IMSL^® FORTRAN NUMERICAL LIBRARY FUNCTION CATALOG VERSION 2025.1

Written for Fortran programmers and based on the world’s most widely called numerical subroutines.

At the heart of the IMSL Libraries lies the comprehensive and trusted set of IMSL mathematical and statistical numerical algorithms. The IMSL Fortran Numerical Library Version 2025.1 includes all of the algorithms from the IMSL family of Fortran libraries including the IMSL F90 Library, the IMSL FORTRAN 77 Library, and the IMSL parallel processing features. With IMSL, we provide the building blocks that eliminate the need to write code from scratch. These pre-written functions allow you to focus on your domain of expertise and reduce your development time.

ONE COMPREHENSIVE PACKAGE

All F77, F90 and parallel processing features are contained within a single IMSL Fortran Numerical Library package.

RELIABLE

High performing and reliable, the IMSL Fortran Numerical Library contains proven technology that has been thoroughly tested, well documented, and continuously maintained and used by developers worldwide for over four decades. Instead of writing, testing and maintaining complex mathematical and statistical algorithms from scratch, developers use the algorithms provided in the IMSL Fortran Numerical Library to help accelerate application development and time to market.

Perforce works with compiler partners and hardware partners to ensure a high degree of reliability and performance optimization. The result of this effort is a robust, sophisticated suite of test methods that allow users to rely on the IMSL numerical analysis functionality and focus their effort on business applications.

PORTABLE

The IMSL Fortran library is available on a wide range of common platform combinations.
We port the Fortran libraries to the latest platform versions, simplifying migrations and upgrades.

EMBEDDABLE

IMSL code embeds easily into your application code:

The IMSL Fortran Library allows developers to write, build, compile, and debug code in a single development environment.
Requires no additional infrastructure such as app/management consoles, servers, or data repository.

INTERFACE MODULES

The IMSL Fortran Numerical Library Version 2025.1 includes powerful and flexible interface modules for all applicable routines. The Interface Modules accomplish the following:

Allow for the use of advanced Fortran syntax and optional arguments throughout.
Only require a short list of required arguments for each algorithm to facilitate development of simpler Fortran applications.
Provide full depth and control via optional arguments for experienced programmers.
Reduce development effort by checking data type matches and array sizing at compile time.
With operators and function modules, provide faster and more natural programming through an object-oriented approach.

This simple and flexible interface to the library routines speeds programming and simplifies documentation. The IMSL Fortran Numerical Library takes full advantage of the intrinsic characteristics and desirable features of the Fortran language.

BACKWARD COMPATIBILITY

The IMSL Fortran Numerical Library Version 2025.1 maintains full backward compatibility with earlier releases of the IMSL Fortran Libraries. No code modifications are required for existing applications that rely on previous versions of the IMSL Fortran Libraries. Calls to routines from the IMSL FORTRAN 77 Libraries with the F77 syntax continue to function as well as calls to the IMSL F90 Library.

SMP/OPENMP SUPPORT

The IMSL Fortran Numerical Library has also been designed to take advantage of symmetric multiprocessor (SMP) systems. Computationally intensive algorithms in areas such as linear algebra will leverage SMP capabilities on a variety of systems. By allowing you to replace the generic Basic Linear Algebra Subprograms (BLAS) contained in the IMSL Fortran Numerical Library with optimized routines from your hardware vendor, you can improve the performance of your numerical calculations.

MPI ENABLED

The IMSL Fortran Numerical Library provides a dynamic interface for computing mathematical solutions over a distributed system via the Message Passing Interface (MPI). MPI enabled routines offer a simple, reliable user interface. The IMSL Fortran Numerical Library provides a number of MPI-enabled routines with an MPI-enhanced interface that provides:

Computational control of the server node.
Scalability of computational resources.
Automatic processor prioritization.
Self-scheduling algorithm to keep processors continuously active.
Box data type application.
Computational integrity.
Dynamic error processing.
Homogeneous and heterogeneous network functionality.
Use of descriptive names and generic interfaces.

LAPACK AND SCALAPACK

LAPACK was designed to make the linear solvers and eigensystem routines run more efficiently on high performance computers. For a number of IMSL routines, the user of the IMSL Fortran Numerical Library has the option of linking to code which is based on either the legacy routines or the more efficient LAPACK routines. To obtain improved performance we recommend linking with vendor High Performance versions of LAPACK and BLAS, if available.

ScaLAPACK includes a subset of LAPACK codes redesigned for use on distributed memory MIMD parallel computers. Use of the ScaLAPACK enhanced routines allows a user to solve large linear systems of algebraic equations at a performance level that might not be achievable on one computer by performing the work in parallel across multiple computers.

IMSL facilitates the use of parallel computing in these situations by providing interfaces to ScaLAPACK routines which accomplish the task. The IMSL Library solver interface has the same look and feel whether one is using the routine on a single computer or across multiple computers.

USER FRIENDLY NOMENCLATURE

The IMSL Fortran Numerical Library uses descriptive explanatory function names for intuitive programming.

ERROR HANDLING

Diagnostic error messages are clear and informative – designed not only to convey the error condition, but also to suggest corrective action if appropriate. These error-handling features:

Allow faster and easier program debugging
Provide more productive programming and confidence that the algorithms are functioning properly.

COST-EFFECTIVE

The IMSL Fortran Numerical Library significantly shortens program development time and promotes standardization. Using the IMSL Fortran Numerical Library saves time in source code development and the design, development, documentation, testing and maintenance of applications.

COMPREHENSIVE DOCUMENTATION

Documentation for the IMSL Fortran Numerical Library is comprehensive, clearly written and standardized. Detailed information about each subroutine consists of the name, purpose, synopsis, exceptions, return values and usage examples.

UNMATCHED PRODUCT SUPPORT

Behind every IMSL license is a team of professionals ready to provide expert answers to questions about the IMSL Libraries. Product support options include product maintenance, ensuring the value and performance of IMSL Library software.

Product support:

Gives users direct access to IMSL resident staff of expert product support specialists
Provides prompt, two-way communication
Includes product maintenance updates

CONSULTING SERVICES

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

Mathematical Functionality Overview

The IMSL Fortran Numerical Library is a collection of the most commonly needed numerical functions customized for your programming needs. The mathematical functionality is organized into eleven 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.

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 - including Adams-Gear and Runge-Kutta methods for stiff and non-stiff ordinary differential equations and support for partial differential equations.
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 and linearly and nonlinearly constrained minimizations and the fastest linear programming algorithm available in a general math library.
Basic Matrix/Vector Operations - including Basic Linear Algebra Subprograms (BLAS) and matrix manipulation operations.
Linear Algebra Operators and Generic Functions - including matrix algebra operations, and matrix and utility functionality.
Utilities- including CPU time used, machine, mathematical, physical constants, retrieval of machine constants and customizable error-handling.

Mathematical Special Functions Overview

The IMSL Fortran Numerical Library includes routines that evaluate the special mathematical functions that arise in applied mathematics, physics, engineering and other technical fields. The mathematical special functions are organized into twelve sections.

Elementary Functions - including complex numbers, exponential functions and logarithmic functions.
Trigonometric and Hyperbolic Functions - including trigonometric functions and hyperbolic functions.
Exponential Integrals and Related Functions - including exponential integrals, logarithmic integrals and integrals of trigonometric and hyperbolic functions.
Gamma Functions and Related Functions, including gamma functions, psi functions, Pochhammer’s function and Beta functions.
Error Functions and Related Functions - including error functions and Fresnel integrals.
Bessel Functions - including real and integer order with both real and complex arguments
Kelvin Functions - including Kelvin functions and their derivatives
Airy Functions - including Airy functions, complex Airy functions, and their derivatives.
Elliptic Integrals - including complete and incomplete elliptic integrals
Elliptic and Related Functions - including Weierstrass P-functions and the Jacobi elliptic function.
Probability Distribution Functions and Inverses - including statistical functions, such as chi-squared and inverse beta and many others.
Mathieu Functions - including eigenvalues and sequence of Mathieu functions

Statistical Functionality Overview

The statistical functionality is organized into nineteen 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 stepwise regression, all best regression, multiple linear regression models, polynomial models and nonlinear models.
Correlation - including sample variance-covariance, partial correlation and covariances, pooled variance-covariance and robust estimates of a covariance matrix and mean factor.
Analysis of Variance - including one-way classification models, a balanced factorial design with fixed effects and the Student-Newman-Keuls multiple comparisons test.
Categorical and Discrete Data Analysis - including chi-squared analysis of a two-way contingency table, exact probabilities in a two-way contingency table and 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 and Randomness - including chi-squared goodness-of-fit tests, Kolmogorov/Smirnov tests and tests for normality.
Time Series Analysis and Forecasting - including analysis and forecasting of time series using a nonseasonal ARMA model, GARCH (Generalized Autoregressive Conditional Heteroskedasticity), Kalman filtering, Automatic Model Selection, Bayesian Seasonal Analysis and Prediction, Optimum Controller Design, Spectral Density Estimation, portmanteau lack of fit test and difference of a seasonal or nonseasonal time series.
Covariance Structures and Factor Analysis - including principal components and factor analysis.
Discriminant Analysis - including analysis of data using a generalized linear model and using various parametric models
Cluster Analysis - including hierarchical cluster analysis and k-means cluster analysis.
Sampling - including analysis of data using a simple or stratified random sample.
Survival Analysis, Life Testing, and Reliability - including Kaplan-Meier estimates of survival probabilities.
Multidimensional Scaling - including alternating least squares methods.
Density and Hazard Estimation - including estimates for density and modified likelihood for hazards.
Probability Distribution Functions and Inverses - including binomial, hypergeometric, bivariate normal, gamma and many more.
Random Number Generation - including the Mersenne Twister generator and a generator for multivariate normal distributions and pseudorandom numbers from several distributions, including gamma, Poisson, beta, and low discrepancy sequence.
Utilities - including CPU time used, machine, mathematical, physical constants, retrieval of machine constants and customizable error-handling.
Mathematical Support - including linear systems, special functions, and nearest neighbors.

IMSL® Libraries Also Available for C and Java

IMSL C Numerical Library

The IMSL C Numerical Library delivers advanced mathematical and statistical functionality for programmers to embed in C/C++ applications. This comprehensive set of functions is based upon the same algorithms contained in the highly regarded IMSL Fortran Library. The IMSL C Library is available on a wide range of development platforms and offers functions in key areas such as optimization, data mining, forecasting and design of experiments analysis. These pre-tested functions result in superior performance, increased scalability, ease of integration and greater reliability for software applications that require advanced mathematics and statistics. Dozens of algorithms take advantage of multi-core hardware using standard OpenMP directives.

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 data analysis and visualization technology for the Java platform and a fast, scalable framework for tailored analytical applications.

IMSL MATH LIBRARY

CHAPTER 1: LINEAR SYSTEMS

LINEAR SOLVERS
	ROUTINE	DESCRIPTION
	LIN_SOL_GEN	Solves a real general system of linear equations Ax = b.
	LIN_SOL_SELF	Solves a system of linear equations Ax = b, where A is a self-adjoint matrix.
	LIN_SOL_LSQ	Solves a rectangular system of linear equations Ax @ b, in a least-squares sense.
	LIN_SOL_SVD	Solves a rectangular least-squares system of linear equations Ax @ b using singular value decomposition.
	LIN_SOL_TRI	Solves multiple systems of linear equations.
	LIN_SVD	Computes the singular value decomposition (SVD) of a rectangular matrix, A.

LARGE-SCALE PARALLEL SOLVERS
	ROUTINE	DESCRIPTION
	PARALLEL_NONNEGATIVE_LSQ	Solves a linear, non-negative constrained least-squares system.
	PARALLEL_BOUNDED_LSQ	Solves a linear least-squares system with bounds on the unknowns

SOLUTION OF LINEAR SYSTEMS, MATRIX INVERSION, AND DETERMINANT EVALUATION

REAL GENERAL MATRICES
	ROUTINE	DESCRIPTION
	LSARG	Solves a real general system of linear equations with iterative refinement.
	LSLRG	Solves a real general system of linear equations without iterative refinement.
	LFCRG	Computes the LU factorization of a real general matrix and estimates its L₁ condition number.
	LFTRG	Computes the LU factorization of a real general matrix.
	LFSRG	Solves a real general system of linear equations given the LU factorization of the coefficient matrix.
	LFIRG	Uses iterative refinement to improve the solution of a real general system of linear equations.
	LFDRG	Computes the determinant of a real general matrix given the LU factorization of the matrix.
	LINRG	Computes the inverse of a real general matrix.

COMPLEX GENERAL MATRICES
	ROUTINE	DESCRIPTION
	LSACG	Solves a complex general system of linear equations with iterative refinement.
	LSLCG	Solves a complex general system of linear equations without iterative refinement.
	LFCCG	Computes the LU factorization of a complex general matrix and estimates its L₁ condition number.
	LFTCG	Computes the LU factorization of a complex general matrix.
	LFSCG	Solves a complex general system of linear equations given the LU factorization of the coefficient matrix.
	LFICG	Uses iterative refinement to improve the solution of a complex general system of linear equations.
	LFDCG	Computes the determinant of a complex general matrix given the LU factorization of the matrix.
	LINCG	Computes the inverse of a complex general matrix.

REAL TRIANGULAR MATRICES
	ROUTINE	DESCRIPTION
	LSLRT	Solves a real triangular system of linear equations.
	LFCRT	Estimates the condition number of a real triangular matrix.
	LFDRT	Computes the determinant of a real triangular matrix.
	LINRT	Computes the inverse of a real triangular matrix.

COMPLEX TRIANGULAR MATRICES
	ROUTINE	DESCRIPTION
	LSLCT	Solves a complex triangular system of linear equations.
	LFCCT	Estimates the condition number of a complex triangular matrix.
	LFDCT	Computes the determinant of a complex triangular matrix.
	LINCT	Computes the inverse of a complex triangular matrix.

REAL POSITIVE DEFINITE MATRICES
	ROUTINE	DESCRIPTION
	LSADS	Solves a real symmetric positive definite system of linear equations with iterative refinement.
	LSLDS	Solves a real symmetric positive definite system of linear equations without iterative refinement.
	LFCDS	Computes the R^TR Cholesky factorization of a real symmetric positive definite matrix and estimates its L₁ condition number.
	LFTDS	Computes the R^TR Cholesky factorization of a real symmetric positive definite matrix.
	LFSDS	Solves a real symmetric positive definite system of linear equations given the R^TR Cholesky factorization of the coefficient matrix.
	LFIDS	Uses the iterative refinement to improve the solution of a real symmetric positive definite system of linear equations.
	LFDDS	Computes the determinant of a real symmetric positive matrix given the R^TR Cholesky factorization of the matrix.
	LINDS	Computes the inverse of a real symmetric positive definite matrix.

REAL SYMMETRIC MATRICES
	ROUTINE	DESCRIPTION
	LSASF	Solves a real symmetric system of linear equations with iterative refinement.
	LSLSF	Solves a real symmetric system of linear equations without iterative refinement.
	LFCSF	Computes the U DU^Tfactorization of a real symmetric matrix and estimates its L₁ condition number.
	LFTSF	Computes the U DU^T factorization of a real symmetric matrix.
	LFSSF	Solves a real symmetric system of linear equations given the U DU^T factorization of the coefficient matrix.
	LFISF	Uses iterative refinement to improve the solution of a real symmetric system of linear equations.
	LFDSF	Computes the determinant of a real symmetric matrix given the U DU^T factorization of the matrix.

COMPLEX HERMITIAN POSITIVE DEFINITE MATRICES
	ROUTINE	DESCRIPTION
	LSADH	Solves a complex Hermitian positive definite system of linear equations with iterative refinement.
	LSLDH	Solves a complex Hermitian positive definite system of linear equations without iterative refinement.
	LFCDH	Computes the R^HR factorization of a complex Hermitian positive definite matrix and estimates its L₁ condition number.
	LFTDH	Computes the R^HR factorization of a complex Hermitian positive definite matrix.
	LFSDH	Solves a complex Hermitian positive definite system of linear equations given the R^HR factorization of the coefficient matrix.
	LFIDH	Uses the iterative refinement to improve the solution of a complex Hermitian positive definite system of linear equations.
	LFDDH	Computes the determinant of a complex Hermitian positive definite matrix given the R^HR Cholesky factorization of the matrix.

COMPLEX HERMITIAN MATRICES
	ROUTINE	DESCRIPTION
	LSAHF	Solves a complex Hermitian system of linear equations with iterative refinement.
	LSLHF	Solves a complex Hermitian system of linear equations without iterative refinement.
	LFCHF	Computes the U DU^H factorization of a complex Hermitian matrix and estimates its L₁ condition number.
	LFTHF	Computes the U DU^H factorization of a complex Hermitian matrix.
	LFSHF	Solves a complex Hermitian system of linear equations given the U DU^H factorization of the coefficient matrix.
	LFIHF	Uses iterative refinement to improve the solution of a complex Hermitian system of linear equations.
	LFDHF	Computes the determinant of a complex Hermitian matrix given the U DU^H factorization of the matrix.

REAL BAND MATRICES IN BAND STORAGE MODE
	ROUTINE	DESCRIPTION
	LSLTR	Solves a real tridiagonal system of linear equations.
	LSLCR	Computes the L DU factorization of a a real tridiagonal matrix A using a cyclic reduction algorithm.
	LSARB	Solves a real system of linear equations in band storage mode with iterative refinement.
	LSLRB	Solves a real system of linear equations in band storage mode without iterative refinement.
	LFCRB	Computes the LU factorization of a real matrix in band storage mode and estimates its L₁ condition number.
	LFTRB	Computes the LU factorization of a real matrix in band storage mode.
	LFSRB	Solves a real system of linear equations given the LU factorization of the coefficient matrix in band storage mode.
	LFIRB	Uses iterative refinement to improve the solution of a real system of linear equations in band storage mode.
	LFDRB	Computes the determinant of a real matrix in band storage mode given the LU factorization of the matrix.

REAL BAND SYMMETRIC POSITIVE DEFINITE MATRICES IN BAND STORAGE MODE
	ROUTINE	DESCRIPTION
	LSAQS	Solves a real symmetric positive definite system of linear equations in band symmetric storage mode with iterative refinement.
	LSLQS	Solves a real symmetric positive definite system of linear equations in band symmetric storage mode without iterative refinement.
	LSLPB	Computes the R^TDR Cholesky factorization of a real symmetric positive definite matrix A in codiagonal band symmetric storage mode. Solves a system Ax = b.
	LFCQS	Computes the R^TR Cholesky factorization of a real symmetric positive definite matrix in band symmetric storage mode and estimates its L₁ condition number.
	LFTQS	Computes the R^TR Cholesky factorization of a real symmetric positive definite matrix in band symmetric storage mode.
	LFSQS	Solves a real symmetric positive definite system of linear equations given the factorization of the coefficient matrix in band symmetric storage mode.
	LFIQS	Uses iterative refinement to improve the solution of a real symmetric positive definite system of linear equations in band symmetric storage mode.
	LFDQS	Computes the determinant of a real symmetric positive definite matrix given the R^TR Cholesky factorization of the matrix in band symmetric storage mode.

COMPLEX BAND MATRICES IN BAND STORAGE MODE
	ROUTINE	DESCRIPTION
	LSLTQ	Solves a complex tridiagonal system of linear equations.
	LSLCQ	Computes the LDU factorization of a complex tridiagonal matrix A using a cyclic reduction algorithm.
	LSACB	Solves a complex system of linear equations in band storage mode with iterative refinement.
	LSLCB	Solves a complex system of linear equations in band storage mode without iterative refinement.
	LFCCB	Computes the LU factorization of a complex matrix in band storage mode and estimates its L₁ condition number.
	LFTCB	Computes the LU factorization of a complex matrix in band storage mode given the coefficient matrix in band storage mode.
	LFSCB	Solves a complex system of linear equations given the LU factorization of the coefficient matrix in band storage mode.
	LFICB	Uses iterative refinement to improve the solution of a complex system of linear equations in band storage mode.
	LFDCB	Computes the determinant of a complex matrix given the LU factorization of the matrix in band storage mode.

COMPLEX BAND POSITIVE DEFINITE MATRICES IN BAND STORAGE MODE
	ROUTINE	DESCRIPTION
	LSAQH	Solves a complex Hermitian positive definite system of linear equations in band Hermitian storage mode with iterative refinement.
	LSLQH	Solves a complex Hermitian positive definite system of linear equations in band Hermitian storage mode without iterative refinement.
	LSLQB	Computes the R^HDR Cholesky factorization of a complex Hermitian positive-definite matrix A in codiagonal band Hermitian storage mode. Solves a system Ax = b.
	LFCQH	Computes the R^H R factorization of a complex Hermitian positive definite matrix in band Hermitian storage mode and estimates its L₁ condition number.
	LFTQH	Computes the R^H R factorization of a complex Hermitian positive definite matrix in band Hermitian storage mode.
	LFSQH	Solves a complex Hermitian positive definite system of linear equations given the factorization of the coefficient matrix in band Hermitian storage mode.
	LFIQH	Uses iterative refinement to improve the solution of a complex Hermitian positive definite system of linear equations in band Hermitian storage mode.
	LFDQH	Computes the determinant of a complex Hermitian positive definite matrix given the R^HR Cholesky factorization in band Hermitian storage mode.

REAL SPARSE LINEAR EQUATION SOLVERS
	ROUTINE	DESCRIPTION
	LSLXG	Solves a sparse system of linear algebraic equations by Gaussian elimination.
	LFTXG	Computes the LU factorization of a real general sparse matrix.
	LFSXG	Solves a sparse system of linear equations given the LU factorization of the coefficient matrix.

COMPLEX SPARSE LINEAR EQUATION SOLVERS
	ROUTINE	DESCRIPTION
	LSLZG	Solves a complex sparse system of linear equations by Gaussian elimination.
	LSTZG	Computes the LU factorization of a complex general sparse matrix.
	LFSZG	Solves a complex sparse system of linear equations given the LU factorization of the coefficient matrix.

REAL SPARSE SYMMETRIC POSITIVE DEFINITE LINEAR EQUATIONS SOLVERS
	ROUTINE	DESCRIPTION
	LSLXD	Solves a sparse system of symmetric positive definite linear algebraic equations by Gaussian elimination.
	LSCXD	Performs the symbolic Cholesky factorization for a sparse symmetric matrix using a minimum degree ordering or a user-specified ordering, and sets up the data structure for the numerical Cholesky factorization.
	LNFXD	Computes the numerical Cholesky factorization of a sparse symmetrical matrix A.
	LFSXD	Solves a real sparse symmetric positive definite system of linear equations, given the Cholesky factorization of the coefficient matrix.

COMPLEX SPARSE HERMITIAN POSITIVE DEFINITE LINEAR EQUATIONS SOLVERS
	ROUTINE	DESCRIPTION
	LSLZD	Solves a complex sparse Hermitian positive definite system of linear equations by Gaussian elimination.
	LNFZD	Computes the numerical Cholesky factorization of a sparse Hermitian matrix A.
	LFSZD	Solves a complex sparse Hermitian positive definite system of linear equations, given the Cholesky factorization of the coefficient matrix.

REAL TOEPLITZ MATRICES IN TOEPLITZ STORAGE MODE
	ROUTINE	DESCRIPTION
	LSLTO	Solves a real Toeplitz linear system.

COMPLEX TOEPLITZ MATRICES IN TOEPLITZ STORAGE MODE
	ROUTINE	DESCRIPTION
	LSLTC	Solves a complex Toeplitz linear system.

COMPLEX CIRCULAR MATRICES IN CIRCULANT STORAGE MODE
	ROUTINE	DESCRIPTION
	LSLCC	Solves a complex circulant linear system.

ITERATIVE METHODS
	ROUTINE	DESCRIPTION
	PCGRC	Solves a real symmetric definite linear system using a preconditioned conjugate gradient method with reverse communication.
	JCGRC	Solves a real symmetric definite linear system using the Jacobi-preconditioned conjugate gradient method with reverse communication.
	GMRES	Uses GMRES with reverse communication to generate an approximate solution of Ax = b.

LINEAR LEAST SQUARES AND MATRIX FACTORIZATION

LEAST SQUARES, QR DECOMPOSITION AND GENERALIZED INVERSE LEAST SQUARES
	ROUTINE	DESCRIPTION
	LSQRR	Solves a linear least-squares problem without iterative refinement.
	LQRRV	Computes the least-squares solution using Householder transformations applied in blocked form.
	LSBRR	Solves a linear least-squares problem with iterative refinement.
	LCLSQ	Solves a linear least-squares problem with linear constraints.
	LQRRR	Computes the QR decomposition, AP = QR, using Householder transformations.
	LQERR	Accumulate the orthogonal matrix Q from its factored form given the QR factorization of a rectangular matrix A.
	LQRSL	Computes the coordinate transformation, projection, and complete the solution of the least-squares problem Ax = b.
	LUPQR	Computes an updated QR factorization after the rank-one matrix αxy^T is added.

CHOLESKY FACTORIZATION
	ROUTINE	DESCRIPTION
	LCHRG	Computes the Cholesky decomposition of a symmetric positive semidefinite matrix with optional column pivoting.
	LUPCH	Updates the R^TR Cholesky factorization of a real symmetric positive definite matrix after a rank-one matrix is added.
	LDNCH	Downdates the R^TR Cholesky factorization of a real symmetric positive definite matrix after a rank-one matrix is removed.

SINGULAR VALUE DECOMPOSITIONS
	ROUTINE	DESCRIPTION
	LSVRR	Computes the singular value decomposition of a real matrix.
	LSVCR	Computes the singular value decomposition of a complex matrix.
	LSGRR	Computes the generalized inverse of a real matrix.

CHAPTER 2: EIGENSYSTEM ANALYSIS

EIGENVALUE DECOMPOSITION
	ROUTINE	DESCRIPTION
	LIN_EIG_SELF	Computes the eigenvalues of a self-adjoint matrix, A.
	LIN_EIG_GEN	Computes the eigenvalues of an n x n matrix, A.
	LIN_GEIG_GEN	Computes the generalized eigenvalues of an n x n matrix pencil, Av = lBv.

EIGENVALUES AND (OPTIONALLY) EIGENVECTORS OF AX = lX

REAL GENERAL PROBLEM AX = lX
	ROUTINE	DESCRIPTION
	EVLRG	Computes all of the eigenvalues of a real matrix.
	EVCRG	Computes all of the eigenvalues and eigenvectors of a real matrix.
	EPIRG	Computes the performance index for a real eigensystem.

COMPLEX GENERAL PROBLEM AX =lX
	ROUTINE	DESCRIPTION
	EVLCG	Computes all of the eigenvalues of a complex matrix.
	EVCCG	Computes all of the eigenvalues and eigenvectors of a complex matrix.
	EPICG	Computes the performance index for a complex eigensystem.

REAL SYMMETRIC GENERAL PROBLEM AX = lX
	ROUTINE	DESCRIPTION
	EVLSF	Computes all of the eigenvalues of a real symmetric matrix.
	EVCSF	Computes all of the eigenvalues and eigenvectors of a real symmetric matrix.
	EVASF	Computes the largest or smallest eigenvalues of a real symmetric matrix.
	EVESF	Computes the largest or smallest eigenvalues and the corresponding eigenvectors of a real symmetric matrix.
	EVBSF	Computes selected eigenvalues of a real symmetric matrix.
	EVFSF	Computes selected eigenvalues and eigenvectors of a real symmetric matrix.
	EPISF	Computes the performance index for a real symmetric eigensystem.

REAL BAND SYMMETRIC MATRICIES IN BAND STORAGE MODE
	ROUTINE	DESCRIPTION
	EVLSB	Computes all of the eigenvalues of a real symmetric matrix in band symmetric storage mode.
	EVCSB	Computes all of the eigenvalues and eigenvectors of a real symmetric matrix in band symmetric storage mode.
	EVASB	Computes the largest or smallest eigenvalues of a real symmetric matrix in band symmetric storage mode.
	EVESB	Computes the largest or smallest eigenvalues and the corresponding eigenvectors of a real symmetric matrix in band symmetric storage mode.
	EVBSB	Computes the eigenvalues in a given interval of a real symmetric matrix stored in band symmetric storage mode.
	EVFSB	Computes the eigenvalues in a given interval and the corresponding eigenvectors of a real symmetric matrix stored in band symmetric storage mode.
	EPISB	Computes the performance index for a real symmetric eigensystem in band symmetric storage mode.

COMPLEX HERMITIAN MATRICES
	ROUTINE	DESCRIPTION
	EVLHF	Computes all of the eigenvalues of a complex Hermitian matrix.
	EVCHF	Computes all of the eigenvalues and eigenvectors of a complex Hermitian matrix.
	EVAHF	Computes the largest or smallest eigenvalues of a complex Hermitian matrix.
	EVEHF	Computes the largest or smallest eigenvalues and the corresponding eigenvectors of a complex Hermitian matrix.
	EVBHF	Computes the eigenvalues in a given range of a complex Hermitian matrix.
	EVFHF	Computes the eigenvalues in a given range and the corresponding eigenvectors of a complex Hermitian matrix.
	EPIHF	Computes the performance index for a complex Hermitian eigensystem.

REAL UPPER HESSENBERG MATRICES
	ROUTINE	DESCRIPTION
	EVLRH	Computes all of the eigenvalues of a real upper Hessenberg matrix.
	EVCRH	Computes all of the eigenvalues and eigenvectors of a real upper Hessenberg matrix.

COMPLEX UPPER HESSENBERG MATRICES
	ROUTINE	DESCRIPTION
	EVLCH	Computes all of the eigenvalues of a complex upper Hessenberg matrix.
	EVCCH	Computes all of the eigenvalues and eigenvectors of a complex upper.

EIGENVALUES AND (OPTIONALLY) EIGENVECTORS OF AX = lBX

REAL GENERAL PROBLEM AX = lX
	ROUTINE	DESCRIPTION
	GVLRG	Computes all of the eigenvalues of a generalized real eigensystem Az = lBz.
	GVCRG	Computes all of the eigenvalues and eigenvectors of a generalized real eigensystem Az = lBz.
	GPIRG	Computes the performance index for a generalized real eigensystem Az = lBz.

COMPLEX GENERAL PROBLEM AX = lBX
	ROUTINE	DESCRIPTION
	GVLCG	Computes all of the eigenvalues of a generalized complex eigensystem Az = lBz.
	GVCCG	Computes all of the eigenvalues and eigenvectors of a generalized complex eigensystem Az = lBz.
	GPICG	Computes the performance index for a generalized complex eigensystem Az = lBz.

REAL SYMMETRIC PROBLEM AX = lBX
	ROUTINE	DESCRIPTION
	GVLSP	Computes all of the eigenvalues of the generalized real symmetric eigenvalue problem Az = lBz, with B symmetric positive definite.
	GVCSP	Computes all of the eigenvalues and eigenvectors of the generalized real symmetric eigenvalue problem Az = lBz, with B symmetric positive definite.
	GPISP	Computes the performance index for a generalized real symmetric eigensystem problem.

EIGENVALUES AND EIGENVECTORS COMPUTED WITH ARPACK
	ROUTINE	DESCRIPTION
	ARPACK_SYMMETRIC	Computes some eigenvalues and eigenvectors of the generalized real symmetric eigenvalue problem Ax = lBx.
	ARPACK_SVD	Computes some singular values and left and right singular vectors of a real rectangular matrix A_{M x N} = USV^T.
	ARPACK_NONSYMMETRIC	Compute some eigenvalues and eigenvectors of the generalized eigenvalue problem Ax = lBx. This can be used for the case B = I.
	ARPACK_COMPLEX	Compute some eigenvalues and eigenvectors of the generalized eigenvalue problem Ax = lBx.

CHAPTER 3: INTERPOLATION AND APPROXIMATION

CURVE AND SURFACE FITTING WITH SPLINES
	ROUTINE	DESCRIPTION
	SPLINE_CONSTRAINTS	Returns the derived type array result.
	SPLINE_VALUES	Returns an array result, given an array of input.
	SPLINE_FITTING	Weighted least-squares fitting by B-splines to discrete One-Dimensional data is performed.
	SURFACE_CONSTRAINTS	Returns the derived type array result given optional input.
	SURFACE_VALUES	Returns a tensor product array result, given two arrays of independent variable values.
	SURFACE_FITTING	Weighted least-squares fitting by tensor product B-splines to discrete two-dimensional data is performed.

CUBIC SPLINE INTERPOLATION
	ROUTINE	DESCRIPTION
	CSIEZ	Computes the cubic spline interpolant with the ‘not-a-knot’ condition and returns values of the interpolant at specified points.
	CSINT	Computes the cubic spline interpolant with the ‘not-a-knot’ condition.
	CSDEC	Computes the cubic spline interpolant with specified derivative endpoint conditions.
	CSHER	Computes the Hermite cubic spline interpolant.
	CSAKM	Computes the Akima cubic spline interpolant.
	CSCON	Computes a cubic spline interpolant that is consistent with the concavity of the data.
	CSPER	Computes the cubic spline interpolant with periodic boundary conditions.

CUBIC SPLINE EVALUATION AND INTEGRATION
	ROUTINE	DESCRIPTION
	CSVAL	Evaluates a cubic spline.
	CSDER	Evaluates the derivative of a cubic spline.
	CS1GD	Evaluates the derivative of a cubic spline on a grid.
	CSITG	Evaluates the integral of a cubic spline.

B-SPLINE INTERPOLATION
	ROUTINE	DESCRIPTION
	SPLEZ	Computes the values of a spline that either interpolates or fits user-supplied data.
	BSINT	Computes the spline interpolant, returning the B-spline coefficients.
	BSNAK	Computes the “not-a-knot” spline knot sequence.
	BSOPK	Computes the “optimal” spline knot sequence.
	BS2IN	Computes a two-dimensional tensor-product spline interpolant, returning the tensor-product B-spline coefficients.
	BS3IN	Computes a three-dimensional tensor-product spline interpolant, returning the tensor-product B-spline coefficients.

SPLINE EVALUATION, INTEGRATION, AND CONVERSION TO PIECEWISE POLYNOMIAL GIVEN THE B-SPLINE REPRESENTATION
	ROUTINE	DESCRIPTION
	BSVAL	Evaluates a spline, given its B-spline representation.
	BSDER	Evaluates the derivative of a spline, given its B-spline representation.
	BS1GD	Evaluates the derivative of a spline on a grid, given its B-spline representation.
	BSITG	Evaluates the integral of a spline, given its B-spline representation.
	BS2VL	Evaluates a two-dimensional tensor-product spline, given its tensor-product B-spline representation.
	BS2DR	Evaluates the derivative of a two-dimensional tensor-product spline, given its tensor-product B-spline representation.
	BS2GD	Evaluates the derivative of a two-dimensional tensor-product spline, given its tensor-product B-spline representation on a grid.
	BS2IG	Evaluates the integral of a tensor-product spline on a rectangular domain, given its tensor-product B-spline representation.
	BS3VL	Evaluates a three-dimensional tensor-product spline, given its tensor-product B-spline representation.
	BS3DR	Evaluates the derivative of a three-dimensional tensor-product spline, given its tensor-product B-spline representation.
	BS3GD	Evaluates the derivative of a three-dimensional tensor-product spline, given its tensor-product B-spline representation on a grid.
	BS3IG	Evaluates the integral of a tensor-product spline in three dimensions over a three-dimensional rectangle, given its tensor-product B-spline representation.
	BSCPP	Converts a spline in B-spline representation to piecewise polynomial representation.

PIECEWISE POLYNOMIAL
	ROUTINE	DESCRIPTION
	PPVAL	Evaluates a piecewise polynomial.
	PPDER	Evaluates the derivative of a piecewise polynomial.
	PP1GD	Evaluates the derivative of a piecewise polynomial on a grid.
	PPITG	Evaluates the integral of a piecewise polynomial.

QUADRATIC POLYNOMIAL INTERPOLATION ROUTINES FOR GRIDDED DATA
	ROUTINE	DESCRIPTION
	QDVAL	Evaluates a function defined on a set of points using quadratic interpolation.
	QDDER	Evaluates the derivative of a function defined on a set of points using quadratic interpolation.
	QD2VL	Evaluates a function defined on a rectangular grid using quadratic interpolation.
	QD2DR	Evaluates the derivative of a function defined on a rectangular grid using quadratic interpolation.
	QD3VL	Evaluates a function defined on a rectangular three-dimensional grid using quadratic interpolation.
	DQ3DR	Evaluates the derivative of a function defined on a rectangular three-dimensional grid using quadratic interpolation.

MULTI-DIMENSIONAL INTERPOLATION
	ROUTINE	DESCRIPTION
	SURF	Computes a smooth bivariate interpolant to scattered data that is locally a quintic polynomial in two variables.
	SURFND	Performs multidimensional interpolation and differentiation for up to 7 dimensions.

LEAST-SQUARES APPROXIMATION
	ROUTINE	DESCRIPTION
	RLINE	Fits a line to a set of data points using least squares.
	RCURV	Fits a polynomial curve using least squares.
	FNLSQ	Computes a least-squares approximation with user-supplied basis functions.
	BSLSQ	Computes the least-squares spline approximation, and returns the B-spline coefficients.
	BSVLS	Computes the variable knot B-spline least squares approximation to given data.
	CONFIT	Computes the least-squares constrained spline approximation, returning the B-spline coefficients.
	BSLS2	Computes a two-dimensional tensor-product spline approximant using least squares, returning the tensor-product B-spline coefficients.
	BSLS3	Computes a three-dimensional tensor-product spline approximant using least squares, returning the tensor-product B-spline coefficients.

CUBIC SPLINE SMOOTHING
	ROUTINE	DESCRIPTION
	CSSED	Smooths one-dimensional data by error detection.
	CSSMH	Computes a smooth cubic spline approximation to noisy data.
	CSSCV	Computes a smooth cubic spline approximation to noisy data using cross-validation to estimate the smoothing parameter.

RATIONAL L_∞ APPROXIMATION
	ROUTINE	DESCRIPTION
	RATCH	Computes a rational weighted Chebyshev approximation to a continuous function on an interval.

CHAPTER 4: INTEGRATION AND DIFFERENTIATION

UNIVARIATE QUADRATURE
	ROUTINE	DESCRIPTION
	QDAGS	Integrates a function (which may have endpoint singularities).
	QDAG	Integrates a function using a globally adaptive scheme based on Gauss-Kronrod rules.
	QDAGP	Integrates a function with singularity points given.
	QDAG1D	Integrates a function with a possible internal or endpoint singularity.
	QDAGI	Integrates a function over an infinite or semi-infinite interval.
	QDAWO	Integrates a function containing a sine or a cosine.
	QDAWF	Computes a Fourier integral.
	QDAWS	Integrates a function with algebraic logarithmic singularities.
	QDAWC	Integrates a function F(X)/(X – C) in the Cauchy principal value sense.
	QDNG	Integrates a smooth function using a nonadaptive rule.

MULTIDIMENSIONAL QUADRATURE
	ROUTINE	DESCRIPTION
	TWODQ	Computes a two-dimensional iterated integral.
	QDAG2D	Integrates a function of two variables with a possible internal or end point singularity.
	QDAG3D	Integrates a function of three variables with a possible internal or endpoint singularity.
	QAND	Integrates a function on a hyper-rectangle.
	QMC	Integrates a function over a hyper-rectangle using a quasi-Monte Carlo method.

GAUSS RULES AND THREE-TERM RECURRENCES
	ROUTINE	DESCRIPTION
	GQRUL	Computes a Gauss, Gauss-Radau, or Gauss-Lobatto quadrature rule with various classical weight functions.
	GQRCF	Computes a Gauss, Gauss-Radau or Gauss-Lobatto quadrature rule given the recurrence coefficients for the monic polynomials orthogonal with respect to the weight function.
	RECCF	Computes recurrence coefficients for various monic polynomials.
	RECQR	Computes recurrence coefficients for monic polynomials given a quadrature rule.
	FQRUL	Computes a Fejér quadrature rule with various classical weight functions.

DIFFERENTIATION
	ROUTINE	DESCRIPTION
	DERIV	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
	ROUTINE	DESCRIPTION
	IVPRK	Solves an initial-value problem for ordinary differential equations using the Runge-Kutta-Verner fifth-order and sixth-order method.
	IVMRK	Solves an initial-value problem y’ = f(t, y) for ordinary differential equations using Runge-Kutta pairs of various orders.
	IVPAG	Solves an initial-value problem for ordinary differential equations using either Adams-Moulton’s or Gear’s BDF method.

SOLUTION OF THE BOUNDARY VALUE PROBLEM FOR ODES
	ROUTINE	DESCRIPTION
	BVPFD	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.
	BVPMS	Solves a (parameterized) system of differential equations with boundary conditions at two points, using a multiple-shooting method.

SOLUTION OF DIFFERENTIAL-ALGEBRAIC SYSTEMS
	ROUTINE	DESCRIPTION
	DAESL	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
	ROUTINE	DESCRIPTION
	IVOAM	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
	ROUTINE	DESCRIPTION
	PDE_1D_MG	Method of lines with Variable Griddings.
	MMOLCH	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 the generalized Feynman-Kac PDE on a rectangular grid using a finite element Galerkin method.
	HQSVAL	This rank-1 array function evaluates a Hermite quintic spline or one of its derivatives for an array of input points.

SOLUTION OF A PDE IN TWO AND THREE DIMENSIONS
	ROUTINE	DESCRIPTION
	FPS2H	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.
	FPS3H	Solves Poisson’s or Helmholtz’s equation on a three-dimensional box using a fast Poisson solver based on the HODIE finite-difference scheme on a uniform mesh.

STURM-LIOUVILLE PROBLEMS
	ROUTINE	DESCRIPTION
	SLEIG	Determines eigenvalues, eigenfunctions and/or spectral density functions for Sturm-Liouville problems.
	SLCNT	Calculates the indices of eigenvalues of a Sturm-Liouville problem.

CHAPTER 6: TRANSFORMS

REAL TRIGONOMETRIC FFT
	ROUTINE	DESCRIPTION
	FAST_DFT	Computes the Discrete Fourier Transform of a rank-1 complex array, x.
	FAST_2DFT	Computes the Discrete Fourier Transform (2DFT) of a rank-2 complex array, x.
	FAST_3DFT	Computes the Discrete Fourier Transform (2DFT) of a rank-3 complex array, x.
	FFTRF	Computes the Fourier coefficients of a real periodic sequence.
	FFTRB	Computes the real periodic sequence from its Fourier coefficients.
	FFTRI	Computes parameters needed by FFTRF and FFTRB.

COMPLEX EXPONENTIAL FFT
	ROUTINE	DESCRIPTION
	FFTCF	Computes the Fourier coefficients of a complex periodic sequence.
	FFTCB	Computes the complex periodic sequence from its Fourier coefficients.
	FFTCI	Computes parameters needed by FFTCF and FFTCB.

REAL SINE AND COSINE FFTS
	ROUTINE	DESCRIPTION
	FSINT	Computes the discrete Fourier sine transformation of an odd sequence.
	FSINI	Computes parameters needed by FSINT.
	FCOST	Computes the discrete Fourier cosine transformation of an even sequence.
	FCOSI	Computes parameters needed by FCOST.

REAL QUARTER SINE AND QUARTER COSINE FFTS
	ROUTINE	DESCRIPTION
	QSINF	Computes the coefficients of the sine Fourier transform with only odd wave numbers.
	QSINB	Computes a sequence from its sine Fourier coefficients with only odd wave numbers.
	QSINI	Computes parameters needed by QSINF and QSINB.
	QCOSF	Computes the coefficients of the cosine Fourier transform with only odd wave numbers.
	QCOSB	Computes a sequence from its cosine Fourier coefficients with only odd wave numbers.
	QCOSI	Computes parameters needed by QCOSF and QCOSB.

TWO AND THREE DIMENSIONAL COMPLEX FFTS
	ROUTINE	DESCRIPTION
	FFT2D	Computes Fourier coefficients of a complex periodic two-dimensional array.
	FFT2B	Computes the inverse Fourier transform of a complex periodic two dimensional array.
	FFT3F	Computes Fourier coefficients of a complex periodic three-dimensional array.
	FFT3B	Computes the inverse Fourier transform of a complex periodic three-dimensional array.

CONVOLUTIONS AND CORRELATIONS
	ROUTINE	DESCRIPTION
	RCONV	Computes the convolution of two real vectors.
	CCONV	Computes the convolution of two complex vectors.
	RCORL	Computes the correlation of two real vectors.
	CCORL	Computes the correlation of two complex vectors.

LAPLACE TRANSFORM
	ROUTINE	DESCRIPTION
	INLAP	Computes the inverse Laplace transform of a complex function.
	SINLP	Computes the inverse Laplace transform of a complex function.

CHAPTER 7: NONLINEAR EQUATIONS

ZEROS OF A POLYNOMIAL
	ROUTINE	DESCRIPTION
	ZPLRC	Finds the zeros of a polynomial with real coefficients using Laguerre’s method.
	ZPORC	Finds the zeros of a polynomial with real coefficients using the Jenkins-Traub three-stage algorithm.
	ZPOCC	Finds the zeros of a polynomial with complex coefficients using the Jenkins-Traub three-stage algorithm.

ZEROS OF A FUNCTION
	ROUTINE	DESCRIPTION
	ZANLY	Finds the zeros of a univariate complex function using Müller’s method.
	ZUNI	Finds a zero of a real univariate function.
	ZBREN	Finds a zero of a real function that changes sign in a given interval.
	ZREAL	Finds the real zeros of a real function using Müller’s method.

ROOT OF A SYSTEM OF EQUATIONS
	ROUTINE	DESCRIPTION
	NEQNF	Solves a system of nonlinear equations using a modified Powell hybrid algorithm and a finite-difference approximation to the Jacobian.
	NEQNJ	Solves a system of nonlinear equations using a modified Powell hybrid algorithm with a user-supplied Jacobian.
	NEQBF	Solves a system of nonlinear equations using factored secant update with a finite-difference approximation to the Jacobian.
	NEQBJ	Solves a system of nonlinear equations using factored secant update with a user-supplied Jacobian.

CHAPTER 8: OPTIMIZATION

UNCONSTRAINED MINIMIZATION

UNIVARIATE FUNCTION
	ROUTINE	DESCRIPTION
	UVMIF	Finds the minimum point of a smooth function of a single variable using only function evaluations.
	UVMID	Finds the minimum point of a smooth function of a single variable using both function evaluations and first derivative evaluations.
	UVMGS	Finds the minimum point of a non-smooth function of a single variable.

MULTIVARIATE FUNCTION
	ROUTINE	DESCRIPTION
	UMINF	Minimizes a function of N variables using a quasi-Newton method and a finite-difference gradient.
	UMING	Minimizes a function of N variables using a quasi-Newton method and a user-supplied gradient.
	UMIDH	Minimizes a function of N variables using a modified Newton method and a finite-difference Hessian.
	UMIAH	Minimizes a function of N variables using a modified Newton method and a user-supplied Hessian.
	UMCGF	Minimizes a function of N variables using a conjugate gradient algorithm and a finite-difference gradient.
	UMCGG	Minimizes a function of N variables using a conjugate gradient algorithm and a user-supplied gradient.
	UMPOL	Minimizes a function of N variables using a direct search polytope algorithm.

NONLINEAR LEAST SQUARES
	ROUTINE	DESCRIPTION
	UNLSF	Solves a nonlinear least-squares problem using a modified Levenberg-Marquardt algorithm and a finite-difference Jacobian.
	UNLSJ	Solves a nonlinear least squares problem using a modified Levenberg-Marquardt algorithm and a user-supplied Jacobian.

MINIMIZATION WITH SIMPLE BOUNDS
	ROUTINE	DESCRIPTION
	BCONF	Minimizes a function of N variables subject to bounds on the variables using a quasi- Newton method and a finite-difference gradient.
	BCONG	Minimizes a function of N variables subject to bounds on the variables using a quasi- Newton method and a user-supplied gradient.
	BCODH	Minimizes a function of N variables subject to bounds on the variables using a modified Newton method and a finite-difference Hessian.
	BCOAH	Minimizes a function of N variables subject to bounds on the variables using a modified Newton method and a user-supplied Hessian.
	BCPOL	Minimizes a function of N variables subject to bounds on the variables using a direct search complex algorithm.
	BCLSF	Solves a nonlinear least squares problem subject to bounds on the variables using a modified Levenberg-Marquardt algorithm and a finite-difference Jacobian.
	BCLSJ	Solves a nonlinear least squares problem subject to bounds on the variables using a modified Levenberg-Marquardt algorithm and a user-supplied Jacobian.
	BCNLS	Solves a nonlinear least-squares problem subject to bounds on the variables and general linear constraints.

LINEARLY CONSTRAINED MINIMIZATION
	ROUTINE	DESCRIPTION
	READ_MPS	Reads an MPS file containing a linear programming problem or a quadratic programming problem.
	MPS_FREE	Deallocates the space allocated for the IMSL derived type s_MPS. This routine is usually used in conjunction with READ_MPS.
	DENSE_LP	Solves a linear programming problem using an active set strategy.
	DLPRS	Solves a linear programming problem via the revised simplex algorithm.
	SLPRS	Solves a sparse linear programming problem via the revised simplex algorithm.
	TRAN	Solves a transportation problem.
	QPROG	Solves a quadratic programming problem subject to linear equality/inequality constraints.
	LCONF	Minimizes a general objective function subject to linear equality/inequality constraints.
	LCONG	Minimizes a general objective function subject to linear equality/inequality constraints and a user-supplied gradient.
	LIN_CON_TRUST_REGION	Minimizes a function of N variables subject to linear constraints using a derivative-free, interpolation-based trust region method.

NONLINEARLY CONSTRAINED MINIMIZATION
	ROUTINE	DESCRIPTION
	NNLPF	Nonlinearly Constrained Minimization using a sequential equality constrained QP method.
	NNLPG	Nonlinearly Constrained Minimization using a sequential equality constrained QP method and a user-supplied gradient.

SERVICE ROUTINES
	ROUTINE	DESCRIPTION
	CDGRD	Approximates the gradient using central differences.
	FDGRD	Approximates the gradient using forward differences.
	FDHES	Approximates the Hessian using forward differences and function values.
	GDHES	Approximates the Hessian using forward differences and a user-supplied gradient.
	DDJAC	Approximates the Jacobian of M functions in N unknowns using divided differences.
	FDJAC	Approximate the Jacobian of M functions in N unknowns using forward differences.
	CHGRD	Checks a user-supplied gradient of a function.
	CHHES	Checks a user-supplied Hessian of an analytic function.
	CHJAC	Checks a user-supplied Jacobian of a system of equations with M functions in N unknowns.
	GGUES	Generates points in an N-dimensional space.

CHAPTER 9: BASIC MATRIX/VECTOR OPERATIONS

BASIC LINEAR ALGEBRA SUBPROGRAMS (BLAS)

LEVEL 1 BLAS
	ROUTINE	DESCRIPTION
	SSET	Sets the components of a vector to a scalar.
	SCOPY	Copies a vector x to a vector y, both single precision.
	SSCAL	Multiplies a vector by a scalar, y ←a y, both single precision.
	SVCAL	Multiplies a vector by a scalar and stores the result in another vector, y ←a x, all single precision.
	SADD	Adds a scalar to each component of a vector, x ← x + a, all single precision.
	SSUB	Subtract each component of a vector from a scalar, x ← a - x, all single precision.
	SAXPY	Computes the scalar times a vector plus a vector, y ← ax+ y, all single precision.
	SSWAP	Interchange vectors x and y, both single precision.
	SDOT	Computes the single-precision dot product x^Ty.
	DSDOT	Computes the single-precision dot product x^Ty using a double precision accumulator.
	SDSDOT	Computes the sum of a single-precision scalar and a single precision dot product, a + x^Ty, using a double-precision accumulator.
	SDDOTI	Computes the sum of a single-precision scalar plus a single precision dot product using a double-precision accumulator, which is set to the result ACC ← a + x^Ty.
	SHPROD	Computes the Hadamard product of two single-precision vectors.
	SXYZ	Computes a single-precision xyz product.
	SSUM	Sums the values of a single-precision vector.
	SASUM	Sums the absolute values of the components of a single-precision vector.
	SNRM2	Computes the Euclidean length or L₂ norm of a single-precision vector.
	SPRDCT	Multiplies the components of a single-precision vector.
	ISMIN	Finds the smallest index of the component of a single-precision vector having minimum value.
	ISMAX	Finds the smallest index of the component of a single-precision vector having maximum value.
	ISAMIN	Finds the smallest index of the component of a single-precision vector having minimum absolute value.
	ISAMAX	Finds the smallest index of the component of a single-precision vector having maximum absolute value.
	SROTG	Constructs a Givens plane rotation in single precision.
	SROT	Applies a Givens plane rotation in single precision.
	SROTM	Applies a modified Givens plane rotation in single precision.
	SROTMG	Constructs a modified Givens plane rotation in single precision.

LEVEL 2 BLAS
	ROUTINE	DESCRIPTION
	SGEMV	Computes one of the matrix-vector operations: y ← αAx + βy, or y ← αA^Tx + βy.
	SGBMV	Computes one of the matrix-vector operations: y ← αAx + βy, or y ← αA^Tx + βy, where A is a matrix stored in band storage mode.
	CHEMV	Compute the matrix-vector operation y ← αAx + βy where A is a Hermitian matrix.
	CHPMV	Compute the matrix-vector operation y ← αAx + βy where A is a packed Hermitian matrix.
	CHBMV	Computes the matrix-vector operation y ← αAx + βy where A is a Hermitian band matrix in band Hermitian storage.
	CTPMV	Performs the matrix-vector operation in packed form.
	CTPSV	Solves the systems of equations in packed form.
	SSYMV	Computes the matrix-vector operation y ← αAx + βy where A is a symmetric matrix.
	SSBMV	Computes the matrix-vector operation y ← αAx + βy where A is a symmetric matrix in band symmetric storage mode.
	SSPMV	Performs the matrix-vector operation y ← αAx + βy in packed form.
	STRMV	Computes one of the matrix-vector operations: x← Ax or x← A^Tx where A is a triangular matrix.
	STBMV	Computes one of the matrix-vector operations: x← Ax or x← A^Tx where A is a triangular matrix in band storage mode.
	STRSV	Solves one of the triangular linear systems: x← A^-1x or x← (A^-1)^Tx where A is a triangular matrix.
	STBSV	Solves one of the triangular systems: x← A^-1x or x← (A^-1)^Tx where A is a triangular matrix in band storage mode.
	STPMV	Performs one of the matrix-vector operations: x← Ax or x← A^Tx where A is in packed form.
	STPSV	Solves one of the systems of equations x← A^-1x or x← (A^-1)^Tx A^Tx where A is in packed form.
	SGER	Computes the rank-one update of a real general matrix: A← A + αxy^T.
	CGERU	Computes the rank-one update of a complex general matrix: A← A + αxy^T.
	CGERC	Computes the rank-one update of a complex general matrix: .
	CHER	Computes the rank-one update of a Hermitian matrix: with x complex and α real.
	CHPR	Computes the rank-one update of a Hermitian matrix: in packed form with x complex and α real.
	CHER2	Computes a rank-two update of a Hermitian matrix: .
	CHPR2	Performs the hermitian rank 2 operation in packed form.
	SSYR	Computes the rank-one update of a real symmetric matrix: A← A + αxx^T.
	SSPR	Performs the symmetric rank 1 operation A← A + αxx^T in packed form.
	SSYR2	Computes the rank-two update of a real symmetric matrix: A← A + αxy+ αyx^T.
	SSPR2	Performs the symmetric rank 2 operation A← A + αxy+ αyx^T in packed form.

LEVEL 3 BLAS
	ROUTINE	DESCRIPTION
	SGEMM	Computes one of the matrix-matrix operations: C← αAB + βC, C← αA^TB + βC, C← αAB^T + βC, or C← αA^TB^T + βC.
	SSYMM	Computes one of the matrix-matrix operations: C← αAB + βC or C← αBA + βC, where A is a symmetric matrix and B and C are m by n matrices.
	CHEMM	Computes one of the matrix-matrix operations: C← αAB + βC or C← αBA + βC, where A is a Hermitian matrix and B and C are m by n matrices.
	SSYRK	Computes one of the symmetric rank k operations: C← αAA^T + βC or C← αA^TA + βC, where C is an n by n symmetric matrix and A is an n by k matrix in the first case and a k by n matrix in the second case.
	CHERK	Computes one of the Hermitian rank k operations: or , where C is an n by n Hermitian matrix and A is an n by k matrix in the first case and a k by n matrix in the second case.
	SSYR2K	Computes one of the symmetric rank 2k operations: C← αAB^T + αBA^T + βC or C← αA^TB + αB^TA + βC, where C is an n by n symmetric matrix and A and B are n by k matrices in the first case and k by n matrices in the second case.
	CHER2K	Computes one of the Hermitian rank 2k operations: or where C is an n by n Hermitian matrix in the first case and k by n matrices in the second case.
	STRMM	Computes one of the matrix-matrix operations: B← αAB, B← αA^TB or B← αBA, B← αBA^T, where B is an m by n matrix and A is a triangular matrix.
	STRSM	Solves one of the matrix equations: B← αA^-1B, B← αBA^-1 or B← α(A^-1)^T B, B← αB(A^-1)^T, where B is an m by n matrix and A is a triangular matrix.
	CTRSM	Solves one of the complex matrix equations: or , where A is a triangular matrix.

OTHER MATRIX/VECTOR OPERATIONS

MATRIX COPY
	ROUTINE	DESCRIPTION
	CRGRG	Copies a real general matrix.
	CCGCG	Copies a complex general matrix.
	CRBRB	Copies a real band matrix stored in band storage mode.
	CCBCB	Copies a complex band matrix stored in complex band storage mode.

MATRIX CONVERSION
	ROUTINE	DESCRIPTION
	CRGRB	Converts a real general matrix to a matrix in band storage mode.
	CRBRG	Converts a real matrix in band storage mode to a real general matrix.
	CCGCB	Converts a complex general matrix to a matrix in complex band storage mode.
	CCBCG	Converts a complex matrix in band storage mode to a complex matrix in full storage mode.
	CRGCG	Copies a real general matrix to a complex general matrix.
	CRRCR	Copies a real rectangular matrix to a complex rectangular matrix.
	CRBCB	Converts a real matrix in band storage mode to a complex matrix in band storage mode.
	CSFRG	Extends a real symmetric matrix defined in its upper triangle to its lower triangle.
	CHFCG	Extends a complex Hermitian matrix defined in its upper triangle to its lower triangle.
	CSBRB	Copies a real symmetric band matrix stored in band symmetric storage mode to a real band matrix stored in band storage mode.
	CHBCB	Copies a complex Hermitian band matrix stored in band Hermitian storage mode to a complex band matrix stored in band storage mode.
	TRNRR	Transposes a rectangular matrix.

MATRIX MULTIPLICATION
	ROUTINE	DESCRIPTION
	MXTXF	Computes the transpose product of a matrix, A^TA.
	MXTYF	Multiplies the transpose of matrix A by matrix B, A^TB.
	MXYTF	Multiplies a matrix A by the transpose of a matrix B, AB^T.
	MRRRR	Multiplies two real rectangular matrices, AB.
	MCRCR	Multiplies two complex rectangular matrices, AB.
	HRRRR	Computes the Hadamard product of two real rectangular matrices.
	BLINF	Computes the bilinear form x^TAy.
	POLRG	Evaluates a real general matrix polynomial.

MATRIX-VECTOR MULTIPLICATION
	ROUTINE	DESCRIPTION
	MURRV	Multiplies a real rectangular matrix by a vector.
	MURBV	Multiplies a real band matrix in band storage mode by a real vector.
	MUCRV	Multiplies a complex rectangular matrix by a complex vector.
	MUCBV	Multiplies a complex band matrix in band storage mode by a complex vector.

MATRIX ADDITION
	ROUTINE	DESCRIPTION
	ARBRB	Adds two band matrices, both in band storage mode.
	ACBCB	Adds two complex band matrices, both in band storage mode.

MATRIX NORM
	ROUTINE	DESCRIPTION
	NRIRR	Computes the infinity norm of a real matrix.
	NR1RR	Computes the 1-norm of a real matrix.
	NR2RR	Computes the Frobenius norm of a real rectangular matrix.
	NR1RB	Computes the 1-norm of a real band matrix in band storage mode.
	NR1CB	Computes the 1-norm of a complex band matrix in band storage mode.

DISTANCE BETWEEN TWO POINTS
	ROUTINE	DESCRIPTION
	DISL2	Computes the Euclidean (2-norm) distance between two points.
	DISL1	Computes the 1-norm distance between two points.
	DISLI	Computes the infinity norm distance between two points.

VECTOR CONVOLUTIONS
	ROUTINE	DESCRIPTION
	VCONR	Computes the convolution of two real vectors.
	VCONC	Computes the convolution of two complex vectors.

EXTENDED PRECISION ARITHMETIC
	ROUTINE	DESCRIPTION
	DQINI	Initializes an extended-precision accumulator with a double-precision scalar.
	DQSTO	Stores a double-precision approximation to an extended-precision scalar.
	DQADD	Adds a double-precision scalar to the accumulator in extended precision.
	DQMUL	Multiplies double-precision scalars in extended precision.
	ZQINI	Initializes an extended-precision complex accumulator to a double complex scalar.
	ZQSTO	Stores a double complex approximation to an extended-precision complex scalar.
	ZQADD	Adds a double complex scalar to the accumulator in extended precision.
	ZQMUL	Multiplies double complex scalars using extended precision.

CHAPTER 10: LINEAR ALGEBRA OPERATORS AND GENERIC FUNCTIONS

OPERATORS
	ROUTINE	DESCRIPTION
	OPERATORS: .x., .tx., .xt., .xh.	Computes matrix-vector and matrix-matrix products.
	OPERATORS: .t., .h.	Computes transpose and conjugate transpose of a matrix.
	OPERATORS: .i.	Computes the inverse matrix, for square non-singular matrices, or the Moore-Penrose generalized inverse matrix for singular square matrices or rectangular matrices.
	OPERATORS: .ix., .xi.	Computes the inverse matrix times a vector or matrix for square non-singular matrices or the corresponding Moore-Penrose generalized inverse matrix for singular square matrices or rectangular matrices.

FUNCTIONS
	ROUTINE	DESCRIPTION
	CHOL	Computes the Cholesky factorization of a positive-definite, symmetric or self-adjoint matrix, A.
	COND	Computes the condition number of a matrix, A.
	DET	Computes the determinant of a rectangular matrix, A.
	DIAG	Constructs a square diagonal matrix from a rank-1 array or several diagonal matrices from a rank-2 array.
	DIAGONALS	Extracts a rank-1 array whose values are the diagonal terms of a rank-2 array argument.
	EIG	Computes the eigenvalue-eigenvector decomposition of an ordinary or generalized eigenvalue problem.
	EYE	Creates a rank-2 square array whose diagonals are all the value one.
	FFT	The Discrete Fourier Transform of a complex sequence and its inverse transform.
	FFT_BOX	The Discrete Fourier Transform of several complex or real sequences.
	IFFT	The inverse of the Discrete Fourier Transform of a complex sequence.
	IFFT_BOX	The inverse Discrete Fourier Transform of several complex or real sequences.
	ISNAN	This is a generic logical function used to test scalars or arrays for occurrence of an IEEE 754 Standard format of floating point (ANSI/IEEE 1985) NaN, or not-a-number.
	NAN	Returns, as a scalar function, a value corresponding to the IEEE 754 Standard format of floating point (ANSI/IEEE 1985) for NaN.
	NORM	Computes the norm of a rank-1 or rank-2 array.
	ORTH	Orthogonalizes the columns of a rank-2 or rank-3 array.
	RAND	Computes a scalar, rank-1, rank-2 or rank-3 array of random numbers.
	RANK	Computes the mathematical rank of a rank-2 or rank-3 array.
	SVD	Computes the singular value decomposition of a rank-2 or rank-3 array, A = USV^T.
	UNIT	Normalizes the columns of a rank-2 or rank-3 array so each has Euclidean length of value one.

CHAPTER 11: UTILITIES

SCALAPACK UTILITIES
	ROUTINE	DESCRIPTION
	SCALAPACK_SETUP	This routine sets up a processor grid and calculates default values for various entities to be used in mapping a global array to the processor grid.
	SCALAPACK_GETDIM	This routine calculates the row and column dimensions of a local distributed array based on the size of the array to be distributed and the row and column blocking factors to be used.
	SCALAPACK_READ	Reads matrix data from a file and transmits it into the two-dimensional block-cyclic form.
	SCALAPACK_WRITE	Writes the matrix data to a file.
	SCALAPACK_MAP	This routine maps array data from a global array to local arrays in the two-dimensional block-cyclic form required by ScaLAPACK routines.
	SCALAPACK_UNMAP	This routine unmaps array data from local distributed arrays to a global array. The data in the local arrays must have been stored in the two-dimensional block-cyclic form required by ScaLAPACK routines.
	SCALAPACK_EXIT	This routine exits ScaLAPACK mode for the IMSL Library routines. All processors in the BLACS context call the routine.

PRINT
	ROUTINE	DESCRIPTION
	ERROR_POST	Prints error messages.
	SHOW	Prints rank-1 or rank-2 arrays of numbers in a readable format.
	WRRRN	Prints a real rectangular matrix with integer row and column labels.
	WRRRL	Prints a real rectangular matrix with a given format and labels.
	WRIRN	Prints an integer rectangular matrix with integer row and column labels.
	WRIRL	Prints an integer rectangular matrix with a given format and labels.
	WRCRN	Prints a complex rectangular matrix with integer row and column labels.
	WRCRL	Prints a complex rectangular matrix with a given format and labels.
	WROPT	Sets or Retrieves an option for printing a matrix.
	PGOPT	Sets or Retrieves page width and length for printing.

PERMUTE
	ROUTINE	DESCRIPTION
	PERMU	Rearranges the elements of an array as specified by a permutation.
	PERMA	Permutes the rows or columns of a matrix.

SORT
	ROUTINE	DESCRIPTION
	SORT_REAL	Sorts a rank-1 array of real numbers x so the y results are algebraically nondecreasing, y₁ ≤ y₂ ≤ … y_n .
	SVRGN	Sorts a real array by algebraically increasing value.
	SVRGP	Sorts a real array by algebraically increasing value and returns the permutation that rearranges the array.
	SVIGN	Sorts an integer array by algebraically increasing value.
	SVIGP	Sorts an integer array by algebraically increasing value and returns the permutation that rearranges the array.
	SVRBN	Sorts a real array by nondecreasing absolute value.
	SVRBP	Sorts a real array by nondecreasing absolute value and returns the permutation that rearranges the array.
	SVIBN	Sorts an integer array by nondecreasing absolute value.
	SVIBP	Sorts an integer array by nondecreasing absolute value and returns the permutation that rearranges the array.

SEARCH
	ROUTINE	DESCRIPTION
	SRCH	Searches a sorted vector for a given scalar and returns its index.
	ISRCH	Searches a sorted integer vector for a given integer and returns its index.
	SSRCH	Searches a character vector, sorted in ascending ASCII order, for a given string and returns its index.

CHARACTER STRING MANIPULATION
	ROUTINE	DESCRIPTION
	ACHAR	Returns a character given its ASCII value.
	IACHAR	Returns the integer ASCII value of a character argument.
	ICASE	Returns the ASCII value of a character converted to uppercase.
	IICSR	Compares two character strings using the ASCII collating sequence but without regard to case.
	IIDEX	Determines the position in a string at which a given character sequence begins without regard to case.
	CVTSI	Converts a character string containing an integer number into the corresponding integer form.

TIME, DATE AND VERSION
	ROUTINE	DESCRIPTION
	CPSEC	Returns CPU time used in seconds.
	TIMDY	Gets time of day.
	TDATE	Gets today’s date.
	NDAYS	Computes the number of days from January 1, 1900, to the given date.
	NDYIN	Gives the date corresponding to the number of days since January 1, 1900.
	IDYWK	Computes the day of the week for a given date.
	VERML	Obtains IMSL MATH LIBRARY-related version and system information.

RANDOM NUMBER GENERATION
	ROUTINE	DESCRIPTION
	RAND_GEN	Generates a rank-1 array of random numbers.
	RNGET	Retrieves the current value of the seed used in the IMSL random number generators.
	RNSET	Initializes a random seed for use in the IMSL random number generators.
	RNOPT	Selects the uniform (0, 1) multiplicative congruential pseudorandom number generator.
	RNIN32	Initializes the 32-bit Mersenne Twister generator using an array.
	RNGE32	Retrieves the current table used in the 32-bit Mersenne Twister generator.
	RNSE32	Sets the current table used in the 32-bit Mersenne Twister generator.
	RNIN64	Initializes the 64-bit Mersenne Twister generator using an array.
	RNGE64	Retrieves the current table used in the 64-bit Mersenne Twister generator.
	RNSE64	Sets the current table used in the 64-bit Mersenne Twister generator.
	RNUNF	Generates a pseudorandom number from a uniform (0, 1) distribution.
	RNUN	Generates pseudorandom numbers from a uniform (0, 1) distribution.

LOW DISCREPANCY SEQUENCES
	ROUTINE	DESCRIPTION
	FAURE_INIT	Generates pseudorandom numbers from a uniform (0, 1) distribution.
	FAURE_FREE	Frees the structure containing information about the Faure sequence.
	FAURE_NEXT	Computes a shuffled Faure sequence.

OPTIONS MANAGER
	ROUTINE	DESCRIPTION
	IUMAG	This routine handles MATH LIBRARY and STAT LIBRARY type INTEGER options.
	UMAG	Gets and puts type REAL options.
	SUMAG	This routine handles MATH LIBRARY and STAT LIBRARY type SINGLE PRECISION options.
	DUMAG	This routine handles MATH LIBRARY and STAT LIBRARY type DOUBLE PRECISION options.

LINE PRINTER GRAPHICS
	ROUTINE	DESCRIPTION
	PLOTP	Prints a plot of up to 10 sets of points.

MISCELLANEOUS
	ROUTINE	DESCRIPTION
	PRIME	Decomposes an integer into its prime factors.
	CONST	Returns the value of various mathematical and physical constants.
	CUNIT	Converts X in units XUNITS to Y in units YUNITS.
	HYPOT	Computes without underflow or overflow.
	MP_SETUP	Initializes or finalizes MPI.

IMSL MATH SPECIAL FUNCTIONS LIBRARY

CHAPTER 1: ELEMENTARY FUNCTIONS

ELEMENTARY FUNCTIONS
	ROUTINE	DESCRIPTION
	CARG	Evaluates the argument of a complex number.
	CBRT	Evaluates the cube root.
	EXPRL	Evaluates the exponential function factored from first order, (EXP(X) – 1.0)/X.
	LOG10	Extends FORTRAN’s generic log10 function to evaluate the principal value of the complex common logarithm.
	ALNREL	Evaluates the natural logarithm of one plus the argument.

CHAPTER 2: HYPERBOLIC FUNCTIONS

TRIGONOMETRIC FUNCTIONS
	ROUTINE	DESCRIPTION
	TAN	Extends FORTRAN’s generic tan to evaluate the complex tangent.
	COT	Evaluates the cotangent.
	SINDG	Evaluates the sine for the argument in degrees.
	COSDG	Evaluates the cosine for the argument in degrees.
	ASIN	Extends FORTRAN’s generic ASIN function to evaluate the complex arc sine.
	ACOS	Extends FORTRAN’s generic ACOS function to evaluate the complex arc cosine.
	ATAN	Extends FORTRAN’s generic function ATAN to evaluate the complex arc tangent.
	ATAN2	This function extends FORTRAN’s generic function ATAN2 to evaluate the complex arc tangent of a ratio.

HYPERBOLIC FUNCTIONS
	ROUTINE	DESCRIPTION
	SINH	Extends FORTRAN’s generic function SINH to evaluate the complex hyperbolic sine.
	COSH	Extends FORTRAN’s generic function COSH to evaluate the complex hyperbolic cosine.
	TANH	Extends FORTRAN’s generic function TANH to evaluate the complex hyperbolic tangent.

TRIGONOMETRIC AND HYPERBOLIC FUNCTIONS
	ROUTINE	DESCRIPTION
	ASINH	Evaluates the arc hyperbolic sine.
	ACOSH	Evaluates the arc hyperbolic cosine.
	ATANH	Evaluates the arc hyperbolic tangent.

CHAPTER 3: EXPONENTIAL INTEGRALS AND RELATED FUNCTIONS

EXPONENTIAL INTEGRALS AND RELATED FUNCTIONS
	ROUTINE	DESCRIPTION
	EI	Evaluates the exponential integral for arguments greater than zero and the Cauchy principal value for arguments less than zero.
	E1	Evaluates the exponential integral for arguments greater than zero and the Cauchy principal value of the integral for arguments less than zero.
	ENE	Evaluates the exponential integral of integer order for arguments greater than zero scaled by EXP(X).
	ALI	Evaluates the logarithmic integral.
	SI	Evaluates the sine integral.
	CI	Evaluates the cosine integral.
	CIN	Evaluates a function closely related to the cosine integral.
	SHI	Evaluates the hyperbolic sine integral.
	CHI	Evaluates the hyperbolic cosine integral.
	CINH	Evaluates a function closely related to the hyperbolic cosine integral.

CHAPTER 4: GAMMA FUNCTION AND RELATED FUNCTIONS

FACTORIAL FUNCTION
	ROUTINE	DESCRIPTION
	FAC	Evaluates the factorial of the argument.
	BINOM	Evaluates the binomial coefficient.

GAMMA FUNCTIONS
	ROUTINE	DESCRIPTION
	GAMMA	Evaluates the complete gamma function.
	GAMR	Evaluates the reciprocal gamma function.
	ALNGAM	Evaluates the logarithm of the absolute value of the gamma function.
	ALGAMS	Returns the logarithm of the absolute value of the gamma function and the sign of gamma.

INCOMPLETE GAMMA FUNCTIONS
	ROUTINE	DESCRIPTION
	GAMI	Evaluates the incomplete gamma function.
	GAMIC	Evaluates the complementary incomplete gamma function.
	GAMIT	Evaluates the Tricomi form of the incomplete gamma function.

PSI FUNCTION
	ROUTINE	DESCRIPTION
	PSI	Evaluates the logarithmic derivative of the gamma function.
	PSI1	Evaluates the second derivative of the log gamma function.

POCHHAMMER'S FUNCTIONS
	ROUTINE	DESCRIPTION
	POCH	Evaluates a generalization of Pochhammer’s symbol.
	POCH1	Evaluates a generalization of Pochhammer’s symbol starting from the first order.

BETA FUNCTION
	ROUTINE	DESCRIPTION
	BETA	Evaluates the complete beta function.
	ALBETA	Evaluates the natural logarithm of the complete beta function for positive arguments.
	BETAI	Evaluates the incomplete beta function ratio.

CHAPTER 5: ERROR FUNCTIONS AND RELATED FUNCTIONS

ERROR FUNCTIONS
	ROUTINE	DESCRIPTION
	ERF	Evaluates the error function.
	ERFC	Evaluates the complementary error function.
	ERFCE	Evaluates the exponentially scaled complementary error function.
	CERFE	Evaluates the complex scaled complemented error function.
	ERFI	Evaluates the inverse error function.
	ERFCI	Evaluates the inverse complementary error function.
	DAWS	Evaluates Dawson’s function.

FRESNEL INTEGRALS
	ROUTINE	DESCRIPTION
	FRESC	Evaluates the cosine Fresnel integral.
	FRESS	Evaluates the sine Fresnel integral.

CHAPTER 6: BESSEL FUNCTIONS

BESSEL FUNCTIONS OF ORDERS 0 AND 1
	ROUTINE	DESCRIPTION
	BSJ0	Evaluates the Bessel function of the first kind of order zero.
	BSJ1	Evaluates the Bessel function of the first kind of order one.
	BSY0	Evaluates the Bessel function of the second kind of order zero.
	BSY1	Evaluates the Bessel function of the second kind of order one.
	BSI0	Evaluates the modified Bessel function of the first kind of order zero.
	BSI1	Evaluates the modified Bessel function of the first kind of order one.
	BSK0	Evaluates the modified Bessel function of the second kind of order zero.
	BSK1	Evaluates the modified Bessel function of the second kind of order one.
	BSI0E	Evaluates the exponentially scaled modified Bessel function of the first kind of order zero.
	BSI1E	Evaluates the exponentially scaled modified Bessel function of the first kind of order one.
	BSK0E	Evaluates the exponentially scaled modified Bessel function of the second kind of order zero.
	BSK1E	Evaluates the exponentially scaled modified Bessel function of the second kind of order one.

SERIES OF BESSEL FUNCTIONS, INTEGER ORDER
	ROUTINE	DESCRIPTION
	BSJNS	Evaluates a sequence of Bessel functions of the first kind with integer order and real or complex arguments.
	BSINS	Evaluates a sequence of modified Bessel functions of the first kind with integer order and real or complex arguments.

SERIES OF BESSEL FUNCTIONS, REAL ORDER AND ARGUMENT
	ROUTINE	DESCRIPTION
	BSJS	Evaluates a sequence of Bessel functions of the first kind with real order and real positive arguments.
	BSYS	Evaluates a sequence of Bessel functions of the second kind with real nonnegative order and real positive arguments.
	BSIS	Evaluates a sequence of modified Bessel functions of the first kind with real order and real positive arguments.
	BSIES	Evaluates a sequence of exponentially scaled modified Bessel functions of the first kind with nonnegative real order and real positive arguments.
	BSKS	Evaluates a sequence of modified Bessel functions of the second kind of fractional order.
	BSKES	Evaluates a sequence of exponentially scaled modified Bessel functions of the second kind of fractional order.

SERIES OF BESSEL FUNCTIONS, REAL ARGUMENT AND COMPLEX ARGUMENT
	ROUTINE	DESCRIPTION
	CBJS	Evaluates a sequence of Bessel functions of the first kind with real order and complex arguments.
	CBYS	Evaluates a sequence of Bessel functions of the second kind with real order and complex arguments.
	CBIS	Evaluates a sequence of modified Bessel functions of the first kind with real order and complex arguments.
	CBKS	Evaluates a sequence of modified Bessel functions of the second kind with real order and complex arguments.

CHAPTER 7: KELVIN FUNCTIONS

KELVIN FUNCTIONS
	ROUTINE	DESCRIPTION
	BER0	Evaluates the Kelvin function of the first kind, ber, of order zero.
	BEI0	Evaluates the Kelvin function of the first kind, bei, of order zero.
	AKER0	Evaluates the Kelvin function of the second kind, ker, of order zero.
	AKEI0	Evaluates the Kelvin function of the second kind, kei, of order zero.
	BERP0	Evaluates the derivative of the Kelvin function of the first kind, ber, of order zero.
	BEIP0	Evaluates the derivative of the Kelvin function of the first kind, bei, of order zero.
	AKERP0	Evaluates the derivative of the Kelvin function of the second kind, ker, of order zero.
	AKEIP0	Evaluates the derivative of the Kelvin function of the second kind, kei, of order zero.
	BER1	Evaluates the Kelvin function of the first kind, ber, of order one.
	BEI1	Evaluates the Kelvin function of the first kind, bei, of order one.
	AKER1	Evaluates the Kelvin function of the second kind, ker, of order one.
	AKEI1	Evaluates the Kelvin function of the second kind, kei, of order one.

CHAPTER 8: AIRY FUNCTIONS

REAL AIRY FUNCTIONS
	ROUTINE	DESCRIPTION
	AI	Evaluates the Airy function.
	BI	Evaluates the Airy function of the second kind.
	AID	Evaluates the derivative of the Airy function.
	BID	Evaluates the derivative of the Airy function of the second kind.
	AIE	Evaluates the exponentially scaled Airy function.
	BIE	Evaluates the exponentially scaled Airy function of the second kind.
	AIDE	Evaluates the exponentially scaled derivative of the Airy function.
	BIDE	Evaluates the exponentially scaled derivative of the Airy function of the second kind.

COMPLEX AIRY FUNCTIONS
	ROUTINE	DESCRIPTION
	CAI	Evaluates the Airy function of the first kind for complex arguments.
	CBI	Evaluates the Airy function of the second kind for complex arguments.
	CAID	Evaluates the derivative of the Airy function of the first kind for complex arguments.
	CBID	Evaluates the derivative of the Airy function of the second kind for complex arguments.

CHAPTER 9: ELLIPTIC FUNCTIONS

ELLIPTIC FUNCTIONS
	ROUTINE	DESCRIPTION
	ELK	Evaluates the complete elliptic integral of the kind K(x).
	ELE	Evaluates the complete elliptic integral of the second kind E(x).
	ELRF	Evaluates Carlson’s incomplete elliptic integral of the first kind R_F(x, y, z).
	ELRD	Evaluates Carlson’s incomplete elliptic integral of the second kind R_D(x, y, z).
	ELRJ	Evaluates Carlson’s incomplete elliptic integral of the third kind R_J(x, y, z, rho).
	ELRC	Evaluates an elementary integral from which inverse circular functions, logarithms and inverse hyperbolic functions can be computed.

CHAPTER 10: ELLIPTIC AND RELATED FUNCTIONS

WEIERSTRASS ELLIPTIC AND RELATED FUNCTIONS
	ROUTINE	DESCRIPTION
	CWPL	Evaluates the Weierstrass ℘ function in the lemniscatic case for complex argument with unit period parallelogram.
	CWPLD	Evaluates the first derivative of the Weierstrass ℘ function in the lemniscatic case for complex argument with unit period parallelogram.
	CWPQ	Evaluates the Weierstrass ℘ function in the equianharmonic case for complex argument with unit period parallelogram.
	CWPQD	Evaluates the first derivative of the Weierstrass ℘ function in the equianharmonic case for complex argument with unit period parallelogram.

JACOBI ELLIPTIC FUNCTIONS
	ROUTINE	DESCRIPTION
	EJSN	Evaluates the Jacobi elliptic function sn(x, m).
	EJCN	Evaluates the Jacobi elliptic function cn(x, m).
	EJDN	Evaluates the Jacobi elliptic function dn(x, m).

CHAPTER 11: PROBABILITY DISTRIBUTIONS FUNCTIONS AND INVERSES

DISCRETE RANDOM VARIABLES: CUMULATIVE DISTRIBUTION FUNCTIONS AND PROBABILITY DENSITY FUNCTIONS
	ROUTINE	DESCRIPTION
	BINDF	Evaluates the binomial cumulative distribution function.
	BINPR	Evaluates the binomial probability density function.
	GEODF	Evaluates the discrete geometric cumulative distribution function.
	GEOIN	Evaluates the inverse of the geometric cumulative distribution function.
	GEOPR	Evaluates the discrete geometric probability density function.
	HYPDF	Evaluates the hypergeometric cumulative distribution function.
	HYPPR	Evaluates the hypergeometric probability density function.
	POIDF	Evaluates the Poisson cumulative distribution function.
	POIPR	Evaluates the Poisson probability density function.
	UNDDF	Evaluates the discrete uniform cumulative distribution function.
	UNDIN	Evaluates the inverse of the discrete uniform cumulative distribution function.
	UNDPR	Evaluates the discrete uniform probability density function.

CONTINUOUS RANDOM VARIABLES: DISTRIBUTION FUNCTIONS AND THEIR INVERSES
	ROUTINE	DESCRIPTION
	AKS1DF	Evaluates the cumulative distribution function of the one-sided Kolmogorov-Smirnov goodness of fit D⁺ or D^– test statistic based on continuous data for one sample.
	AKS2DF	Evaluates the cumulative distribution function of the one-sided Kolmogorov-Smirnov goodness of fit Dtest statistic based on continuous data for two samples.
	ALNDF	Evaluates the lognormal cumulative distribution function.
	ALNIN	Evaluates the inverse of the lognormal cumulative distribution function.
	ALNPR	Evaluates the lognormal probability density function.
	ANORDF	Evaluates the standard normal (Gaussian) cumulative distribution function.
	ANORIN	Evaluates the inverse of the standard normal (Gaussian) cumulative distribution function.
	ANORPR	Evaluates the normal probability density function.
	BETDF	Evaluates the beta cumulative distribution function.
	BETIN	Evaluates the inverse of the beta cumulative distribution function.
	BETPR	Evaluates the beta probability density function.
	BETNDF	Evaluates the noncentral beta cumulative distribution function (CDF).
	BETNIN	Evaluates the inverse of the noncentral beta cumulative distribution function (CDF).
	BETNPR	Evaluates the noncentral beta probability density function.
	BNRDF	Evaluates the bivariate normal cumulative distribution function.
	CHIDF	Evaluates the chi-squared cumulative distribution function.
	CHIIN	Evaluates the inverse of the chi-squared cumulative distribution function.
	CHIPR	Evaluates the chi-squared probability density function.
	CSNDF	Evaluates the noncentral chi-squared cumulative distribution function.
	CSNIN	Evaluates the inverse of the noncentral chi-squared cumulative distribution function.
	CSNPR	Evaluates the noncentral chi-squared probability density function.
	EXPDF	Evaluates the exponential cumulative distribution function.
	EXPIN	Evaluates the inverse of the exponential cumulative distribution function.
	EXPPR	Evaluates the exponential probability density function.
	EXVDF	Evaluates the extreme value cumulative distribution function.
	EXVIN	Evaluates the inverse of the extreme value cumulative distribution function.
	EXVPR	Evaluates the extreme value probability density function.
	FDF	Evaluates the Fcumulative distribution function.
	FIN	Evaluates the inverse of the Fcumulative distribution function.
	FPR	Evaluates the Fprobability density function.
	FNDF	Evaluates the noncentral F cumulative distribution function (CDF).
	FNIN	Evaluates the inverse of the noncentral F cumulative distribution function (CDF).
	FNPR	Evaluates the noncentral F probability density function.
	GAMDF	Evaluates the gamma cumulative distribution function.
	GAMIN	Evaluates the inverse of the gamma cumulative distribution function.
	GAMPR	Evaluates the gamma probability density function.
	RALDF	Evaluates the Rayleigh cumulative distribution function.
	RALIN	Evaluates the inverse of the Rayleigh cumulative distribution function.
	RALPR	Evaluates the Rayleigh probability density function.
	TDF	Evaluates the Student’s tcumulative distribution function.
	TIN	Evaluates the inverse of the Student’s tcumulative distribution function.
	TPR	Evaluates the Student’s tprobability density function.
	TNDF	Evaluates the noncentral Student’s tcumulative distribution function.
	TNIN	Evaluates the inverse of the noncentral Student’st cumulative distribution function.
	TNPR	Evaluates the noncentral Student's t probability density function.
	UNDF	Evaluates the uniform cumulative distribution function.
	UNIN	Evaluates the inverse of the uniform cumulative distribution function.
	UNPR	Evaluates the uniform probability density function.
	WBLDF	Evaluates the Weibull cumulative distribution function.
	WBLIN	Evaluates the inverse of the Weibull cumulative distribution function.
	WBLPR	Evaluates the Weibull probability density function.

GENERAL CONTINUOUS RANDOM VARIABLE
	ROUTINE	DESCRIPTION
	GCDF	Evaluates a general continuous cumulative distribution function given ordinates of the density.
	GCIN	Evaluates the inverse of a general continuous cumulative distribution function given ordinates of the density.
	GFNIN	Evaluates the inverse of a general continuous cumulative distribution function given in a subprogram.

CHAPTER 12: MATHIEU FUNCTIONS

MATHIEU FUNCTIONS
	ROUTINE	DESCRIPTION
	MATEE	Evaluates the eigenvalues for the periodic Mathieu functions.
	MATCE	Evaluates a sequence of even, periodic, integer order, real Mathieu functions.
	MATSE	Evaluates a sequence of odd, periodic, integer order, real Mathieu functions.

CHAPTER 13: MISCELLANEOUS FUNCTIONS

MISCELLANEOUS FUNCTIONS
	ROUTINE	DESCRIPTION
	SPENC	Evaluates a form of Spence’s integral.
	INITS	Initializes the orthogonal series so the function value is the number of terms needed to insure the error is no larger than the requested accuracy.
	CSEVL	Evaluates the N-term Chebyshev series.

REFERENCE MATERIAL: LIBRARY ENVIRONMENTS UTILITIES

The following routines are documented in the Reference Material sections of the IMSL™ MATH LIBRARY and IMSL™ STAT LIBRARY User's Manual.
	ROUTINE	DESCRIPTION
	ERSET	Sets error handler default print and stop actions.
	IERCD	Retrieves the code for an informational error.
	N1RTY	Retrieves an error type for the most recently called IMSL routine.
	IMACH	Retrieves integer machine constants.
	AMACH	Retrieves single precision machine constants.
	DMACH	Retrieves double precision machine constants.
	IFNAN	Checks if a floating-point number is NaN (not a number).
	UMACH	Sets or Retrieves input or output device unit numbers.

IMSL STAT LIBRARY

CHAPTER 1: BASIC STATISTICS

FREQUENCY TABULATIONS
	ROUTINE	DESCRIPTION
	OWFRQ	Tallies observations into a one-way frequency table.
	TWFRQ	Tallies observations into a two-way frequency table.
	FREQ	Tallies multivariate observations into a multiway frequency table.

UNIVARIATE SUMMARY STATISTICS
	ROUTINE	DESCRIPTION
	UVSTA	Computes basic univariate statistics.

RANKS AND ORDER STATISTICS
	ROUTINE	DESCRIPTION
	RANKS	Computes the ranks, normal scores, or exponential scores for a vector of observations
	LETTR	Produces a letter value summary.
	ORDST	Determines order statistics.
	EQTIL	Computes empirical quantiles.

PARAMETRIC ESTIMATES AND TESTS
	ROUTINE	DESCRIPTION
	TWOMV	Computes statistics for mean and variance inferences using samples from two normal populations.
	BINES	Estimates the parameter pof the binomial distribution.
	POIES	Estimates the parameter of the Poisson distribution.
	NRCES	Computes maximum likelihood estimates of the mean and variance from grouped and/or censored normal data.

GROUPED DATA
	ROUTINE	DESCRIPTION
	GRPES	Computes basic statistics from grouped data.

CONTINOUS DATA IN A TABLE
	ROUTINE	DESCRIPTION
	CSTAT	Computes cell frequencies, cell means, and cell sums of squares for multivariate data.
	MEDPL	Computes a median polish of a two-way table.

CHAPTER 2: REGRESSION

SIMPLE LINEAR REGRESSION
	ROUTINE	DESCRIPTION
	RLINE	Fits a line to a set of data points using least squares.
	RONE	Analyzes a simple linear regression model.
	RINCF	Performs response control given a fitted simple linear regression model.
	RINPF	Performs inverse prediction given a fitted simple linear regression model.

MULTIVARIATE GENERAL LINEAR MODEL ANALYSIS

MODEL FITTING
	ROUTINE	DESCRIPTION
	RLSE	Fits a multiple linear regression model using least squares.
	RCOV	Fits a multivariate linear regression model given the variance-covariance matrix.
	RGIVN	Fits a multivariate linear regression model via fast Givens transformations.
	RGLM	Fits a multivariate general linear model.
	RLEQU	Fits a multivariate linear regression model with linear equality restrictions H B = Gimposed on the regression parameters given results from routine RGIVNafter IDO= 1 and IDO= 2 and prior to IDO= 3.

STATISTICAL INFERENCE AND DIAGNOSTICS
	ROUTINE	DESCRIPTION
	RSTAT	Computes statistics related to a regression fit given the coefficient estimates.
	RCOVB	Computes the estimated variance-covariance matrix of the estimated regression coefficients given the Rmatrix.
	CESTI	Constructs an equivalent completely testable multivariate general linear hypothesis H BU = Gfrom a partially testable hypothesis H_pBU =G_p.
	RHPSS	Computes the matrix of sums of squares and crossproducts for the multivariate general linear hypothesis H BU = Ggiven the coefficient estimates and the R matrix.
	RHPTE	Performs tests for a multivariate general linear hypothesis H BU = Ggiven the hypothesis sums of squares and crossproducts matrix S_Hand the error sums of squares and crossproducts matrix S_E.
	RLOFE	Computes a lack of fit test based on exact replicates for a fitted regression model.
	RLOFN	Computes a lack of fit test based on near replicates for a fitted regression model.
	RCASE	Computes case statistics and diagnostics given data points, coefficient estimates and the R matrix for a fitted general linear model.
	ROTIN	Computes diagnostics for detection of outliers and influential data points given residuals and the Rmatrix for a fitted general linear model.

UTILITIES FOR CLASSIFICATION VARIABLES
	ROUTINE	DESCRIPTION
	GCLAS	Gets the unique values of each classification variable.
	GRGLM	Generates regressors for a general linear model.

VARIABLES SELECTION
	ROUTINE	DESCRIPTION
	RBEST	Selects the best multiple linear regression models.
	RSTEP	Builds multiple linear regression models using forward selection, backward selection or stepwise selection.
	GSWEP	Performs a generalized sweep of a row of a nonnegative definite matrix.
	RSUBM	Retrieves a symmetric submatrix from a symmetric matrix.

POLYNOMINAL REGRESSION AND SECOND-ORDER MODELS

POLYNOMINAL REGRESSION ANALYSIS
	ROUTINE	DESCRIPTION
	RCURV	Fits a polynomial curve using least squares.
	RPOLY	Analyzes a polynomial regression model.

SECOND-ORDER MODEL DESIGN
	ROUTINE	DESCRIPTION
	RCOMP	Generates an orthogonal central composite design.

UTILITY ROUTINES FOR POLYNOMIAL MODELS AND SECOND-ORDER MODELS
	ROUTINE	DESCRIPTION
	RFORP	Fits an orthogonal polynomial regression model.
	RSTAP	Computes summary statistics for a polynomial regression model given the fit based on orthogonal polynomials.
	RCASP	Computes case statistics for a polynomial regression model given the fit based on orthogonal polynomials.
	OPOLY	Generates orthogonal polynomials with respect to x-values and specified weights.
	GCSCP	Generates centered variables, squares, and crossproducts.
	TCSCP	Transforms coefficients from a second order response surface model generated from squares and crossproducts of centered variables to a model using uncentered variables.

NONLINEAR REGRESSION ANALYSIS
	ROUTINE	DESCRIPTION
	RNLIN	Fits a nonlinear regression model.

FITTING LINEAR MODELS BASED ON CRITERIA OTHER THAN LEAST SQUARES
	ROUTINE	DESCRIPTION
	RLAV	Fits a multiple linear regression model using the least absolute values criterion.
	RLLP	Fits a multiple linear regression model using the L_p norm criterion.
	RLMV	Fits a multiple linear regression model using the minimax criterion.
	PLSR	Performs partial least squares regression for one or more response variables and one or more predictor variables.

CHAPTER 3: CORRELATION

THE CORRELATION MATRIX
	ROUTINE	DESCRIPTION
	CORVC	Computes the variance-covariance or correlation matrix.
	COVPL	Computes a pooled variance-covariance matrix from the observations.
	PCORR	Computes partial correlations or covariances from the covariance or correlation matrix.
	RBCOV	Computes a robust estimate of a covariance matrix and mean vector.

CORRELATION MEASURES FOR A CONTINGENCY TABLE
	ROUTINE	DESCRIPTION
	CTRHO	Estimates the bivariate normal correlation coefficient using a contingency table.
	TETCC	Categorizes bivariate data and computes the tetrachoric correlation coefficient.

A DICHOTOMOUS VARIABLE WITH A CLASSIFICATION VARIABLE
	ROUTINE	DESCRIPTION
	BSPBS	Computes the biserial and point-biserial correlation coefficients for a dichotomous variable and a numerically measurable classification variable.
	BSCAT	Computes the biserial correlation coefficient for a dichotomous variable and a classification variable.

MEASURES BASED UPON RANKS
	ROUTINE	DESCRIPTION
	CNCRD	Calculates and tests the significance of the Kendall coefficient of concordance.
	KENDL	Computes and tests Kendall’s rank correlation coefficient.
	KENDP	Computes the frequency distribution of the total score in Kendall’s rank correlation coefficient.

CHAPTER 4: ANALYSIS OF VARIANCE

GENERAL ANALYSIS
	ROUTINE	DESCRIPTION
	AONEW	Analyzes a one-way classification model.
	AONEC	Analyzes a one-way classification model with covariates.
	ATWOB	Analyzes a randomized block design or a two-way balanced design.
	ABIBD	Analyzes a balanced incomplete block design or a balanced lattice design.
	ALATN	Analyzes a Latin square design.
	ANWAY	Analyzes a balanced n-way classification model with fixed effects.
	ABALD	Analyzes a balanced complete experimental design for a fixed, random, or mixed model.
	ANEST	Analyzes a completely nested random model with possibly unequal numbers in the subgroups.

INFERENCE ON MEANS AND VARIANCE COMPONENTS
	ROUTINE	DESCRIPTION
	CTRST	Computes contrast estimates and sums of squares.
	SCIPM	Computes simultaneous confidence intervals on all pairwise differences of means.
	SNKMC	Performs Student-Newman-Keuls multiple comparison test.
	CIDMS	Computes a confidence interval on a variance component estimated as proportional to the difference in two mean squares in a balanced complete experimental design.

SERVICE ROUTINE
	ROUTINE	DESCRIPTION
	ROREX	Reorders the responses from a balanced complete experimental design.

CHAPTER 5: CATEGORICAL AND DISCRETE DATA ANALYSIS

STATISTICS IN THE TWO-WAY CONTINGENCY TABLE
	ROUTINE	DESCRIPTION
	CTTWO	Performs a chi-squared analysis of a 2 by 2 contingency table.
	CTCHI	Performs a chi-squared analysis of a two-way contingency table.
	CTPRB	Computes exact probabilities in a two-way contingency table.
	CTEPR	Computes Fisher’s exact test probability and a hybrid approximation to the Fisher exact test probability for a contingency table using the network algorithm.

LOG-LINEAR MODELS
	ROUTINE	DESCRIPTION
	PRPFT	Performs iterative proportional fitting of a contingency table using a log-linear model.
	CTLLN	Computes model estimates and associated statistics for a hierarchical log-linear model.
	CTPAR	Computes model estimates and covariances in a fitted log-linear model.
	CTASC	Computes partial association statistics for log-linear models in a multidimensional contingency table.
	CTSTP	Builds hierarchical log-linear models using forward selection, backward selection, or stepwise selection.

RANDOMIZATION TESTS
	ROUTINE	DESCRIPTION
	CTRAN	Performs generalized Mantel-Haenszel tests in a stratified contingency table.

GENERALIZED CATEGORICAL MODELS
	ROUTINE	DESCRIPTION
	CTGLM	Analyzes categorical data using logistic, Probit, Poisson, and other generalized linear models.

WEIGHTED LEAST SQUARES ANALYSIS
	ROUTINE	DESCRIPTION
	CTWLS	Performs a generalized linear least-squares analysis of transformed probabilities in a two-dimensional contingency table.

CHAPTER 6: NONPARAMETRIC STATISTICS

ONE SAMPLE OR MATCHED SAMPLES

TESTS OF LOCATION
	ROUTINE	DESCRIPTION
	SIGNT	Performs a sign test of the hypothesis that a given value is in a specified quantile of a distribution.
	SNRNK	Performs a Wilcoxon signed rank test.

TESTS OF TREND
	ROUTINE	DESCRIPTION
	NCTRD	Performs the Noether test for cyclical trend.
	SDPLC	Performs the Cox and Stuart sign test for trends in dispersion and location.

TIES
	ROUTINE	DESCRIPTION
	NTIES	Computes tie statistics for a sample of observations.

MORE THAN TWO SAMPLES

ONE-WAY TESTS OF LOCATION
	ROUTINE	DESCRIPTION
	KRSKL	Performs a Kruskal-Wallis test for identical population medians.
	BHAKV	Performs a Bhapkar V test.

TWO-WAY TESTS OF LOCATION
	ROUTINE	DESCRIPTION
	FRDMN	Performs Friedman’s test for a randomized complete block design.
	QTEST	Performs a Cochran Q test for related observations.

TESTS FOR TREND
	ROUTINE	DESCRIPTION
	KTRND	Performs k-sample trends test against ordered alternatives.

CHAPTER 7: TESTS OF GOODNESS-OF-FIT AND RANDOMNESS

GENERAL GOODNESS-OF-FIT TESTS FOR A SPECIFIED DISTRIBUTION
	ROUTINE	DESCRIPTION
	KSONE	Performs a Kolmogorov-Smirnov one-sample test for continuous distributions.
	CHIGF	Performs a chi-squared goodness-of-fit test.
	SPWLK	Performs a Shapiro-Wilk W-test for normality.
	LILLF	Performs Lilliefors test for an exponential or normal distribution.
	MVMMT	Computes Mardia’s multivariate measures of skewness and kurtosis and tests for multivariate normality.
	ADNRM	Performs an Anderson-Darling test for normality.
	CVMNRM	Performs a Cramer-von Mises test for normality.

TWO SAMPLE TESTS
	ROUTINE	DESCRIPTION
	KSTWO	Performs a Kolmogorov-Smirnov two-sample test.

TESTS FOR RANDOMNESS
	ROUTINE	DESCRIPTION
	RUNS	Performs a runs up test.
	PAIRS	Performs a pairs test.
	DSQAR	Performs a d² test.
	DCUBE	Performs a triplets test.

CHAPTER 8: TIME SERIES ANALYSIS AND FORECASTING

GENERAL METHODOLOGY

TIME SERIES TRANSFORMATION
	ROUTINE	DESCRIPTION
	BCTR	Performs a forward or an inverse Box-Cox (power) transformation.
	DIFF	Differences a time series.
	ESTIMATE_MISSING	Estimates missing values in a time series.
	SEASONAL_FIT	Determines an optimal differencing for seasonal adjustments of a time series.

SAMPLE CORRELATION FUNCTION
	ROUTINE	DESCRIPTION
	ACF	Computes the sample autocorrelation function of a stationary time series.
	PACF	Computes the sample partial autocorrelation function of a stationary time series.
	CCF	Computes the sample cross-correlation function of two stationary time series.
	MCCF	Computes the multichannel cross-correlation function of two mutually stationary multichannel time series.

TIME DOMAIN METHODOLOGY

NONSEASONAL TIME SERIES MODEL ESTIMATION
	ROUTINE	DESCRIPTION
	ARMME	Computes method of moments estimates of the autoregressive parameters of an ARMA model.
	MAMME	Computes method of moments estimates of the moving average parameters of an ARMA model.
	NSPE	Computes preliminary estimates of the autoregressive and moving average parameters of an ARMA model.
	NSLSE	Computes least-squares estimates of parameters for a nonseasonal ARMA model.
	MAX_ARMA	Exact maximum likelihood estimation of the parameters in a univariate ARMA (autoregressive, moving average) time series model.
	REG_ARIMA	Fits a univariate, non-seasonal ARIMA time series model with the inclusion of one or more regression variables.
	GARCH	Computes estimates of the parameters of a GARCH(p,q) model.
	SPWF	Computes the Wiener forecast operator for a stationary stochastic process.
	NSBJF	Computes Box-Jenkins forecasts and their associated probability limits for a nonseasonal ARMA model.

TRANSFER FUNCTION MODEL
	ROUTINE	DESCRIPTION
	IRNSE	Computes estimates of the impulse response weights and noise series of a univariate transfer function model.
	TFPE	Computes preliminary estimates of parameters for a univariate transfer function model.

MULTICHANNEL TIME SERIES
	ROUTINE	DESCRIPTION
	MLSE	Computes least-squares estimates of a linear regression model for a multichannel time series with a specified base channel.
	MWFE	Computes least-squares estimates of the multichannel Wiener filter coefficients for two mutually stationary multichannel time series.
	KALMN	Performs Kalman filtering and evaluates the likelihood function for the state-space model.

AUTOMATIC MODEL SELECTION FITTING
	ROUTINE	DESCRIPTION
	AUTO_UNI_AR	Automatic selection and fitting of a univariate autoregressive time series model.
	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, associated probability limits and weights for an outlier contaminated time series.
	AUTO_ARIMA	Automatically identifies time series outliers, determines parameters of a multiplicative seasonal ARIMA model and produces forecasts that incorporate the effects of outliers whose effects persist beyond the end of the series.
	AUTO_FPE_UNI_AR	Automatic selection and fitting of a univariate autoregressive time series model using Akaike’s Final Prediction Error (FPE) criteria.
	AUTO_PARM	Estimates structural breaks in non-stationary univariate time series.
	AUTO_MUL_AR	Automatic selection and fitting of a multivariate autoregressive time series model.
	AUTO_FPE_MUL_AR	Automatic selection and fitting of a multivariate autoregressive time series model using Akaike’s Multivariate Final Prediction Error (MFPE) criteria.

BAYESIAN TIME SERIES ESTIMATION
	ROUTINE	DESCRIPTION
	BAY_SEA	Bayesian seasonal adjustment modeling. The model allows for a decomposition of a time series into trend, seasonal, and an error component.

CONTROLLER DESIGN
	ROUTINE	DESCRIPTION
	OPT_DES	Optimal controller design which allows for multiple channels for both the controlled and manipulated variables.

DIAGNOSTICS
	ROUTINE	DESCRIPTION
	LOFCF	Performs lack-of-fit test for a univariate time series or transfer function given the appropriate correlation function.

FREQUENCY DOMAIN METHODOLOGY

SMOOTHING FUNCTIONS
	ROUTINE	DESCRIPTION
	DIRIC	Computes the Dirichlet kernel.
	FEJER	Computes the Fejér kernel.

SPECTRAL DENSITY ESTIMATION
	ROUTINE	DESCRIPTION
	ARMA_SPEC	Calculates the rational power spectrum for an ARMA model.
	PFFT	Computes the periodogram of a stationary time series using a fast Fourier transform.
	SSWD	Estimates the nonnormalized spectral density of a stationary time series using a spectral window given the time series data.
	SSWP	Estimates the nonnormalized spectral density of a stationary time series using a spectral window given the periodogram.
	SWED	Estimates the nonnormalized spectral density of a stationary time series based on specified periodogram weights given the time series data.
	SWEP	Estimates the nonnormalized spectral density of a stationary time series based on specified periodogram weights given the periodogram.

CROSS-SPECTRAL DENSITY ESTIMATION
	ROUTINE	DESCRIPTION
	CPFFT	Computes the cross periodogram of two stationary time series using a fast Fourier transform.
	CSSWD	Estimates the nonnormalized cross-spectral density of two stationary time series using a spectral window given the time series data.
	CSSWP	Estimates the nonnormalized cross-spectral density of two stationary time series using a spectral window given the spectral densities and cross periodogram.
	CSWED	Estimates the nonnormalized cross-spectral density of two stationary time series using a weighted cross periodogram given the time series data.
	CSWEP	Estimates the nonnormalized cross-spectral density of two stationary time series using a weighted cross periodogram given the spectral densities and cross periodogram.

CHAPTER 9: COVARIANCE STRUCTURES AND FACTOR ANALYSIS

PRINCIPAL COMPONENTS
	ROUTINE	DESCRIPTION
	PRINC	Computes principal components from a variance-covariance matrix or a correlation matrix.
	KPRIN	Maximum likelihood or least-squares estimates for principal components from one or more matrices.

FACTOR ANALYSIS

FACTOR EXTRACTION
	ROUTINE	DESCRIPTION
	FACTR	Extracts initial factor loading estimates in factor analysis.

FACTOR ROTATION AND SUMMARIZATION
	ROUTINE	DESCRIPTION
	FROTA	Computes an orthogonal rotation of a factor loading matrix using a generalized orthomax criterion, including quartimax, varimax, and equamax rotations.
	FOPCS	Computes an orthogonal Procrustes rotation of a factor-loading matrix using a target matrix.
	FDOBL	Computes a direct oblimin rotation of a factor loading matrix.
	FPRMX	Computes an oblique Promax or Procrustes rotation of a factor loading matrix using a target matrix, including pivot and power vector options.
	FHARR	Computes an oblique rotation of an unrotated factor loading matrix using the Harris-Kaiser method.
	FGCRF	Computes direct oblique rotation according to a generalized fourth-degree polynomial criterion.
	FIMAG	Computes the image transformation matrix.
	FRVAR	Computes the factor structure and the variance explained by each factor.

FACTOR SCORES
	ROUTINE	DESCRIPTION
	FCOEF	Computes a matrix of factor score coefficients for input to the routine FSCOR.
	FSCOR	Computes a set of factor scores given the factor score coefficient matrix.

RESIDUAL CORRELATION
	ROUTINE	DESCRIPTION
	FRESI	Computes communalities and the standardized factor residual correlation matrix.

INDEPENDENCE OF SETS OF VARIABLES AND CANONICAL CORRELATION ANALYSIS
	ROUTINE	DESCRIPTION
	MVIND	Computes a test for the independence of k sets of multivariate normal variables.
	CANCR	Performs canonical correlation analysis from a data matrix.
	CANVC	Performs canonical correlation analysis from a variance-covariance matrix or a correlation matrix.

CHAPTER 10: DISCRIMINANT ANALYSIS

PARAMETRIC DISCRIMINATION
	ROUTINE	DESCRIPTION
	DSCRM	Performs a linear or a quadratic discriminant function analysis among several known groups.
	DMSCR	Uses Fisher’s linear discriminant analysis method to reduce the number of variables.

NONPARAMETRIC DISCRIMINATION
	ROUTINE	DESCRIPTION
	NNBRD	Performs knearest neighbor discrimination.

CHAPTER 11: CLUSTER ANALYSIS

HIERARCHICAL CLUSTER ANALYSIS
	ROUTINE	DESCRIPTION
	CDIST	Computes a matrix of dissimilarities (or similarities) between the columns (or rows) of a matrix.
	CLINK	Performs a hierarchical cluster analysis given a distance matrix.
	CNUMB	Computes cluster membership for a hierarchical cluster tree.

K-MEANS CLUSTER ANALYSIS
	ROUTINE	DESCRIPTION
	KMEAN	Performs a K-means (centroid) cluster analysis.

CHAPTER 12: SAMPLING

SAMPLING
	ROUTINE	DESCRIPTION
	SMPPR	Computes statistics for inferences regarding the population proportion and total given proportion data from a simple random sample.
	SMPPS	Computes statistics for inferences regarding the population proportion and total given proportion data from a stratified random sample.
	SMPRR	Computes statistics for inferences regarding the population mean and total using ratio or regression estimation, or inferences regarding the population ratio given a simple random sample.
	SMPRS	Computes statistics for inferences regarding the population mean and total using ratio or regression estimation given continuous data from a stratified random sample.
	SMPSC	Computes statistics for inferences regarding the population mean and total using single stage cluster sampling with continuous data.
	SMPSR	Computes statistics for inferences regarding the population mean and total, given data from a simple random sample.
	SMPSS	Computes statistics for inferences regarding the population mean and total, given data from a stratified random sample.
	SMPST	Computes statistics for inferences regarding the population mean and total given continuous data from a two-stage sample with equisized primary units.

CHAPTER 13: SURVIVAL ANALYSIS, LIFE TESTING AND RELIABILITY

SURVIVAL ANALYSIS
	ROUTINE	DESCRIPTION
	KAPMR	Computes Kaplan-Meier estimates of survival probabilities in stratified samples.
	KTBLE	Prints Kaplan-Meier estimates of survival probabilities in stratified samples.
	TRNBL	Computes Turnbull’s generalized Kaplan-Meier estimates of survival probabilities in samples with interval censoring.
	PHGLM	Analyzes time event data via the proportional hazards model.
	SVGLM	Analyzes censored survival data using a generalized linear model.
	STBLE	Estimates survival probabilities and hazard rates for various parametric models.

ACTUARIAL TABLES
	ROUTINE	DESCRIPTION
	ACTBL	Produces population and cohort life tables.

CHAPTER 14: MULTIDIMENSIONAL SCALING

MULTIDIMENSIONAL SCALING ROUTINES
	ROUTINE	DESCRIPTION
	MSIDV	Performs individual-differences multidimensional scaling for metric data using alternating least squares.

UTILITY ROUTINES
	ROUTINE	DESCRIPTION
	MSDST	Computes distances in a multidimensional scaling model.
	MSSTN	Transforms dissimilarity/similarity matrices and replaces missing values by estimates to obtain standardized dissimilarity matrices.
	MSDBL	Obtains normalized product-moment (double centered) matrices from dissimilarity matrices.
	MSINI	Computes initial estimates in multidimensional scaling models.
	MSTRS	Computes various stress criteria in multidimensional scaling.

CHAPTER 15: DENSITY AND HAZARD ESTIMATION

ESTIMATES FOR A DENSITY
	ROUTINE	DESCRIPTION
	DESPL	Performs nonparametric probability density function estimation by the penalized likelihood method.
	DESKN	Performs nonparametric probability density function estimation by the kernel method.
	DNFFT	Computes Gaussian kernel estimates of a univariate density via the fast Fourier transform over a fixed interval.
	DESPT	Estimates a probability density function at specified points using linear or cubic interpolation.

MODIFIED LIKELIHOOD ESTIMATES FOR HAZARDS
	ROUTINE	DESCRIPTION
	HAZRD	Performs nonparametric hazard rate estimation using kernel functions and quasi-likelihoods.
	HAZEZ	Performs nonparametric hazard rate estimation using kernel functions. Easy-to-use version of HAZRD.
	HAZST	Performs hazard rate estimation over a grid of points using a kernel function.

CHAPTER 16: LINE PRINTER GRAPHICS

HISTOGRAMS
	ROUTINE	DESCRIPTION
	VHSTP	Prints a vertical histogram.
	VHS2P	Prints a vertical histogram with every bar subdivided into two parts.
	HHSTP	Prints a horizontal histogram.

SCATTER PLOTS
	ROUTINE	DESCRIPTION
	SCTP	Prints a scatter plot of several groups of data.

EXPLORATORY DATA ANALYSIS
	ROUTINE	DESCRIPTION
	BOXP	Prints boxplots for one or more samples.
	STMLP	Prints a stem-and-leaf plot.

EMPIRICAL PROBABILITY DISTRIBUTION
	ROUTINE	DESCRIPTION
	CDFP	Prints a sample cumulative distribution function (CDF), a theoretical CDF, and confidence band information.
	CDF2P	Prints a plot of two sample cumulative distribution functions.
	PROBP	Prints a probability plot.

OTHER GRAPHICS ROUTINES
	ROUTINE	DESCRIPTION
	PLOTP	Prints a plot of up to 10 sets of points.
	TREEP	Prints a binary tree.

CHAPTER 17: PROBABILITY DISTRIBUTIONS FUNCTIONS AND INVERSES

PROBABILITY DISTRIBUTION FUNCTIONS AND INVERSES
	ROUTINE	DESCRIPTION
	BINDF	Evaluates the binomial cumulative distribution function.
	BINPR	Evaluates the binomial probability density function.
	GEODF	Evaluates the discrete geometric cumulative distribution function.
	GEOIN	Evaluates the inverse of the geometric cumulative distribution function.
	GEOPR	Evaluates the discrete geometric probability density function.
	HYPDF	Evaluates the hypergeometric cumulative distribution function.
	HYPPR	Evaluates the hypergeometric probability density function.
	POIDF	Evaluates the Poisson cumulative distribution function.
	POIPR	Evaluates the Poisson probability density function.
	UNDDF	Evaluates the discrete uniform cumulative distribution function.
	UNDIN	Evaluates the inverse of the discrete uniform cumulative distribution function.
	UNDPR	Evaluates the discrete uniform probability density function.

CONTINUOUS RANDOM VARIABLES: DISTRIBUTION FUNCTIONS AND THEIR INVERSES
	ROUTINE	DESCRIPTION
	AKS1DF	Evaluates the cumulative distribution function of the one-sided Kolmogorov-Smirnov goodness of fit D⁺ or D^– test statistic based on continuous data for one sample.
	AKS2DF	Evaluates the cumulative distribution function of the one-sided Kolmogorov-Smirnov goodness of fit Dtest statistic based on continuous data for two samples.
	ALNDF	Evaluates the lognormal cumulative distribution function.
	ALNIN	Evaluates the inverse of the lognormal cumulative distribution function.
	ALNPR	Evaluates the lognormal probability density function.
	ANORDF	Evaluates the standard normal (Gaussian) cumulative distribution function.
	ANORIN	Evaluates the inverse of the standard normal (Gaussian) cumulative distribution function.
	ANORPR	Evaluates the normal probability density function.
	BETDF	Evaluates the beta cumulative distribution function.
	BETIN	Evaluates the inverse of the beta cumulative distribution function.
	BETPR	Evaluates the beta probability density function.
	BETNDF	Evaluates the noncentral beta cumulative distribution function (CDF).
	BETNIN	Evaluates the inverse of the noncentral beta cumulative distribution function (CDF).
	BETNPR	Evaluates the noncentral beta probability density function.
	BNRDF	Evaluates the bivariate normal cumulative distribution function.
	CHIDF	Evaluates the chi-squared cumulative distribution function.
	CHIIN	Evaluates the inverse of the chi-squared cumulative distribution function.
	CHIPR	Evaluates the chi-squared probability density function.
	CSNDF	Evaluates the noncentral chi-squared cumulative distribution function.
	CSNIN	Evaluates the inverse of the noncentral chi-squared cumulative distribution function.
	CSNPR	Evaluates the noncentral chi-squared probability density function.
	EXPDF	Evaluates the exponential cumulative distribution function.
	EXPIN	Evaluates the inverse of the exponential cumulative distribution function.
	EXPPR	Evaluates the exponential probability density function.
	EXVDF	Evaluates the extreme value cumulative distribution function.
	EXVIN	Evaluates the inverse of the extreme value cumulative distribution function.
	EXVPR	Evaluates the extreme value probability density function.
	FDF	Evaluates the Fcumulative distribution function.
	FIN	Evaluates the inverse of the Fcumulative distribution function.
	FPR	Evaluates the F probability density function.
	FNDF	Evaluates the noncentral F cumulative distribution function (CDF).
	FNIN	Evaluates the inverse of the noncentral F cumulative distribution function (CDF).
	FNPR	Evaluates the noncentral F probability density function.
	GAMDF	Evaluates the gamma cumulative distribution function.
	GAMIN	Evaluates the inverse of the gamma cumulative distribution function.
	GAMPR	Evaluates the gamma probability density function.
	RALDF	Evaluates the Rayleigh cumulative distribution function.
	RALIN	Evaluates the inverse of the Rayleigh cumulative distribution function.
	RALPR	Evaluates the Rayleigh probability density function.
	TDF	Evaluates the Student’s tcumulative distribution function.
	TIN	Evaluates the inverse of the Student’s tcumulative distribution function.
	TPR	Evaluates the Student’s tprobability density function.
	TNDF	Evaluates the noncentral Student’s tcumulative distribution function.
	TNIN	Evaluates the inverse of the noncentral Student’s tcumulative distribution function.
	TNPR	Evaluates the noncentral Student's t probability density function.
	UNDF	Evaluates the uniform cumulative distribution function.
	UNIN	Evaluates the inverse of the uniform cumulative distribution function.
	UNPR	Evaluates the uniform probability density function.
	WBLDF	Evaluates the Weibull cumulative distribution function.
	WBLIN	Evaluates the inverse of the Weibull cumulative distribution function.
	WBLPR	Evaluates the Weibull probability density function.

GENERAL CONTINUOUS RANDOM VARIABLES
	ROUTINE	DESCRIPTION
	GCDF	Evaluates a general continuous cumulative distribution function given ordinates of the density.
	GCIN	Evaluates the inverse of a general continuous cumulative distribution function given ordinates of the density.
	GFNIN	Evaluates the inverse of a general continuous cumulative distribution function given in a subprogram.

PARAMETER ESTIMATION
	ROUTINE	DESCRIPTION
	MLE	Calculates maximum likelihood estimates for the parameters of one of several univariate probability distributions.

CHAPTER 18: RANDOM NUMBER GENERATION

UTILITY ROUTINES FOR RANDOM NUMBER GENERATORS
	ROUTINE	DESCRIPTION
	RNOPT	Selects the uniform (0,1) multiplicative congruential pseudorandom number generator.
	RNOPG	Retrieves the indicator of the type of uniform random number generator.
	RNSET	Initializes a random seed for use in the IMSL random number generators.
	RNGET	Retrieves the current value of the seed used in the IMSL random number generators.
	RNSES	Initializes the table in the IMSL random number generators that use shuffling.
	RNGES	Retrieves the current value of the table in the IMSL random number generators that use shuffling.
	RNSEF	Retrieves the array used in the IMSL GFSR random number generator.
	RNGEF	Retrieves the current value of the array used in the IMSL GFSR random number generator.
	RNISD	Determines a seed that yields a stream beginning 100,000 numbers beyond the beginning of the stream yielded by a given seed used in IMSL multiplicative congruential generators (with no shufflings).
	RNIN32	Initializes the 32-bit Mersenne Twister generator using an array.
	RNGE32	Retrieves the current table used in the 32-bit Mersenne Twister generator.
	RNSE32	Sets the current table used in the 32-bit Mersenne Twister generator.
	RNIN64	Initializes the 64-bit Mersenne Twister generator using an array.
	RNGE64	Retrieves the current table used in the 64-bit Mersenne Twister generator.
	RNSE64	Sets the current table used in the 64-bit Mersenne Twister generator.

BASIC UNIFORM DISTRIBUTION
	ROUTINE	DESCRIPTION
	RNUN	Generates pseudorandom numbers from a uniform (0, 1) distribution.
	RNUNF	Generates a pseudorandom number from a uniform (0, 1) distribution.

UNIVARIATE DISCRETE DISTRIBUTIONS
	ROUTINE	DESCRIPTION
	RNBIN	Generates pseudorandom numbers from a binomial distribution.
	RNGDA	Generates pseudorandom numbers from a general discrete distribution using an alias method.
	RNGDS	Sets up table to generate pseudorandom numbers from a general discrete distribution.
	RNGDT	Generates pseudorandom numbers from a general discrete distribution using a table lookup method.
	RNGEO	Generates pseudorandom numbers from a geometric distribution.
	RNHYP	Generates pseudorandom numbers from a hypergeometric distribution.
	RNLGR	Generates pseudorandom numbers from a logarithmic distribution.
	RNNBN	Generates pseudorandom numbers from a negative binomial distribution.
	RNPOI	Generates pseudorandom numbers from a Poisson distribution.
	RNUND	Generates pseudorandom numbers from a discrete uniform distribution.

UNIVARIATE CONTINUOUS DISTRIBUTIONS
	ROUTINE	DESCRIPTION
	RNBET	Generates pseudorandom numbers from a beta distribution.
	RNCHI	Generates pseudorandom numbers from a chi-squared distribution.
	RNCHY	Generates pseudorandom numbers from a Cauchy distribution.
	RNEXP	Generates pseudorandom numbers from a standard exponential distribution.
	RNEXV	Generates pseudorandom numbers from an extreme value distribution.
	RNFDF	Generates pseudorandom numbers from the Fdistribution.
	RNEXT	Generates pseudorandom numbers from a mixture of two exponential distributions.
	RNGAM	Generates pseudorandom numbers from a standard gamma distribution.
	RNGCS	Sets up table to generate pseudorandom numbers from a general continuous distribution.
	RNGCT	Generates pseudorandom numbers from a general continuous distribution.
	RNLNL	Generates pseudorandom numbers from a lognormal distribution.
	RNNOA	Generates pseudorandom numbers from a standard normal distribution using an acceptance/rejection method.
	RNNOF	Generates a pseudorandom number from a standard normal distribution.
	RNNOR	Generates pseudorandom numbers from a standard normal distribution using an inverse CDF method.
	RNRAL	Generates pseudorandom numbers from a Rayleigh distribution.
	RNSTA	Generates pseudorandom numbers from a stable distribution.
	RNSTT	Generates pseudorandom numbers from a Student’s tdistribution.
	RNTRI	Generates pseudorandom numbers from a triangular distribution on the interval (0, 1).
	RNVMS	Generates pseudorandom numbers from a von Mises distribution.
	RNWIB	Generates pseudorandom numbers from a Weibull distribution.

MULTIVARIATE DISTRIBUTIONS
	ROUTINE	DESCRIPTION
	RNCOR	Generates a pseudorandom orthogonal matrix or a correlation matrix.
	RNDAT	Generates pseudorandom numbers from a multivariate distribution determined from a given sample.
	RNMTN	Generates pseudorandom numbers from a multinomial distribution.
	RNMVN	Generates pseudorandom numbers from a multivariate normal distribution.
	RNSPH	Generates pseudorandom points on a unit circle or K-dimensional sphere.
	RNTAB	Generates a pseudorandom two-way table.
	RNMVGC	Given a Cholesky factorization of a correlation matrix, generates pseudorandom numbers from a Gaussian Copula distribution.
	RNMVTC	Given a Cholesky factorization of a correlation matrix, generates pseudorandom numbers from a Student‘s t Copula distribution.
	CANCOR	Given an input array of deviate values, generates a canonical correlation array.

ORDER STATISTICS
	ROUTINE	DESCRIPTION
	RNNOS	Generates pseudorandom order statistics from a standard normal distribution.
	RNUNO	Generates pseudorandom order statistics from a uniform (0, 1) distribution.

STOCHASTIC PROCESSES
	ROUTINE	DESCRIPTION
	RNARM	Generates a time series from a specified ARMA model.
	RNNPP	Generates pseudorandom numbers from a nonhomogenous Poisson process.

SAMPLES AND PERMUTATIONS
	ROUTINE	DESCRIPTION
	RNPER	Generates a pseudorandom permutation.
	RNSRI	Generates a simple pseudorandom sample of indices.
	RNSRS	Generates a simple pseudorandom sample from a finite population.

LOW DISCREPANCY SEQUENCES
	ROUTINE	DESCRIPTION
	FAURE_FREE	Frees the structure containing information about the Faure sequence.
	FAURE_INIT	Shuffled Faure sequence initialization.
	FAURE_NEXT	Computes a shuffled Faure sequence.

CHAPTER 19: UTILITIES

PRINT
	ROUTINE	DESCRIPTION
	PGOPT	Sets or retrieves page width and length for printing.
	WRIRL	Prints an integer rectangular matrix with a given format and labels.
	WRIRN	Prints an integer rectangular matrix with integer row and column labels.
	WROPT	Sets or retrieves an option for printing a matrix.
	WRRRL	Prints a real rectangular matrix with a given format and labels.
	WRRRN	Prints a real rectangular matrix with integer row and column labels.

PERMUTE
	ROUTINE	DESCRIPTION
	MVNAN	Moves any rows of a matrix with the IMSL missing value code NaN (not a number) in the specified columns to the last rows of the matrix.
	PERMA	Permutes the rows or columns of a matrix.
	PERMU	Rearranges the elements of an array as specified by a permutation.
	RORDM	Reorders rows and columns of a symmetric matrix.

SORT
	ROUTINE	DESCRIPTION
	SCOLR	Sorts columns of a real rectangular matrix using keys in rows.
	SROWR	Sorts rows of a real rectangular matrix using keys in columns.
	SVIGN	Sorts an integer array by algebraically increasing value.
	SVIGP	Sorts an integer array by algebraically increasing value and returns the permutation that rearranges the array.
	SVRGN	Sorts a real array by algebraically increasing value.
	SVRGP	Sorts a real array by algebraically increasing value and returns the permutation that rearranges the array.

SEARCH
	ROUTINE	DESCRIPTION
	ISRCH	Searches a sorted integer vector for a given integer and returns its index.
	SRCH	Searches a sorted vector for a given scalar and returns its index.
	SSRCH	Searches a character vector, sorted in ascending ASCII order, for a given string and returns its index.

CHARACTER STRING MANIPULATION
	ROUTINE	DESCRIPTION
	ACHAR	Returns a character given its ASCII value.
	CVTSI	Converts a character string containing an integer number into the corresponding integer form.
	IACHAR	Returns the integer ASCII value of a character argument.
	ICASE	Returns the ASCII value of a character converted to uppercase.
	IICSR	Compares two character strings using the ASCII collating sequence but without regard to case.
	IIDEX	Determines the position in a string at which a given character sequence begins without regard to case.

TIME, DATE AND VERSION
	ROUTINE	DESCRIPTION
	CPSEC	Returns CPU time used in seconds.
	IDYWK	Computes the day of the week for a given date.
	NDAYS	Computes the number of days from January 1, 1900, to the given date.
	NDYIN	Gives the date corresponding to the number of days since January 1, 1900.
	TDATE	Gets today’s date.
	TIMDY	Gets time of day.
	VERSL	Obtains STAT/LIBRARY-related version and system information.

RETRIEVAL OF DATA SETS
	ROUTINE	DESCRIPTION
	GDATA	Retrieves a commonly analyzed data set.

CHAPTER 20: MATHEMATICAL SUPPORT

LINEAR SYSTEMS
	ROUTINE	DESCRIPTION
	CHFAC	Cholesky factorization R^TRof a nonnegative definite matrix.
	GIRTS	Solves a triangular linear system given R.
	MCHOL	Modified Cholesky factorization.

SPECIAL FUNCTIONS
	ROUTINE	DESCRIPTION
	AMILLR	Mill’s ratio.
	ENOS	Expected value of a normal order statistic.

NEAREST NEIGHBORS
	ROUTINE	DESCRIPTION
	NGHBR	Searches a k-dtree for the m nearest neighbors.
	QUADT	Forms a k-dtree.

Visual Numerics, IMSL, PV-WAVE, JMSL, JWAVE, TS-WAVE, and PyIMSL are registered trademarks of Rogue Wave Software, Inc.

IMPORTANT NOTICE: Information contained in this documentation is subject to change without notice. Use of this document is subject to the terms and conditions of a Rogue Wave Software License Agreement, including, without limitation, the Limited Warranty and Limitation of Liability.

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CHAPTER 1: LINEAR SYSTEMS

LINEAR SOLVERS

LARGE-SCALE PARALLEL SOLVERS

SOLUTION OF LINEAR SYSTEMS, MATRIX INVERSION, AND DETERMINANT EVALUATION

REAL GENERAL MATRICES

COMPLEX GENERAL MATRICES

REAL TRIANGULAR MATRICES

COMPLEX TRIANGULAR MATRICES

REAL POSITIVE DEFINITE MATRICES

REAL SYMMETRIC MATRICES

COMPLEX HERMITIAN POSITIVE DEFINITE MATRICES

COMPLEX HERMITIAN MATRICES

REAL BAND MATRICES IN BAND STORAGE MODE

REAL BAND SYMMETRIC POSITIVE DEFINITE MATRICES IN BAND STORAGE MODE

COMPLEX BAND MATRICES IN BAND STORAGE MODE

COMPLEX BAND POSITIVE DEFINITE MATRICES IN BAND STORAGE MODE

REAL SPARSE LINEAR EQUATION SOLVERS

COMPLEX SPARSE LINEAR EQUATION SOLVERS

REAL SPARSE SYMMETRIC POSITIVE DEFINITE LINEAR EQUATIONS SOLVERS

COMPLEX SPARSE HERMITIAN POSITIVE DEFINITE LINEAR EQUATIONS SOLVERS

REAL TOEPLITZ MATRICES IN TOEPLITZ STORAGE MODE

COMPLEX TOEPLITZ MATRICES IN TOEPLITZ STORAGE MODE

COMPLEX CIRCULAR MATRICES IN CIRCULANT STORAGE MODE

ITERATIVE METHODS

LINEAR LEAST SQUARES AND MATRIX FACTORIZATION

LEAST SQUARES, QR DECOMPOSITION AND GENERALIZED INVERSE LEAST SQUARES

CHOLESKY FACTORIZATION

SINGULAR VALUE DECOMPOSITIONS

CHAPTER 2: EIGENSYSTEM ANALYSIS

EIGENVALUE DECOMPOSITION

EIGENVALUES AND (OPTIONALLY) EIGENVECTORS OF AX = lX

REAL GENERAL PROBLEM AX = lX

COMPLEX GENERAL PROBLEM AX =lX

REAL SYMMETRIC GENERAL PROBLEM AX = lX

REAL BAND SYMMETRIC MATRICIES IN BAND STORAGE MODE

COMPLEX HERMITIAN MATRICES

REAL UPPER HESSENBERG MATRICES

COMPLEX UPPER HESSENBERG MATRICES

EIGENVALUES AND (OPTIONALLY) EIGENVECTORS OF AX = lBX

REAL GENERAL PROBLEM AX = lX

COMPLEX GENERAL PROBLEM AX = lBX

REAL SYMMETRIC PROBLEM AX = lBX

EIGENVALUES AND EIGENVECTORS COMPUTED WITH ARPACK

CHAPTER 3: INTERPOLATION AND APPROXIMATION

CURVE AND SURFACE FITTING WITH SPLINES

CUBIC SPLINE INTERPOLATION

CUBIC SPLINE EVALUATION AND INTEGRATION

B-SPLINE INTERPOLATION

SPLINE EVALUATION, INTEGRATION, AND CONVERSION TO PIECEWISE POLYNOMIAL GIVEN THE B-SPLINE REPRESENTATION

PIECEWISE POLYNOMIAL

QUADRATIC POLYNOMIAL INTERPOLATION ROUTINES FOR GRIDDED DATA

MULTI-DIMENSIONAL INTERPOLATION

LEAST-SQUARES APPROXIMATION

CUBIC SPLINE SMOOTHING

RATIONAL L∞ APPROXIMATION

CHAPTER 4: INTEGRATION AND DIFFERENTIATION

UNIVARIATE QUADRATURE

IMSL^® FORTRAN NUMERICAL LIBRARY FUNCTION CATALOG VERSION 2025.1

SPLINE EVALUATION, INTEGRATION, AND CONVERSION TO PIECEWISE POLYNOMIAL
GIVEN THE B-SPLINE REPRESENTATION

RATIONAL L_∞ APPROXIMATION