b.
lin_sol_gen_posdef_coordinate (complex)	Solves a sparse Hermitian positive definite system of linear equations Ax = b.
sparse_cholesky_smp	Computes the Cholesky factorization of a sparse real symmetric positive definite matrix A by an OpenMP parallelized supernodal algorithm and solves the sparse real positive definite system of linear equations Ax = b.
sparse_cholesky_smp (complex)	Computes the Cholesky factorization of a sparse (complex) Hermitian positive definite matrix A by an OpenMP parallelized supernodal algorithm and solves the sparse Hermitian positive definite system of linear equations Ax = b.
lin_sol_gen_min_residual	Solves a linear system Ax = b using the restarted generalized minimum residual (GMRES) method .
lin_sol_def_cg	Solves a real symmetric definite linear system using a conjugate gradient method.

ITERATIVE METHODS
FUNCTION	DESCRIPTION
lin_sol_gen_min_residual	Solves a linear system Ax = b using the restarted generalized minimum residual (GMRES) method .
lin_sol_def_cg	Solves a real symmetric definite linear system using a conjugate gradient method.

LINEAR LEAST-SQUARES WITH FULL MATRICES
FUNCTION	DESCRIPTION
lin_least_squares_gen	Solves a linear least-squares problem Ax = b.
nonneg_least_squares	Computes the non-negative least squares (NNLS) solution of an m × n real linear least squares system, Ax ≅ b,x ≥ 0.
lin_lsq_lin_constraints	Solves a linear least-squares problem with linear constraints.
nonneg_matrix_factorization	Given an m × n real matrix A ≥ 0 and an integer k ≤ min(m,n), computes a factorization A ≅ FG.
lin_svd_gen	Computes the SVD, A = USVᵀ, of a real rectangular matrix A.
lin_svd_gen (complex)	Computes the SVD, A = USVᵀ, of a complex rectangular matrix A.
lin_sol_nonnegdef	Solves a real symmetric nonnegative definite system of linear equations Ax = b.

CHAPTER 2: EIGENSYSTEM ANALYSIS

ORDINARY LINEAR EIGENSYSTEM PROBLEMS
FUNCTION	DESCRIPTION
eig_gen	Computes the eigenexpansion of a real matrix A.
eig_gen (complex)	Computes the eigenexpansion of a complex matrix A.
eig_sym	Computes the eigenexpansion of a real symmetric matrix A.
eig_sym_band	Computes all eigenvalues or eigenpairs of a real symmetric matrix A in band storage format. Optionally, interval and extreme eigenvalues or eigenpairs of A can be computed.
eig_herm (complex)	Computes the eigenexpansion of a complex Hermitian matrix A.
eig_herm_band (complex)	Computes the eigenexpansion of a complex Hermitian matrix A in band storage format.

GENERALIZED LINEAR EIGENSYSTEM PROBLEMS
FUNCTION	DESCRIPTION
eig_symgen	Computes the generalized eigenexpansion of a system Ax =λBx. A and B are real and symmetric. B is positive definite.
geneig	Computes the generalized eigenexpansion of a system Ax =λBx, with A and B real.
geneig (complex)	Computes the generalized eigenexpansion of a system Ax =λBx, with A and B complex.

EIGENVALUES AND EIGENVECTORS COMPUTED WITH ARPACK
FUNCTION	DESCRIPTION
arpack_symmetric	Computes some of the eigenvalues and eigenvectors of the generalized real symmetric eigenvalue problem Ax =λBx using an implicitly restarted Arnoldi method (IRAM).
arpack_svd	Computes selected singular values and singular vectors of a real rectangular matrix A = UΣV^T .
arpack_general	Computes some of the eigenvalues and eigenvectors of the generalized real nonsymmetric eigenvalue problem Ax =λBx using an implicitly restarted Arnoldi method (IRAM).
arpack_general (complex)	Computes selected eigenvalues and eigenvectors of the generalized complex eigenvalue problem Ax = λBx.

CHAPTER 3: INTERPOLATION AND APPROXIMATION

CUBIC SPLINE INTERPOLATION
FUNCTION	DESCRIPTION
cub_spline_interp_e_cnd	Computes a cubic spline interpolant, specifying various endpoint conditions.
cub_spline_interp_shape	Computes a shape-preserving cubic spline.
cub_spline_tcb	Computes a tension-continuity-bias (TCB) cubic spline interpolant. This is also called a Kochanek - Bartels spline and is a generalization of the Catmull-Rom spline.

CUBIC SPLINE EVALUATION AND INTEGRATION
FUNCTION	DESCRIPTION
cub_spline_value	Computes the value of a cubic spline or the value of one of its derivatives.
cub_spline_integral	Computes the integral of a cubic spline.

SPLINE INTERPOLATION
FUNCTION	DESCRIPTION
spline_interp	Computes a spline interpolant.
spline_knots	Computes the knots for a spline interpolant.
spline_2d_interp	Computes a two-dimensional, tensor-product spline interpolant from two - dimensional, tensor - product data.

SPLINE EVALUATION AND INTEGRATION
FUNCTION	DESCRIPTION
spline_value	Computes the value of a spline or the value of one of its derivatives.
spline_integral	Computes the integral of a spline.
spline_2d_value	Computes the value of a tensor-product spline or the value of one of its partial derivatives.
spline_2d_integral	Evaluates the integral of a tensor-product spline on a rectangular domain.

MULTI-DIMENSIONAL INTERPOLATION
FUNCTION	DESCRIPTION
spline_nd_interp	Performs multidimensional interpolation and differentiation for up to 7 dimensions.

LEAST-SQUARES APPROXIMATION AND SMOOTHING
FUNCTION	DESCRIPTION
user_fcn_least_squares	Computes a least-squares fit using user-supplied functions.
spline_least_squares	Computes a least-squares spline approximation.
spline_2d_least_squares	Computes a two-dimensional, tensor-product spline approximant using least squares.
cub_spline_smooth	Computes a smooth cubic spline approximation to noisy data by using cross - validation to estimate the smoothing parameter or by directly choosing the smoothing parameter.
spline_lsq_constrained	Computes a least-squares constrained spline approximation.
smooth_1d_data	Smooth one-dimensional data by error detection.

SCATTERED DATA INTERPOLATION
FUNCTION	DESCRIPTION
scattered_2d_interp	Computes a smooth bivariate interpolant to scattered data that is locally a quintic polynomial in two variables.

SCATTERED DATA LEAST SQUARES
FUNCTION	DESCRIPTION
radial_scattered_fit	Computes an approximation to scattered data in Rⁿ for n≥ 1 using radial-basis functions.
radial_evaluate	Evaluates a radial basis fit.

CHAPTER 4: QUADRATURE

UNIVARIATE QUADRATURE
FUNCTION	DESCRIPTION
int_fcn_sing	Integrates a function, which may have endpoint singularities, using a globally adaptive scheme based on Gauss - Kronrod rules.
int_fcn_sing_1d	Integrates a function with a possible internal or endpoint singularity.
int_fcn	Integrates a function using a globally adaptive scheme based on Gauss - Kronrod rules.
int_fcn_sing_pts	Integrates a function with singularity points given.
int_fcn_alg_log	Integrates a function with algebraic-logarithmic singularities.
int_fcn_inf	Integrates a function over an infinite or semi-infinite interval.
int_fcn_trig	Integrates a function containing a sine or a cosine factor.
int_fcn_fourier	Computes a Fourier sine or cosine transform.
int_fcn_cauchy	Computes integrals of the form in the Cauchy principal value sense.
int_fcn_smooth	Integrates a smooth function using a nonadaptive rule.

MULTIDIMENSIONAL QUADRATURE
FUNCTION	DESCRIPTION
int_fcn_2d	Computes a two - dimensional iterated integral.
int_fcn_sing_2d	Integrates a function of two variables with a possible internal or endpoint singularity.
int_fcn_sing_3d	Integrates a function of three variables with a possible internal or endpoint singularity.
int_fcn_hyper_rect	Integrate a function on a hyper- rectangle,
int_fcn_qmc	Integrates a function over a hyper - rectangle using a quasi-Monte Carlo method.

GAUSS RULES AND THREE-TERM RECURRENCES
FUNCTION	DESCRIPTION
gauss_quad_rule	Computes a Gauss, Gauss - Radau, or Gauss - Lobatto quadrature rule with various classical weight functions.

DIFFERENTIATION
FUNCTION	DESCRIPTION
fcn_derivative	Computes the first, second or third derivative of a user-supplied function.

CHAPTER 5: DIFFERENTIAL EQUATIONS

FIRST-ORDER ORDINARY DIFFERENTIAL EQUATIONS
SOLUTION OF THE INITIAL VALUE PROBLEM FOR ODES
FUNCTION	DESCRIPTION
ode_runge_kutta	Solves an initial-value problem for ordinary differential equations using the Runge - Kutta - Verner fifth-order and sixth-order method.

SOLUTION OF THE BOUNDARY VALUE PROBLEM FOR ODES
FUNCTION	DESCRIPTION
bvp_finite_difference	Solves a (parameterized) system of differential equations with boundary conditions at two points, using a variable order, variable step size finite difference method with deferred corrections.

SOLUTION OF DIFFERENTIAL-ALGEBRAIC SYSTEMS

FUNCTION

DESCRIPTION

differential_algebraic_eqs

Solves a first order differential-algebraic system of equations,

g(t, y, y’) = 0, with optional additional constraints and user-defined linear system solver.

FIRST-AND-SECOND ORDER ORDINARY DIFFERENTIAL EQUATIONS
SOLUTION OF THE INITIAL VALUE PROBLEM FOR ODES
FUNCTION	DESCRIPTION
ode_adams_krogh	Solves an initial-value problem for a system of ordinary differential equations of order one or two using a variable order Adams method.

PARTIAL DIFFERENTIAL EQUATIONS
SOLUTION OF SYSTEMS OF PDES IN ONE DIMENSION
FUNCTION	DESCRIPTION
pde_1d_mg	Solves a system of one-dimensional time-dependent partial differential equations using a moving - grid interface.
modified_method_of_lines	Solves a system of partial differential equations of the form u_t = f(x, t, u, u_x, u_xx) using the method of lines.
feynman_kac	Solves a generalized Feynman-Kac equation on a finite interval using Hermite quintic splines.
feynman_kac_evaluate	Computes the value of a Hermite quintic spline or the value of one of its derivatives .

SOLUTION OF A PDE IN TWO DIMENSIONS
FUNCTION	DESCRIPTION
fast_poisson_2d	Solves Poisson’s or Helmholtz’s equation on a two-dimensional rectangle using a fast Poisson solver based on the HODIE finite-difference scheme on a uniform mesh.

CHAPTER 6: TRANSFORMS

REAL TRIGONOMETRIC FFT
FUNCTION	DESCRIPTION
fft_real	Computes the discrete Fourier transform of a real sequence.
fft_real_init	Computes the parameters for imsl_f_fft_real.

COMPLEX EXPONENTIAL FFT
FUNCTION	DESCRIPTION
fft_complex	Computes the complex discrete Fourier transform of a complex sequence.
fft_complex_init	Computes the parameters for imsl_c_fft_complex.

REAL SINE AND COSINE FFTS
FUNCTION	DESCRIPTION
fft_cosine	Computes the discrete Fourier cosine transformation of an even sequence.
fft_cosine_init	Computes parameters needed by imsl_f_fft_cosine.
fft_sine	Computes the discrete Fourier sine transformation of an odd sequence.
fft_sine_init	Computes parameters needed by imsl_f_fft_cosine.

TWO - DIMENSIONAL FFTS
FUNCTION	DESCRIPTION
fft_2d_complex	Computes the complex discrete two-dimensional Fourier transform of a complex two-dimensional array.

CONVOLUTIONS AND CORRELATIONS
FUNCTION	DESCRIPTION
convolution	Computes the convolution of two real vectors.
convolution (complex)	Computes the convolution, and optionally, the correlation of two complex vectors.

LAPLACE TRANSFORM
FUNCTION	DESCRIPTION
inverse_laplace	Computes the inverse Laplace transform of a complex function.

CHAPTER 7: NONLINEAR EQUATIONS

ZEROS OF A POLYNOMIAL
FUNCTION	DESCRIPTION
zeros_poly	Finds the zeros of a polynomial with real coefficients using the Jenkins-Traub three-stage algorithm.
zeros_poly (complex)	Finds the zeros of a polynomial with complex coefficients using the Jenkins-Traub three-stage algorithm.

ZEROS OF A FUNCTION
FUNCTION	DESCRIPTION
zero_univariate	Finds a zero of a real univariate function.
zero_function	Finds the real zeros of a real, continuous, univariate function.

ROOT OF A SYSTEM OF EQUATIONS
FUNCTION	DESCRIPTION
zeros_sys_eqn	Solves a system of n nonlinear equations f(x) = 0 using a modified Powell hybrid algorithm.

CHAPTER 8: OPTIMIZATION

UNCONSTRAINED MINIMIZATION
UNIVARIATE FUNCTION
FUNCTION	DESCRIPTION
min_uncon	Finds the minimum point of a smooth function f(x) of a single variable using only function evaluations.
min_uncon_deriv	Finds the minimum point of a smooth function of a single variable using both function and first derivative evaluations.
min_uncon_golden	Finds the minimum point of a nonsmooth function of a single variable using the golden selection search method.

MULTIVARIATE FUNCTION
FUNCTION	DESCRIPTION
min_uncon_multivar	Minimizes a function f(x) of n variables using a quasi-Newton method.
min_uncon_polytope	Minimizes a function of n variables using a direct search polytope algorithm.

NONLINEAR LEAST SQUARES
FUNCTION	DESCRIPTION
nonlin_least_squares	Solves a nonlinear least-squares problem using a modified Levenberg-Marquardt algorithm.

LINEARLY CONSTRAINED MINIMIZATION
FUNCTION	DESCRIPTION
read_mps	Reads an MPS file containing a linear programming problem or a quadratic programming problem.
linear_programming	Solves a linear programming problem.
lin_prog	Solves a linear programming problem using the revised simplex algorithm.
quadratic_prog	Solves a quadratic programming problem subject to linear equality or inequality constraints.
sparse_lin_prog	Solves a sparse linear programming problem by an infeasible primal-dual interior-point method.
sparse_quadratic_prog	Solves a sparse convex quadratic programming problem by an infeasible primal-dual interior-point method.
min_con_gen_lin	Minimizes a general objective function subject to linear equality/inequality constraints.
bounded_least_squares	Solves a nonlinear least-squares problem subject to bounds on the variables using a modified Levenberg-Marquardt algorithm.
transport	Solves a transportation problem.
min_con_lin_trust_region	Minimizes a function of n variables subject to linear constraints using a derivative-free, interpolation-based trust-region method.
min_con_polytope	Minimizes a function of n variables subject to bounds on the variables using a direct search complex algorithm.

NONLINEARLY CONSTRAINED MINIMIZATION
FUNCTION	DESCRIPTION
constrained_nlp	Solves a general nonlinear programming problem using a sequential equality constrained quadratic programming method.

SERVICE ROUTINES
FUNCTION	DESCRIPTION
jacobian	Approximates the Jacobian of m functions in n unknowns using divided differences.

CHAPTER 9: SPECIAL FUNCTIONS

ERROR AND GAMMA FUNCTIONS
ERROR FUNCTIONS
FUNCTION	DESCRIPTION
erf	Evaluates the real error function erf(x).
erfc	Evaluates the real complementary error function erfc(x).
erf_inverse	Evaluates the real inverse error function erf^-1(x).
erfce	Evaluates the exponentially scaled complementary error function.
erfe	Evaluates a scaled function related to erfc(z).
erfc_inverse	Evaluates the real inverse complementary error function erfc^-1(x).
beta	Evaluates the real beta function β(x, y).
log_beta	Evaluates the logarithm of the real beta function ln β(x, y) .
beta_incomplete	Evaluates the real incomplete beta function Ix = βx(a,b)/β(a,b).

GAMMA FUNCTIONS
FUNCTION	DESCRIPTION
gamma	Evaluates the real gamma function Γ(x).
log_gamma	Evaluates the logarithm of the absolute value of the gamma function log \|Γ(x)\|.
gamma_incomplete	Evaluates the incomplete gamma function γ(a,x).

PSI FUNCTIONS
FUNCTION	DESCRIPTION
psi	Evaluates the derivative of the log gamma function.
psi1	Evaluates the second derivative of the log gamma function.

BESSEL FUNCTIONS
FUNCTION	DESCRIPTION
bessel_J0	Evaluates the real Bessel function of the first kind of order zero J₀(x).
bessel_J1	Evaluates the real Bessel function of the first kind of order one J₁(x).
bessel_Jx	Evaluates a sequence of Bessel functions of the first kind with real order and complex arguments.
bessel_Y0	Evaluates the real Bessel function of the second kind of order zero Y₀(x).
bessel_Y1	Evaluates the real Bessel function of the second kind of order one Y₁(x).
bessel_Yx	Evaluates a sequence of Bessel functions of the second kind with real order and complex arguments.
bessel_I0	Evaluates the real modified Bessel function of the first kind of order zero I₀(x).
bessel_exp_I0	Evaluates the exponentially scaled modified Bessel function of the first kind of order zero.
bessel_I1	Evaluates the real modified Bessel function of the first kind of order one I₁(x).
bessel_exp_I1	Evaluates the exponentially scaled modified Bessel function of the first kind of order one.
bessel_Ix	Evaluates a sequence of modified Bessel functions of the first kind with real order and complex arguments.
bessel_K0	Evaluates the real modified Bessel function of the second kind of order zero K₀(x).
bessel_exp_K0	Evaluates the exponentially scaled modified Bessel function of the second kind of order zero.
bessel_K1	Evaluates the exponentially scaled modified Bessel function of the second kind of order one.
bessel_exp_K1	Evaluates the exponentially scaled modified Bessel function of the second kind of order one.
bessel_Kx	Evaluates a sequence of modified Bessel functions of the second kind with real order and complex arguments.

ELLIPTIC INTEGRALS
FUNCTION	DESCRIPTION
elliptic_integral_K	Evaluates the complete elliptic integral of the kind K(x).
elliptic_integral_E	Evaluates the complete elliptic integral of the second kind E(x).
elliptic_integral_RF	Evaluates Carlson’s elliptic integral of the first kind R_F(x,y,z).
elliptic_integral_RD	Evaluates Carlson’s elliptic integral of the second kind R_D(x,y,z).
elliptic_integral_RJ	Evaluates Carlson’s elliptic integral of the third kind R_J(x,y,z,ρ).
elliptic_integral_RC	Evaluates an elementary integral from which inverse circular functions, logarithms, and inverse hyperbolic functions can be computed.

FRESNEL INTEGRALS
FUNCTION	DESCRIPTION
fresnel_integral_C	Evaluates the cosine Fresnel integral.
fresnel_integral_S	Evaluates the sine Fresnel integral.

AIRY FUNCTIONS
FUNCTION	DESCRIPTION
airy_Ai	Evaluates the Airy function.
airy_Bi	Evaluates the Airy function of the second kind.
airy_Ai_derivative	Evaluates the derivative of the Airy function.
airy_Bi_derivative	Evaluates the derivative of the Airy function of the second kind.

KELVIN FUNCTIONS
FUNCTION	DESCRIPTION
kelvin_ber0	Evaluates the Kelvin function of the first kind, ber, of order zero.
kelvin_bei0	Evaluates the Kelvin function of the first kind, bei, of order zero.
kelvin_ker0	Evaluates the Kelvin function of the second kind, ker, of order zero.
kelvin_kei0	Evaluates the Kelvin function of the second kind, kei, of order zero.
kelvin_ber0_derivative	Evaluates the derivative of the Kelvin function of the first kind, ber, of order zero.
kelvin_bei0_derivative	Evaluates the derivative of the Kelvin function of the first kind, bei, of order zero.
kelvin_ker0_derivative	Evaluates the derivative of the Kelvin function of the second kind, ker, of order zero.
kelvin_kei0_derivative	Evaluates the derivative of the Kelvin function of the second kind, kei, of order zero.

STATISTICAL FUNCTIONS
FUNCTION	DESCRIPTION
normal_cdf	Evaluates the standard normal (Gaussian) distribution function.
normal_inverse_cdf	Evaluates the inverse of the standard normal (Gaussian) distribution function.
chi_squared_cdf	Evaluates the chi-squared distribution function.
chi_squared_inverse_cdf	Evaluates the inverse of the chi-squared distribution function.
F_cdf	Evaluates the F distribution function.
F_inverse_cdf	Evaluates the inverse of the F distribution function.
t_cdf	Evaluates the Student’s t distribution function.
t_inverse_cdf	Evaluates the inverse of the Student’s t distribution function.
gamma_cdf	Evaluates the gamma distribution function.
binomial_cdf	Evaluates the binomial distribution function.
hypergeometric_cdf	Evaluates the hypergeometric distribution function.
poisson_cdf	Evaluates the Poisson distribution function.
beta_cdf	Evaluates the beta distribution function.
beta_inverse_cdf	Evaluates the inverse of the beta distribution function.
bivariate_normal_cdf	Evaluates the bivariate normal distribution function.

FINANCIAL FUNCTIONS
FUNCTION	DESCRIPTION
cumulative_interest	Evaluates the cumulative interest paid between two periods.
cumulative_principal	Evaluates the cumulative principal paid between two periods.
depreciation_db	Evaluates the depreciation of an asset using the fixed-declining balance method.
depreciation_ddb	Evaluates the depreciation of an asset using the double-declining balance method.
depreciation_sln	Evaluates the depreciation of an asset using the straight-line method.
depreciation_syd	Evaluates the depreciation of an asset using the sum-of-years digits method.
depreciation_vdb	Evaluates the depreciation of an asset for any given period using the variable-declining balance method.
dollar_decimal	Converts a fractional price to a decimal price.
dollar_fraction	Converts a decimal price to a fractional price.
effective_rate	Evaluates the effective annual interest rate.
future_value	Evaluates an investment’s future value.
future_value_schedule	Evaluates the future value of an initial principal taking into consideration a schedule of compound interest rates.
interest_payment	Evaluates the interest payment for an investment for a given period.
interest_rate_annuity	Evaluates an annuity’s interest rate per period.
internal_rate_of_return	Evaluates the internal rate of return for a schedule of cash flows.
internal_rate_schedule	Evaluates the internal rate of return for a schedule of cash flows. It is not necessary that the cash flows be periodic.
modified_internal_rate	Evaluates the modified internal rate of return for a schedule of periodic cash flows.
net_present_value	Evaluates an investment’s net present value. The calculation is based on a schedule of periodic cash flows and a discount rate.
nominal_rate	Evaluates the nominal annual interest rate.
number_of_periods	Evaluates the number of periods for an investment for which periodic and constant payments are made and the interest rate is constant.
payment	Evaluates the periodic payment for an investment.
present_value	Evaluates the net present value of a stream of equal periodic cash flows, which are subject to a given discount rate.
present_value_schedule	Evaluates the present value for a schedule of cash flows. It is not necessary that the cash flows be periodic.
principal_payment	Evaluates the payment on the principal for a specified period.

BOND FUNCTIONS
FUNCTION	DESCRIPTION
accr_interest_maturity	Evaluates the interest that has accrued on a security, which pays interest at maturity.
accr_interest_periodic	Evaluates the interest that has accrued on a security, which pays interest periodically.
bond_equivalent_yield	Evaluates a Treasury bill’s bond-equivalent yield.
convexity	Evaluates the convexity for a security.
coupon_days	Evaluates the number of days in the coupon period containing the settlement date.
coupon_number	Evaluates the number of coupons payable between the settlement date and the maturity date.
days_before_settlement	Evaluates the number of days starting with the beginning of the coupon period and ending with the settlement date.
days_to_next_coupon	Evaluates the number of days starting with the settlement date and ending with the next coupon date.
depreciation_amordegrc	Evaluates the depreciation for each accounting period .
depreciation_amorlinc	Evaluates the depreciation for each accounting period. This function is similar to depreciation amordegrc, except that depreciation_amordegrc has a depreciation coefficient that is applied during the evaluation that is based on the asset life.
discount_price	Evaluates a discounted security’s price per $100 face value.
discount_rate	Evaluates a security’s discount rate.
discount_yield	Evaluates a discounted security’s annual yield.
duration	Evaluates a security’s annual duration where the security has periodic interest payments.
interest_rate_security	Evaluates a fully invested security’s interest rate.
modified_duration	Evaluates a security’s modified Macauley duration assuming a par value of $100.
next_coupon_date	Evaluates the first coupon date that follows the settlement date.
previous_coupon_date	Evaluates the coupon date that immediately precedes the settlement date.
price	Evaluates a security’s price per $100 face value. The security pays periodic interest.
price_maturity	Evaluates a security’s price per $100 face value. The security pays interest at maturity.
received_maturity	Evaluates the amount one receives when a fully invested security reaches the maturity date.
treasury_bill_price	Evaluates a Treasury bill’s price per $100 face value.
treasury_bill_yield	Evaluates a Treasury bill’s yield.
year_fraction	Evaluates the fraction of a year represented by the number of whole days between two dates.
yield_maturity	Evaluates a security’s annual yield. The security pays interest at maturity.
yield_periodic	Evaluates a security’s yield. The security pays periodic interest.

CHAPTER 10: STATISTICS AND RANDOM NUMBER GENERATION

STATISTICS
FUNCTION	DESCRIPTION
simple_statistics	Computes basic univariate statistics.
table_oneway	Tallies observations into a one-way frequency table.
chi_squared_test	Performs a chi-squared goodness-of-fit test.
covariances	Computes the sample variance-covariance or correlation matrix.
regression	Fits a multiple linear regression model using least squares.
poly_regression	Performs a polynomial least-squares regression.
ranks	Computes the ranks, normal scores, or exponential scores for a vector of observations.

RANDOM NUMBERS
FUNCTION	DESCRIPTION
random_seed_get	Retrieves the current value of the seed used in the IMSL random number generators.
random_seed_set	Initializes a random seed for use in the IMSL random number generators.
random_option	Selects the uniform (0,1) multiplicative congruential pseudorandom number generator.
random_uniform	Generates pseudorandom numbers from a uniform (0,1) distribution.
random_normal	Generates pseudorandom numbers from a standard normal distribution using an inverse CDF method.
random_poisson	Generates pseudorandom numbers from a Poisson distribution.
random_gamma	Generates pseudorandom numbers from a standard gamma distribution.
random_beta	Generates pseudorandom numbers from a beta distribution .
random_exponential	Generates pseudorandom numbers from a standard exponential distribution.
faure_next_point	Computes a shuffled Faure sequence.

CHAPTER 11: PRINTING FUNCTIONS

PRINT
FUNCTION	DESCRIPTION
write_matrix	Prints a rectangular matrix (or vector) stored in contiguous memory locations.
page	Sets or retrieves the page width or length.
write_options	Sets or retrieves an option for printing a matrix.

CHAPTER 12: UTILITIES

SET OUTPUT FILES
FUNCTION	DESCRIPTION
output_file	Sets the output file or the error message output file.
version	Returns integer information describing the version of the library, license number, operating system, and compiler.

TIME AND DATE
FUNCTION	DESCRIPTION
ctime	Returns the number of CPU seconds used.
date_to_days	Computes the number of days from January 1, 1900, to the given date.
days_to_date	Gives the date corresponding to the number of days since January 1, 1900.

ERROR HANDLING
FUNCTION	DESCRIPTION
error_options	Sets various error handling options.
error_type	Gets the type corresponding to the error message from the last function called.
error_message	Gets the text of the error message from the last function called.
error_code	Gets the code corresponding to the error message from the last function called.
initialize_error_handler	Initializes the IMSL C Numerical Library error handling system.
set_user_fcn_return_flag	Indicates a condition has occurred in a user-supplied function necessitating a return to the calling C Numerical Library function.

C RUNTIME LIBRARY
FUNCTION	DESCRIPTION
free	Frees memory returned from an IMSL C Math Library function.
fopen	Opens a file using the C runtime library used by the IMSL C Math Library.
fclose	Closes a file opened by imsl_fopen.

OPEN MP
FUNCTION	DESCRIPTION
omp_options	Sets various OpenMP options.

CONSTANTS
FUNCTION	DESCRIPTION
constant	Returns the value of various mathematical and physical constants.
machine (float)	Returns information describing the computer’s floating-point arithmetic.
machine (integer)	Returns integer information describing the computer’s arithmetic.
sort	Sorts a vector by algebraic value. Optionally, a vector can be sorted by absolute value, and a sort permutation can be returned.
sort_integer	Sorts an integer vector by algebraic value. Optionally, a vector can be sorted by absolute value, and a sort permutation can be returned.

COMPUTING VECTOR NORMS
FUNCTION	DESCRIPTION
vector_norm	Computes various norms of a vector or the difference of two vectors.
vector_norm (complex)	Computes various norms of a vector or the difference of two vectors.

LINEAR ALGEBRA SUPPORT
FUNCTION	DESCRIPTION
mat_mul_rect	Computes the transpose of a matrix, a matrix-vector product, a matrix-matrix product, the bilinear form, or any triple product.
mat_mul_rect (complex)	Computes the transpose of a matrix, the conjugate-transpose of a matrix, a matrix-vector product, a matrix-matrix product, the bilinear form, or any triple product.
mat_mul_rect_band	Computes the transpose of a matrix, a matrix-vector product, or a matrix-matrix product, all matrices stored in band form.
mat_mul_rect_band (complex)	Computes the transpose of a matrix, a matrix-vector product, or a matrix-matrix product, all matrices of complex type and stored in band form.
mat_mul_rect_coordinate	Computes the transpose of a matrix, a matrix-vector product, or a matrix-matrix product, all matrices stored in sparse coordinate form.
mat_mul_rect_coordinate (complex)	Computes the transpose of a matrix, a matrix-vector product or a matrix-matrix product, all matrices stored in sparse coordinate form.
mat_add_band	Adds two band matrices, both in band storage mode, C← αA + βB.
mat_add_band (complex)	Adds two band complex matrices, both in band storage mode, C← αA + βB.
mat_add_coordinate	Performs element-wise addition of two real matrices stored in coordinate format, C← αA + βB.
mat_add_coordinate (complex)	Performs element-wise addition on two complex matrices stored in coordinate format, C← αA + βB.
matrix_det	Computes the determinant of a square, real-valued matrix.
matrix_det (complex)	Computes the determinant of a square, complex matrix.
matrix_norm	Computes various norms of a rectangular matrix.
matrix_norm_band	Computes various norms of a matrix stored in band storage mode.
matrix_norm_coordinate	Computes various norms of a matrix stored in coordinate format.
generate_test_band	Generates test matrices of class E(n,c). Returns in band or band symmetric format .
generate_test_band (complex)	Generates test matrices of class E_c(n,c). Returns in band or band symmetric format.
generate_test_coordinate	Generates test matrices of class D(n,c) and E(n,c). Returns in either coordinate format.
generate_test_coordinate (complex)	Generates test matrices of class D(n,c) and E(n,c). Returns in either coordinate or band storage format, where possible.

NUMERIC UTILITIES
FUNCTION	DESCRIPTION
c_neg	Changes the sign of a complex number.
c_add	Adds two complex numbers.
c_sub	Subtracts a complex number from a complex number.
c_mul	Multiplies two complex numbers.
c_div	Divides a complex number by a complex number.
c_eq	Tests for equality of two complex numbers.
cz_convert	Truncates a double precision complex number to a single precision complex number.
zc_convert	Increases precision of a single precision complex number to a double precision complex number.
cf_convert	Makes a complex number from an ordered pair.
c_conjg	Conjugates a complex number.
c_abs	Computes a magnitude of a complex number.
c_arg	Computes an angle of a complex number.
c_sqrt	Computes a square root of a complex number.
c_cos	Computes a trigonometric cosine of a complex number.
c_sin	Computes a trigonometric sine of a complex number.
c_exp	Computes an exponential function of a complex number.
c_log	Computes a natural logarithm of a complex number.
cf_power	Computes a complex number raised to a real power.
cc_power	Computes a complex number raised to a complex power.
fi_power	Computes a real number raised to an integral power.
ii_power	Computes an integer raised to an integral power.

IMSL C STAT LIBRARY

CHAPTER 1: BASIC STATISTICS

SIMPLE SUMMARY STATISTICS
FUNCTION	DESCRIPTION
simple_statistics	Computes basic univariate statistics.
empirical_quantiles	Computes empirical quantiles.
normal_one_sample	Computes statistics for mean and variance inferences using a sample from a normal population.
normal_two_sample	Computes statistics for mean and variance inferences using samples from two normal populations.

TABULATE, SORT, AND RANK
FUNCTION	DESCRIPTION
table_oneway	Tallies observations into a one-way frequency table.
table_twoway	Tallies observations into a two-way frequency table.
sort_data	Sorts observations by specified keys, with option to tally cases into a multi-way frequency table.
ranks	Computes the ranks, normal scores, or exponential scores for a vector of observations.

CHAPTER 2: REGRESSION

MULTIVARIATE LINEAR REGRESSION—MODEL FITTING
FUNCTION	DESCRIPTION
regressors_for_glm	Generates regressors for a general linear model.
regression	Fits a multiple linear regression model using least squares.

MULTIVARIATE LINEAR REGRESSION — STATISTICAL INFERENCE AND DIAGNOSTICS
FUNCTION	DESCRIPTION
regression_summary	Produces summary statistics for a regression model given the information from the fit.
regression_prediction	Computes predicted values, confidence intervals, and diagnostics after fitting a regression model.
hypothesis_partial	Constructs a completely testable hypothesis.
hypothesis_scph	Sums of cross products for a multivariate hypothesis.
hypothesis_test	Tests for the multivariate linear hypothesis.

VARIABLE SELECTION
FUNCTION	DESCRIPTION
regression_selection	Selects the best multiple linear regression models.
regression_stepwise	Builds multiple linear regression models using forward selection, backward selection or stepwise selection.

POLYNOMIAL AND NONLINEAR REGRESSION
FUNCTION	DESCRIPTION
poly_regression	Performs a polynomial least-squares regression.
poly_prediction	Computes predicted values, confidence intervals, and diagnostics after fitting a polynomial regression model.
nonlinear_regression	Fits a nonlinear regression model.
nonlinear_optimization	Fits a nonlinear regression model using Powell's algorithm.

ALTERNATIVES TO LEAST SQUARES
FUNCTION	DESCRIPTION
Lnorm_regression	Fits a multiple linear regression model using L p criteria other than least squares.
pls_regression	Performs partial least squares (PLS) regression for one or more response variables and one or more predictor variables.

CHAPTER 3: CORRELATION AND COVARIANCE

VARIANCES, COVARIANCES, AND CORRELATIONS
FUNCTION	DESCRIPTION
covariances	Computes the variance-covariance or correlation matrix.
partial_covariances	Computes a pooled variance-covariance matrix from the observations.
pooled_covariances	Computes partial correlations or covariances from the covariance or correlation matrix.
robust_covariances	Computes a robust estimate of a covariance matrix and mean vector.

CHAPTER 4: ANALYSIS OF VARIANCE AND DESIGNED EXPERIMENTS

GENERAL ANALYSIS
FUNCTION	DESCRIPTION
anova_oneway	Analyzes a one-way classification model.
ancovar	Analyzes a one-way classification model with covariates.
anova_factorial	Analyzes a balanced factorial design with fixed effects.
anova_nested	Analyzes a completely nested random effects model with possibly unequal numbers in the subgroups.
anova_balanced	Analyzes a balanced complete experimental design for a fixed, random, or mixed model.

DESIGNED EXPERIMENTS
FUNCTION	DESCRIPTION
crd_factorial	Analyzes data from balanced and unbalanced completely randomized experiments.
rcbd_factorial	Analyzes data from balanced and unbalanced randomized complete-block experiments.
latin_square	Analyzes data from latin-square experiments.
lattice	Analyzes balanced and partially-balanced lattice experiments.
split_plot	Analyzes a wide variety of split-plot experiments with fixed, mixed or random factors.
split_split_plot	Analyzes data from split-split-plot experiments.
strip_plot	Analyzes data from strip-plot experiments.
strip_split_plot	Analyzes data from strip-split-plot experiments.

UTILITIES
FUNCTION	DESCRIPTION
homogeneity	Conducts Bartlett’s and Levene’s tests of the homogeneity of variance assumption in analysis of variance.
multiple_comparisons	Compares differences among averages using the SNK, LSD, Tukey's, Duncan's and Bonferroni's multiple comparisons tests.
false_discovery_rates	Calculates the False Discovery Rate (FDR) q-values corresponding to a set of p-values resulting from multiple simultaneous hypothesis tests.
yates	Estimates missing observations in designed experiments using Yate’s method.

CHAPTER 5: CATEGORICAL AND DISCRETE DATA ANALYSIS

STATISTICS IN THE TWO-WAY CONTINGENCY TABLE
FUNCTION	DESCRIPTION
contingency_table	Performs a chi-squared analysis of a two-way contingency table.
exact_enumeration	Computes exact probabilities in a two-way contingency table, using the total enumeration method.
exact_network	Computes exact probabilities in a two-way contingency table using the network algorithm.

CATEGORICAL MODELS
FUNCTION	DESCRIPTION
categorical_glm	Analyzes categorical data using logistic, Probit, Poisson, and other generalized linear models.
logistic_regression	Fits a binomial or multinomial logistic regression model using iteratively reweighted least squares.
logistic_regression_free	Frees the memory associated with a logistic regression model structure.
logistic_reg_predict	Predicts a binomial or multinomial outcome given an estimated model and new values of the independent variables.

CHAPTER 6: NONPARAMETRIC STATISTICS

ONE SAMPLE TESTS-NONPARAMETRIC STATISTICS
FUNCTION	DESCRIPTION
sign_test	Performs a sign test.
wilcoxon_sign_rank	Performs a Wilcoxon signed rank test.
noether_cyclical_trend	Performs the Noether’s test for cyclical trend.
cox_stuart_trends_test	Performs the Cox and Stuart sign test for trends in location and dispersion.
tie_statistics	Computes tie statistics for a sample of observations.

TWO OR MORE SAMPLES
FUNCTION	DESCRIPTION
wilcoxon_rank_sum	Performs a Wilcoxon rank sign test.
kruskal_wallis_test	Performs a Kruskal-Wallis test for identical population medians.
friedmans_test	Performs Friedman’s test for a randomized complete block design.
cochran_q_test	Performs Cochran’s Q test for related observations.
k_trends_test	Performs k -sample trends test against ordered alternatives.

CHAPTER 7: TESTS OF GOODNESS OF FIT

GENERAL GOODNESS-OF-FIT TESTS FOR A SPECIFIED DISTRIBUTION
FUNCTION	DESCRIPTION
chi_squared_test	Performs a chi-squared goodness-of-fit test.
shapiro_wilk_normality_test	Performs the Shapiro-Wilk test for normality.
lilliefors_normality_test	Performs a Lilliefors test for normality.
chi_squared_normality_test	Performs a chi-squared test for normality.
kolmogorov_one	Performs a Kolmogorov-Smirnov’s one-sample test for continuous distributions.
kolmogorov_two	Performs a Kolmogorov-Smirnov’s two-sample test.
multivar_normality_test	Computes Mardia’s multivariate measures of skewness and kurtosis and tests for multivariate normality.
ad_normality_test	Performs an Anderson - Darling test for normality.
cvm_normality_test	Performs a Cramer-von Mises test for normality.

TESTS FOR RANDOMNESS
FUNCTION	DESCRIPTION
randomness_test	Performs a test for randomness.

CHAPTER 8: TIME SERIES ANALYSIS AND FORECASTING

ARIMA MODELS
FUNCTION	DESCRIPTION
arma	Computes least-square estimates of parameters for an ARMA model.
max_arma	Exact maximum likelihood estimation of the parameters in a univariate ARMA (autoregressive, moving average) time series model.
arma_forecast	Computes forecasts and their associated probability limits for an ARMA model.
arima	Fits a univariate seasonal or non-seasonal ARIMA time series model.
regression_arima	Fits a univariate ARIMA (p ,d ,q ) time series model with the inclusion of one or more regression variables.

AUTOMATIC ARIMA SELECTION AND FITTING UTILITIES
FUNCTION	DESCRIPTION
auto_uni_ar	Automatic selection and fitting of a univariate autoregressive time series model. The lag for the model is automatically selected using Akaike’s information criterion (AIC).
seasonal_fit	Estimates the optimum seasonality parameters for a time series using an autoregressive model, AR (p), to represent the time series.
ts_outlier_identification	Detects and determines outliers and simultaneously estimates the model parameters in a time series whose underlying outlier-free series follows a general seasonal or nonseasonal ARMA model.
ts_outlier_forecast	Computes forecasts, their associated probability limits and weights for an outlier contaminated time series whose underlying outlier free series follows a general seasonal or nonseasonal ARMA model.
auto_arima	Automatically identifies time series outliers, determines parameters of a multiplicative seasonal ARIMA (p ,0, q )×(0, d ,0)_S model and produces forecasts that incorporate the effects of outliers whose effects persist beyond the end of the series.
auto_parm	Estimates structural breaks in non-stationary univariate time series .

BAYESIAN TIME SERIES ESTIMATION
FUNCTION	DESCRIPTION
bayesian_seasonal_adj	Decomposes a time series into trend, seasonal, and an error component.

MODEL CONSTRUCTION AND EVALUATION UTILITIES
FUNCTION	DESCRIPTION
box_cox_transform	Performs a Box-Cox transformation.
difference	Differences a seasonal or nonseasonal time series.
autocorrelation	Computes the sample autocorrelation function of a stationary time series.
crosscorrelation	Computes the sample cross-correlation function of two stationary time series.
multi_crosscorrelation	Computes the multichannel cross-correlation function of two mutually stationary multichannel time series.
partial_autocorrelation	Computes the sample partial autocorrelation function of a stationary time series.
lack_of_fit	Performs lack-of-fit test for an univariate time series or transfer function given the appropriate correlation function.
estimate_missing	Estimates missing values in a time series.

EXPONENTIAL SMOOTHING METHODS
FUNCTION	DESCRIPTION
hw_time_series	Calculates parameters and forecasts using the Holt-Winters Multiplicative or Additive forecasting method for seasonal data.

GARCH MODELING
FUNCTION	DESCRIPTION
garch	Computes estimates of the parameters of a GARCH(p ,q) model.

STATE-SPACE MODELS
FUNCTION	DESCRIPTION
kalman	Performs Kalman filtering and evaluates the likelihood function for the state-space model.

AUTO-REGRESSION AND ERROR CORRECTION
FUNCTION	DESCRIPTION
vector_autoregression	Estimates a vector auto-regressive time series model with optional moving average components.

CHAPTER 9: MULTIVARIATE ANALYSIS

HIERARCHICAL CLUSTER ANALYSIS
FUNCTION	DESCRIPTION
dissimilarities	Computes a matrix of dissimilarities (or similarities) between the columns (or rows) of a matrix.
cluster_hierarchical	Performs a hierarchical cluster analysis given a distance matrix.
cluster_number	Computes cluster membership for a hierarchical cluster tree.

K-MEANS CLUSTER ANALYSIS
FUNCTION	DESCRIPTION
cluster_k_means	Performs a K-means (centroid) cluster analysis.

PRINCIPAL COMPONENT ANALYSIS
FUNCTION	DESCRIPTION
principal_components	Computes principal components.

FACTOR ANALYSIS
FUNCTION	DESCRIPTION
factor_analysis	Extracts initial factor-loading estimates in factor analysis with rotation options.
discriminant_analysis	Performs discriminant function analysis.

CHAPTER 10: SURVIVAL AND RELIABILITY ANALYSIS

SURVIVAL ANALYSIS
FUNCTION	DESCRIPTION
kaplan_meier_estimates	Computes Kaplan-Meier estimates of survival probabilities in stratified samples.
prop_hazards_gen_lin	Analyzes survival and reliability data using Cox’s proportional hazards model.
survival_glm	Analyzes censored survival data using a generalized linear model.
survival_estimates	Estimates survival probabilities and hazard rates for the various parametric models.

RELIABILITY ANALYSIS
FUNCTION	DESCRIPTION
nonparam_hazard_rate	Estimates a reliability hazard function using a nonparametric approach.

ACTUARIAL TABLES
FUNCTION	DESCRIPTION
life_tables	Produces population and cohort life tables.

CHAPTER 11: PROBABILITY DISTRIBUTION FUNCTIONS AND INVERSES

DISCRETE RANDOM VARIABLES
FUNCTION	DESCRIPTION
binomial_cdf	Evaluates the binomial distribution function.
binomial_pdf	Evaluates the binomial probability function.
neg_binomial_cdf	Evaluates the cumulative distribution function (CDF) of the negative binomial distribution.
neg_binomial_inverse_cdf	Evaluates the inverse cumulative distribution function (CDF) of the negative binomial distribution.
neg_binomial_pdf	Evaluates the probability density (mass) function (PDF) of the negative binomial distribution.
geometric_cdf	Evaluates the discrete geometric cumulative distribution function.
geometric_inverse_cdf	Evaluates the inverse of the discrete geometric cumulative distribution function.
geometric_pdf	Evaluates the discrete geometric probability density function.
hypergeometric_cdf	Evaluates the hypergeometric distribution function.
hypergeometric_pdf	Evaluates the hypergeometric probability function.
poisson_cdf	Evaluates the Poisson distribution function.
poisson_pdf	Evaluates the Poisson probability function.
discrete_uniform_cdf	Evaluates the discrete uniform cumulative distribution function.
discrete_uniform_inverse_cdf	Evaluates the inverse of the discrete uniform cumulative distribution function.
discrete_uniform_pdf	Evaluates the discrete uniform probability density function.

CONTINUOUS RANDOM VARIABLES
FUNCTION	DESCRIPTION
beta_cdf	Evaluates the beta probability distribution function.
beta_inverse_cdf	Evaluates the inverse of the beta distribution function.
non_central_beta_cdf	Evaluates the noncentral beta cumulative distribution function.
non_central_beta_inverse_cdf	Evaluates the inverse of the noncentral beta cumulative distribution function.
non_central_beta_pdf	Evaluates the noncentral beta probability density function.
bivariate_normal_cdf	Evaluates the bivariate normal distribution function.
chi_squared_cdf	Evaluates the chi-squared distribution function.
chi_squared_inverse_cdf	Evaluates the inverse of the chi-squared distribution function.
complementary_chi_squared_ cdf	Evaluates the complement of the chi-squared distribution.
complementary_F_cdf	Evaluates the complement of the F distribution function.
complementary_t_cdf	Evaluates the complement of the Student’s t distribution function.
exponential_cdf	Evaluates the exponential cumulative distribution function.
exponential_inverse_cdf	Evaluates the inverse of the exponential cumulative distribution function.
exponential_pdf	Evaluates the exponential probability density function.
F_cdf	Evaluates the F distribution function.
F_inverse_cdf	Evaluates the inverse of the F distribution function.
gamma_cdf	Evaluates the gamma distribution function.
gamma_inverse_cdf	Evaluates the inverse of the gamma distribution function.
generalized_gaussian_cdf	Evaluates the generalized Gaussian cumulative distribution function (CDF).
generalized_gaussian_inverse_cdf	Evaluates the inverse cumulative distribution function (CDF) of the generalized Gaussian distribution.
generalized_gaussian_pdf	Evaluates the generalized Gaussian probability density function (PDF).
lognormal_cdf	Evaluates the lognormal cumulative distribution function.
lognormal_inverse_cdf	Evaluates the inverse of the lognormal cumulative distribution function.
lognormal_pdf	Evaluates the lognormal probability density function.
multivariate_normal_cdf	Evaluates the cumulative distribution function for the multivariate normal distribution.
non_central_chi_sq	Evaluates the noncentral chi-squared distribution function.
non_central_chi_sq_inv	Evaluates the inverse of the noncentral chi-squared function.
non_central_chi_sq_pdf	Evaluates the noncentral chi-squared probability density function.
non_central_F_cdf	Evaluates the noncentral F cumulative distribution function.
complementary_non_central_ F_cdf	Evaluates the complementary noncentral F cumulative distribution function .
non_central_F_inverse_cdf	Evaluates the inverse of the noncentral F cumulative distribution function.
non_central_F_pdf	Evaluates the noncentral F probability density function.
non_central_t_cdf	Evaluates the noncentral Student’s t distribution function.
non_central_t_inv_cdf	Evaluates the inverse of the noncentral Student’s t distribution function.
non_central_t_pdf	Evaluates the noncentral Student's t probability density function.
pareto_cdf	Evaluates the Pareto cumulative probability distribution function.
pareto_pdf	Evaluates the Pareto probability density function.
normal_cdf	Evaluates the standard normal (Gaussian) distribution function.
normal_inverse_cdf	Evaluates the inverse of the standard normal (Gaussian) distribution function.
t_cdf	Evaluates the Student's t distribution function.
t_inverse_cdf	Evaluates the inverse of the Student's t distribution function.

PARAMETER ESTIMATION
FUNCTION	DESCRIPTION
max_likelihood_estimates	Calculates maximum likelihood estimates (MLE) for the parameters of one of several univariate probability distributions.

CHAPTER 12: RANDOM NUMBER GENERATION

UNIVARIATE DISCRETE DISTRIBUTIONS
FUNCTION	DESCRIPTION
random_binomial	Generates pseudorandom binomial numbers from a binomial distribution.
random_geometric	Generates pseudorandom numbers from a geometric distribution.
random_hypergeometric	Generates pseudorandom numbers from a hypergeometric distribution.
random_logarithmic	Generates pseudorandom numbers from a logarithmic distribution.
random_neg_binomial	Generates pseudorandom numbers from a negative binomial distribution.
random_poisson	Generates pseudorandom numbers from a Poisson distribution.
random_uniform_discrete	Generates pseudorandom numbers from a discrete uniform distribution.
random_general_discrete	Generates pseudorandom numbers from a general discrete distribution using an alias method or, optionally, a table lookup method.
discrete_table_setup	Sets up a table to generate pseudorandom numbers from a general discrete distribution.

UNIVARIATE CONTINUOUS DISTRIBUTIONS
FUNCTION	DESCRIPTION
random_beta	Generates pseudorandom numbers from a beta distribution.
random_cauchy	Generates pseudorandom numbers from a Cauchy distribution.
random_chi_squared	Generates pseudorandom numbers from a chi-squared distribution.
random_exponential	Generates pseudorandom numbers from a standard exponential distribution.
random_exponential_mix	Generates pseudorandom mixed numbers from a standard exponential distribution.
random_gamma	Generates pseudorandom numbers from a standard gamma distribution.
random_generalized_gaussian	Generates pseudorandom numbers from a generalized Gaussian distribution.
random_lognormal	Generates pseudorandom numbers from a lognormal distribution.
random_normal	Generates pseudorandom numbers from a standard normal distribution.
random_stable	Generates pseudorandom numbers from a stable distribution.
random_student_t	Generates pseudorandom numbers from a Student's t distribution.
random_triangular	Generates pseudorandom numbers from a triangular distribution.
random_uniform	Generates pseudorandom numbers from a uniform (0, 1) distribution.
random_von_mises	Generates pseudorandom numbers from a von Mises distribution.
random_weibull	Generates pseudorandom numbers from a Weibull distribution.
random_general_continuous	Generates pseudorandom numbers from a general continuous distribution.
continuous_table_setup	Sets up a table to generate pseudorandom numbers from a general continuous distribution.

MULTIVARIATE CONTINUOUS DISTRIBUTIONS
FUNCTION	DESCRIPTION
random_normal_multivariate	Generates pseudorandom numbers from a multivariate normal distribution.
random_orthogonal_matrix	Generates a pseudorandom orthogonal matrix or a correlation matrix.
random_mvar_from_data	Generates pseudorandom numbers from a multivariate distribution determined from a given sample.
random_multinomial	Generates pseudorandom numbers from a multinomial distribution.
random_sphere	Generates pseudorandom points on a unit circle or K-dimensional sphere.
random_table_twoway	Generates a pseudorandom two-way table.
random_mvar_gaussian_ copula	Given a Cholesky factorization of a correlation matrix, generates pseudorandom numbers from a Gaussian Copula distribution.
random_mvar_t_copula	Given a Cholesky factorization of a correlation matrix, generates pseudorandom numbers from a Student’s t Copula distribution.
canonical_correlation	Given an input array of deviate values, generates a canonical correlation array.

ORDER STATISTICS
FUNCTION	DESCRIPTION
random_order_normal	Generates pseudorandom order statistics from a standard normal distribution.
random_order_uniform	Generates pseudorandom order statistics from a uniform (0, 1) distribution.

STOCHASTIC PROCESSES
FUNCTION	DESCRIPTION
random_arma	Generates a time series from a specific ARMA model.
random_npp	Generates pseudorandom numbers from a nonhomogeneous Poisson process.

SAMPLES AND PERMUTATIONS
FUNCTION	DESCRIPTION
random_permutation	Generates a pseudorandom permutation.
random_sample_indices	Generates a simple pseudorandom sample of indices.
random_sample	Generates a simple pseudorandom sample from a finite population.

UTILITY FUNCTIONS
FUNCTION	DESCRIPTION
random_option	Selects the uniform (0, 1) multiplicative congruential pseudorandom number generator.
random_option_get	Retrieves the uniform (0, 1) multiplicative congruential pseudorandom number generator.
random_seed_get	Retrieves the current value of the seed used in the IMSL random number generators.
random_substream_seed_get	Retrieves a seed for the congruential generators that do not do shuffling that will generate random numbers beginning 100,000 numbers farther along.
random_seed_set	Initializes a random seed for use in the IMSL random number generators.
random_table_set	Sets the current table used in the shuffled generator.
random_table_get	Retrieves the current table used in the shuffled generator.
random_GFSR_table_set	Sets the current table used in the GFSR generator.
random_GFSR_table_get	Retrieves the current table used in the GFSR generator.
random_MT32_init	Initializes the 32-bit Mersenne Twister generator using an array.
random_MT32_table_get	Retrieves the current table used in the 32-bit Mersenne Twister generator.
random_MT32_table_set	Sets the current table used in the 32-bit Mersenne Twister generator.
random_MT64_init	Initializes the 64-bit Mersenne Twister generator using an array.
random_MT64_table_get	Retrieves the current table used in the 64-bit Mersenne Twister generator.
random_MT64_table_set	Sets the current table used in the 64-bit Mersenne Twister generator.

LOW-DISCREPANCY SEQUENCE
FUNCTION	DESCRIPTION
faure_next_point	Computes a shuffled Faure sequence.

CHAPTER 13: DATA MINING

APRIORI – MARKET BASKET ANALYSIS
FUNCTION	DESCRIPTION
apriori	Computes the frequent itemsets in a transaction set.
aggr_apriori	Computes the frequent itemsets in a transaction set using aggregation.
write_apriori_itemsets	Prints frequent itemsets.
write_association_rules	Prints association rules.
free_apriori_itemsets	Frees the memory allocated within a frequent itemsets structure.
free_association_rules	Frees the memory allocated within an association rules structure.

DECISION TREE
FUNCTION	DESCRIPTION
decision_tree	Generates a decision tree or a random forest of decision trees for a single response variable and two or more predictor variables
decision_tree_predict	Computes predicted values using a decision tree.
decision_tree_print	Prints a decision tree.
decision_tree_free	Frees the memory associated with a decision tree.
gradient_boosting	Performs stochastic gradient boosting for decision trees.
gradient_boosting_predict	Uses a previously trained gradient boosting model to predict a univariate response variable based on new data.
gradient_boosting_model_ free	Frees the memory associated with a gradient boosting model structure.
gradient_boosting_model_ read	Retrieves a gradient boosting model previously filed using imsls_f_gradient_boosting_model_write.
gradient_boosting_model_ write	Writes a gradient boosting model to an ASCII file for later retrieval using imsls_f_gradient_boosting_model_read.

GENETIC ALGORITHM DATA STRUCTURES
FUNCTION	DESCRIPTION
ga_chromosome	Creates an Imsls_f_chromosome data structure containing unencoded and encoded phenotype information.
ga_copy_chromosome	Copies the contents of one chromosome into another chromosome.
ga_clone_chromosome	Clones an existing chromosome.
ga_individual	Creates an Imsls_f_individual data structure from user supplied phenotypes.
ga_copy_individual	Copies the contents of one individual into another individual.
ga_clone_individual	Clones an existing individual.
ga_mutate	Performs the mutation operation on an individual's chromosome.
ga_decode	Decodes an individual's chromosome into its binary, nominal, integer and real phenotypes.
ga_encode	Encodes an individual's binary, nominal, integer and real phenotypes into its chromosome.
ga_free_individual	Frees memory allocated to an existing individual.
ga_population	Creates an Imsls_f_population data structure from user supplied individuals.
ga_random_population	Creates an Imsls_f_population data structure from randomly generated individuals.
ga_copy_population	Copies the contents of one population into another population.
ga_clone_population	Clones an existing population.
ga_grow_population	Adds individuals to an existing population.
ga_merge_population	Creates a new population by merging two populations with identical chromosome structures.
ga_free_population	Frees memory allocated to an existing population.
genetic_algorithm	Optimizes a user defined fitness function using a tailored genetic algorithm.

NAIVE BAYES
FUNCTION	DESCRIPTION
naive_bayes_trainer	Trains a Naïve Bayes classifier.
naive_bayes_classification	Classifies unknown patterns using a previously trained Naïve Bayes classifier.
nb_classifier_free	Frees memory allocated to an Imsls_f_nb_classifier data structure.
nb_classifier_write	Writes a Naïve Bayes Classifier to an ASCII file for later retrieval using imsls_f_nb_classifier_read.
nb_classifier_read	Retrieves a Naïve Bayes Classifier from a file previously saved using imsls_f_nb_classifier_write.

NEURAL NETWORK DATA STRUCTURES
FUNCTION	DESCRIPTION
mlff_network_init	Initializes a data structure for training a neural network.
mlff_network	Multilayered feedforward neural network.
mlff_network_free	Frees memory allocated for an Imsls_f_NN_Network data structure.
mlff_network_write	Writes a trained neural network to an ASCII file.
mlff_network_read	Retrieves a neural network from a file previously saved.
mlff_initialize_weights	Initializes weights for multilayered feedforward neural networks prior to network training using one of four user selected methods.

FORECASTING NEURAL NETWORKS
FUNCTION	DESCRIPTION
mlff_network_trainer	Trains a multilayered feedforward neural network.
mlff_network_forecast	Calculates forecasts for trained multilayered feedforward neural networks.

CLASSIFICATION NEURAL NETWORKS
FUNCTION	DESCRIPTION
mlff_classification_trainer	Trains a multilayered feedforward neural network for classification.
mlff_pattern_classification	Calculates classifications for trained multilayered feedforward neural networks.

PREPROCESSING FILTERS
FUNCTION	DESCRIPTION
scale_filter	Scales or unscales continuous data prior to its use in neural network training, testing, or forecasting.
time_series_filter	Converts time series data to the format required for processing by a neural network.
time_series_class_filter	Converts time series data sorted within nominal classes in decreasing chronological order to a useful format for processing by a neural network.
unsupervised_nominal_filter	Converts nominal data into a series of binary encoded columns for input to a neural network. Optionally, it can also reverse the binary encoding, accepting a series of binary encoded columns and returning a single column of nominal classes.
unsupervised_ordinal_filter	Converts ordinal data into proportions. Optionally, it can also reverse encoding, accepting proportions and converting them into ordinal values.

SELF ORGANIZING MAPS
FUNCTION	DESCRIPTION
kohonenSOM_trainer	Trains a Kohonen network.
kohonenSOM_forecast	Calculates forecasts using a trained Kohonen network.

SUPPORT VECTOR MACHINES
FUNCTION	DESCRIPTION
support_vector_trainer	Trains a Support Vector Machines (SVM) classifier.
support_vector_classification	Classifies unknown patterns using a previously trained Support Vector Machines (SVM) model computed by support_vector_trainer.
svm_classifier_free	Frees memory allocated to an Imsls_f_svm_model / Imsls_d_svm_model data structure.

UTILITIES
FUNCTION	DESCRIPTION
multiclass_auc	Calculates the Area Under the Curve (AUC) or its multiclass analog for classification problems.

CHAPTER 14: PRINTING FUNCTIONS

PRINT
FUNCTION	DESCRIPTION
write_matrix	Prints a rectangular matrix (or vector) stored in contiguous memory locations.

SET
FUNCTION	DESCRIPTION
page	Sets or retrieves the page width or length.
write_options	Sets or retrieves an option for printing a matrix.

CHAPTER 15: UTILITIES

SET OUPUT FILES
FUNCTION	DESCRIPTION
output_file	Sets the output file or the error message output file.
version	Returns integer information describing the version of the library, license number, operating system, and compiler.

ERROR HANDLING
FUNCTION	DESCRIPTION
error_options	Sets various error handling options.
error_type	Gets the type corresponding to the error message from the last function called.
error_message	Gets the text of the error message from the last function called.
error_code	Returns the code corresponding to the error message from the last function called.
initialize_error_handler	Initializes the IMSL C Stat Library error handling system.
set_user_fcn_return_flag	Indicates a condition has occurred in a user-supplied function necessitating a return to the calling function.

C RUNTIME LIBRARY
FUNCTION	DESCRIPTION
free	Frees memory returned from an IMSL C Stat Library function.
fopen	Opens a file using the C runtime library used by the IMSL C Stat Library.
fclose	Closes a file opened by imsls_fopen.
ascii_read	Reads freely-formatted ASCII files.
data_read	Reads column-oriented data from a delimited ASCII file and returns a structure with the number of rows and columns and a double matrix containing the data.
free_data_matrix	Frees the memory allocated for an Imsls_data_matrix structure.
free_column_info	Frees the memory allocated for an Imsls_column_info structure.

OPENMP
FUNCTION	DESCRIPTION
omp_options	Sets various OpenMP options.

CONSTANTS
FUNCTION	DESCRIPTION
machine (integer)	Returns integer information describing the computer’s arithmetic.
machine (float)	Returns information describing the computer’s floating-point arithmetic.
data_sets	Retrieves a commonly analyzed data set.

MATHEMATICAL SUPPORT
FUNCTION	DESCRIPTION
mat_mul_rect	Computes the transpose of a matrix, a matrix-vector product, a matrix-matrix product, a bilinear form, or any triple product.
permute_vector	Rearranges the elements of a vector as specified by a permutation.
permute_matrix	Permutes the rows or columns of a matrix.
impute_missing	Locates and optionally replaces dependent variable missing values with nearest neighbor estimates.
binomial_coefficient	Evaluates the binomial coefficient.
beta	Evaluates the real regularized incomplete beta function.
beta_incomplete	Evaluates the real regularized incomplete beta function.
log_beta	Evaluates the logarithm of the real beta function ln β(x,y).
gamma	Evaluates the real gamma function.
gamma_incomplete	Evaluates the incomplete gamma function γ(a,x).
log_gamma	Evaluates the logarithm of the absolute value of the gamma function log \|Γ(x)\|.
ctime	Returns the number of CPU seconds used.

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IMSL® C Numerical Library Function Catalog