Public Domain Software

C.7 Public Domain Software

Below is a selective list indicating the scope of software available from Netlib. The first few libraries here are widely regarded as being of high quality. The likelihood of your encoun- tering a bug is relatively small; if you do, report it by email to ehg@research.att.com

Algorithms published in ACM Transactions on Mathematical Software can also be downloaded from www.acm.org/pubs/calgo . As of October 2007, 866 algorithms were available.

BLAS : Basic Linear Algebra Subprograms levels 1, 2, and 3, and machine constants. FFTPACK : A package of Fortran programs for the fast Fourier transform of periodic and

other symmetric sequences. This package consists of programs which perform fast Fourier transforms for both complex and real periodic sequences and certain other symmetric se- quences. Developed by Paul Swarztrauber, NCAR.

VFFTPK : A vectorized version of FFTPACK for multiple sequences. Developed by Sweet, Lindgren, and Boisvert.

FISHPACK : A package of Fortran subprograms providing finite difference approximations for elliptic boundary value problems. Developed by Paul Swarztrauber and Roland Sweet.

FN : Wayne Fullerton’s special function library (single and double).

C.7. Public Domain Software C-11 GO : Golden Oldies: Routines that have been widely used but aren’t available through the

standard libraries. HARWELL : Sparse matrix routine MA28 from the Harwell library made available by Iain

Duff. LAPACK : For the most common problems in numerical linear algebra such as linear equa-

tions, linear least squares problems, eigenvalue problems, and singular value problems. Designed to be efficient on a wide range of modern high-performance computers. De- veloped by Ed Anderson, Z. Bai, Chris Bischof, Jim Demmel, Jack Dongarra, Jeremy Du Croz, Anne Greenbaum, Sven Hammarling, Alan McKenney, Susan Ostrouchov, and Danny Sorensen.

PPPACK : Subroutines from the book A Practical Guide to Splines, by Carl de Boor. Some calling sequences differ slightly from those in the book.

TOMS : Collected algorithms of the ACM. When requesting a specific item, please refer to the algorithm number.

In contrast to the above libraries, the following are collections of codes from a variety of sources. Most are excellent, but you should exercise caution. We include research codes that we haven’t tested and codes that may not be state of the art but are useful for comparisons. The following list is alphabetical, not by merit:

AMOS : Bessel and Airy functions of complex arguments and nonnegative order. BIHAR : Biharmonic solver in rectangular geometry and polar coordinates. Made available

by Petter Bjørstad, University of Bergen. BMP : Multiple precision package. By Richard P. Brent. C++ : Miscellaneous codes written in C++. Eric Grosse, editor, Bell Laboratories.

C : Miscellaneous codes written in C. Not all C software is in this miscellaneous library. If it clearly fits into a domain-specific library, it is assigned there. Eric Grosse, editor.

CONFORMAL : Routines to solve the “parameter problem” associated with conformal map- ping. Includes SCPACK (polygons with straight sides) from Nick Trefethen; CAP (circular arc polygons) from Petter Bjorstad and Eric Grosse; gear-like domains by Kent Pearce, and CONFPACK (Symm’s integral equation) by Hough and Gutknecht.

CONTIN : Methods for continuation and limit points, notably PITCON, by Werner Rhein- boldt and John Burkardt, University of Pittsburgh.

DDSV : Programs from Linear Algebra Computations on Vector and Parallel Computers, by Jack Dongarra, Iain Duff, Danny Sorensen, and Henk Van der Vorst.

DIERCKX : Spline fitting routines for various kinds of data and geometries. Paul Dierckx, Leuven.

ELEFUNT : Transportable Fortran programs for testing the elementary function programs provided with Fortran compilers. Reference: Software Manual for the Elementary Func- tions by W. J. Cody and W. Waite, Prentice–Hall, 1980.

FITPACK : Splines under tension (an early version). Developed by Alan K. Cline.

C-12 Online Appendix C. Guide to Literature FMM : Routines from the book Computer Methods for Mathematical Computations, by

George Forsythe, Mike Malcolm, and Cleve Moler. GCV : Generalized cross validation spline smoothing and ridge regression. Developed by

Grace Wahba. HOMPACK : Fortran 77 subroutines for solving nonlinear systems of equations by homo-

topy methods. There are subroutines for fixed point, zero finding, and general homotopy curve tracking problems, utilizing both dense and sparse Jacobian matrices. Three different algorithms are implemented: ODE-based, normal flow, and augmented Jacobian. Layne T. Watson, Blacksburg, VA.

ITPACK : Iterative linear system solver based on a number of methods: Jacobi method, SOR, and SSOR with conjugate gradient or Chebyshev (semi-iteration) acceleration. David Young, David Kincaid, and the group at the University of Texas, Austin.

JAKEF : A precompiler that analyzes a given Fortran 77 source code for the evaluation of

a scalar or vector function and then generates an expanded Fortran subroutine that simul- taneously evaluates the gradient or Jacobian, respectively. For scalar functions the ratio between the run time of the resulting gradient routine and that of the original evaluation routine is never greater than a fixed bound of about five. The storage requirement may

be considerable, as it is also proportional to the run time of the original routine. Since no differencing is done, the partial derivative values obtained are exact up to roundoff errors. By Andreas Griewank.

LANZ : Large Sparse Symmetric Generalized Eigenproblem. Mark T. Jones, Argonne Na- tional Laboratory and Merrell L. Patrick, Duke University.

LANCZOS : For computing a few eigenvalues/eigenvectors of large (sparse) real symmetric and Hermitian matrices, and singular values and vectors of rectangular matrices. By Jane Cullum and Ralph Willoughby.

LAWSON–HANSON : Least squares codes from the book Solving Least Squares Problems, by C. L. Lawson and R. J. Hanson, SIAM, 1995.

LP : A set of test problems for linear programming in MPS format. David Gay, Bell Labo- ratories.

MINPACK : Solution of systems of nonlinear equations and nonlinear least squares prob- lems. Consists of five algorithmic paths, each including a core subroutine and an easy-to-use driver. The algorithms proceed either from an analytic specification of the Jacobian matrix or directly from the problem functions. The paths include facilities for systems of equations with a banded Jacobian matrix, for least squares problems with a large amount of data, and for checking the consistency of the Jacobian matrix with the functions. Developed by Jorge Moré, Burt Garbow, and Ken Hillstrom, Argonne National Laboratory.

MISC : Contains various pieces of software collected over time. Jack Dongarra. MPFUN : Multiple precision arithmetic. David Bailey. NAPACK : Solving linear systems; estimating the condition number or the norm of a ma-

trix; computing determinants, matrix inverse, least squares problems. Also for performing unconstrained minimization, compute eigenvalues, eigenvectors, the singular value de-

C.7. Public Domain Software C-13 composition, or the QR decomposition. The package has special routines for general,

band, symmetric, indefinite, tridiagonal, upper Hessenberg, and circulant matrices. By Bill Hager, University of Florida, Gainesville. Related book: Applied Numerical Linear Alge- bra , Prentice–Hall, 1988.

NUMERALGO : Algorithms from the journal Numerical Algorithms. ODE : Various initial and boundary value ordinary differential equation solvers: colsys,

dverk, rksuite, ode. Erik Grosse. ODEPACK : The ODE package from Hindmarch and others. Alan Hindmarch, Lawrence

Livermore National Laboratory. ODRPACK : Orthogonal Distance Regression. A portable collection of Fortran subprograms

for fitting a model to data. It is designed primarily for instances when the independent as well as the dependent variables have significant errors, implementing a highly efficient algo- rithm for solving the weighted orthogonal distance regression problem, i.e., for minimizing the sum of the squares of the weighted orthogonal distances between each data point and the curve described by the model equation. By Boggs, Byrd, Rogers, and Schnabel.

PARANOIA : A program to explore the floating-point system on your computer. Devised by W. Kahan, University of California, Berkeley.

PDES : A compact package for solving systems of linear equations using multigrid or aggregation–disaggregation methods. Imbedded in the algorithms are implementations for sparse Gaussian elimination and symmetric Gauss–Seidel (unaccelerated or accelerated by conjugate gradients or Orthomin(1)). This package is particularly useful for solving problems which arise from discretizing partial differential equations, regardless of whether finite differences, finite elements, or finite volumes are used. Craig Douglas.

PLTMG : Elliptic partial differential equations in general regions of the plane. It features adaptive local mesh refinement, multigrid iteration, and a pseudoarclength continuation option for parameter dependencies. The package includes an initial mesh generator and several graphics packages. By Randy Bank. Reference: PLTMG: A Software Package for Solving Elliptic Partial Differential Equations : Users’ Guide 8.0, SIAM, 1998.

POLYHEDRA : A database of angles, vertex locations, and so on for over 100 hundred geo- metric solids. Compiled by Andrew Hume.

PORT : Public subset of the PORT library, which includes the latest version of David Gay’s NL2SOL nonlinear least squares. The rest of the PORT3 library is available by license from Lucent Technologies.

RANDOM : Random number generators. Eric Grosse, editor. QUADPACK : Univariate quadrature. By Robert Piessens (Leuven), Elise de Donker (Leu-

ven), and David Kahaner (National Bureau of Standards). SLAP : Sparse linear algebra package for iterative symmetric and nonsymmetric linear sys-

tem solutions. Included are core routines to do iterative refinement, preconditioned conju- gate gradient, preconditioned conjugate gradient on the normal equations, preconditioned biconjugate gradient, preconditioned biconjugate gradient squared, orthomin, and general- ized minimum residual. Mark K. Seager and Anne Greenbaum.

C-14 Online Appendix C. Guide to Literature SLATEC : Comprehensive software library containing over 1400 general purpose mathe-

matical and statistical routines written in Fortran 77. SPARSPAK : Subroutines from the book Computer Solution of Large Sparse Positive Definite

Systems by Alan George and Joseph Liu, Prentice–Hall, 1981. SPARSE : Subroutines written in C that solve large sparse systems of linear equations using

LU factorization. The package is able to handle arbitrary real and complex square matrix equations. Besides being able to solve linear systems, it solves transposed systems, finds determinants, multiplies a vector by a matrix, and estimates errors due to ill-conditioning in the system of equations and instability in the computations. SPARSE does not require or assume symmetry and is able to perform numerical pivoting (either diagonal or complete) to avoid unnecessary error in the solution. SPARSE also has an optional interface that allow it to be called from FORTRAN programs. Ken Kundert, Alberto Sangiovanni-Vincentelli, Berkeley.

SPARSE-BLAS : An extension to the set of Basic Linear Algebra Subprograms (BLAS). The extension is targeted at sparse vector operations, with the goal of providing efficient, but portable, implementations of algorithms for high-performance computers. By Dave Dodson.

SPECFUN : Fortran programs for special functions, and accompanying test programs simi- lar in concept to those in ELEFUNT. W. J. Cody, Argonne National Laboratory.

SVDPACK : Singular values and singular vectors of large sparse matrices. By Mike Berry. TEXTBOOK : Codes associated with numerical analysis textbooks. Erik Grosse, editor. TOEPLITZ : Solution of Toeplitz or circulant systems of linear equations and for orthogonal

factorization of column-circulant matrices. A Soviet–American collaborative effort. Burt Garbow, Argonne National Laboratory,

TRANSFORM : Fast Fourier Transform (FFT) and other digital processing tools. Erik Grosse, editor.

UNCON : Unconstrained optimization. Problems from Moré, Garbow, and others. VANHUFFEL : Total least squares (TLS) problem by using a partial singular value decom-

position (PSVD). By Sabine Van Huffel.