Newsgroups: sci.math.num-analysis,sci.math.symbolic,sci.answers,news.answers Subject: FAQ: Numerical Analysis and Associated Fields Resource Guide (1/1) Summary: From: sullivan@mathcom.com (Steve Sullivan) Distribution: world Followup-To: sci.math.num-analysis Keywords: Approved: news-answers-request@MIT.EDU Archive-name: num-analysis/faq/part1 Last-modified: 1997 August 14 q10. FAQ: Numerical Analysis & Associated Fields Resource Guide Welcome! My intent here is to provide reviews of software, texts, and other resources instead of simply a listing. My experience is that for someone looking for a package or system, reviews by previous users can be a lifesaver. If you have any suggestions, comments, or contributions please send them to me at: sullivan@mathcom.com Other reviews would be most welcome! If you use a mathematical package or set of programs and would care to write one to twenty sentences on it, please let me know. If you have a favorite text or two you'd like to recommend, please let me know. Sigh, and now the legalities ... The information contained in this document is believed to be true, but no guarantees of accuracy are made, and there is no liability of any sort for any consequences of its use. This document may be copied and/or reproduced providing that: * the use is for non-commercial purposes only, and * all copies contain this copyright notice: * Copyright 1995-7 S. J. Sullivan See: * q20, "NA FAQ: Introduction" * q30, "NA FAQ: Overview of Recent Additions" * q40, "NA FAQ: Table of Contents" * q50, "NA FAQ: Acknowledgements" Steve Sullivan Mathcom, Inc. sullivan@mathcom.com ========================================================================= q20. NA FAQ: Introduction Where to find this FAQ: On the web: http://www.indra.com/~sullivan/q10.html Mathcom This FAQ is usually available from MIT's rtfm and its mirrors: ftp://rtfm.mit.edu/pub/usenet/news.answers/num-analysis/faq/part1 MIT's rtfm If not, a compressed (with gzip) version is at: ftp://ftp.mathcom.com/mathcom/nafaq.txt.gz Mathcom ftp Abbreviations used in this document: NA Numerical Analysis ### Denotes "to be filled in later". This is work in progress, and probably always will be. [] Reviews are associated with the name of the reviewer in brackets. Those reviews marked [SJS] are by myself. [author] indicates text taken from a package documentation. 10^12 10 to the power 12. In Fortran, that's 10**12; in C that's pow(10,12). x(i) the i'th element of vector x. In C, that would be x[i]. Instead of the normal question/answer form, this FAQ is organized as an outline ... hopefully, you'll find your questions answered here. ========================================================================= q30. NA FAQ: Overview of Recent Additions The Oxford BSP (Bulk Synchronous Protocol) Toolset and Profiling system and the Oxford BSPlib. See q290, "Miscellaneous NA Software" Semidefinate programming: SDPpack. See q265.1, "Optimization, Linear and Non-Linear Programming: General Resources" Jack Dongarra's list of Linear Algebra Software See q205, "Dense (Non-Sparse) Linear Algebra Systems" and q207, "Sparse Linear Algebra Systems". O-Matrix: See q125.12, "O-Matrix" UCALC: q125.13, "UCALC" SACLIB is a library of C programs for computer algebra derived from the SAC2 system. Hoon Hong was the q520.2.8, "SACLIB" NTL: q520.2.9, "NTL - A Library for doing Number Theory" As well as numerous other updates. ========================================================================= q40. NA FAQ: Table of Contents * q10, "FAQ: Numerical Analysis & Associated Fields Resource Guide" * q20, "NA FAQ: Introduction" * q30, "NA FAQ: Overview of Recent Additions" * q40, "NA FAQ: Table of Contents" * q50, "NA FAQ: Acknowledgements" * * q105, "What is Numerical Analysis?" * q110, "Indices of NA Software on the Net" * q112, "Indices of Commercial NA Software" * q115, "Libraries of NA Software on the Net" * q120, "NA Packages on the Net" * q125, "Commercial NA Libraries and Packages" * q135, "Newsgroups for NA" * q140, "Professional Societies for NA" * q145, "Electronic Newsletters for NA" * q150, "Electronic Journals for NA" * q155, "Online Preprints for NA" * q160, "Miscellaneous Web Sites for NA" * q165, "Books, With and Without Software, for NA" Specialized Subfields Within Numerical Analysis * q205, "Dense (Non-Sparse) Linear Algebra Systems" * q207, "Sparse Linear Algebra Systems" * q210, "Random Number Generators (RNGs)" * q215, "Function Evaluation" * q220, "Finding Roots" * q230, "Curve Fitting, Data Modelling, Interpolation, Extrapolation" * q240, "Transforms (FFT, etc) and digital signal processing (DSP)" * q245, "Wavelets" * q250, "Integration and Ordinary Differential Equations (ODEs)" * q253, "Stochastic Differential Equations" * q255, "N-Body and Particle Simulation" * q260, "Partial Differential Equations (PDEs) and Finite Element Modeling (FEM)" * q265, "Operations Research: Minimization, Optimization" * q270, "Computational Geometry" * q285, "Graphics and Scientific Visualization" * q290, "Miscellaneous NA Software" Associated Fields * q505, "Probability and Statistics" * q510, "Chaos Theory (Nonlinear Dynamics)" * q520, "Symbolic Algebra" * q530, "Cryptography (Cryptology)" * q540, "Fractals" * q550, "Neural Networks" * q560, "Discrete algorithms" * q570, "Constraints" * q580, "Genetic Algorithms" * q590, "Simulated Annealing" Teaching and Academic Software * q800, "Teaching and Academic Software" =========================================================================== q50. NA FAQ: Acknowledgements Many thanks to all those who've given their time and advice in creating this FAQ. In order to save contributors from unwanted spam, I do not include their email addresses. Bob Berman Ronald F Boisvert Ted Brown John Chandler Luiz Henrique de Figueiredo Bill Frensley Pawel Gora Amara Graps Vijay Gupta Doug Hart Albert Hines Charles Knechtel Zdislav V. Kovarik Dave Linder George Marsaglia Pierre Maxted Allen Mcintosh Sean O riordain Daniel Pfenniger Daniel Pick Brian Ripley Ramin Samadani Robert Schneiders Peter Somlo Tim Strotman N. Sukumar Stephen Vavasis Dave Watson Many thanks also to the organizers of the many services listed herein - Netlib, the NIST guide, NA-Net, CAIN, the NASA Graphics site, and numerous other indices and informative web pages. =========================================================================== q105. What is Numerical Analysis? NA is the union of theoretical and computational investigation into the computer solution of mathematical problems. NA generally includes those problems involving continuous functions of real or complex variables, as opposed to solely discrete variables and functions. The mixing of theoretical and computational concerns leads to a strong emphasis on algorithms: what are the time and memory usage properties of a certain algorithm? What errors are introduced by an algorithm? The compuational aspects of NA usually take place within the scope of floating-point arithmetic, and are implemented on machines ranging from super-computers through PCs to hand-calculators. The theoretical aspects extend into fields such as Calculus, Differential Equations, and Analysis. The field of Linear Algebra is so often used to model physical systems that the theoretical study of Linear Algebra is in itself often considered to be NA at work. Primary areas of theoretical concern in NA are: * global/local error bounding * stability of algorithms * rates of convergence of algorithms Primary areas of computational concern in NA are: * roundoff error * global/local error and its tolerance * time and memory requirements of computation * High Performance Computing (HPC) * parallel computing * architechture/platform specific details. =========================================================================== q110. Indices of NA Software on the Net For indices of packages oriented towards symbolic algebra, see q520, "Symbolic Algebra". The NIST Guide to Available Mathematical Software (Formerly called GAMS) http://gams.nist.gov/ NIST Guide to Mathematical Software or telnet to: gams.nist.gov [SJS]: Maintained by National Institute of Standards and Technology (NIST) An index and server for a wide variety of mathematical software, including most of netlib (see q115.1, "Netlib"). Much of the software is in Fortran. If you prefer to speak C++ or C, see q160.1, "C++ Resources", and q115.2, "Fortran, C, and f2c". [Ronald Boisvert]: The main focus is on fine-grained software components, e.g. subroutines, although information about some larger packages are included. As of November 1995, nearly 10,000 components from more than 90 packages have been cross-indexed using a detailed tree-structured problem classification system. Both freely available software (from netlib or developed at NIST) and commercial packages (used by NIST) are indexed, although source code is available only for non-commercial software. =================================== q112. Indices of Commercial NA Software A large list of commercial NA products may be found at: http://www.cray.com/PUBLIC/APPS/DAS/ Cray The Directory of commercial software, by International Computer Programs, Inc., is at: http://www.icp.com/softinfo/ ICP Finally, for packages oriented towards symbolic algebra, see q520, "Symbolic Algebra". =========================================================================== q115. Libraries of NA Software on the Net Libraries are collections of source code, and source code packages. Much of the code is in Fortran. If you prefer to speak C++ or C, see q160.1, "C++ Resources", and q115.2, "Fortran, C, and f2c". The main library by far is q115.1, "Netlib". For statistical software, the best resource is q115.3, "Statlib". Other libraries are q115.4, "NCAR's Mathematical and Statistical Libraries" and q115.5, "Hensa Unix Parallel Archive". * q115.1, "Netlib" * q115.2, "Fortran, C, and the f2c Translator" * q115.3, "Statlib" * q115.4, "NCAR's Mathematical and Statistical Libraries" * q115.5, "Hensa Unix Parallel Archive" * q115.6, "Modula-3 NA Library" * q115.7, "Forth Numerical/Scientific Library" * q115.8, "Eiffel Numerical/Scientific Library" * q115.9, "Lisp Numerical/Scientific Libraries" * q115.10, "Java Numerical/Scientific Libraries" =========================================================================== q115.1. Netlib NetLib is probably the world's largest repository of numerical methods programs. It is located at Oak Ridge National Laboratory, Knoxville, Tennessee, and at AT&T Bell Laboratories, Murray Hill, NJ. email: send message "help" to either: netlib@ornl.gov netlib@research.att.com http://www.netlib.org Netlib main http://www.netlib.org/netlib/netlib_faq.html Netlib FAQ http://www.netlib.org/master/expanded_liblist.html Netlib index ftp://netlib.att.com/netlib Netlib via ftp Netlib mirrors: http://www.netlib.no/ Netlib in Norway or email to: netlib@nac.no http://www.hensa.ac.uk/ftp/mirrors/netlib/master/ Netlib in England or email to: netlib@ukc.ac.uk http://elib.zib.de/netlib/master/readme.html Netlib in Germany or: http://elib.zib-berlin.de/netlib Netlib in Germany or email to: anonymous@elib.zib-berlin.de ftp://draci.cs.uow.edu.au/netlib/ Netlib in Australia or email to: netlib@draci.cs.uow.edu.au Netlib in Taiwan: email only: netlib@nchc.edu.tw Some gems of netlib: Machine/architecture dependant Basic Linear Algebra Subroutines (BLAS) are the keystone of Netlib. LAPACK, in Fortran 77, is the modern replacement of EISPACK, LINPACK, etc. CLAPACK is a C version of LAPACK. See the Caution on Using Arrays in q115.2, "Fortran, C, and f2c". LAPACK++ is a C++ version of, sadly, only a subset of LAPACK. LAPACK++ is work in progress, and hopefully the full functionality of LAPACK will be supported soon. ScaLAPACK is for distributed memory machines. =================================== q115.2. Fortran, C, and the f2c Translator For C++ and C resources, see q160.1, "C++ Resources". Most of the programs in netlib are in Fortran. However, netlib contains an excellent Fortran-to-C conversion utility, f2c. While f2c produces working C code, it is visually complex and ugly. Using f2c on a large package like LAPACK can require a good deal of time to get all the options correct. Fortunately, LAPACK has already be converted to C: see CLAPACK. The utility f2c can also be invoked by email. Send email to netlib@research.att.com, with the subject "execute f2c", and body containing the non-confidential Fortran program to be converted. But the email option is of use only for very small, simple programs, since a resulting C program of any size must be linked with the f2c libraries. Usually one will have to download the f2c package anyway to generate the libraries. Generally it's easier to download the f2c package, build the libraries and the f2c conversion program, and do the conversion locally. CAUTION: Programs created by f2c conversion use parameter passing conventions different from most C or C++ programs. Their callers must create the appropriate parameters before using them. See the file f2c.ps in the f2c distribution. A good description of this issue may also be found in the "readme" file for clapack in netlib. =================================== q115.3. Statlib Statlib is a huge repository of statistics related software and info. Probability, statistics, random variables, distribution functions. http://lib.stat.cmu.edu/ Statlib at CMU ftp://lib.stat.cmu.edu Statlib via ftp email: send message "send index" to statlib@lib.stat.cmu.edu =================================== q115.4. NCAR's Mathematical and Statistical Libraries NCAR's libraries contain some overlap with netlib. http://www.ucar.edu/SOFTLIB/mathlib.html NCAR =================================== q115.5. Hensa Unix Parallel Archive General info, software, articles, etc., on parallel computing. http://www.hensa.ac.uk/parallel/environments/pcn/ Hensa Note: this web server can be very slow! =================================== q115.6. Modula-3 NA Library http://www.eskimo.com/~hgeorge/ Modula-3 NA and pick the link to m3na. This is a libraried collection of numerical analysis routines written in Modula-3. Includes linear algebra, roots, ffts, and a bit of statistics. =================================== q115.7. Forth Numerical/Scientific Library http://www.taygeta.com/fsl/sciforth.html Skip Carter's Forth Library at Taygeta =================================== q115.8. Eiffel Numerical/Scientific Library http://www.eiffel.com/products/math.html Commercial Eiffel library at I.S.E. =================================== q115.9. Lisp Numerical/Scientific Libraries http://euler.bd.psu.edu/lispstat/ statistical tools. http://setosa.uwaterloo.ca/~ftp/Quail/features.html U. Waterloo http://eksl-www.cs.umass.edu/research/clip-clasp-overview.html instrumentation and statistical analysis packages ftp://ftp.cs.cmu.edu/user/ai/lang/lisp/code/math/0.html CMU's library =================================== q115.10. Java Numerical/Scientific Libraries http://www.vni.com/products/wpd/jnl/jnl_1_0.html Visual Numerics' Java package [author]: JNL, a Numerical Library for Java, is a set of classes for the most important numerical functions missing in Java. The library is comprised of one numerical type class, Complex, and three categories of numerical functions classes: the special functions class, the linear algebra classes, and the statistics class. All classes use double precision floating point as the underlying float type. =========================================================================== q120. NA Packages on the Net Packages generally include an NA library and an interpretive language for a front end. Also see q520, "Symbolic Algebra", for free symbolic algebra packages. * q120.1, "Octave" * q120.2, "RLaB" * q120.3, "Scilab" * q120.4, "Tela" * q120.6, "Medal" * q120.7, "Euler" * q120.8, "Prophet" * q120.9, "Yorick" * q120.10, "PETSc" =================================== q120.1. Octave http://www.che.wisc.edu/octave Octave ftp://ftp.che.wisc.edu/pub/octave Octave via ftp [Dave Lindner]: Octave is considered the closest-to-Matlab of the Matlab clones. [author]: Octave is a high-level language, primarily intended for numerical computations. It provides a convenient command line interface for solving linear and nonlinear problems numerically. Octave can do arithmetic for real and complex scalars and matrices, solve sets of nonlinear algebraic equations, integrate functions over finite and infinite intervals, and integrate systems of ordinary differential and differential-algebraic equations. The Octave distribution includes a 200+ page Texinfo manual. Two and three dimensional plotting is fully supported using gnuplot. The underlying numerical solvers are currently standard Fortran ones like Lapack, Linpack, Odepack, the Blas, etc., packaged in a library of C++ classes. =================================== q120.2. RLaB http://www.eskimo.com/~ians/rlab.html RLaB ftp://csi.jpl.nasa.gov/pub/matlab/RLaB RLaB via ftp ftp://evans.ee.adfa.oz.au/pub/RLaB RLaB via ftp in Australia [author]: Rlab is an interactive, interpreted scientific programming environment. Rlab is a very high level language intended to provide fast prototyping and program development, as well as easy data-visualization, and processing. Rlab is not a clone of languages such as those used by tools like Matlab or Matrix_X/Xmath. However, as Rlab focuses on creating a good experimental environment (or laboratory) in which to do matrix math, it can be called "MATLAB-like" since the programming language possesses similar operators and concepts. =================================== q120.3. Scilab http://www-rocq.inria.fr/scilab Scilab ftp://ftp.inria.fr/INRIA/Scilab Scilab via ftp [Dave Lindner]: Scilab is another good Matlab clone. [author]: Scilab is a high-level language for numerical computations in a user-friendly environment. It features: Elaborate data structures (polynomial, rational and string matrices, lists, multivariable linear systems,...). Sophisticated interpreter and programming language with Matlab-like syntax. Hundreds of built-in math functions (new primitives can easily be added). Stunning graphics (2d, 3d, animation). Open structure (easy interfacing with Fortran and C via online dynamic link). Many built-in libraries : * Linear Algebra (including sparse matrices, Kronecker form, ordered Schur,...). * Control (Classical, LQG, H-infinity, ...). * Signal processing. * Simulation (various ode's, dassl,...). * Optimization (differentiable and non-differentiable, LQ solver). * Metanet (network analysis and optimization). Symbolic capabilities through Maple interface. =================================== q120.4. Tela http://www.geo.fmi.fi/prog/tela.html Tela ftp://ftp.funet.fi/pub/sci/math/tela Tela via ftp General NA package with graphics, linear algebra, FFT, etc. Is this another Matlab clone? [author]: It is mainly targeted for prototyping large-scale numerical simulations and doing pre- and postprocessing for them, and it replaces a compiled language like C++ or Fortran in this respect. The feature set is therefore biased to operations needed in partial differential equation solvers. =================================== q120.6. Medal ftp://excel2.uwaterloo.ca/pub Medal Apparently there is also available is a commercial version of Medal: Email : medal@excel2.uwaterloo.ca [author]: MEDAL is a novel expert system development environment which is integrated within a control system design environment, and which supports a tight coupling of symbolic and numeric processing. MEDAL supports the development of coupled systems in engineering and science. MEDAL (Matrix and Expert system Development Aid Language) is an interactive program. The language syntax of MEDAL is similar to the popular MATLAB (Matrix Laboratory) language. MEDAL retains all of the main features of MATLAB, including the MATLAB syntax and M-files. In addition, MEDAL includes an integrated expert system shell for the development of knowledge-based systems which can perform sophisticated numeric calculations. Hence, the additional expert system predicates extends the MATLAB command language syntax. Also, MEDAL supports a rich set of data structure for representing objects in the programming environment. Knowledge can be represented using facts, rules and frames. Main features of MEDAL : ------------------------ * interactive computing environment ( command-drive ) * language syntax and user-interface similar to MATLAB * all basic MATLAB-type of matrix functions are provided * flexible 2-D graphics * design of linear control systems * packed matrix representation, as well as regular matrices * automatic loading of M-files ( open philosophy ) * build-in knowledge base development facilities (expert shell ) * knowledge repesentation : rules, facts, objects ( frames ) * simple knowledge base of the Systematic Design Approach is included * runs on Sun Sparc workstations (X-window), PC (DOS), DEC (Ultrix) References: (1) Pang, G.K.H.,``Knowledge-based Control System Design'', in Recent Advances in Computer-Aided Control Systems Engineering, Jamshidi, M and Herget, C.J. (ed.), Elsevier Science Publishers, 1992. (2) Pang, G.K.H., ``A Knowledge Environment for an Interactive Control System Design Package'', Automatica, Vol. 28. No. 3, pp. 473-491, May 1992. =================================== q120.7. Euler ftp://am.ku-eichstaett.de/pub Euler via ftp [author]: EULER started as a MatLab clone. It is now a program, which can handle real, complex and interval numbers and matrices, has a 2D/3D graphics, a builtin modern programming language (extension of MatLab's), an exact scalar product, and the Windows 95 version can call functions in an external DLL. The OS/2 and Windows versions interact nicely with the GUI, and have a notebook style interface. The Unix version is free, the OS/2 version free for educational use, and the Windows version cheap shareware. These features make EULER an ideal tool for the tasks such as * Inspecting and discussing functions of one real or complex variable. * Viewing surfaces in parameter representation. * Linear algebra and eigenvalue computation. * Testing numerical algorithms. * Solving differential equations numerically. * Computing polynomials. =================================== q120.8. Prophet http://www-prophet.bbn.com/ Prophet ftp://www-prophet.bbn.com Prophet via ftp email: prophet-info@bbn.com [author]: Prophet is an NIH-sponsored Unix workstation software package for life science computing. Prophet includes tools for data management, statistical analysis, curve fitting, data graphing, mathematical modeling, and genetic sequence analysis. One of PROPHET's greatest assets is its new graphical user interface . Employing the latest advances in software technology, PROPHET lets you store, analyze and present Data Tables, Graphs, Statistical Analyses and Mathematical Modeling, and Sequence Analyses with high-resolution graphics and multiple windows. Anyone, from the computer-naive to the computer-sophisticate, can learn to use it quickly and effectively. PROPHET is a National Computing Resource for Life Science Research sponsored by the National Center for Research Resources of the National Institutes of Health. Unfortunately, prophet is distributed in binary form only. It is large: it takes something like 65 MB disk space. =================================== q120.9. Yorick wuarchive.wustl.edu: /languages/yorick/yorick-1.2.tar.gz sunsite.unc.edu: /pub/languages/yorick/yorick-1.2.tar.gz sunsite.unc.edu: /pub/Linux/apps/math/matrix/yorick-1.2.tar.gz netlib.att.com: /netlib/env/yorick-1.2.tar.gz netlib2.cs.utk.edu: /env/yorick-1.2.tar.gz [author] Yorick is an interpreted language. It has: * A C-like language, but without declarative statements. Operations between arrays require no explicit loops, which accounts for Yorick's high speed. Scientific computing and numerical analysis are the goals of most Yorick sessions. * An X window system interactive graphics package. * A library of functions written in the Yorick language. Because Yorick can read either text or binary files, it can be used "out of the box" as a pre- and post-processor for most existing physics simulation programs. As a pre-processor, you can write a Yorick program that produces complicated input files for a simulation. These might be based on output from other programs, or might require evaluation of complicated functions or involve a lot of repetition. As a post-processor, Yorick allows you to compare the results of several simulations or to analyze results of a single simulation in ways you did not forsee when you ran it. =================================== q120.10. PETSc ftp://info.mcs.anl.gov/pub/petsc PETSc by ftp http://www.mcs.anl.gov/petsc/petsc.html PETSc by www [author]: Portable, Extensible Toolkit for Scientific Computation (PETSc). PETSc provides many tools for the parallel (and uniprocessor), numerical solution of PDEs that require solving large-scale, sparse nonlinear systems of equations. PETSc includes nonlinear and linear equation solvers that employ a variety of Newton techniques and Krylov subspace methods. In addition, PETSc provides several parallel sparse matrix formats, including compressed row, block compressed row, and block diagonal storage. PETSc is fully usable from Fortran, C and C++, and runs portably on on most UNIX systems. PETSc uses MPI for all parallel communication. One of the unique features of PETSc is that it enables the application programmer to easily and efficiently assemble parallel vectors and sparse matrices. Users can create complete application programs for the parallel solution of nonlinear PDEs without writing much explicit message-passing code themselves. In addition, PETSc is designed to facilitate extensibility. Thus, users can incorporate customized solvers and data structures when using the package. =========================================================================== q125. Commercial NA Libraries and Packages Commercial libraries and packages tend to merge, so I've combined them in one category. Typically a commercial product contains: * a library of numerical routines * graphics routines * an interactive interpreted language Many symbolic algebra packages also contain NA packages. For info on these packages, see q520, "Symbolic Algebra". An good article on commercial software is: Braham, Robert. "Math & Visualization: new tools, new frontiers", IEEE Spectrum 32, 11 (November 1995), p. 19-36. The article contains tables comparing large number of commercial products. There is no mention of the many excellent free products though. * q125.1, "NAG" * q125.2, "IMSL and PV-WAVE" * q125.3, "Matlab and Simulink" * q125.4, "WavBox" * q125.5, "CraySoft Libraries" * q125.6, "IDL" * q125.7, "Comparison of IDL and Matlab" * q125.8, "Mlab" * q125.9, "Gauss" * q125.10, "MathViews" * q125.11, "Matcom: Matlab to C++ Compiler" =================================== q125.1. NAG http://www.nag.co.uk NAG in England http://www.nag.com/ NAG in USA [SJS]: Numerical, symbolic, statistical, and visualization libraries in Fortran 77, Fortran 90, C, Pascal, Ada, and parallel machine versions. High performance Fortran 90 and Fortran 77 compilers. NAG Ltd (The Numerical Algorithms Group) Wilkinson House Jordan Hill Road OXFORD OX2 8DR UK Tel: +44 1865 511245 NAG Inc 1400 Opus Place Suite 200 Downers Grove IL 60515-5702 USA Tel: +1 708 971 2337 =================================== q125.2. IMSL and PV-WAVE http://www.vni.com Visual Numerics, Inc. [SJS]: IMSL is a set of routines in C, C++, and Fortran libraries for general NA, statistics and graphics. PV-WAVE is a visual programming environment that includes IMSL as a "plug-in". Visual Numerics, Inc. IMSL and Stanford Graphics Products 9990 Richmond Avenue, suite 400 Houston, Texas 77042-4548 USA Tel: 800-222-4675 Tel: 713-784-3131 FAX: 713-781-9260 e-mail: marketing@houston.vni.com Visual Numerics, Inc PV-WAVE Products Division 6230 Lookout Road Boulder, Colorado 80301 USA Tel: 800-447-7147 Tel: 303-530-9000 FAX: 303-530-9329 info@boulder.vni.com [author]: * Comprehensive Mathematical Functionality * integration and differentiation * transforms * differential equations * linear systems * interpolation and approximation * eigensystem analysis * optimization * special functions * basic matrix/vector operations * nonlinear equations * utilities * Extensive Statistical Functionality * basic statistics * tests of goodness-of-fit * time series analysis and forecasting * analysis of variance * regression * nonparametric statistics * correlation * random number generation * cluster analysis * categorical and discrete data analysis * probability distribution functions and inverses * factor analysis * utilities * Exponent Graphics includes: * Presentation quality graphs for application development * Application program interface provides easy access to either FORTRAN or C * Two function calls can automatically produce one of over 30 different plot types. * Maximum flexibility for modifying plot chacteristics * Powerful interactive editing and customization tools * CGM, PostScript, HPGL and other device drivers * Support for popular graphics accelerators and output systems * Full Windows-based online documentation with hypertext links PV-WAVE is a software environment for solving problems requiring the application of graphics, mathematics, numerics and statistics to data and equations. PV-WAVE uses an intuitive fourth generation language (4GL) that analyzes and displays data as you enter commands. With it you can perform complex analysis, visualization, and application development quickly and interactively. Robust integrated graphics, numerics, data I/O, and data management has made PV-WAVE the number one selling Visual Data Analysis software family. PV-WAVE and the IMSL numerical and statistical routines, which are seamlessly integrated in PV-WAVE Advantage, are being used by more than 300,000 technical professionals on workstations worldwide. =================================== q125.3. Matlab and Simulink http://www.mathworks.com/ Mathworks The MathWorks, Inc. 24 Prime Park Way Natick, MA 01760-1500 (508) 653-1415 For a comparison of Matlab and IDL, see q125.7, "Comparison of IDL and Matlab". [SJS]: Matlab is an interactive general NA package, including graphics. A huge variety of "toolboxes" are available, both from the vendor and on the net, for various specialized NA areas: control systems, neural nets, optimization, symbolic math, and on and on. Simulink is modeling, simulation, and system analysis tool. [author]: MATLAB is a technical computing environment for high-performance numeric computation and visualization. MATLAB integrates numerical analysis, matrix computation, signal processing, and graphics in an easy-to-use environment where problems and solutions are expressed just as they are written mathematically - without traditional programming. MATLAB has evolved over a period of years with input from many users. In university environments, it has become the standard instructional tool for introductory courses in applied linear algebra, as well as advanced courses in other areas. In industrial settings, MATLAB is used for research and to solve practical engineering and mathematical problems. Typical uses include general purpose numeric computation, algorithm prototyping, and special purpose problem solving with matrix formulations that arise in disciplines such as automatic control theory, statistics, and digital signal processing (time-series analysis). MATLAB also features a family of application-specific solutions that we call toolboxes. Very important to most users of MATLAB, toolboxes are comprehensive collections of MATLAB functions (M-files) that extend the MATLAB environment in order to solve particular classes of problems. Areas in which toolboxes are available include signal processing, control systems design, dynamic systems simulation, systems identification, neural networks, and others. SIMULINK is a tool for modeling, analyzing, and simulating an extraordinarily wide variety of physical and mathematical systems, including those with nonlinear elements and those which make use of continuous and discrete time. As an extension of MATLAB, SIMULINK adds many features specific to dynamic systems while retaining all of MATLAB's general purpose functionality. Using SIMULINK, you model a system graphically, sidestepping much of the nuisance associated with conventional programming. =================================== q125.4. WavBox http://www.wavbox.com/ Wavbox email: info@wavbox.com A wavelet Toolbox for Matlab. [author]: A software toolbox for wavelet transforms and adaptive wavelet packet decompositions with new satisficing search algorithms. Requires Matlab. =================================== q125.5. CraySoft Libraries http://www.cray.com/PUBLIC/product-info/craysoft/CS_home_txt.html Cray product info http://www.cray.com/ Cray main http://www.cray.com/craysoft/ Craysoft main email: crayinfo@cray.com Corporate Headquarters: Cray Research, Inc. 655 Lone Oak Drive Eagan, Minnesota 55121 (800) 289-2729 or (612) 683-3030, [author] Fortran 90 compilers and NA library for Cray, Sparc, Macintosh, and Windows environments. * Seismic migration * Structural analysis * Financial modeling * Decision support analysis * General scientific * Computational chemistry * Computational physics * Intelligence, signal and image processing * Electronic simulation =================================== q125.6. IDL Research Systems Inc. http://www.rsinc.com/ Research Systems, Inc. Research Systems, Inc. 2995 Wilderness Place Boulder, CO 80301 USA Phone: 303-786-9900 email: info@rsinc.com For a comparison of IDL and Matlab, see q125.7, "Comparison of IDL and Matlab". IDL binaries are available at: ftp://ftp.rsinc.com/pub/idl Research Systems, Inc. ftp://boulder.colorado.edu/pub/idl U. of Colorado ftp://ftp.Germany.EU.net/shop/CreaSo/IDL Germany Following are two sets of comments on IDL: 1. By Pierre Maxted 2. By Amara Graps ================ 1. Comments by Pierre Maxted I find that IDL is good for "playing" with data. This works well for astronomers who seem to end up always wanting to do something a little different to last time to data that always has slightly different quirks everytime. I also find that it is a rather easy language in which to write my own routines. This is probably because I can start with interactive IDL to get the feel for what the data is like and what I want to do with it - this then becomes a simple batch file which can be turned into a routine if the procedure is useful - this seems to be a natural way to develop things. These libraries of routines are what makes IDL really powerful in my opinion. I found that adding the astronomy user's library to IDL was like adding wheels to a car. I would recommend to anyone considering using IDL to find out what libraries are out there (e.g. starting at the IDL WWW homme page). Whatever you add to the FAQ, make one point clear - calling IDL a fancy plotting package is like calling a Formula 1 racing car good for picking up the kids from school - IDL can do plotting, but that is not its strength. Well, I agree that the hard copy manuals are rather opaque but Version 4 of IDL has online help (Hyperhelp) that is rather good - especially since it had text searching capabilites so that you can go straight to the bit you need (usually). ================ 2. Comments by Amara Graps Following is an excerpt of comments by [Amara Graps]: For the full text of her review, please see: http://www.amara.com/papers/miscpap.html Amara Graps' Papers ftp://ftp.amara.com/papers/IDL_Matlab.txt Amara Graps' Papers via ftp If you install IDL without a valid license, you will get IDL's 7 minute demo mode. This mode is designed for users who are considering buying the package. IDL is a vector-based language that makes it easy to manipulate arrays and matrices. I've done testing comparing IDL speed to Fortran in various actions, and IDL was as fast as a Fortran program for the IDL array computations where loops were removed (i.e., when using implicit loops in IDL instead of explicit FOR statments). The scientific functions and procedures that come with IDL are often all that scientists need. In addition, there are net archives containing contributed routines. The archives at John Hopkins and at Goddard are especially good (see below). The language, for the most part is "open", i.e. you can see the text of any particular procedure or function, in case you doubt the technique, or want to modify it. Some functions and procedures are black-box, intrinsic functions or procedures, but not nearly as many as Matlab (see below) are. Most work in IDL is done at the command line level. However, IDL supplies rudimentary "widgets" to wrap a GUI around your procedures and functions. You can create buttons, menus, scrollboxes etc. Three-d plotting is currently not very well documented, and the way that IDL does it is very convoluted. Other users and I have complained about it, and I think RSI are taking steps to better document how to do it. Image procesing and animation is pretty slick. If you need to do "slicing and dicing" of a volume, in a way like Spyglass Dicer, IDL has a really great widget routine to do it. The IDL plots are high quality enough to use in initial journal submissions. RSI's support (writing to support@rsinc.com) is pretty good, I usually get responses within 24-34 hours. You have to pay yearly technical support costs, though- about $200 year (don't remember exactly how much). The Usenet group: comp.lang.idl-pvwave has some smart programmers giving answers if you don't want to pay for the IDL technical support. RSI usually doesn't answer questions on that newsgroup (they have a company policy against promoting IDL there because it's shared by two products: IDL and PV-WAVE). I've never liked the IDL documention very much. The information that you need probably *is* in the manuals, but it's somewhat hard to find (the manuals are organized in a wierd way). [Note, however, the comments by Pierre Maxted above]. The anonymous ftp sites below contain public domain IDL code. http://fermi.jhuapl.edu/www/s1r/idl/idl.html JHU/APL/S1R IDL library ftp://fermi.jhuapl.edu/pub/idl JHU/APL/S1R IDL library via ftp NASA IDL Astronomy User's Library, run by Wayne Landsman: http://idlastro.gsfc.nasa.gov/homepage.html NASA IDL Astro Library ftp://idlastro.gsfc.nasa.gov/pub NASA IDL Astro Library via ftp ftp://iuesn1.gsfc.nasa.gov IUE RDAF library at NASA ftp://cetus.colorado.edu/pub IUE RDAF library at U. of Colorado ftp://ftp.astro.psu.edu/pub/nefftp/icur ICUR Spectral Analysis Software ftp://legacy.gsfc.nasa.gov/rosat/software/idl IDL ROSAT software ftp://ftp.sma.ch/pub/idlmeteo IDLmeteo library ftp://eos.crseo.ucsb.edu/pub/idl ESRG library Hal Mueller has a Digital U.S. Map browser based on images created by Ray Sterner at Johns Hopkins University using IDL: http://www.zilker.net/~hal/apl-us// Map browser E. Loren Buhle, Jr. Ph.D. made a page on AVS IN MEDICAL TREATMENT PLANNING which also discusses IDL: http://archive.xrt.upenn.edu/0h/buhle/manuscripts/avs94_paper.html Medical Treatment Planning =================================== q125.7. Comparison of IDL and Matlab Following is an excerpt of a paper by [Amara Graps]: For the full text of her review, please see: http://www.amara.com/papers/miscpap.html Amara Graps' Paper ftp://ftp.amara.com/papers/IDL_Matlab.txt Amara Graps' Paper via ftp IDL is a package that began life as an image-processing utility that has grown to be a general-purpose numerical analysis tool. Matlab started as a numerical analysis package that now includes [at extra cost] image processing tools. Now the two have a similar scientific data-analysis environment, with capabililties to build GUI programs and do very robust data analysis. (Note: all prices are approximate October 1995 prices - SJS) They each cost about the same: ~$1500 for Mac and PC versions and more for Unix (~4000 -- single user to $15,000 -- unlimited number of users). Matlab is popular among education institutions because it has exceptional educational discounts. If you are an academic, Matlab can be had for $495 and each toolbox only $195. My NASA colleagues thought that MathWorks "nickled- and-dimed" them with the costs of the Toolkits (like the signal processing toolkit), but given what you get, it probably isn't that unreasonable. IDL seems to be more widespread in the NASA communities probably because the original developer used several spacecraft teams (Pioneer Venus and Voyager) as test beds for the IDL software. IDL is more of a true programming language. Matlab has scripts and functions and no way to explicitly type a variable. IDL has programs, procedures, and functions and a language syntax sort of like a cross between Fortran, Pascal, and APL. If you have programmed in Fortran before, then the syntax will be a snap to learn. Matlab's syntax is much more compact than IDL's. For example: x = transpose(y) in IDL is x=y' in Matlab. Matlab has many more built-in, intrinsic functions than IDL. MatLab has many optional Toolkits, such as a Signal Processing Toolkit and an Image Processing Toolkit, which are libraries of more intrinsic functions. Reading and writing files, and handling formats such as GIF, PICT, GDF, and custom formats, seems much easier in IDL than MATLAB. Handling directories is difficult in MATLAB when run on non-unix machines. Matlab has more types of graph types than IDL, and handling colors is simpler than IDL. However, I found most other Matlab graphical programming non-intuitive. It uses a system where each element in a graph is an "object." These objects can have sub-objects. So to change an element in a graph, say the axis color, you have to first find the object (a "get" function), and then set it to the color you want. IDL has system variables storing all graphics elements which can be easily changed. One can also customize a graph upon making the graph, with a keyword. IDL's technical support is pretty good, but Matlab's is better. Post a question on comp.soft-sys.matlab and either a developer, the company president, or a tech support person will respond that day. You can call them, too, but it's not a toll-free call. =================================== q125.8. Mlab http://www.civilized.com/MLAB.htmld/ Civilized Software Civilized Software, Inc. 7735 Old Georgetown Rd. #410 Bethesda, MD 20815 U.S.A. 1-301-656-4714 1-301-656-1069 fax Email: csi@civilized.com [author]: MLAB, (for Modeling LABoratory), is a program for interactive mathematical and statistical modeling. MLAB was originally developed at the National Institutes of Health. It includes curve-fitting, differential equations, statistics and graphics as some of its major capabilities. =================================== q125.9. Gauss email: info@aptech.com Aptech Systems has a web page on Gauss at: http://www.netaxis.qc.ca/~j.breslaw Aptech Systems Aptech Systems, Inc., Tel: (206) 432-7855, Fax: (206) 432-7832 23804 South East Kent-Kangley Road Maple Valley, WA 98038 USA (206) 432-7855 [author]: The GAUSS Mathematical and Statistical System is available for IBM PCs and compatibles as well as UNIX workstations As a complete programming language, the GAUSS system is both flexible and powerful. Immediately available to the GAUSS user is a wide variety of statistical, mathematical and matrix handling routines. Powerful data handling capabilities including a data loop allow transformations in a data set by directly using variable names inexpressions. This greatly simplifies data transformations and makes for shorter more readable programs. GAUSS can be used in either command mode(interactively) or in edit mode. In command mode; one-line commands, or small screen-resident programs, can be issued and the results of calculations seen immediately. In edit mode you can write complex programs and store them in files. GAUSS has over 400 functions built in, including LINPACK and EISPACK routines. =================================== q125.10. MathViews http://www.mathwizards.com MathViews [author] MathViews for Windows is matlab look-alike. It has a full set of linear algebra and signal processing functionality. It provides easy access to: matrix and linear algebra, digital signal processing, instrument control, image processing, time series analysis, data visualization and waveform display and editing. MathViews is highly compatible with the matlab syntax and will execute most matlab m-files with no changes. We also have WaveTool. WaveTool is an interactive software tool for creating, editing and analyzing captured waveshapes. Waveforms can be created using any combination of drawing, math expressions (matlab syntax), insertion from a library of waveforms or data values pasted from other applications such as Microsoft Excel. =================================== q125.11. Matlab to C++ Compiler and C++ Matrix Class Library http://www.mathtools.com Mathtools or email: info@mathtools.com [author]: MATCOM V2 is a Matlab(R) to C++ compiler. MATCOM creates MEX files and standalone C++ applications, with royalty free distribution. MATCOM translates Matlab code to C++, which is compiled by your optimizing C++ compiler. The resulting code runs significantly faster than the original interpreted source. Prior knowledge of C++ is not necessary to use MATCOM. The compilation is fully automated by a smart project manager. Fully functional, time limited evaluation version of MATCOM V2 can be downloaded freely from the MathTools web site. MAT, a Matlab Compatible C++ Matrix Class Library, is designed for development of advanced scientific high-level C++ code. Evalution version of the MAT can be downloaded from the home page noted above. The library includes Complex math, Binary and unary operators, Powerful indexing capabilites, Signal processing, File I/O, Linear algebra, String operations and Graphics. Over 300 mathematical functions are included in MAT. MAT supports matrices of doubles, floats, ints and chars mixed in the program. Images can be stored in matrices of chars, using 1/8 memory storage. On many applications, where 8 digits of precision are sufficient, float-precision matrices can save half the memory usage. Memory allocation and de-allocation is managed automatically. =================================== q125.12. O-Matrix http://www.omatrix.com Harmonic Software O-Matrix For Windows: [author]: O-Matrix is a complete solution for analysis, visualization, and rapid application development, (RAD). The interactive environment enables both point-and-shoot oriented analysis for rapid solutions and a powerful language and debugger for large demanding applications. The integrated matrix language provides performance that far exceeds typical integrated environments and often rivals compiled code for numerically-intensive applications. SPT - The Signal Processing Toolbox for O-Matrix: SPT for O-Matrix provides a broad, extensible set of functions and utilities that expands the capabilities of O-Matrix in the area of digital signal processing. Built on the high-performance capabilities and flexibility of O-Matrix, the toolbox contains tools for algorithm development, data analysis, and visual presentation. SPT enables the rapid development of robust, high-performance applications in areas including digital filtering, spectral estimation, digital communication system simulation, time series analysis, real time control, geophysics, and more. The package comes with complete source code, online tutorials and examples, and unlimited free technical support. KBF - The Kalman Filter Interface Pack for O-Matrix: The KBF interface simplifies the design of a filter or smoother by dividing the design process into simple steps with each step corresponding to an input window or dialog. Extensive plotting of results, including residuals and correlations is also automated. In addition, a simulation feature is included to aid in testing the validity of the design. KBF is used in a wide range of applications such as tracking, weather and earth process modeling, economic forecasting and bioengineering. Harmonic Software Inc. 800-895-4546 / 206-367-8742 =================================== q125.13. UCALC http://www.ucalc.com UCALC for Windows [author]: UCALC includes many features useful for scientific calculations and graphing: * Scientific Expression Evaluator * Eq graphing: Cartesian, polar, 3D, parametric, data files * Equation Solver * Numerical Integrator * Many scientific functions * Supports user functions and variables * Built-in and user-defined numeric formats * Unit Converter * Summation Tables * Financial Modules * General Ledger In addition to the above, UCALC introduces an innovative feature - User Solution Modules (USM). USMs are created by simply providing a math formula, and giving it a name. UCALC parses the formula and creates a template form which allows the user to solve for any item by simply filling in the blanks. Useful USMs are included to get you started. =========================================================================== q135. Newsgroups for NA Newsgroups related to numerical analysis are: sci.math.num-analysis The primary group for NA issues. sci.math.symbolic Covers symbolic algebra: Mathematica, Maple, Macsyma, Derive, Reduce, Mcad, etc. comp.soft-sys.math.mathematica: Devoted to Mathematica. sci.op-research Covers operations research, linear programming, non-linear programming. sci.stat.math Covers probability and statistics. sci.math Covers a broad range of mathematical subjects, at levels from trivial to advanced. sci.math.research Covers advanced mathematics, and is generally theoretical as opposed to applied. =========================================================================== q140. Professional Societies for NA * q140.1, "The (AMS) American Mathematical Society" * q140.2, "(SIAM) The Society for Industrial and Applied Mathematics" * q140.3, "ACM, Inc. (Association for Computing Machinery)" * q140.4, "IEEE The Institute of Electrical and Electronic Engineers" =================================== q140.1. The (AMS) American Mathematical Society http://www.ams.org/ AMS email: ams@math.ams.org General organization information, preprint titles, pointers to other preprint servers and net resources. Also includes: MathDoc, the document delivery service offered by the AMS, provides copies of original journal, collection and conference proceedings articles from publications covered by Mathematical Reviews, Current Mathematical Publications, and the MathSci database. This costs roughly US$14. per ten pages, as of October 1995. MathSciNet is a searchable database available on the World Wide Web. It is based on the data in Mathematical Reviews and Current Mathematical Publications, leading publications that catalog and review research literature in mathematics. This costs roughly US$5500. per year, as of October 1995. =================================== q140.2. (SIAM) The Society for Industrial and Applied Mathematics http://www.siam.org/ SIAM email: siam@siam.org General organizational information, tables of contents of SIAM journals, and recently accepted articles. Society for Industrial and Applied Mathematics 3600 University City Science Center Philadelphia, PA 19104-2688 (215) 382-9800 Journals include: SIAM Scientific Computing SIAM Matrix Analysis SIAM Control and Optimization =================================== q140.3. ACM, Inc. (Association for Computing Machinery) http://acm.org/ ACM email: ACMHELP@acm.org General organizational information, info on journals and conferences. Of particular interest are: Transactions on Mathematical Software (TOMS) http://www.acm.org/pubs/toms/ ACM TOMS Collected Algorithms of the ACM (CALGO) Software can be found in netlib (toms directory); see q115.1, "Netlib". SIGNUM (Special Interest Group in Numerical Mathematics) http://www.acm.org/sig_hp/SIGNUM.html ACM SIGNUM ACM Headquarters One Astor Plaza 1515 Broadway New York, New York 10036 212-869-7440 =================================== q140.4. IEEE The Institute of Electrical and Electronic Engineers http://www.ieee.org IEEE email: member.services@ieee.org General organizational information, journals, books, conferences. Tel: (800) 678-IEEE Tel: (212) 705-7900 =========================================================================== q145. Electronic Newsletters for NA http://www.netlib.org/na-net/na_home.html NA-Net http://www.netlib.org/na-digest/topics NA-Net Index email: nanet@na-net.stanford.edu [author]: The NA-Net is a system developed to serve the community of numerical analysts and other researchers. The Na-Net provides two independent databases and a weekly digest to its members. The Email Database is the electronic mail address of each of its members, and is capable of forwarding mail to them. In addition, this database serves as the distribution list for the NA Digest (see below). The White Pages Database is basically a directory service. It provides a way to exchange personal information among its members. Contained in the database are phone numbers, postal mailing addresses, research interests, affiliations, etc. The NA Digest is a way to provide its members with a weekly collection of articles on topics related to numerical analysis and those who practice it. To get on the mailing list for the digest and enter yourself in their database, you can use email or the World Wide Web. Take advantage of this very useful service! =========================================================================== q150. Electronic Journals for NA Indices of Journals See the large list of online journals, and other resources, at Penn State's Mathematics web site. http://www.math.psu.edu/OtherMath.html Penn State Mathematics See also: http://rattler.cameron.edu/swjpam/ The Southwest Journal of Pure and Applied Mathematics =================================== BIT http://math.liu.se/BIT/ BIT BIT emphasizes numerical methods in approximation, linear algebra, and ordinary and partial differential equations, but also publishes papers in areas such as numerical functional analysis and numerical optimization. =================================== ETNA (Electronic Transactions in Numerical Analysis). http://etna.mcs.kent.edu/ ETNA An online peer reviewed journal. Keyword searching. Most documents are postscript and may be downloaded. Started in 1993. Indexes only itself. =================================== EJDE, The Electronic Journal of Differential Equations http://ejde.math.swt.edu/ EJDE A purely on-line peer-reviewed journal. =================================== The Electronic Journal of Linear Algebra http://gauss.technion.ac.il/iic/ela/ Electronic J. of Linear Algebra =================================== New York Journal of Mathematics http://nyjm.albany.edu:8000/nyjm.html NY J. of Mathematics Appears more abstract than applied. Started in 1994. Indexes only itself. =========================================================================== q155. Online Preprints for NA General See the listings for professional societies, especially the AMS, in q140, "Professional Societies for NA". Springer-Verlag Preprints: See the Springer-Verlag preprint service via email. Not free. http://www.springer.de/server/services.html Springer Verlag Virtual Library Math Journals Preprints http://euclid.math.fsu.edu/Science/Preprints.html Virtual Lib Math Jnls Preprints Links to numerous organizations offering preprints. =========================================================================== q160. Miscellaneous Web Sites for NA See also: * q160.1, "C++ Resources for NA" * q160.2, "Math FAQ" * q160.3, "Math Dictionary" Caltech guide to mathematics resources http://www.ama.caltech.edu/resources.html Caltech Guide to Math Resources Good collection of pointers to quality sites. Penn State's Math Guide http://www.math.psu.edu/OtherMath.html Penn State Math Guide Huge site with information on many fields within mathematics. U. C. Berkeley gopher://math.berkeley.edu U.C. Berkeley gopher site (large) ftp://math.berkeley.edu /pub U.C. Berkeley ftp site (large) http://math.berkeley.edu/ U.C. Berkeley ftp site (small) Berkeley has a large gopher & ftp site, including courseware, pointers to inet libraries, lecture notes, seminars, and software. Indiana University: Mathematical Computing Resources Guide http://www.indiana.edu/~statmath/mathsites.html Indiana University. An excellent large site. The World-Wide Web Virtual Library: Mathematics http://euclid.math.fsu.edu/Science/math.html Virtual Lib: Mathematics Specialized fields (topology, cryptography, optimization, etc), academic departments, miscellaneous math societies and institutes, pointers to commercial software, newsgroups, nice collection of preprints pointers, electronic journals U. Tennessee Knoxville Mathematics Archives WWW Server http://archives.math.utk.edu/ U. Tenn Knoxville Math Archives MathSoft's Favorite Mathematical Constants http://www.mathsoft.com/asolve/constant/constant.html Mathsoft Constants Constants and algorithms for their generation. The reclusive Dr. TP's list of www sites for numerical methods http://tonic.physics.sunysb.edu/docs/num_meth.html Dr. TP's NA page, USA http://www.math.psu.edu/dna/num_methods.html Dr. TP's NA page, USA http://zar.unizar.es/www/num_meth.html Dr. TP's NA page, Spain http://www.labyrinth.net.au/~ctrans/tomasz.html Dr. TP's NA page, Australia Amara Graps' list of science links http://www.amara.com/science/science.html Amara Graps' list A Catalog of Mathematics Resources on WWW and the Internet http://mthwww.uwc.edu/wwwmahes/files/math01.html Catalog of Math Resources By M. Maheswaran, University of Wisconsin Marathon Center. Another large site, with a sizeable section on Applied Mathematics. Altug Koker's list of simulation software http://piranha.eng.buffalo.edu/simulation/comp.simulation/FAQ.html Simulation Software (See his Q15.). Contains pointers to software for: aerospace, automotive, chemistry / biotechnology, graphics and imaging, electronics / electrical engineering, petroleum The Yahoo server's index of Mathematics topics. http://www.yahoo.com/Science/Mathematics Yahoo's Math index Includes commercial products, conferences, journals, and various subfields of mathematics, primarily in applied mathematics. Scientific Applications on Linux Web Page http://lusk1.mines.edu/hjjou/linux_old.html Scientific Apps on Linux Contents: * Commercial Scientific Software * MatLab Alike and Related Packages * Mathematics and Statistics * Finite or Boundary Element * Numerical Analysis * Signal, Communication, Data and Image Processing/Visualization * CAD, Graph, Drawing and Modelling Tools * Scientific Data Plotting Packages * Scientific Data Plotting Libraries * General Purpose Graphic Libraries * Word Processing, Typesetting And Office Software * X-Window GUI Construction * Misc Scientific Packages or Libraries and Links * Other Links For a wide variety of links to mathematical and scientific software, see: http://www-ocean.tamu.edu/~baum/linuxlist-m.html S. Baum's site =================================== q160.1. C++ Resources for NA Ajay Shah's index of resources for NA in C or C++ http://www.math.psu.edu/FAQ/numcomp-free-c.txt Ajay Shah's C++ Resources ftp://usc.edu/pub/C-numanal/numcomp-free-c.gz Ajay Shah's C++ Resources via ftp ftp://ftp.math.psu.edu/pub/FAQ/numcomp-free-c Ajay Shah's C++ Resources via ftp The Object-Oriented Numerics Page http://monet.uwaterloo.ca/blitz/oon.html Object-Oriented NA Pointers to C++ libraries and classes. Also see q590, "Skip Carter's Home Page". Also see Roldan Pozo's page: http://math.nist.gov/acmd/Staff/RPozo/index.html Pozo's page Also see Joerg Arndt's web page on FFT code, at q240, "Transforms (FFT, etc) and digital signal processing (DSP)" =================================== q160.2. Math FAQ The sci.math FAQ by Alex Lopez-Ortiz is a good reference for many mathematical questions. It is more oriented towards pure mathematics than NA. http://daisy.uwaterloo.ca/~alopez-o/math-faq/math-faq.html Alex Lopez-Ortiz's list ftp://rtfm.mit.edu/pub/usenet-by-group/news.answers/sci-math-faq/ Alex Lopez-Ortiz's list via ftp =================================== q160.3. Math Dictionary For an on-line mathematics dictionary, see: http://www.gps.caltech.edu/~eww/math/math.html Eric's Treasure Trove =========================================================================== q165. Books, With and Without Software, for NA See also specific subject areas in this FAQ at q80, "NA FAQ: Table of Contents". For an on-line mathematics dictionary, see: q160.3, "Math Dictionary". Acton, Forman S. 1990 Numerical methods that [usually] work Harper & Row, Publishers ISBN 0883854503. [Daniel Pick] This book is almost worth its price just for the cathartic interlude in the middle of the book on what not to compute. You should require your students to read it, learn it, live it. You may find just giving them the railroad problem found at the beginning of the book a worthwhile exercise. [Bill Frensley] Amen, brother! The only complaint that I have about Acton's interlude is that after demolishing the notion of "fitting exponential data," he fails to point out that this is the inverse Laplace transform problem. Perhaps if everyone read this and made the connection, we would be spared the monthly "is there any good algorithm for the inverse Laplace transform?" Arge, Bruaset and Langtangen, editors Modern Software Tools for Scientific Computing Contains selected contributions from the SciTools'96 conference. Ssee http://www.oslo.sintef.no/SciTools96/ SciTools96 This book consists of papers discussing topics related to computational differential equations, computational geometry and software development. For further information, see http://www.birkhauser.com/cgi-win/ISBN/0-8176-3974-8 birkhauser Baker, Louis. 1991 C Mathematical Function Handbook Daehlen and Tveito, editors Numerical Methods and Software Tools in Industrial Mathematics Birkhauser It includes an introduction to object-oriented numerics and a presentation of the software tools Diffpack and Siscat. See http://www.oslo.sintef.no/NAM software tools Also a series of challenging applications are discussed. For more information, see http://www.birkhauser.com/cgi-win/ISBN/0-8176-3973-X birkhauser Dahlquist, Germund; Bjorck, Ake 1974 Numerical Methods translated by Ned Anderson, Prentice-Hall, 1974. A nice mix of theory and practice. Used as a text at Stanford, among other places.[John Chandler] Dubois, Paul. 1996 Object Technology for Scientific Computing Object-Oriented Numerical Software in Eiffel and C Prentice Hall, 1996, paper, 350 pages ISBN 0-13-267808-X Comes with CD-ROM Price: $40.00 Forsythe, George; Moler, Cleve B. 1967 "Computer Solution of Linear Algebraic Systems" Prentice-Hall I consider this possibly the best textbook I have ever seen in any field. Covers only linear systems, of course.[John Chandler] Golub, Gene H.; Van Loan, Charles F. 1996 Matrix Computations, Third edition Johns Hopkins, Baltimore ISBN 0-8018-3739-1 Telephone: 410-516-6900 [SJS] A classic for handling matrices. Many current programs are based on this text. Good mix of theory and implementation. Golub, Gene H. 1984 Studies in Numerical Analysis Mathematical Association of America ISBN 0883851261. [Daniel Pick] This contains several outstanding essays from several numerical analysts, including Wilkinson's The Perfidious Polynomial, which explains why rootfinding of polynomials numerically is such a tricky problem. It gives an great introduction to the thinking of recent numerical analysts. [Amara Graps] All of the chapters are really good- my favorites are: "Fast Poisson Solvers" and "Multigrid Methods for Partial Differential Equations." Kahaner, David; Moler, Cleve; Nash, Stephen. 1989 Numerical Methods and Software Prentice Hall, Englewood Cliffs, NJ ISBN 0-13-627258-4 Telephone: 800-947-7700 An excellent book which touches on a variety of topics and makes use of the publicly available software like the QUADPACK and SLATEC libraries to illustrate the points. [Vijay Gupta] Knuth, Donald E. 1981 The Art of Computer Programming: Seminumerical algorithms, 3rd edition. Addison-Wesley. Once was the reference; now a bit dated. Lau, H. T. 1995 A Numerical Library in C for Scientists and Engineers CRC Press, Boca Raton, FL ISBN 0-8493-7376-X Telephone: 407-994-0555 This book is basically a compilation of program listings, with a diskette containing source code. The listings are accompanied by brief overviews of the algorithms involved, and generally include references. There is no discussion of theory. While the text by Stoer & Bulirsch is at the theoretical end of the NA spectrum, this text is at the application end. Although the program calling parameters are well described, as far as I could see the programs contain no internal documentation whatsoever. Although this book is copyright 1995, the references contain one source dated 1992 (Press et al's volume), one source dated 1981 (NUMAL in Fortran), and one source dated 1980 (NUMAL in Algol). The remainder of the references are dated 1976 and earlier. It's not clear to me that this book offers anything over Press et al's text. Lau has far less discussion of theory and methodology, and while Press's internal documentation of programs is poor, Lau's book has none whatsoever. [SJS] Mathews, John H. 1992 NUMERICAL METHODS: for Mathematics, Science & Engineering Prentice Hall, Englewood Cliffs, NJ ISBN 0-13-624990-6 and ISBN 0-13-625047-5 Source for the programs is available in several languages: ftp://ftp.mathworks.com/pub/books/mathews/matlab Matlab (ftp) ftp://ftp.mathworks.com/pub/books/mathews/c C (ftp) ftp://ftp.mathworks.com/pub/books/mathews/fortran Fortran (ftp) ftp://ftp.mathworks.com/pub/books/mathews/pascal Pascal (ftp) ftp://ftp.wri.com/pub/Publications/BookSupplements/Mathews-1996/ Mathematica (ftp) http://www.wri.com/MathSource/Publications/BookSupplements/Mathews-1996/0207-874 Mathematica (http) Muller, Jean-Michel, 1997 Elementary functions, algorithms and Implementation Birkhauser Boston. See: http://www.birkhauser.com/cgi-win/ISBN/0-8176-3990-X Birkhauser http://www.ens-lyon.fr/~jmmuller/book_functions.html Muller Nash, John C., 1987, 1996 Nonlinear Parameter Estimation: an integrated system in BASIC Sample chapters and portions of the code are at: http://www.nashinfo.com/~nis/ Nash's Sample Chapters Peters, Martin, 1997 Solving Problems in Scientific Computing Using Maple and MATLAB All Maple and MATLAB programs can be obtained from: ftp://ftp.inf.ethz.ch/pub/software/SolvingProblems/ed3/ Peters text Petkovsek, Marko; Wilf, Herbert; Zeilberger, Doron. 1995 "A=B" Publisher: AK PETERS, Ltd., 289 Linden Street, Wellesley, MA 02181 Telephone to (617) 235-2210. $39. ISBN 1-56881-063-6 [Donald Knuth] Science is what we understand well enough to explain to a computer. Art is everything else we do. During the past several years an important part of mathematics has been transformed from an Art to a Science: No longer do we need to get a brilliant insight in order to evaluate sums of binomial coefficients, and many similar formulas that arise frequently in practice; we can now follow a mechanical procedure and discover the answers quite systematically. I'm especially pleased to see the appearance of this book, because its authors have not only played key roles in the new developments, they are also master expositors of mathematics. It is always a treat to read their publications, especially when they are discussing really important stuff. Science advances whenever an Art becomes a Science. And the state of the Art advances too, because people always leap into new territory once they have understood more about the old. This book will help you reach new frontiers. Press, William H.; Teukolsky, Saul A.; Vetterling, William A.; Flannery, Brian P. 1992 Numerical Recipes in C, Second edition Cambridge University Press, Cambridge and New York ISBN 0-521-43108-5 Text ISBN 0-521-43720-2 Example book ISBN 0-521-43714-8 PC diskette, 5.25 inch ISBN 0-521-43724-5 PC diskette, 3.5 inch ISBN 0-521-43715-6 Mac diskette, 3.5 inch Telephone: 212-924-3900, 800-872-7423 Seperately purchasable diskette contains C source code. A compendium of a wide variety of NA areas. Contains some good introductions to theory and overviews of algorithms. The bridge from algorithm overview to implementation is often missing. The programs should be viewed with some skepticism. They are often poorly documented, and some users have reported numerical problems with the various programs. [SJS] Additional information may be at: http://nr.harvard.edu/numerical-recipes Numerical Recipes ftp://ftp.std.com/vendors/Numerical-Recipes Numerical Recipes via ftp email: nr@nr.com Some Numerical Recipes Reviews are at: http://www.lysator.liu.se/c/num-recipes-in-c.html N.R. Review http://math.jpl.nasa.gov/nr N.R. Reviews http://math.jpl.nasa.gov/nr/nr.html N.R. Review Sedgewick, Robert. 1988 Algorithms, Second edition Addison-Wesley, Reading, Mass ISBN 0-201-06673-4 Telephone: 617-944-3700, 800-822-6339 Stoer, Josef; Bulirsch, Roland 1980 Introduction to Numerical Analysis Springer-Verlag, New York, 1980 ISBN 0-387-90420-4 Telephone: 212-460-1500, 800-777-4643 The classic NA text. A standard for graduate and upper undergraduate courses in NA. Difficult going, but covers a wide set of fields in depth. Strong theoretical orientation. [SJS] Strang, Gilbert 1988 Linear Algebra and It's Applications, Third Edition Harcourt Brace, San Diego ISBN 0-15-551005-3 A well-written introduction to theory. Trefethen, Nick, and Bau, David 1997 Numerical Linear Algebra Siam Tyrtyshnikov, Eugene E, 1997 A Brief Introduction to Numerical Analysis. Birkhauser, Boston. [author]: "Without any doubt, there are many quite good and excellent books on the subject. But I know definitely that I did not realize this when I was a student. In this book, my first desire was to present those lectures that I wished I would have heard when I was a student." Watkins, David S. 1991 Fundamentals of Matrix Computations John Wiley, New York, 1991. ISBN 0-471-61414-9 Telephone: 212-850-6000, 800-225-5945 More readable than Stoer & Bulirsch or Golub & Van Loan, and contains some implementation techniques not present in Golub & Van Loan. Has good descriptions of theory and implementations, and many implementations are covered as straightforward exercises. Not as wide a variety of fields as either Golub & Van Loan or Stoer & Bulirsch. [SJS] ### many others! =========================================================================== q205. Dense (Non-Sparse) Linear Algebra Systems The best resources for linear algebra are: The texts by Golub & Van Loan and by Watkins. On the net, library package LAPACK, with BLAS, from netlib (see q115.1, "Netlib") is a widely recommended replacement for EISPACK and LINPACK. It handles dense matrices only. As far as complete packages, nearly all NA packages, both on the net and commercial, include linear algebra as part of their core. See the listings above. See also: Jack Dongarra's list of Linear Algebra Software http://www.netlib.org/utk/people/JackDongarra/la-sw.html Dongarra's list =================================== q207. Sparse Linear Algebra Systems Netlib (see q115.1, "Netlib") has a number of libraries for handling sparse systems. See the netlib directories: sparse, sparse-blas, sparsepak. See also: Jack Dongarra's list of Linear Algebra Software http://www.netlib.org/utk/people/JackDongarra/la-sw.html Dongarra's list [N. Sukumar]: Recommends the TEMPLATES book ["TEMPLATES for the soln of linear systems: building blocks for iterative methods"] that is availabe in postscript format at netlib. Also in the same dir is code (in C and Fortran) for algorithms discussed in the book. "The book is awesome (easy to read, good pointers on selection of solvers etc.), especially for one who is not aware of how and why sparse solvers work." netlib, in the directory: templates [N. Sukumar] also recommends: The sparse package SPARSKIT which also has the solvers built-in; there are many other feature in addition [matrix conversion/ formatting, plotting, statistics etc]. ftp://ftp.cs.umn.edu/.archive2/users/saad/SPARSKIT U. Minnesota SPARSKIT ftp://ftp.cs.umn.edu/.archive2/sparse/SPARSKIT2 U. Minnesota SPARSKIT ftp://icarus.riacs.edu/pub/SPARSKIT U. Minnesota SPARSKIT =========================================================================== q210. Random Number Generators (RNGs) * q210.1, "Web Sites for Random Number Generators" * q210.2, "References for Random Number Generators" * q210.3, "Types of Random Number Generators" * q210.6.1, "Linear Congruential Generators (LCG)" * q210.6.2, "Add-with-carry and Subtract-with-borrow Generators (AWCG, SWBG)" * q210.6.3, "Multiply-with-carry Generators (MWCG)" * q210.6.4, "Inversive Conguential Generators (ICG)" * q210.7, "Tests for Randomness" * q210.8, "Commercial RNGs and Hardware RNGs" =================================== q210.1. Web Sites for Random Number Generators ftp://odin.mda.uth.tmc.edu/pub/source RANLIB pLab is an excellent web site created by the Department of Mathematics at the Salzburg University. It covers RNGs and tests for randomness, and contains publications, software, and pointers to other resources. Use either: http://random.mat.sbg.ac.at/ Salzburg Dept. Mathematics http://www.mat.sbg.ac.at/home.html Salzburg Dept. Mathematics Additional services may be available from pLab -- see: http://random.mat.sbg.ac.at/team pLab Overview Another web page with info on RNGs is Skip Carter's page at Taygeta: http://www.taygeta.com/random.html Skip Carter's page See also the Diehard page, described at: q210.7, "Tests for Randomness" Also see Pierre L'Ecuyer's papers: http://www.iro.umontreal.ca/people/lecuyer/papers.doc L'Ecuyer ftp://ftp.iro.umontreal.ca/pub/simulation/lecuyer/papers L'Ecuyer ftp Info on 1/f noise, called "flicker noise" or "pink noise", is at: http://linkage.rockefeller.edu/wli/1fnoise Wentian Li's site =================================== q210.2. References for Random Number Generators References: V.S.Anashin. Uniformly distributed sequences over $p$-adic integers. - In:" Number Theoretic and Algebraic Methods in Computer Science. Proc. Int'l Conf. Moscow, June - July 1993". Alf J van der Poorten, Igor Shparlinsky and Horst G. Zimmer - editors. Published by World Scientific, 1995. Pp. 1 -18. Anashin, V. S., Uniformly distributed sequences of $p$-adic integers (Russian), Mat. Zametki 55 (1994), no. 2, 3--46, 188; MR 95f:11096 There is an English translation of this paper made by Plenum Publ. Corp. Anashin, V.S. Uniformly distributed sequences in computer algebra or how to construct random number generators. Translated from Itogi Nauki i Tekhniki, Seria Sovremennaya Matematika i Ee Prilozheniya. Tematicheskie Obzory, Vol. 31, Computing Mathematics and Cybernetics - 2, 1995. 1072 - 3374/96/0000 - 0001. Plenum Publisning Corp., 1996 Anashin, V. S., Solvable groups with operators and commutative rings having transitive polynomials (Russian), Algebra i Logika 21 (1982), no. 6, 627--646; MR 85d:20028 Law, Averill M, and Kelton, W. David. 1991 Simulation Modeling & Analysis, Second edition McGraw Hill, New York Banks, Jerry. Handbook on Simulation Wiley. Bratley, P., Fox, B.L. & Schrage, L.E. 1987 A guide to simulation, 2nd edition Springer Devroye, Luc. 1986 Non-uniform random variate generation Springer-Verlag, New York [SJS] This is the most complete book I've found on generating non-uniform random values. L'Ecuyer, Pierre. Random numbers for simulation. Comm. ACM 33, 85-97 (1990) . L'Ecuyer, Pierre. Uniform random number generation. Annals of operations research 53 (1994), 77. Marsaglia, George. JACM 12 (1965), 83-89. Marsaglia, George. "Random numbers fall mainly in the planes", Proc. Nat. Acad. Sciences USA, 61 (1968), 25-28. Marsaglia, George. "Remarks on choosing and implementing random number generators", Communications of the ACM v 36 n 7 (July 1993), p 105-107. Marsaglia, George and Zaman, Arif. "A new class of random number generators". The annals of applied probability 1, 3, (1991), p. 462-480. Motwani, Rajeev and Raghavan, Prabhakar 1995 Randomized Algorithms Cambridge University Press Sullivan, Stephen. "Another test for randomness", Communications of the ACM 36, 7 (July 1993), p 107. Tezuka, Hsh, L'Ecuyer, Pierre, and Couture, Raymond. "On the lattice structure of add-with-carry and subtract-with- borrow random number generators", ACM Trans on Modeling and Computer Simulation 3, 4 (October 1993), p. 315-331. Still more references, courtesy of [Ripley]: James, F. (1990) A review of pseudorandom numbers. Comp. Phys. Comm. 60 329--344. Morgan, B.J.T. (1984) Elements of simulation. Chapman & Hall. Ripley, B.D. (1983) The computer generation of random variables - a tutorial. Int. Statist. Rev. 51 301--319. Ripley, B.D. (1987) Stochastic Simulation. Wiley, New York Ripley, B.D. (1990) Thoughts on pseudorandom number generators. J. Comput. Appl. Math. 31, 153--163. A revised version of the last is available by anonymous ftp from ftp://markov.stats.ox.ac.uk/pub/simul/simul/prng.ps.Z Ripley's Paper Eichenauer-Herrmann, J. (1992) Inversive congruential pseudorandom numbers: a tutorial. Int. Statist. Rev. 60, 167-176 =================================== q210.3. Types of Random Number Generators Random number generators typically consist of three components: * The basic generator, described further below. * Some generators contain a shuffle box. First described in Marsaglia 1965. Also described in Knuth 1981 and Press et al 1992. * A transformation to the desired probability distribution. See Press et al 1992 or, better yet, Law 1991 or Devroye 1986. Thisted's text as well? ### There are four common types of basic generators. * q210.6.1, "linear congruential (LCG)" * q210.6.2, "add-with-carry and subtract-with-borrow (AWCG, SWBG)" * q210.6.3, "multiply-with-carry (MWCG)" * q210.6.4, "inversive conguential (ICG)" =================================== q210.6.1. Linear Congruential Generators (LCG) Linear congruential generators are of the form x(n) = a * x(n-1) + b mod M A good discussion of this type is in the text by Press et al. These are by far the most common form in use, and have periods in the range 10^6 to 10^9 when using 32 bit words. Unfortunately, they have some unpleasant properties. When taken in pairs, triplets, or n-tuples, the random values often fall on only a few planes in n-space. Using a shuffle box can break up this uniformity. For more information on the problems associated with linear congruential generators, see Marsaglia 1968, Marsaglia 1993 and Sullivan 1993. See also Marsaglia's web site, described under q210.7, "Tests for Randomness". =================================== q210.6.2. Add-with-carry and Subtract-with-borrow Generators (AWCG, SWBG) Add-with-carry generators have the form: x(n) = x(n-s) + x(n-r) + carry mod M Subtract-with-borrow generators have the form: x(n) = x(n-s) - x(n-r) - carry mod M See Marsaglia 1991. These generators have much longer periods, from 10^200 to 10^500, than LCGs, and they are almost as fast as LCGs. Unfortunately they too have the problem of falling mainly on the planes. See Tezuka 1993. Again, a shuffle box, as described in Press et al, can eliminate this problem. The implementation by Marsaglia and Zaman may be found at: ftp://ftp.wustl.edu/systems/ibmpc/msdos/math/fsultra1.zip Marsaglia =================================== q210.6.3. Multiply-with-carry Generators (MWCG) Multiply-with-carry generators have the form: x(n) = a*x(n-1) + carry mod M [George Marsaglia]: Here is a simple version, one so simple and good I predict it will be the system generator for many future computers: x(n)=a*x(n-1)+carry mod 2^32 With multiplier 'a' chosen from a large set of easily found integers, the period is a*2^31-1, around 2^60, and I have yet to find a test it will not pass! [Charles Knechtel]: George Marsaglia has some interesting new ideas for pseudorandom number generation using MWCG and MWCG combined with other pseudorandom number generators (RNGs); these new ideas are implemented as part of the Diehard suite of RNG tests. The best of these seem to pass all the Diehard tests, even tests that many common pseudorandom number generators fail. Source is at: ftp://stat.fsu.edu/pub/diehard Diehard Also see: http://stat.fsu.edu/~geo/diehard.html Diehard documentation =================================== q210.6.4. Inversive Conguential Generators (ICG) Inversive congruential generators are of the form x(n) = a * ~(x(n-1)) + b mod M where: M is prime "~y" denotes the multiplicative inverse of y in the field over {0, 1, ..., M-1} using arithmetic modulo M, and ~0 is 0. ICGs do not have the "mainly in the planes" problem. See the pLab, described above at q210.1, "Web Sites for Random Number Generators", for more info on ICGs. [Charles Knechtel]: Marsaglia's Diehard suite of RNG tests, at q210.7, "Tests for Randomness" also contains a subroutine named makeinvc which implements an ICG and generates a file of pseudorandom numbers named INVCONG.32; however, examination of the FORTRAN source code for makeinvc shows that a modulus M equal to 2^32 was used (see file makewhat.f. Eichenauer-Herrmann (1992, p. 173, 175) notes that certain ICGs with power of two modulus have distributional disadvantages compared to the "excellent quality" of ICGs with prime modulus. Indeed, the documentation for INVCONG.32 remarks that makeinvc fails to pass many of the Diehard tests (see the last section of file makef.txt from the Diehard archive fortran.tar.gz. An ICG with prime modulus should have better uniform properties than makeinvc, and Otmar Lendl's ICG implementation might be speedier than makeinvc. =================================== q210.7. Tests for Randomness The Diehard suite of RNG tests, by George Marsaglia, is available with a rotating 3-D graph showing the collinearities of tuples from: http://stat.fsu.edu/~geo/diehard.html Diehard overview For snapshots of some of the graphs, see: http://euler.bd.psu.edu/~naras/diehard/snapshots.html Diehard snapshots For just the source or executables, use: ftp://stat.fsu.edu/pub/diehard/ Diehard source A GUI version of Diehard is in preparation by Dr. Balasubramanian Narasimhan at: http://stat.stanford.edu/~naras/diehard/snapshots.html Diehard GUI Also see pLab, described above at q210.1, "Web Sites for Random Number Generators", for descriptions of some tests. =================================== q210.8. Commercial RNGs and Hardware RNGs http://www.protego.se Protego Hardware Generator [author]: No more unreliable generation of crypto keys and random numbers in software, the viable alternative is here! SG100 Security Generator is an easy to use easy to integrate hardware random number generator that connects to the standard serial port. Complete with driver software for Windows 95/Windows NT and example programs in source. SG100 is the choice if you want to strengthen and enhance your encryption, statistics and simulation software. =========================================================================== q215. Function Evaluation Point to some sources in netlib, statlib and elsewhere? If you'd like to write a paragraph for the FAQ on function evaluation, please contact me ... =========================================================================== q220. Finding Roots This is a standard topic in nearly all general texts on NA. If you'd like to write a paragraph for the FAQ on finding roots, please contact me ... =========================================================================== q230. Curve Fitting, Data Modelling, Interpolation, Extrapolation This vague heading covers a multitude of closely related endeavors. There are many approaches, described in the following sections. * q230.1, "Interpolation" * q230.2, "Statistical Curve Fitting" * q230.4, "Time series analysis" * q230.6, "Splines" * q230.7, "Nearest Neighbor algorithms" * q230.8, "Fitting a circle to a set of points" Other approaches to data modelling are: * q550, "Neural Networks". * q245, "Wavelets". =================================== q230.1. Interpolation For one dimensional work, see Stoer & Bulirsch 1980 or Press et al 1992. No doubt some of the techniques described there can be found in netlib (see q115.1, "Netlib") by using the NIST guide (see q110.1, "Indices of NA Software"). For greater than or equal one dimensions, some references are: Dave Watson's home page: http://maths.uwa.edu.au/~watson/homepage.html Dave Watson Watson, Dave 1992 Contouring: A guide to the analysis and display of spatial data, Pergamon Press ISBN 0 08 040286 0 Text includes a floppy with source code in Basic (sigh). Subject areas: isoline maps, isochor maps, methodology, data sorting, subset selection, local coordinates, binary local coordinates, barycentric coordinates, rectangular local coordinates, natural neighbour coordinates, gradient estimation, least squares gradients, least squares quadratics, spline gradients, cross product gradients, neighbourhood-based gradients, interpolation, inverse distance weighting, inverse distance weighted gradients, minimum curvature splines, neighbourhood-based interpolation, selected references to contouring literature [Dave Watson] writes: Linear triangle-based interpolation is quick and dirty - probably the best compromise available if you are in a hurry. Natural neighbor interpolation is much slower but does provide a result that most people consider to be closest to that which an experienced manual draftsman would generate. The 'kriging' method is a variation on the splines technique - the main difference being that a subjectively selected probabilistic function is used rather than one of the analytically derived radial basis functions. This class of method generates discontinuities at points where the interpolation subset changes, and kriging attempts to ameliorate this effect be recomputing the coefficients for each interpolation point - this makes it very slow. Interpolation on spheres: See the FAQ by Dave Rusin: http://www.math.niu.edu/~rusin/known-math/spheres/index.html Rusin's FAQ ftp://math.niu.edu/pub/papers/Rusin/known-math/spheres/sphere.faq Rusin's FAQ via ftp See also the comp.graphics.algorithms FAQ: http://www.cis.ohio-state.edu/hypertext/faq/usenet/graphics/algorithms-faq graphics FAQ Software: [Albrecht Preusser] wrote: You could take routines from ACM Alg. 624 "Triangulation and Interpolation of Arbitrarily Distributed Points in the Plane" by Robert J. Renka. This Algorithm is available from netlib (see q115.1, "Netlib") in the toms directory. Another algorithm in FORTRAN is contained in Akima's ACM Alg. 526, it is faster, but takes much more memory. By the way, I have developed methods based on the Delaunay Triangulation from both algorithms for computing nonlinear contours and nonlinear interpolation, which are published as ACM Alg. 626 and 684. Spatial and Geometric Analysis toolbox (SaGA) - a MATLAB package for various aspects of spatial data interpolation and analysis and geometric modeling. It is available at: http://puddle.mit.edu/~glenn/kirill/saga.html Glenn Kirill =================================== q230.2. Statistical Curve Fitting See also: q505, "Probability and Statistics". Books Jobson, J.D. Applied Multivariate Data Analysis, volumes 1 and 2. Springer-Verlag, New York. 1991. Johnson, Richard A.; Wichern, Dean W. Applied Multivariate Statistical Analysis, Third Edition [Ramin Samadani] writes: I like the book by Lawson and Hanson, solving least squares problems. I think its supposed to be back in print now or soon. Lawson, Charles L.; Hanson, Richard J. Prentice-Hall, Englewood Cliffs, N.J. 1974 Press et al 1991 also has a description of the field. ### Need a review of Marquardt-Levenberg algorithms. Anybody want to write a paragraph? Software ODRPACK, from netlib [author]: ODRPACK is a portable collection of Fortran subprograms for fitting a model to data. It is designed primarily for instances when the explanatory as well as the response variables have significant errors, implementing a highly efficient algorithm 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. =================================== q230.4. Time series analysis Time series analysis may be used for some types of data. See: Brockwell, Peter J.; Davis, Richard A. 1991 Time Series: Theory and Methods, Second Edition Springer-Verlag, New York. ISBN 0-387-97429-6 [SJS]: Beautiful approach with emphasis on theory. Emphasis on the linear model. Hamilton, James D. 1994 Time Series Analysis Princeton U. Press, Princeton, NJ ISBN 0-691-04289-6 [SJS]: Applied approach, with heavy emphasis on applications from economics. Not having an economics background is a detriment in reading this text. Broad mix of models. Montgomery, Douglas C. / Forecasting and time series analysis (1990) Pankratz, Alan / Forecasting with Univariate Time Series Models: Concepts and Cases / (1983) / good, clear Vandaele, Walter / Applied Time Series and Box-Jenkins Models (1983) / / good; pedagogical and practical Also see q115.3, "Statlib". Also see q505, "Probability and Statistics". ### others? =================================== q230.6. Splines Useful for modelling single and multiple dimensional data. Books: de Boor, Carl 1978 A Practical Guide to Splines Springer-Verlag, New York. ISBN 0-540-90356-9 [Tim Strotman]: Provides an excellent blending of theory and practical implementation. Dierckx, Paul 1993 Curve and surface fitting with splines Clarendon Press, Oxford England and New York ISBN 0198534418 Farin, Gerald E. 1995 NURB curves and surfaces : from projective geometry to practical use Wellesley, Mass. : A.K. Peters ISBN 1568810385 : Farin, Gerald E. 1993 Curves and surfaces for computer aided geometric design : a practical guide, third edition. Boston : Academic Press Nurnberger, Gunther 1989 Approximation by Spline Functions Springer-Verlag, Berlin ISBN 3-540-51618-2 Berlin ISBN 0-387-51618-2 New York Piegl, Les; Tiller, Wayne 1995 The NURBS Book Springer-Verlag, New York. ISBN 0-387-55069-0 [Tim Strotman]: Provides an excellent blending of theory and practical implementation. Spath, Helmuth 1995 One Dimensional Spline Interpolation Algorithms A.K. Peters, Wellesley, MA ISBN 1-56881-016-4 Software: A search of the NIST guide (see q110.1, "Indices of NA Software") turns up numerous references. =================================== q230.7. Nearest Neighbor algorithms Books: Dasarathy, Belur V. 1991 Nearest Neighbor (NN) Norms: NN Pattern Classification Techniques IEEE Computer Society Press, Los Alamitos, CA [SJS]: Excellent. Other references: The following Technical Reports are available from the International Computer Science Institute via anonymous FTP from ftp.ICSI.Berkeley.EDU Berkeley Tech Reports tr-89-063.ps.Z Five Balltree Construction Algorithms tr-90-001.ps.Z The Delaunay Triangulation and Function Learning Teillaud, Monique Towards Dynamic Randomized Algorithms in Computational Geometry Lecture Notes in Computer Science 758 Springer-Verlag Mulmuley, K.; Sen, S. Dynamic point location in arrangements of hyperplanes 7th ACM Symposium of Computational Geometry in North Conway 1991 M. Dickerson, R. L. Drysdale and J.-R. Sack Simple algorithms for enumerating interpoint distances and finding k nearest neighbors. Internat. J. Computational Geometry & Applications 2:3 (1992) 221--239. P. B. Callahan and S. R. Kosaraju A decomposition of multi-dimensional point-sets with applications to k-nearest-neighbors and n-body potential fields. 24th ACM Symp. Theory of Computing, 1992, 546--556. M. T. Dickerson and D. Eppstein Algorithms for proximity problems in higher dimensions. Comp. Geom. Theory & Applications, to appear. P. M. Vaidya An $O(n \log n)$ algorithm for the all-nearest-neighbors problem. Discrete and Computational Geometry 4 (1989) 101--115. =================================== q230.8. Fitting a circle to a set of points Problem: Given N Points: (x1,y1); (x2,y2).. (xN,yN), we want to find for best-fit circle: (X0,Y0), R. (Note: for fitting an *ellipse*, substitute the equation for an ellipse for the equation for a circle in the "Brute Force Approach"). Brute Force Approach (leads to a non-linear system): [Amara Graps] Idea: Minimize by least squares the root-mean-squared error of the radius in the equation for a circle. In this method, one minimizes the sum of the squares of the *length* differences, which gives you a non-linear problem with all the associated pitfalls. (x-X0)^2 + (y-Y0)^2 = R^2 Equation for a circle R = SQRT[ (x-X0)^2 + (y-Y0)^2) ] Radius of the circle where: (X0,Y0) = center of circle (x,y) = point coordinates R = radius 1) Get first estimate for (X0,Y0,R). (Details: Find some points to make first estimates- either solve the circle exactly (3 equations, 3 unknowns) to get a first estimate of the center and radius, or just do a kind of centroid calculation on all points- to get a rough estimate of the center and radius.) 2) Calculate r (r1, r2,.. rN) for each of your N points from the equation for a radius of a circle. 3) Calculate the root-mean-squared error For example, for 5 given points on the circle: RMS error = SQRT[ [ (r1-R)^2 + (r2-R)^2 + (r3-R)^2 + (r4-R)^2 + (r5-R)^2] / 3 ] (dividing by "3" because we have 3 free parameters.) 4) Change (X0,Y0,R) slightly in your minimization algorithm to try a new (X0,Y0,R). (Details: Because minimization algorithms can get very computationally intensive, if one's problem is a simple one, I would look for a "canned" minimization routine. Some commercial computer programs for plotting and spreadsheets do this sort of thing. For example, the Excel spreadsheet has a built-in "solver" that will perform minimzation. Other possibilties for software: Matlab with the optimization toolbox, MACSYMA, ODRPACK from Netlib, and the recent L-BFGS-B package which allows you to specify bounds on the variables, from: ftp://eecs.nwu.edu/pub/lbfgs L-BFGS-B 5) Calculate r (r1, r2 etc.) again from new (X0,Y0,R) above. 6) Calculate RMS error again. 7) Compare current RMS error with previous RMS error. If it doesn't vary by more some small amount, say 10^{-3} then you're done, otherwise continue steps 4 -- 7. Other References: Berman & Somlo: "Efficient procedures for fitting circles..." IEEE Instrum & Meast., IM-35, no.1, pp. 31-35, 1986. [Peter Somlo] Other (more elegant) approaches that reduce to a linear system. If you choose to minimize the squares of the *area* differences, you get a linear problem, which is a much safer way. [Pawel Gora, Zdislav V. Kovarik, Daniel Pfenniger, Condensed by Amara Graps] 1. Function to minimize is (sum of the area differences): Q = Sum { [ (xi - X0)^2 + (yi -Y0)^2 - R^2 ]^2 , i=1..N } 2. A necessary condition is the system of 3 equations with 3 unknowns X0, Y0, R. Calculate the partial derivatives of Q, with respect to X0, Y0, R. (all d's are partial) dQ / dX0 = 0 dQ / dY0 = 0 dQ / dR = 0 3. Developing we get the linear least-squares problem: | x1 y1 1 | | a | | -x1^2-y1^2 | | x2 y2 1 | | b | =~ | -x2^2-y2^2 | | x3 y3 1 | | c | | -x3^2-y3^2 | | x4 y4 1 | | -x4^2-y4^2 | | x5 y5 1 | | -x5^2-y5^2 | ..... ......... (for example, for 5 points) where a = 2 X0; b = 2 Y0 ; c = X0^2 + Y0^2 - R^2. Take any good least-squares algorithm to solve it, yielding a,b,c. So the final circle solution will be given with X0 = a/2; Y0 = b/2; R^2 = X0^2+Y0^2 - c. By the way, with 5 points you can also find the unique quadratic form (ellipse, hyperbola) which passes exactly through 5 points. With more than 5 points one can do a linear least-squares as well. The problem is then to minimize: | x1^2-y1^2 x1y1 x1 y1 1 | | a | | -x1^2-y1^2 | | x2^2-y2^2 x2y2 x2 y2 1 | | b | =~ | -x2^2-y2^2 | | x3^2-y3^2 x3y3 x3 y3 1 | | c | | -x3^2-y3^2 | | x4^2-y4^2 x4y4 x4 y4 1 | | e | | -x4^2-y4^2 | | x5^2-y5^2 x5y5 x5 y5 1 | | f | | -x5^2-y5^2 | ..... ......... There are Fortran programs fcircle.f, fellipse.f and the Lawson & Hanson least-squares routines ls.f showing how to implement these least-squares problems at: ftp://obsftp.unige.ch/fit Circle Programs The robust or L1 or least-first-power approximation [Zdislav V. Kovarik]. If you try to minimize W(a,b,r) = SUM(j=1:N) ABS (((x_j-a)^2 + (y_j-b)^2)^(1/2) - r) all you have to do is set up the 10 (i.e. if 5, choose 3) circles passing through every choice of 3 of 5 points, calculate W(a,b,r) for each of them and pick the minimizing circle. The extra feature is that this procedure separates and discards points which are conspicuously far from the majority trend. (Of course, it becomes increasingly time-consuming when the number of given points increases.) [Amara Graps] This method of determining the minimum bounding circle from a set of _circles_ is solved, and with code available at: http://www.intergalact.com/circles.html Sky Coyote =========================================================================== q240. Transforms (FFT, etc) and digital signal processing (DSP) FFTs are a standard part of nearly every NA package. For more info: See the comp.dsp FAQ: http://dsp.ee.adfa.oz.au/sigproc.html comp.dsp FAQ ftp://evans.ee.adfa.oz.au/pub/dsp/comp.dsp.faq comp.dsp FAQ via ftp Newsgroup: comp.dsp See also Frigo and Johnson's library of FFT software: http://theory.lcs.mit.edu/~fftw Frigo and Johnson's library [author]: FFTW is a C library for performing Discrete Fourier Transforms in one or more dimensions. We have performed extensive benchmarks of the speed and accuracy of available FFT software on a variety of platforms. The results are available from the web page mentioned above, and show that FFTW is typically superior to other public-domain Fourier Transform codes. It is our hope that these benchmarks will allow users to intelligently select among the myriad existing FFT software. See also Dan Cross' page and FFT library: http://www.intersrv.com/~dcross/fft.html Dan Cross' page See also Joerg Arndt's page and his FFT library: http://www.spektracom.de/~arndt/fxt/fxtpage.html Joerg Arndt's page other resources? ### =========================================================================== q245. Wavelets [Amara Graps] writes: Wavelets are functions that satisfy certain mathematical requirements and are used in representing data or other functions. They have worked well as an alternative to fourier sine and cosine functions in data analysis in many different scientific fields. Some internet resources are: Dept. of Mathematics at Salzburg University http://www.mat.sbg.ac.at/~uhl/wav.html Salzburg U. Mathematics Dept. An extensive wavelet bibliography list can be found at Mathsoft: http://www.mathsoft.com/wavelets.html Mathsoft A large software list, as well as a bibliography list, can be found at Steve Baum's site at Texas A&M University: http://www-ocean.tamu.edu/~baum/wavelets.html Steve Baum's page Amara Graps has a good wavelets page on the Web: http://www.amara.com/current/wavelet.html Amara Graps' page Also, she has an introductory paper at: http://www.amara.com/IEEEwave/IEEEwavelet.html Amara Graps' paper ftp://ftp.best.com/pub/agraps/papers/IEEEwavelet.ps.gz Amara Graps' paper via ftp Newsletters: Wavelet Digest. Subscriptions: E-mail to wavelet@math.scarolina.edu with "subscribe" as subject. Preprints, references, and back issues can be obtained from: http://www.math.sc.edu/~wavelet/ Wavelet Digest ftp://ftp.math.sc.edu/pub Wavelet Digest via ftp gopher://gopher.math.sc.edu Wavelet Digest via gopher =========================================================================== q250. Integration and Ordinary Differential Equations (ODEs) Most of the general NA texts, such as Stoer & Bulirsch 1980, have chapters on integration techniques. See also: Davis, Philip J.; Rabinowitz, Philip 1984 Methods of Numerical Integration Academic Press, Orlando, Florida ISBN 0122063600 ODEPACK, from netlib (see q115.1, "Netlib"). [Dave Linder]: Well known and widely used. Allows error-based adaptive step-size control. [author] A systematized collection of ODE solvers. Handles stiff and nonstiff systems, sparse systems, explicit and linearly implicit forms. Fortran IV, double precision. A single precision version may be found in sodepack, also in netlib. RKSUITE, from netlib ode/rksuite (see q115.1, "Netlib") [Dave Lindner]: Also good. Allows error-based adaptive step-size control and easy to use for explicit systems. [author]: For initial value problem for first order ordinary differential equations. A suite of codes for solving IVPs in ODEs. A choice of RK methods is available. Includes an error assessment facility and a sophisticated stiffness checker. Template programs and example results provided. Supersedes RKF45, DDERKF, D02PAF. LSODE and DVODE, from netlib (see q115.1, "Netlib"): [Jean Claude Boettner] The algorithm is the same but the jacobian matrix is stored in DVODE allowing better efficiency, especially for big systems of ODE (100-300 typically in my case). So expect a slow down (2 ?) when using LSODE. It might be interesting to test VODEPK (on NETLIB) with Krylov methods. See also many other packages in the directory ode, in netlib. Ernst/Wanner package: ftp://ftp.unige.ch/pub/doc/math/ Ernst/Wanner [author]: Separate Fortran codes for stiff, nonstiff, and mechanical systems. For the description see the book by the authors: Hairer, Ernst; Norsett; Wanner, Gerhard (1993): Solving Ordinary Differential Equations. Nonstiff Problems. 2nd edition. Springer Series in Comput. Math., vol. 8. =========================================================================== q253. Stochastic Differential Equations [Sasha Cyganowski]: I have a library package for Maple called "stochastic" that solves Stochastic Differential Equations explicitly and also constructs numerical schemes for them. People can download it from http://www.cm.deakin.edu.au/~sash/maple.html Stochastic DE package =========================================================================== q255. N-Body and Particle Simulation * q255.1, "N-Body Simulation Web Sites" * q255.2, "N-Body Simulation Software" =================================== q255.1. N-Body Simulation Web Sites [Amara Graps] writes: N-body problems occur in fields such as cosmology, solar system dynamics, molecular dynamics, and plasma physics. My summary of N-body simulation methods contains info on the following methods: Particle-Particle (PP), Particle-Mesh (PM), Particle-Particle/Particle-Mesh (P3M), Nested Grid Particle-Mesh (NGPM), Tree-Code (TC)- Top Down, Tree-Code (TC)- Bottom Up, Fast-Multipole-Method (FMM), Tree-Code Particle-Mesh (TPM), Self-Consistent Field (SCF), and the Symplectic Method. I also list Internet sites for research groups, some papers, some code, and other NBody-related links. It is at: http://www.amara.com/papers/nbody.html Amara Graps' page ftp://ftp.best.com/pub/agraps/papers/nbody.txt Amara Graps' page via ftp =================================== q255.2. N-Body Simulation Software NEMO, by Peter Teuben http://www.astro.umd.edu/nemo/ NEMO [author] NEMO is an extendible Stellar Dynamics Toolbox. It has various programs to create, integrate, analyze and visualize N-body and SPH like systems. In addition there are various tools to operate on images, tables and orbits, including FITS files to export/import to/from other astronomical data reduction packages. We also advertise other software packages , which work on similar problems. =========================================================================== q260. Partial Differential Equations (PDEs) and Finite Element Modeling (FEM) * q260.1, "PDE and FEM Web Sites" * q260.2, "PDE and FEM Software on the net" * q260.3, "Commercial Packages for FEM" * q260.4, "Comparison of Meshing Software Packages" * q260.5, "Newsgroups for PDE and FEM" * q260.6, "Books and References for PDE and FEM" =================================== q260.1. PDE and FEM Web Sites "Mesh Generation and Grid Generation on the Web": http://www-users.informatik.rwth-aachen.de/~roberts/meshgeneration.html mesh generation You can find the same list with hyperlinks at http://www-users.informatik.rwth-aachen.de/~roberts/latest_news.html mesh generation Ian MacPhedran and Roger Young's pages on finite element resources: http://duke.usask.ca/~macphed/finite/finite.html FEM Resources http://www.engr.usask.ca/%7Emacphed/finite/fe_resources/fe_resources.html FEM Resources The geometry center at U. of Minnesota: http://www.geom.umn.edu U. Minnesota Geometry Center MGNet at Yale. MGNet has codes, preprints, virtual proceedings, a large bibliography, and more dealing with multigrid and/or domain decomposition methods for solving PDE's. There has also been a monthly electronic newslettter for the past 6 years. http://casper.cs.yale.edu/mgnet/www/mgnet.html MGNet The reclusive Dr. TP's CFD page: http://www.fges.demon.co.uk/cfd/CFD_codes.html Dr. TP's CFD page, U.K. http://www.math.psu.edu/dna/CFD_codes.html Dr. TP's CFD page, USA http://icemcfd.com/cfd/CFD_codes.html Dr. TP's CFD page, USA Robert Schneiders site on mesh generation. http://www-users.informatik.rwth-aachen.de/~roberts/meshgeneration.html Mesh Generation Large site with info on people, literature, software, and numerous research efforts worldwide. For Delaunay triangulation & Voronoi diagram and more geometry algorithms, including interactive demos and Java source codes, see: http://ra.cfm.ohio-state.edu/grad/zhao/algorithms/algorithms.html Ohio State There is a Maple package for working with PDEs, solving systems of ODEs and making general changes of variables at: http://lie.uwaterloo.ca/pdetools.html U. Waterloo =================================== q260.2. PDE and FEM Software on the net PDE and FEM Software on the net: (See also q270, "Computational Geometry") * q260.2.1, "FEMLAB" * q260.2.2, "Fec" * q260.2.3, "FElt" * q260.2.4, "Femlib" * q260.2.5, "Kaskade" * q260.2.6, "Tri" * q260.2.7, "QMG" * q260.2.8, "Sinda/Fluint" * q260.2.9, "Physica" * q260.2.10, "Madpack5" * q260.2.11, "Triangle" * q260.2.12, "FreeFEM" =================================== q260.2.1. FEMLAB http://www.math.chalmers.se/Research/Femlab/ FEMLAB ftp://ftp.md.chalmers.se/pub/Femlab/ FEMLAB via ftp [author]: From the Department of mathematics at Chalmers University of Technology and Gvteborg university. FEMLAB is an interactive program for the numerical solution of ordinary and partial differential equations based on the Finite Element Method in adaptive form with automatic error control. Femlab is a part of an educational program based on the Leibniz vision of integration of Calculus, Computation and Application. The educational program is presented in the texts: Computational Differential Equations, Cambridge University Press , to appear 1996 Introduction to Adaptive Methods for Differential Equations, Acta Numerica (1995) pp. 105-158. =================================== q260.2.2. Fec ftp://karazm.math.uh.edu/pub/Math Fec A collection of finite element libraries in C++ =================================== q260.2.3. FElt http://www-cse.ucsd.edu:80/users/atkinson/FElt/felt.html FElt ftp://cs.ucsd.edu/pub/felt FElt via ftp [author]: FElt is a free system for introductory level finite element analysis. FElt is intended largely as a teaching tool. At this stage it should be able to handle most static and dynamic linear analysis problems (structural and thermal) that you'd find in a one or two term introductory class in finite element analysis; it also has some capabilities for modal and spectral analysis. The FElt element library currently contains fifteen elements ranging from a simple spring to an 8-node brick. The main FElt applications are all built around a single intuitive, powerful, and easy-to-use input syntax. =================================== q260.2.4. Femlib ftp://usc.edu/pub/C-numanal/femlib-1.1.tar.gz Femlib Set of C++ classes for finite element work, garbage collection algorithms, and sparse matrix algorithms. A bit rough; incomplete in some areas. =================================== q260.2.5. Kaskade ftp://elib.zib-berlin.de/pub/kaskade/3.x Kaskade in Germany ftp://elib.zib-berlin.de/pub/kaskade/Manuals/3.x Kaskade Manuals in Germany ftp://na.cs.yale.edu/mgnet/Codes/kaskade/3.x Kaskade in USA [author]: The KASKADE 3.1 software package solves linear scalar elliptic and parabolic problems in 1, 2, 3 space dimensions with adaptive finite element methods. Furthermore, the toolbox includes extensions for handling systems of equations and example algorithms for nonlinear methods used in obstacle, porous media or Stefan problems. Core of the program is a variety og multilevel/multigrid preconditioners for the arising linear systems. This object-oriented code is written in C++ and can be compiled with Gnu g++, version 2.7.2, and some other compilers. If you want to compile with Gnu g++, version 2.6.3, you have to change the definition of the complex-type in the file general.h. The program solves the same mathematical problem classes as its predecessor KASKADE 2.x, which is written in C. We provided a graphical user interface ZGUI to the numerical program based on the interface language Tcl/Tk of j. Ousterhout. =================================== q260.2.6. Tri ftp://ftp.cs.cornell.edu/pub/scott/tri Tri [author]: Tripoint was first developed by David Eppstein to triangulate point set input in two dimensions, following the algorithm in "Provably Good Mesh Generation" by Bern, Eppstein, and Gilbert[1]. During the summer of 1991, Scott Mitchell extended the program to triangulate polygonal regions with holes, again in two dimensions. The algorithm followed borrows ideas both from [1] and "Quality Mesh Generation in Three Dimensions" by Mitchell and Vavasis[2]. Tripoint takes input from text files as the polygon to triangulate. Output is also as text files, using the same data format. Points are represented by their coordinates, and edges by the indecies of their endpoints. There is a matlab code front end, called drawmesh.m. This allows the graphical input of the input polygon using the mouse, and the display with zooming of the output triangulation. There is also matlab code called dispmesh.m, which allows the displaying of output only. This allows the user freedom over how to generate the input. The algorithm is similar to one in "Provably Good Mesh Generation"[1]. The main differences include: Tripoint uses connected component information while generating the quadtree, as in [2]. Tripoint does not cut dangling acute triangles from the input as a first step as in [1]. Ideally, as in [2], tripoint would center input verticies in boxes, and use a very general and easy algorithm for triangulating individual boxes. Instead, vertices are not centered, and the ideal algorithm is used with added special case analysis for boxes near an input vertex. Scott Mitchell continues to support tripoint. We would eventually like to implement a three dimentional algorithm following [2]. =================================== q260.2.7. QMG http://www.cs.cornell.edu/home/vavasis/qmg-home.html QMG [author]: QMG is free software for fully automatic unstructured finite element mesh generation in two and three dimensions. It can generate meshes for complex polyhedral domains with nonmanifold features. It includes geometric modeling routines for polyhedral domains, two mesh generators and a finite element solver. QMG is written in primarily in C++ and is a collection of m-files and mex-files that run under Matlab 4.2. =================================== q260.2.8. Sinda/Fluint http://www.webcom.com/crtech Sinda/Fluint ftp://ftp.csn.net/crtech Sinda/Fluint via ftp [author]: SINDA/FLUINT is a comprehensive finite-difference, lumped parameter (circuit or network analogy) tool for analyzing complex thermal/fluid systems. It is used at over 300 sites in the aerospace, electronics, petrochemical, and automotive industries. =================================== q260.2.9. Physica http://www.gre.ac.uk/~physica Physica A three dimensional unstructured mesh software framework for the modelling of multi-physics phenomena. =================================== q260.2.10. Madpack5 http://casper.cs.yale.edu/mgnet/www/mgnet-codes.html Madpack at MGNet in USA http://www.cerfacs.fr/~douglas/mgnet-codes.html Madpack at MGNet in France [author]: Version 5 of Craig Douglas' multigrid package. This is an abstract solver. It is PDE, domain, and discretization independent. It only handles linear problems, however. It is an ongoing project with a number of contributors from around the world. Some of these wish to remain anonymous. Serial, parallel, and semi-chaotic solvers are or will be included during 1994. A paper describing this is in the file mgnet/papers/Douglas/mad5.ps. This is an object oriented code. The user interface is written in C. Most of the solvers are written in Fortran-77+m4. The same calling sequence is used independent of the data's type (real and complex, single and double precision are supported). The user interface builds all of the truly nasty data structures needed by the code. The ownership of this code is convoluted. =================================== q260.2.11. Triangle A Two-Dimensional Quality Mesh Generator and Delaunay Triangulator. http://www.cs.cmu.edu/~quake/triangle.html Mesh Generator Triangle generates exact Delaunay triangulations, constrained Delaunay triangulations, and quality conforming Delaunay triangulations. The latter can be generated with no small angles, and are thus suitable for finite element analysis. =================================== q260.2.12. FreeFEM http://www.asci.fr/~prudhomm/gfem-html/gfemenglish.html FreeFEM, in English http://www.asci.fr/~prudhomm/gfem-html/ FreeFEM, in French FreeFEM is a graphical software which is built around a programming language dedicated to the partial differential equations. FreeFEM solves,with the finite element method,scalar linear elliptic PDEs of order 2,the time dependant equations and more generally all iterative sheme with PDE combination for example the heat equation,convection-diffusion and even the Navier-Stokes equations.The program is written in C,it is shareware and portable. Domains are defined by analytic equations of the boundary,and triangulated by a Delaunay-Voronoi algorithm. The language allows the manipulation of the complex numbers with the reserved words I,Re,Im. Systems of equations are also supported. Thus one can solve,for example the problems of the linear elasticity. =================================== q260.3. Commercial Packages for FEM A large list of commercial FEM products may be found at: http://www.cray.com/PUBLIC/APPS/DAS/DAS4.html List of FEM Products =================================== q260.4. Comparison of Meshing Software Packages [Albert M. Hines, Feb 1996]: This table reflects the best information that I can gather to date on some of the more popular meshers. Many others exist and may be better or worse than those listed here. This study was conducted by Howmet, a manufacturing corporation with no incentive to support or reject any package over another. Portions of the study were also funded by your generous tax donations through an ICCA program designed to enhance the capability of US investment casting through (among many other things) automeshing software. The meshes were used for heat transfer and fluid flow predominantly. A limited amount of stress analysis and electromagnetics were also investigated. The desired modeling analysis is a crucial factor in determining whether a meshing package will support the mesh quality and refinement necessary for a simulation. (e.g. mesh quality is almost a non-issue for heat transfer, but not for stress!) The geometries that I have considered are aerospace turbine engine components: complex 3-D thin walled structures. Bulky or spindly geometries may behave differently (e.g. engine blocks, oil rigs, etc.). The scale used is 0 to 10. A zero means that it meets none of my expectations. A 10 means that it meets all of my expectations. A cumulative score should not be obtained by adding columns. Many entries are more important than others. Weighting for the various tasks are different for each analyst/application. The scores are often subjective and should be considered at best approximate. They do not necessarily reflect the opinion of Howmet Corporation or, for that matter, of anyone other than myself. They are, however, the result of careful and expensive investigation into the market. Any questions or comments should directed to me at "ahines@howmet.com". Albert M. Hines, Howmet Corporation, 1500 South Warner Street, Whitehall, MI 49461, 616-894-7864. SOFTWARE(5): OCTREE PATRAN MESHCAST HYPERMESH ALG ---------------------------------------------------------------------------- 3-D SURFACE MESH (*) automesh robustness (a) 9 8 7 4 3 automesh flexibilty (b) 4 6 8 7 5 number of elements (c) 10 6 7 6 8 meshing speed (d) 3 1 9 5 3 typical element quality (e) 1 8 7 4 5 semi-auto effectiveness N/A 7 3 10 6 mesh editing N/A 8 1 10 2 3-D SOLID MESH automesh robustness (a) 8 7 (4) 7 N/A 4 automesh options (b) 6 7 7 N/A 6 number of elements (c) 10 4 (4) 5 N/A 3 meshing speed (d) 4 1 9 N/A 3 typical element quality (e) 2 6 (4) 7 N/A 4 semi-auto effectiveness N/A 4 N/A 9 6 mesh editing N/A 8 3 10 6 software vendor meshing (f) 8 2 9 5 8 auto-hex meshing N/A N/A N/A N/A 3 GENERAL Ease of use (g) 3 4 9 8 4 I/O options 4 8 7 9 7 Error reporting 3 4 3 3 3 Barrier-free tech. support 8 1 10 6 3 Competent/helpful tech. support 6 6 8 7 8 Ease of install/maintenance 8 4 8 7 8 "Bug-free-ness" 6 7 3 4 4 COST(1) $12,000 $6800(2) $10,000(3) $4500 $5,525 NOTES ----- * OCTREE surface mesh obtained by extracting faces of its solid elements. (a) Should mesh the first time with given parameters. This refers to tetrahedra only. (b) Includes things like a finely meshed boundary with coarsely meshed interior, ignoring features smaller than a given size, multiple element layers through thin sections, multiple meshing algorithms, etc. Refers to tetrahedral elements. (c) Being in industry, practicality is a must. Meshes > ~100,000 nodes do not run in a reasonable amount of time in our lab. If a program cannot mesh a part within this limitation, I consider it unable to mesh the part, even if it might successfully generate the mesh. Automeshers should allow the specification of a target number of nodes. Any mesh above this size should send a flag to remesh, ignoring small features. (d) Again, from a practical point of view, there are limits beyond which I consider the program to fail. The most glaring comparison is between PATRAN and MeshCAST. A typical part that meshes less than 10 minutes with MeshCAST normally takes several days to mesh in PATRAN. It is likely that given infinite time, PATRAN would succeed (after all, it contains the RPI finite octree mesher as one of its algorithms!), however, I can't justify tying a machine up for a week to find out if it will mesh (and often it crashes at the end of the meshing cycle!). (e) There are many if's and's & but's here. Basically I use aspect ratio and dihedral angle for tetrahedra, jacobian at the gauss points for hex'es, wedge's, and quad's, and interior angle for triangles. These are the only element types that I use. (f) For many problems, I could not successfully mesh the part, so I sent the geometry to the software vendor. In other cases, I sent it specifically to evaluate the software run under the developer's care. Score reflects willingness, speed, size, and quality of the mesh received. (g) I am partial to a Mac-like interface, which I consider to be the computer world's 'reference standard'. Program should require minimal training and manuals. All options should be available on the menus (no hidden or cryptic commands). This is not just personal preference, but time and dollars in training. (1) Cost is annual lease, US dollars, except as noted. Platform is HP-735 network license. Cost is what we pay, not necessarily list price. (2) Unigraphics common database module $3,000 extra (i.e. $9,800). Base license includes one translator, we chose IGES. (3) This price includes the fluids, thermal, radiation, solver modules. I am not sure of the price of just MeshCAST by itself. (4) This is very approximated assuming infinite meshing time. (5) Versions tested: OCTREE: March 1,1995, P3: v1.4, Meshcast: v3.0.3, Hypermesh: v2.00b, Algor: July, 1995. =================================== q260.5. Newsgroups for PDE and FEM Computational Fluid Dynamics (CFD) newsgroups: * sci.mech.fluids * sci.geo.fluids * sci.mech.fluids * sci.physics.computational.fluid-dynamics * sci.engr.marine.hydrodynamics Some of these groups are archived at: http://www.Fluent.COM/cgi-bin/fetch CFD Newsgroups Archives =================================== q260.6. Books and References for PDE and FEM Axelsson, O.; Barker, V.A. 1984. Finite Element Solution of Boundary Value Problems: Theory and Computation Orlando FL: Academic Press, Inc. Bornemann, F. An Adaptive Multilevel Approach to Parabolic Equations in Two Space Dimensions. Dissertation, Freie Universitaet Berlin, 1991. Bornemann, F.; Erdmann, B.; Kornhuber, R. Adaptive Multilevel Methods in Three Space Dimensions. Int. J. Numer. Meths. in Eng., 36, 1993. Braess, Dietrich. 1992 Finite Elemente, Springer (In German) Brenner; Scott. 1994. The Mathematical Theory of Finite Elements Springer-Verlag Celia; Grey. Numerical Methods for Differential Equations [G. Scott Lett] "very good". Ciarlet, Philippe G. 1978 The finite element method for elliptic problems Amsterdam: North-Holland Deuflhard, P.; Leinen, P.; Yserentant, H. Concepts of an Adaptive Hierarchical Finite Element Code. IMPACT, 1, 1989. Grossmann; Roos. Numerik Partieller Differentialgleichungen Teubner. (In German). Johnson, Claes. Numerical Solution of Partial Differential Equations by the Finite Element Method. [Hans Sandholt] I found great pleasure to read it. Hackbusch, Wolfgang Elliptic Differential Equations. Theory and Numerical Treatment Springer Series in Computational Mathematics 18 Springer-Verlag, Berlin Heidelberg New York. 1992. ISBN 3-540-54822-X See: http://www.numerik.uni-kiel.de/wh/ Hackbush's page Hackbusch, Wolfgang Iterative Solution of Large Sparse Systems of Equations Applied Mathematical Sciences, Vol. 95. Springer-Verlag, New York, U.S.A., 1993. ISBN 3-540-94064-2 (Berlin ...) ISBN 0-387-94064-2 (New York ...) See: http://www.numerik.uni-kiel.de/wh/ Hackbush's page [G. Scott Lett] A good book to start; helping to bridge the gap between recipes and understanding. Hughes, T.J.R. 1987. The Finite Element Method Kornhuber, R. Monotone Multigrid Methods for Nonlinear Variational Problems. Habilitationsschrift, Freie Universitaet Berlin, 1995. Oden, J.T.; Reddy, J. N. 1976. An introduction to the mathematical theory of finite elements New York: Wiley-Interscience Schwarz, H.R. 1984. Methode der Finiten Elemente Teubner (In German) Strang; Fix. 1973. An Analysis of the Finite Element Method Prentice Hall Wait, R.; Mitchell, A.R. 1985. Finite Element Analysis and Applications John Wiley & sons. Zienkiewicz, O.C.; Morgan, K. 1983. Finite Elements and Approximation J. Wiley & Sons =========================================================================== q265. Operations Research: Minimization, Optimization, Etc. * q265.1, "Optimization, Linear and Non-Linear Programming: General Resources" * q265.2, "Optimization, Linear and Non-Linear Programming: References" * q265.3, "Queueing Theory and Performance Analysis." =================================== q265.1. Optimization, Linear and Non-Linear Programming: General Resources See the FAQs maintained by Robert Fourer and John Gregory: http://www.mcs.anl.gov/home/otc/Guide/faq/ LP and NLP FAQs See also: Decision Tree for Optimization Software by Hans D. Mittelmann, Dept of Mathematics, Arizona State U., and P. Spellucci, Dept of Mathematics, Technical U. Darmstadt. http://plato.la.asu.edu/guide.html Decision Tree for Optimization Software NEOS Guide to Optimization Software By the OTC, a joint effort of Argonne National Laboratory and Northwestern University. http://www.mcs.anl.gov/home/otc/Guide/SoftwareGuide/ NEOS Guide The Optimization Technology Center at Argonne National Laboratory (ANL). http://www.mcs.anl.gov/home/otc/ ANL Optimization Center Xu's list of public optimization codes: http://ucsu.colorado.edu/~xu/software.html Xu's list Arnold Neumaier's overview: http://solon.cma.univie.ac.at/~neum/glopt.html Neumaier Simon Streltsov's pages: http://cad.bu.edu/go/ Streltsov Janos Pinter's pages: http://www.tuns.ca/~pinter/gobook.html Pinter http://www.tuns.ca/~pinter/lgoinf.html Pinter Michael Trick's Operations Research Page http://mat.gsia.cmu.edu/ Michael Trick Semidefinate programming: http://cs.nyu.edu/cs/faculty/overton/sdppack/sdppack.html SDPpack We would like to announce a new version of our code SDPpack (Version 0.9 Beta for Matlab 5.0). This version extends the previous release for semidefinite programming (SDP) to mixed semidefinite-quadratic-linear programs (SQLP), i.e. linear optimization problems over a product of semidefinite cones, quadratic cones and the nonnegative orthant. =================================== q265.2. Optimization, Linear and Non-Linear Programming: References Here are only a few popular and/or new references. It's a huge field! See also q265.1, "Optimization, Linear and Non-Linear Programming Resources" Chvatal, Vasek, 1983 Linear Programming W.H. Freeman A current classic for graduate and upper level undergraduate courses. Stephen J. Wright Primal-dual Interior-point Methods Siam 1997 / xx+289 pages / Softcover / ISBN 0-89871-382-X / Order Code OT54 For more information see http://www.siam.org/books/swright/ Wright Robert J. Vanderbei Linear Programming: Foundations and Extensions Kluwer Academic Publishers, Boston Hardbound, ISBN 0-7923-9804-1 September 1996, 440 pp. NLG 240.00 USD 129.95 GBP 92.50 This book is an introductory graduate textbook on linear programming although upper-level graduate students and researchers will find plenty of material here that cannot be found in other books. It has also been used successfully to teach undergraduates majoring in Operations Research. Balanced treatment of the simplex method and interior-point methods. Efficient source code (in C) for all the algorithms presented in the text, available from: http://www.princeton.edu/~rvdb/ Vanderbei Stephen G. Nash and Ariela Sofer Linear and Nonlinear Programming McGraw-Hill (1996) ISBN: 0-07-046065-5 See: http://bass.gmu.edu/site/ORE/books/Nash-Sofer.html Nash & Sofer Tam\'as Terlaky (Ed.) Interior Point Methods of Mathematical Programming Kluwer Academic Publishers (September 1996) ISBN 0-7923-4201-1 This book primarily intends to give an introduction to the theory of Interior Point Methods (IPMs) in Mathematical Programming. At the same time we try to give a quick overview of the impact, of the extensions of IPMs to smooth nonlinear optimization and to give an impression of the potentials of IPMs in solving difficult practical problems. Practical Methods of Optimization R. Fletcher John Wiley, 1987 Excellent practical text on non-linear programming. J.E. Dennis Jr. and R.B. Schnabel Numerical Methods for Nonlinear Optimization and Nonlinear Equations Siam, 1983 Gill, Murray and Wright 2 volume book on Nonlinear Programming. K.G.Murty, 1988 Linear Complementarity, Linear and Nonlinear Programming Heldermann Verlag Bazraa and Shetty. Nonlinear Programming, theory and algorithms, Luenberger: Linear and Nonlinear Programming =================================== q265.3. Queueing Theory and Performance Analysis. The only thing close to a FAQ is at: ftp://rtfm.mit.edu/pub/usenet-by-group/comp.benchmarks/ comp.benchmarks FAQ References: By far the most often referenced works are the classics by Kleinrock: Kleinrock, Leonard 1975 Queueing Systems, Volumes 1 and 2 John Wiley, New York Excellent theoretical development of the field. This is the standard text in the area. Kleinrock is apparently working on an updated version of his texts, but when they'll be published is unknown. Other good texts are: Allen, Arnold O. 1990 Probability, Statistics, and Queueing Theory with Computer Science Applications, Second Edition Academic Press, Boston. This is a common text in the field and has an applied approach. King, Peter J. 1990. Computer and Communication Systems Performance Modelling Prentice Hall Brief intro to prob theory, MG1, priority queues, networks of queues, approximations. Also chapters on numerical solutions, local area networks. Nelson, Randolph. 1995. Probability, stochastic processes, and queueing theory Springer Verlag Good treatment of prob, combinatorics, RVs and some distributions ... but only uniform, binomial, exponential, poisson. Not the normal distribution! Also, expectation, a big treatment of MG1, markov processes, matrix geometric solutions, and queueing networks. Perros, Harry G. 1995. Queueing Networks with Blocking. Oxford press Brings together many results for different types of blocking. Blocking occurs when server i cannot continue serving because the queue at server j is full. =================================== Queueing Theory and Performance Newsgroups sci.op-research sci.math.num-analysis =================================== Queueing Theory and Performance Indices Decision Tree for Optimization Software by Hans D. Mittelmann, Dept of Mathematics, Arizona State U., and P. Spellucci, Dept of Mathematics, Technical U. Darmstadt. http://plato.la.asu.edu/guide.html Decision Tree for Optimization Software =========================================================================== q270. Computational Geometry Directory of Computational Geometry Software http://www.geom.umn.edu/software/cglist/ Computational Geometry Directory This page contains a list of free computational geometry programs and packages. See also q260, "Partial Differential Equations (PDEs) and Finite Element Modeling (FEM)". =========================================================================== q285. Graphics and Scientific Visualization This is a huge field. Rather than attempt to review it, I've simply noted a few resources. All text is [author]. An good article on commercial math & visualization software is: Braham, Robert. "Math & Visualization: new tools, new frontiers", IEEE Spectrum 32, 11 (November 1995), p. 19-36. The article contains tables comparing large number of commercial products. There is no mention of the many excellent free products though. * q285.1, "NASA Index on Scientific Visualization" * q285.2, "Other Web Sites on Graphics and Sci Vis" * q285.3, "Software for Graphics and Sci Vis" =================================== q285.1. NASA Index on Scientific Visualization The best resource I found is an annotated list of scientific visualization sites, courtesy of NASA's Numerical Aerodynamic Simulation program. http://www.nas.nasa.gov/RNR/Visualization/annotatedURLs.html NASA Graphics Index or: http://www.nas.nasa.gov/NAS/Visualization/visWeblets.html NASA Graphics Index Excerpting from [NASA], some of the large general purpose scientific visualization web sites are: (Thanks NASA!) Software Support Lab software archive at the Laboratory for Atmospheric and Space Physics at the University of Colorado in Boulder. This web site contains descriptions of and access to a great deal of software, including visualization packages such as AVS, IRIS Explorer, Vis-5D, HDF, NCSA Image, NIH Image, Interactive NCAR Graphics, and many others. Many of the descriptions are incomplete and still contain some automatically generated boilerplate. Hopefully this will change soon. http://sslab.colorado.edu:2222/software.html U. Colorado Graphics, Visualization, and Usability Center at Georgia Tech. This extensive web site includes scivis work along with material from related fields such as animation, virtual environments, medical informatics, software visualization, user interface software, multimedia, educational technology, human factors, and hypertext. Plenty of content here. http://www.cc.gatech.edu/gvu/gvutop.html Georgia Tech MIT Aero/Astro Scientific Visualization This web site is home to Visual2, Visual3, and pV3. These are visualization systems for unsteady, unstructured (and structured) CFD visualization (mostly). Visual2 is for 2D flows, Visual3 for 3D flows, and pV3 takes data from solvers on distributed workstations on the fly. There are papers, software, and users manuals. The author assures me that pictures will be coming. The software is binary and libraries only, not source code. http://raphael.mit.edu/haimes.html MIT The University of Minnesota Supercomputing Institute. This web site contains pointers to URLs of interest to the scientific visualization community. http://web.msi.umn.edu/WWW/SciVis/scivis.html U. Minnesota Superconducting The Geometry Center, University of Minnesota. This excellent web site contains examples of, software for, and technical and other information about some of the premier mathematical visualizations on the planet. http://www.geom.umn.edu/ U. Minnesota Geometry Center A Gallery of Interactive On-Line Geometry The Geometry Center also has an incredible page with links to their interactive, web-based, visualizations of various mathematical objects. Interaction is slow due to the network, but these forms-based programs are well worth looking at. http://www.geom.umn.edu/apps/gallery.html U. Minnesota Geometry Center State University of New York at Stony Brook has a very nice web site with excellent information about their program which is primarily centered around the VolVis software. The source and executables are available along with many full papers in compressed PostScript format. http://www.cs.sunysb.edu/~volvis/ State U. of NY at Stony Brook Stanford Computer Graphics Laboratory. Good projects, pictures, movies, software, technical papers and descriptions of some of the graphics work at Stanford University. http://www-graphics.stanford.edu/ Stanford Computer Graphics Lab CRS4: Centre for Advanced Studies Research and Development in Sardinia (Cagliari, Italy). This extensive web site contains pictures, movies, projects, staff, research papers, and hypertextual MPEG info. A few papers are in Italian, but most of the web site is in English. http://www.crs4.it/~zip/group_homepage.html CRS4 Lawrence Livermore National Laboratory's web site has lots of images, papers, and some software. Lots of interesting visualization techniques here! http://www.llnl.gov/graphics/sciviz.html LLNL The National Center for Supercomputing Applications (NCSA) NCSA Visualization and Virtual Environments page . This extensive web site contains pictures, movies, descriptive text, and research papers. Visualization work covers a wide variety of application areas. http://www.ncsa.uiuc.edu/General/ThisIsNCSA/VizVR.html NCSA ftp://ftp.ncsa.uiuc.edu NCSA via ftp NCSA Digital Information Systems Overview contains many visualizations. http://www.ncsa.uiuc.edu/SCMS/DigLib/text/overview.html NCSA visualizations. ftp://ftp.ncsa.uiuc.edu NCSA NCSA Virtual Reality Lab briefly describes some VR projects including some scientific visualization. There are also some research papers. http://www.ncsa.uiuc.edu/Viz/VR/VRHomePage.html NCSA VR lab ftp://ftp.ncsa.uiuc.edu NCSA VR lab via ftp The Beckman Institute Visualization Facility web site describes local visualization facilities available on campus. There are some substantial miscroscopy facilities. http://delphi.beckman.uiuc.edu/ Beckman NASA's Numerical Aerodynamic Simulation Division (NAS) http://www.nas.nasa.gov/home.html NASA's NAS Mathematical Visualization by David Banks This web site contains Dr. Banks' dissertation and pointers to related work. A number of interesting mathematical visualizations of 4-dimensional spaces can be found here. http://www.icase.edu/~banks/math.html David Banks The Army High Performance Computing Research Center. This web site contains pictures, movies, descriptions of software, projects, and staff, but no research papers. Many of the visualizations come with enough information to gain at least a superficial understanding. A wide variety of application areas are represented. http://www.arc.umn.edu/html/ahpcrc.html Army Other good web sites are: http://www-ocean.tamu.edu/~baum/ocean_graphics.html Texas A&M U. =================================== q285.2. Other Web Sites on Graphics and Sci Vis For more general graphics questions, less related to scientific visualization: See the several FAQs relating to computer graphics: http://www.cis.ohio-state.edu/hypertext/faq/usenet/graphics/top Ohio State See the comp.graphics.misc FAQ: http://www.primenet.com/~grieggs/cg_faq.html Grieggs ftp://rtfm.mit.edu/pub/usenet/news.answers/graphics/faq comp.graphics.misc FAQ A huge general overview of computer graphics is at LS VII, Computer Graphics, in the Department of Computer Science at the University of Dortmund. * Other Overviews * Conferences and Workshops * Research related servers * Inquiries * Organizations * Commercial Sites * Software and Data * News * FAQs http://ls7-www.informatik.uni-dortmund.de/html/englisch/servers U. of Dortmund For commercial software, see the following sites: http://www.cray.com/PUBLIC/APPS/DAS/DAS8.html Cray http://theyellowpages.com/Comp_graphics.htm Misc =================================== q285.3. Software for Graphics and Sci Vis The most common free software package is gnuplot: ftp://prep.ai.mit.edu/pub/gnu/gnuplot Gnu Archives For commercial software, see q125, "Commercial Packages", and q520, "Symbolic Algebra". Also see: ftp://ftp.x.org/contrib/applications/Plotmtv1.4.1.tar.Z Plotmt for Unix Also see: ftp://ftp.archives.math.utk.edu GRAPHMATH Also see: http://www.maths.soton.ac.uk/mrd/panda.htm Panda [author]: Panda is an interactive graphics visualization tool for plotting and manipulating numerical data, for Win 3.1 or Win 95. It is primarily designed to animate time-dependent data in one spatial dimension, such as might be obtained from the numerical solution of partial differential equations. Panda is a 16 bit application for Windows 3.1 or 95. It requires VBRUN300.DLL to be installed on your system. Panda is freeware for private, non-commercial use. Also see q285.2, "Other Web Sites". =========================================================================== q290. Miscellaneous NA Software The NRAO Astronomical Image Processing System (AIPS) National Radio Astronomy Observatory home page http://www.nrao.edu/ NRAO The NRAO Astronomical Image Processing System (AIPS) is a software package for interactive (and, optionally, batch) calibration and editing of radio interferometric data and for the calibration, construction, display and analysis of astronomical images made from those data using Fourier synthesis methods. Design and development of the package began in Charlottesville, Virginia in 1978. It presently consists of over 800,000 lines of code, 80,000 lines of on-line documentation, and 400,000 lines of other documentation. It contains over 300 distinct applications "tasks," representing approximately 50 person-years of effort since 1978. AIPS ("Classic", not aips++) Home Page http://info.cv.nrao.edu/aips/aips-home.html AIPS The Oxford BSP Toolset and Profiling system -- version 1.1 We are pleased to announce the first official release of the Oxford BSP Toolset which conforms to the BSPlib programming library definition. BSPlib is an SPMD communications library, and is based on the Bulk Synchronous Parallel (BSP) model of parallel computation. The main feature of BSPlib is two modes of communication, one capturing a BSP oriented message passing approach, and the other reflecting a (one-sided) direct remote memory access paradigm. The core BSP library consists of just 20 primitives. Sources are freely available by anonymous FTP. For more information on the toolset distribution see: http://www.bsp-worldwide.org/implmnts/oxtool/ Oxford BSP Toolset Oxford BSPlib Parallel programmers looking for a simple but efficient approach to developing scalable applications software may be interested in the new BSPlib programming library. BSPlib is an alternative to MPI and PVM, and is based on the BSP model of parallel computation. It is already being used by a rapidly growing community of software developers in universities and in industry. The BSP approach to parallel programming is applicable to all kinds of parallel architecture: distributed memory machines, shared memory multiprocessors, and networks of workstations. It provides a consistent, and very general, framework within which to develop portable parallel software for scalable architectures. One particular advantage of BSP is that it provides _predictable_ high performance. BSPlib can be used with C or Fortran. It supports SPMD parallelism based on efficient one-sided communications. The core library (excluding collective communications) consists of just 20 primitives. The final BSPlib Definition (with C or Fortran Examples) can be obtained from any one of the WWW sites listed below. Information on implementations and their availability will be posted to this newsgroup in the next few days. Bill McColl (for The BSPlib Team) BSP Worldwide (Oxford, England) C source: http://www.bsp-worldwide.org/standard/bsplib_C_examples.ps.Z England ftp://ftp.das.harvard.edu/pub/bsp/bsplib_C_examples.ps.Z USA ftp://plato.clas.suffolk.edu/pub/bsp/bsplib_C_examples.ps.Z USA ftp://ftp.cs.ucf.edu/pub/bsp/bsplib_C_examples.ps.Z USA http://www.math.ruu.nl/people/bisselin/bsplib_C_examples.ps.gz Netherlands F77 source: http://www.bsp-worldwide.org/standard/bsplib_f77_examples.ps.Z England ftp://ftp.das.harvard.edu/pub/bsp/bsplib_f77_examples.ps.Z USA ftp://plato.clas.suffolk.edu/pub/bsp/bsplib_f77_examples.ps.Z USA ftp://ftp.cs.ucf.edu/pub/bsp/bsplib_f77_examples.ps.Z USA http://www.math.ruu.nl/people/bisselin/bsplib_f77_examples.ps.gz Netherlands =========================================================================== q505. Probability and Statistics Books: There are hundreds of prob/stat texts, but I'm interested in the marriage of statistics and computing: Thisted, Ronald A. 1986 Elements of statistical computing: numerical computation Chapman and Hall, New York A good text, and inexpensive. [Allen Mcintosh] Griffiths, Paul; Hill, Ian David, editors. 1985 Applied statistics algorithms E. Horwood Publishing, Chichester, England Algorithms are available on statlib. Moshier, Stephen Lloyd Baluk. 1989 Methods and programs for mathematical functions E. Horwood Publishing, Chichester, England Halsted Press, New York. Trivedi, Kishor Shridharbhai 1982 Probability and statistics with reliability, queuing, and computer science applications Prentice-Hall, Englewood Cliffs, NJ Kennedy, W. J.; Gentle, J. E. 1980 Statistical Computing Dekker, New York others? Newsgroup: sci.stat.math sci.math.stat FAQs, if any? Web sites: Statistics and Statistical Graphics Resources, by York University http://www.math.yorku.ca/SCS/StatResource.html York U. Contents: General statistical resources || York stuff || Statistical Associations || Statistics Departments || SAS stuff || SPSS || LispStat || S Plus || Mathematica || Data Visualization & Statistical Graphics || Psychology & Psychometrics || Online courses || New Online WWW statistics || Data || New Categorical Data Analysis || New Other Statistical Packages || New Unix Statistical Services Software Sites http://www.utexas.edu/cc/stat/world/softwaresites.html U. Texas Pointers to various commercial and free packages. Software: StatLib, by the Carnegie Mellon University Statistics Department. see q115.3, "Statlib". University of Minnesota School of Statistics http://stat.umn.edu/ARCHIVES/archives.html U. Minnesota Archives for Xlisp-Stat, MacAnova, R-Code. Xlisp-Stat Resources http://www.stat.umn.edu/~rcode/xlispstat-resources.html U. Minnesota http://lib.stat.cmu.edu/xlispstat/ CMU XlispStat Archive (Alternate site for Xlisp-Stat) Xlisp-Stat Information Xlisp-Stat is an object oriented environment for statistical computing and dynamic graphics. Written by Professor Luke Tierney (School of Statistics, University of Minnesota), Xlisp-Stat was motivated by the "S" system, with the basic principal that an extendible system is necessary for researching new computationally based statistical methods. Xlisp-Stat provides a set of high-level tools to develop new dynamic graphics techniques, such as those found in the R-code. Unlike S, Xlisp-Stat is based on Lisp, a well-established, complete and flexible programming language. Like S, Xlisp-Stat is an interpreted language, which is much more suited towards exploration than a compiled language (such as C/C++ or Pascal -- these require lengthy recompilations to fix bugs or test simple new ideas). When greater speed is required, a byte-code compiler can be run from inside Xlisp-Stat. This compiler can give increase the speed of execution by an order of magnitude. The defining reference book on Xlisp-Stat is Lisp-Stat by Luke Tierney, 1990, J. Wiley and Sons, ISBN 0-471-50916-7. Since Xlisp-Stat is founded on Lisp, almost any book on general Lisp programming can help you get started. Statistical power analysis software http://www.interchg.ubc.ca/cacb/power/ Power Analysis This page is an attempt to provide an up-to-date list of microcomputer software that can be used to calculate the power of statistical hypothesis tests. It is maintained by Centre for Applied Conservation Biology, University of British Columbia. Ox, by Jurgen A. Doornik http://www.nuff.ox.ac.uk/Users/Doornik/ Ox Ox is an object oriented matrix programming language, with a C and C++ like syntax. Ox currently has versions for Windows (PC and Alpha), MS-DOS, Linux, SunOS, Solaris and HP-UX. Packages include: Estimation and forecasting of ARFIMA(p,d,q) and ARMA(p,q) models; QuadPack is a Fortran library for univariate numerical integration (`quadrature') using adaptive rules SSFPack is a package for analysing univariate Gaussian and non-Gaussian time series which can be placed in the state space form (SSF); MaxBFGS() can be used to maximize functions of many parameters such as likelihood functions; The PcFiml class contains code for VARs, cointegration, simultaneous equations estimation, (multivariate) diagnostic tests; the Simulation class allows for easy implementation of simulation experiments. Some examples are in ox/samples/simula. U. Texas Dept of Biomathematics software. This is mostly Fortran, but some is also in C. DCDFLIB is a good set of functions for computing cumulative distribution function values. http://odin.mdacc.tmc.edu/anonftp/ U. Texas Biomath via www ftp://odin.mdacc.tmc.edu/pub/index U. Texas Biomath via ftp =========================================================================== q510. Chaos Theory (Nonlinear Dynamics) * q510.1, "FAQs for Chaos Theory" * q510.2, "Newsletters for Chaos Theory" * q510.3, "Bibliography for Chaos Theory" q510.1. FAQs for Chaos Theory http://amath.colorado.edu/appm/faculty/jdm/faq.html FAQ http://www.fen.bris.ac.uk/engmaths/research/nonlinear/faq.html FAQ http://amath.colorado.edu/appm/faculty/jdm/faq.html FAQ ftp://rtfm.mit.edu/pub/usenet/news.answers/sci/nonlinear-faq FAQ See also: http://t13.lanl.gov/~nxt/sites.html FAQ http://cnls-www.lanl.gov/nbt/sites.html FAQ =================================== q510.2. Newsletters for Chaos Theory UK Nonlinear News The primary goal of UK Nonlinear News is to allow researchers in the applied and theoretical sides of nonlinear mathematics to keep abreast of the wide variety of nonlinear activities throughout the UK. To join the mailing list, send email to uk-nonl-subs@ucl.ac.uk with the word SUBSCRIBE in the subject field. Or see: http://www.amsta.leeds.ac.uk/Applied/news.dir/index.html Nonlinear News =================================== q510.3. Bibliography for Chaos Theory Peter E. Beckmann (beckmann@nemo.physik.uni-mainz.de) at the Department of Physics, University of Mainz, Mainz, Germany has a nonlinear papers bibliography containing thousands of entries. http://www.uni-mainz.de/FB/Physik/Chaos/chaosbib.html Nonlinear biblio ftp://ftp.uni-mainz.de/pub/chaos/chaosbib Nonlinear biblio, BibTex-style ftp://ftp.uni-mainz.de/pub/chaos/chaosref Nonlinear biblio, Refs-style =========================================================================== q520. Symbolic Algebra Since the symbolic algebra systems have been well documented elsewhere, I simply provide pointers instead of reviewing them here. An good recent article on commercial math & visualization software is: Braham, Robert. "Math & Visualization: new tools, new frontiers", IEEE Spectrum 32, 11 (November 1995), p. 19-36. The article contains tables comparing large number of commercial products. There is no mention of the many excellent free products though. * q520.1, "Comparative Reviews on Symbolic Algebra Packages" Free Software for Symbolic Algebra: * q520.2.1, "MuPAD" * q520.2.2, "Jacal" * q520.2.3, "GAP" * q520.2.4, "PARI/GP" * q520.2.5, "Form" * q520.2.6, "GRTensorII" * q520.2.7, "SAML" =================================== * q520.3, "Automatic Differentiation Tools" * q520.4, "Web sites for Symbolic Algebra" =================================== q520.1. Comparative Reviews on Symbolic Algebra Packages Michael Wester maintains a web page with his detailed review of Axiom, Derive, Macsyma, Maple, Mathematica, Mupad, and Reduce, as well as references and links to other reviews. Wester's review compares the packages on 131 problems, mostly from symbolic algebra. http://math.unm.edu/~wester/cas_review.html Wester's www page ftp://math.unm.edu/pub/wester/cas/Paper.ps Wester's paper via ftp See the articles in Computers in Physics, Vol 6 #4 and #5 [Jul/Aug, Sep/Oct, 1992]. See the web pages at Indiana University Center for Statistical and Mathematical Computing for a several comparisons and reviews of symbolic math and general math/stat packages: http://www.indiana.edu/~statmath/mathsites.html Indiana U. math overview http://www.indiana.edu/~statmath/math/index.html Indiana U. symbolic math review Several sites devoted to "Comparison of Mathematica on Various Computers" can be reached via: http://smc.vnet.net/mathbench.html Christensen or http://fampm201.tu-graz.ac.at/karl/timings.html Karl There are some comparisons kept by Paulo Ney deSouza on the Berkeley math gopher (in particular the file Comparison, but also others): gopher://math.berkeley.edu/11/Symbolic_Soft Berkeley Math gopher See also the paper by Laurent Bernardin, ``A Review of Symbolic Solvers'', SIGSAM bulletin 31(1), 1996. Available in postscript form at http://www.inf.ethz.ch/personal/bernardi/publications/review.ps Bernardin's review Macsyma also has comparisons of Macsyma's commercial product vs. others at: http://www.macsyma.com Macsyma =================================== q520.2.1. MuPAD http://math-www.uni-paderborn.de/~cube/ MuPAD ftp://math-ftp.uni-paderborn.de:/pub/MuPAD MuPAD via ftp ftp mirrors: * Deutschland ftp://ftp.uni-paderborn.de:/pub/MuPAD MuPAD (daily mirror) ftp://ftp.ask.uni-karlsruhe.de:/pub/education/mathematics/MuPAD MuPAD ftp://ftp.germany.eu.net:/pub/comp/applications/math/mupad MuPAD * France ftp://ftp.inria.fr:/lang/MuPAD MuPAD * Switzerland ftp://ftp.switch.ch:/mirror/MuPAD MuPAD * USA ftp://archives.math.utk.edu:/software/multi-platform/MuPAD MuPAD ftp://ftp.math.utah.edu:/pub/mupad MuPAD MuPAD has been strongly recommended by users. From the [author]: MuPAD is a system for symbolic and numeric computation, parallel mathematical programming and mathematical visualization. It is intended to be a 'general purpose' computer algebra system. MuPAD has easy-to-use language constructs for parallel programming. A prerelease Version for parallel programming exists for Sequent and Sun multiprocessor machines. Programming in MuPAD's own programming language is supported by a comfortable source code debugger. Window-based user interfaces for MuPAD exist for the X-Window-System and the Apple Macintosh. MuPAD is distributed for free (for non-commercial use). It is not in the public domain; a registration is required. =================================== q520.2.2. Jacal ftp://prep.ai.mit.edu/pub/gnu/jacal Jacal From the [author]: JACAL is a symbolic mathematics system for the simplification and manipulation of equations and single and multiple valued algebraic expressions constructed of numbers, variables, radicals, and algebraic functions, differential, and holonomic functions. In addition, vectors and matrices of the above objects are included. JACAL is written in Scheme. A version of Scheme (IEEE P1178 and R4RS compliant) written in C is available with JACAL. SCM runs on Amiga, Atari-ST, MacOS, MS-DOS, OS/2, NOS/VE, Unicos, VMS, Unix and similar systems. JACAL source is available via FTP (detailed instructions follow) from: ftp://altdorf.ai.mit.edu:archive/scm/jacal1a4.tar.gz JACAL ftp://prep.ai.mit.edu:pub/gnu/jacal/jacal1a4.tar.gz JACAL ftp://ftp.maths.tcd.ie:pub/bosullvn/jacal/jacal1a4.tar.gz JACAL ftp://ftp.cs.indiana.edu:/pub/scheme-repository/scm/jacal1a4.tar.gz JACAL SLIB is a portable scheme library which JACAL requires: ftp://altdorf.ai.mit.edu:archive/scm/slib2a1.tar.gz SLIB ftp://prep.ai.mit.edu:pub/gnu/jacal/slib2a1.tar.gz SLIB ftp://ftp.maths.tcd.ie:pub/bosullvn/jacal/slib2a1.tar.gz SLIB ftp://ftp.cs.indiana.edu:/pub/scheme-repository/imp/slib2a1.tar.gz SLIB SCM is a small Scheme implementation under which JACAL will run. ftp://altdorf.ai.mit.edu:archive/scm/scm4e1.tar.gz SCM ftp://prep.ai.mit.edu:pub/gnu/jacal/scm4e1.tar.gz SCM ftp://ftp.maths.tcd.ie:pub/bosullvn/jacal/scm4e1.tar.gz SCM ftp://ftp.cs.indiana.edu:/pub/scheme-repository/imp/scm4e1.tar.gz SCM =================================== q520.2.3. GAP ftp sites: ftp://ftp.math.rwth-aachen.de/pub/gap/ GAP ftp://archives.math.utk.edu/software/multi-platform/gap/ GAP ftp://dehn.mth.pdx.edu/pub/math/gap/ GAP ftp://pell.anu.edu.au/pub/gap/ GAP [author]: GAP is a system for computational discrete algebra, which we have developed with particular emphasis on computational group theory, but which has already proved useful also in other areas. The name GAP is an acronym for *Groups, Algorithms, and Programming*. =================================== q520.2.4. PARI/GP ftp://megrez.math.u-bordeaux.fr/pub/pari/ PARI/GP Also at math.ucla.edu [author]: PARI/GP is a package which is aimed at efficient computations in number theory, but also contains a large number of functions unrelated to number theory. It is somewhat related to a Computer Algebra System, but is not really one since it treats symbolic expressions as mathematical entities such as polynomials, series, matrices, etc..., and not as expressions per se. However it is often much faster than other CAS, and contains a huge number of specific functions not found elsewhere, essentially for use in number theory. In particular, and especially so in the present release, there is a very large package for working in general algebraic number fields. =================================== q520.2.5. Form http://rulgm4.LeidenUniv.nl/gj/form.html Form ftp://ftp.nikhef.nl/pub/form/ Form via ftp [author]: The symbolic manipulation program Form is a powerful tool to do large algebraic calculations. It is an easy-to-learn language which is complementary to large programs such as Maple and Mathematica in that not much knowledge is built in, but Form provides you with the means to grind quickly through large formulae. In this introductory course the most-used commands are introduced and useful algorithms are discussed. Many examples illustrate the text. =================================== q520.2.6. GRTensorII http://astro.queensu.ca/~grtensor GRTensorII via www ftp://astro.queensu.ca/pub/grtensor GRTensorII via ftp [author]: GRTensorII is a computer algebra package for performing calculations in the general area of differential geometry. Its purpose is the calculation of tensor components on curved spacetimes specified in terms of a metric or set of basis vectors. It is available in both MapleV and Mathematica versions, and is distributed free of charge =================================== q520.2.7. SAML ftp://topo.math.u-psud.fr:/pub/bousch/saml-960828.tgz SAML [author]: SAML, the Simple Algebraic Math Library, is free. Keep in mind that it's a work in progress. That's for Unix only. =================================== q520.2.8. SACLIB ftp://ftp.risc.uni-linz.ac.at/pub/saclib SACLIB [Back in 1994, Andre Heck wrote]: SACLIB is a library of C programs for computer algebra derived from the SAC2 system. Hoon Hong was the main instigator. Sometime early in 1990 he proposed to translate SAC2 (which was written in the ALDES language) into C instead of Fortran (as it had been since 1976), and he quickly wrote the required translator. The results were rewarding in several ways. Hoon Hong, George E. Collins and Jeremy Johnson, working together at Ohio State University, observed a speedup by a factor of about two in most applications and the powerful debugging facilities associated with C became available. Later that year Hoon finished his doctorate and moved to RISC, where Bruno Buchberger was writing a book on Groebner bases and working on a set of programs to go with it. He found that SAC2 was the only computer algebra system in which he could write these programs without an unacceptable sacrifice in computational efficiency. It became apparent that for similar reasons other researchers would benefit greatly from the availability of a library of C programs derived from SAC2. Subsequently Bruno did much to promote and facilitate the preparation of the library for distribution. Although the translated programs were correct, they needed to be reformatted for user consumption, a users guide was required, and the developers had compulsions to make some minor improvements. Jeremy Johnson made many recent improvements to the algebraic number algorithms and wrote the corresponding chapter of the User Guide, among other things. Werner Krandick made improvements to the polynomial real root algorithms and wrote the corresponding chapter in the User Guide. Mark Encarnacion wrote three chapters of the User Guide and also converted the polynomial input and output algorithms to modern notation from the original "Fortran notation". Ana Mandache, Andreas Neubacher and Hoon Hong all toiled long hours editing and reformatting programs. Andreas deserves special recognition. He initiated the writing of the manual, wrote three chapters of the manual and two of the appendices, and did all the required system maintenance. To facilitate experimenting with the functions in the library, Herbert Vielhaber implemented isac, the interactive shell for SACLIB. He also wrote the corresponding appendix of the manual. This initial version of SACLIB is just the beginning of what is to come. The developers know how to improve several of the programs in the current system and will do it for subsequent versions. Some basic functionalities are largely undeveloped in the currrent system (e.g. linear algebra) but they will be supplied in subsequent versions. Some more advanced functionalities (e.g. polynomial complex roots and quantifier elimination) are nearly ready and will be forthcoming soon. Also it is expected that users of the system will write programs based on the ones we distribute and offer them to other users. =================================== q520.2.9. NTL - A Library for doing Number Theory http://www.cs.wisc.edu/~shoup/ntl NTL [author]: * NTL is a high-performance, portable C++ library providing data structures and algorithms for manipulating signed, arbitrary length integers, and for vectors, matrices, and polynomials over the integers and over finite fields. * NTL uses state-of-the-art algorithms. In particular, its code for polynomial arithmetic is one of the fastest available. Early versions of NTL have been used to set "world records" for polynomial factorization and point counting on elliptic curves. * NTL is written entirely in C++, and can be easily installed on just about any Unix platform, including PCs, and 32- and 64-bit workstations. Despite the fact that NTL is written in C++ and avoids assembly, NTL's performance is generally much better than is typical of such portable libraries. * NTL is relatively easy to use, and it provides a good environment for easily and quickly implementing new number-theoretic algorithms, without sacrificing performance. * NTL is free software that is intended for research and educational purposes only. =================================== q520.3. Automatic Differentiation Tools [Luiz Henrique de Figueiredo]: A good starting point for automatic differentiation tools is: http://www.mcs.anl.gov/autodiff Argonne National Lab =================================== q520.4. Web sites for Symbolic Algebra U.C. Berkeley gopher://math.berkeley.edu U.C. Berkeley Math Dept. via gopher ftp://math.berkeley.edu/pub U.C. Berkeley Math Dept. via ftp A large site of courses, archives, pointers to other sites. The Symbolic_Soft directory contains info on: ALJABR, AMP, Articles_and_Books/, Available_Systems, Axiom Bibliography, CALC, CLA, Calculus, Cayley, CoCoA, Comparison/ DELiA, DOE-Macsyma, Derive, FLAC, Form, GANITH, GAP, GNU-calc GRTensorII, Galois, Gmp, JACAL, KAN, KANT, LIE, LiE, MALM, MAS, MPQS Macaulay, Macsyma, Magma/, Maple/, Mathematica/, Maxima, Mercury Mock-Mma, NCAlgebra, Numbers, On_Going/, PARI, PFSA, Paramacs Reduce/, Reviews/, Ricci, SENAC/, SIMATH, STENSOR, Schoonschip Schur, SymbMath, Theorist, UBASIC, Vaxima, Weyl, XPL, cas.tex CAIN: The Computer Algebra Information Network http://www.can.nl/cain.html CAIN CAIN contains information on symbolic algebra packages, conferences, newsletters, bibliographies and tools. It also contains pointers to a number of related information servers. As of December 1995, it contains info on the following: * General purpose systems: ALJABR, AXIOM, Derive, FORM, GNU-calc, MACSYMA Descendants, Macsyma, Magma, Maple, Mathematica, MAXIMA, MuPAD, PARAMAX, PUNIMAX, REDUCE, SENAC, Theorist, VAXIMA * (Non)Commutative Algebra & Algebraic Geometry: Albert, Bergman, CALI, CASA, CoCoA, FELIX, GANITH, GB, GRB, GROEBNER (from RISC-Linz), GROEBNER (REDUCE package), IDEALS, KAN, Macaulay, MAS, NCALGEBRA, SACLIB, Singular, WU * Differential Equation Solvers & Tools: List of Symmetry Programs (PostScript, gzip-compressed), CRACK, DELiA, DESIR, Diffgrob2 (Manual: PostScript, gzip-formatted), DIMSYM, FIDE, LIE (A.K. Head, in MuMath), Lie (Baumann, in Mathematica), Lie-Baecklund Symmetries (Baumann, in Mathematica), liesymm, ODESOLVE, PDELIE, SPDE, , StandardForm, SYM_DE, SYMMGRP.MAX (Manual: PostScript, gzip-formatted) * Finite Element Analysis: MathFE, PDEase, SENAC/FEM (PostScipt, gzip-formatted); see also SENAC, * Group Theory: ANU Software, Cayley, CHEVIE, GAP, GRAPE, GUAVA, LiE, LIE (REDUCE package), Magma, MeatAxe, Schur, Sisyphos, Symmetrica, Weyl Groups and Hecke Algebras * High Energy Physics: FeynArts, FeynCalc, FORM, HEP, Schoonschip, Tracer * Number Theory: Galois, KANT, KASH, MALM, Numbers, PARI, SIMATH, UBASIC * Tensor Calculus: CARTAN, Classi, GRTensor, MathTensor, Redten, Ricci, SHEEP, STENSOR * Experimental systems: PC Shareware with Symbolic Features: AMP, Calculus and Differential Equations, CC4, CLA, Mathomatic, PFSA, SymbMath, X(PLORE), * Experimental Systems: Various Systems AUTOMATA, QUOTPIC & TESTISOM, Computer Algebra Kit, FLAC, JACAL, Mock-Mma, ORME, RepTiles, Asir, SimLab, Computer Tools for Analysis and Simulation SymbolicNet http://symbolicnet.mcs.kent.edu/ SymbolicNet Like CAIN, SymbolicNet contains information on symbolic algebra packages, conferences, newsletters, bibliographies and tools. As of October 1995, it contains info on the following packages: Axiom, Derive, GANITH, GRTensor, Macsyma, Magma, Maple, Mathematica MathSoft, MathTensor, Milo, MuPAD, Pari-1.39, Reduce, Schur, SymbMath Indiana U. Mathematical Computing Resources on the Internet http://www.indiana.edu/~statmath/mathsites.html Indiana U. Contains pointers to a number of reviews of mathematics packages, and to other mathematics related sites. Also contains a number of downloadable shareware math packages. Number Theory Web A large web site devoted to number theory resources. http://www.math.uga.edu/~ntheory/ Number Theory Web =========================================================================== q530. Cryptography (Cryptology) See newsgroups sci.crypt, sci.crypt.research. There are numerous cryptography FAQs. See: ftp://rtfm.mit.edu/Index-byname MIT's rtfm FAQ index =========================================================================== q540. Fractals Although generating fractals usually involves floating point numbers, fractals are generally not considered part of NA. The FAQ is at: ftp://rtfm.mit.edu/pub/usenet-by-group/news.answers/fractal-faq MIT's rtfm newsgroups: sci.fractals =========================================================================== q550. Neural Networks Although neural nets use optimization techniques, they are generally regarded as a separate field. The FAQ is at: ftp://rtfm.mit.edu/pub/usenet-by-group/comp.answers/ai-faq/neural-nets MIT's rtfm newsgroups: comp.ai.neural-nets =========================================================================== q560. Discrete algorithms A good intro text for discrete algorithms is: Thomas H. Cormen, Charles E. Leiserson, and Ronald L. Rivest. Introduction to Algorithms MIT Press, 1990. ISBN 0-262-03141-8 Telephone: 617-253-5641, 800-356-0343 See also the newsgroup comp.theory. See: Center for Discrete Mathematics and Theoretical Computer Science (DIMACS) at: http://dimacs.rutgers.edu/ DIMACS Discrete algorithms include: * Sorting algorithms * Network traversal (traveling salesman, etc) * Primality testing (see the cryptography FAQs mentioned above). * Automata Theory * Many other fields =========================================================================== q570. Constraints newsgroup: comp.constraints ftp://rtfm.mit.edu/pub/usenet-by-group/comp.answers/constraints-faq FAQ University of New Hampshire Constraint Computation Center Configuration involves selecting and arranging parts to fit problem constraints. Configuration problems may involve design, manufacturing, sales, installation and maintenance. The parts need not be physical, e.g. they may be actions in plans. http://www.cs.unh.edu/ccc/config/ U. of New Hampshire Constraints archive, containing publications, benchmarks, biblio, faq, ftp sites & www pages: http://web.cs.city.ac.uk/archive/constraints/constraints.html Constraints Archive =========================================================================== q580. Genetic Algorithms For a light-hearted FAQ and overview, see the Hitch-Hiker's Guide to Evolutionary Computation http://research.Germany.EU.net:8080/encore/www/ Hitch-Hiker's Guide via www ftp://ftp.Germany.EU.net/pub/research/softcomp/EC/FAQ/www/Q20_1.htm Hitch-Hiker's Guide via ftp PGAPack, Parallel Genetic Algorithm Library, by David Levine [David Levine] PGAPack is a general-purpose, data-structure-neutral, parallel genetic algorithm library. It is intended to provide most capabilities desired in a genetic algorithm library, in an integrated, seamless, and portable manner. Key features include: * Callable from Fortran or C. * Runs on uniprocessors, parallel computers, and workstation networks. * Binary-, integer-, real-, and character-valued native data types. * Full extensibility to support custom operators and new data types. * Easy-to-use interface for novice and application users. * Multiple levels of access for expert users. * Parameterized population replacement. * Multiple crossover, mutation, and selection operators * Easy integration of hill-climbing heuristics. * Extensive debugging facilities. * Large set of example problems. * Detailed users guide PGAPack is available from: http://www.mcs.anl.gov/pgapack.html PGAPack ftp://ftp.mcs.anl.gov/pub/pgapack/pgapack.tar.Z PGAPack via ftp David Levine can be reached at: levine@mcs.anl.gov MCS 221 C-216 Argonne National Laboratory Argonne, Illinois 60439 (708)-252-6735 Fax: (708)-252-5986 =========================================================================== q590. Simulated Annealing Adaptive Simulated Annealing Package (ASA), by Lester Ingber http://www.alumni.caltech.edu/~ingber/ ASA ftp://ftp.alumni.caltech.edu/pub/ingber ASA via ftp An optimization algorithm for nonlinear and stochastic systems. Also, Skip Carter's home page has info and software on simulated annealing, as well as other topics: digital filters, Kalman filters, neural nets, and C++ software. http://taygeta.com/skips_home.html Skip Carter's page =========================================================================== q800. Teaching and Academic Software * q805, "Ted Brown's Work on Physics and Engineering" * q810, "Gleb Beliakov's Work on Numerical Analysis" q805. Ted Brown's Work on Physics and Engineering Ted Brown has written a set of tutorials on vectors, dynamics, electricity and magnetism. They are implemented for the PC DOS environment, but he might be convinced to write a more general version. email: tbrown@tekotago.ac.nz [Ted Brown]: The tutorial, on VECTORS, is an interactive program suitable for first year students, in that it presumes no previous knowledge of the area. The principal sections are on Addition and Difference of vectors by graphical construction, and by components. All the construction is done on the screen, with magnitudes and angles being presented dynamically in a box, as the mouse is moved about. Magnitudes and directions of resultants are read directly from the screen. Students are required to logon, and records are kept of who has been using the program, for how long, and what their current score is. This information is only available through an instructor module. The program runs in Windows, resolution 640*480, 256 colours, on a standalone machine, or on a network, and its size is around 5 or 6 Meg. If anyone is interested in getting more details, I can be contacted on "tbrown@tekotago.ac.nz" I have, over the last few years written a number of physics tutorials, in the general areas of dynamics, electricity and magnetism, but they have all been written for DOS. If I thought there was some interest, I would re-write them for Windows. Ted. =================================== q810. Gleb Beliakov's Work on Numerical Analysis PNA is designed for the Maple V (release 2 or 3) environment. "Practicum in Numerical Analysis (PNA)" is a set of laboratory tasks designed to be a supplement to the course of numerical analysis. The exercises illustrate the basic numerical methods, show their advantages and limitations and help to understand the behavior of numerical solutions. The interactive use of a computer permits one to understand the properties of the algorithms to an extent impossible to achieve reading textbooks. First, it is possible to present more realistic examples of the usage of numerical methods (bigger systems of equations, more iterations), and second, the students can freely change given illustrations in order to try them out and to clarify the behavior of the solutions. Finally, the discussed algorithms can be used by the students in their further studies by either linking them to bigger programs as a library or by copying the text into another programming environment with slight changes in the syntax. It should be noted that PNA is not a substitute for a textbook but a complement to classical educational tools. ===========================================================================