Meschach Library
Version 1.2b
David E. Stewart
([email protected])
and
Zbigniew Leyk
([email protected])
School of Mathematical Sciences
Australian National University
Canberra ACT 0200
Australia
[last revised: 6th April, 1994]
1. INTRODUCTION
The Meschach Library is a numerical library of C routines for performing calculations on matrices and vectors. It is intended for solving systems of linear equations (dense and sparse), solve least squares problems, computing eigenvalues and eigenvectors, etc. We do not claim that it contains every useful algorithm in numerical linear algebra, but it does provide a basis on which more advanced algorithms can be built. The library is for people who know something about the C programming language, something of how to solve the numerical problem they are faced with but do not want to have the hassle of building all the necessary routines from the scratch. The library is not a loose collection of numerical routines but it comprises a coherent system. The current version is enhanced with many features comparing with previous versions. Since the memory requirements are nontrivial for large problems we have paid more attention to allocation/deallocation of memory.
The source code is available to be perused, used and passed on without cost, while ensuring that the quality of the software is not compromised. The software is copyrighted; however, the copyright agreement follows in the footsteps of the Free Software Foundation in preventing abuse that occurs with totally public domain software.
Detailed instructions for installing Meschach are contained below.
Pronunciation: if in doubt, say "me-shark". This is close enough. Don't ask us "Why call it that?" Have a look at the quote at the front of the manual.
2. AVAILABILITY
The authors make this code openly available to others, in the hope that
it will prove to be a useful tool. We ask only that:
-
If you publish results obtained using Meschach, please consider acknowledging the source of the code.
-
If you discover any errors in the code, please promptly communicate them to the authors.
We also suggest that you send email to the authors identifying yourself as a user of Meschach; this will enable the authors to notify you of any corrections/improvements in Meschach.
3. HOW TO GET ITThere are several different forms in which you might receive Meschach. To provide a shorthand for describing collections of files, the Unix convention of putting alternative letters in [...] will be used. (So, fred[123] means the collection fred1, fred2 and fred3.) Meschach is available over Internet/AARnet via netlib, or at the anonymous ftp site thrain.anu.edu.au in the directory pub/meschach. There are five .shar files: meschach[01234].shar (which contain the library itself), meschach0.shar (which contains basic documentation and machine dependent files for a number of machines). Of the meschach[1234].shar files, only meschach[12].shar are needed for the basic Meschach library; the third .shar file contains the sparse matrix routines, and the the fourth contains the routines for complex numbers, vectors and matrices. There is also a README file that you should get from meschach0.shar.
If you need the old iterative routines, the file oldmeschach.shar contains the files conjgrad.c, arnoldi.c and lanczos.c.
To get the library from netlib,
mail [email protected] send all from c/meschach
There are a number of other netlib sites which mirror the main netlib sites. These include [email protected] (Oak Ridge, TN, USA), [email protected] (Oslo, Norway), ftp.cs.uow.edu.au (Wollongong, Australia; ftp only), [email protected] (Taiwan), elib.zib-berlin.de (Berlin, Germany; ftp only). (For anonymous ftp sites the directory containing the Meschach .shar files is pub/netlib/c/meschach or similar, possibly depending on the site.)
Meschach is available in other forms on thrain.anu.edu.au by ftp in the directory pub/meschach. It is available as a .tar file (mesch12a.tar for version 1.2a), or as a collection of .shar files, or as a .zip file. The .tar and .zip versions each contain the entire contents of the Meschach library.
There is a manual called "Meschach: Matrix Computations in C" which has been published by
Centre for Mathematics and its Applications
School of Mathematical Sciences
Australian National University
Canberra, ACT 0200
Australia
and costs A$30 (about US$22) + postage/handling. You can order it by writing there or you can send email messages to one of us ([email protected] or [email protected]) and we can pass it on.
If you don't have any money, as a stop gap you can get the OLD manual, although it is out of date, by anonymous ftp from
thrain.anu.edu.au : /pub/meschach/version1.1b/bookdvi.tar [.Z or .gz]
In addition, don't forget that the distribution includes a DOC directory which contains tutorial.txt and fnindex.txt which are respectively, the tutorial chapter (text version) and the function index (text version).
4. INSTALLATION
a) On Unix machines
To extract the files from the .shar files, put them all into a suitable directory and use
sh .shar
to expand the files. (Use one sh command per file; sh *.shar will not work in general.)
For the .tar file, use
tar xvf mesch12a.tar
and for the .zip file use
unzip mesch12a.zip
On a Unix system you can use the configure script to set up the machine-dependent files. The script takes a number of options which are used for installing different subsets of the full Meschach. For the basic system, which requires only meschach[012].shar, use
configure make basic make clean
For including sparse operations, which requires meschach[0123].shar, use
configure --with-sparse make sparse make clean
For including complex operations, which requires meschach[0124].shar, use
configure --with-complex make complex make clean
For including everything, which requires meschach[01234].shar, use
configure --with-all make all make clean
To compile the complete library in single precision (with Real equivalent to float), add the --with-float option to configure, use
configure --with-all --with-float make all make clean
Some Unix-like systems may have some problems with this due to bugs or incompatibilities in various parts of the system. To check this use make torture and run torture. In this case use the machine-dependent files from the machines directory. (This is the case for RS/6000 machines, the -O switch results in failure of a routine in schur.c. Compiling without the -O switch results in correct results.)
If you have problems using configure, or you use a non-Unix system, check the MACHINES directory (generated by meschach0.shar) for your machine, operating system and/or compiler. Save the machine dependent files makefile, machine.c and machine.h. Copy those files from the directory for your machine to the directory where the source code is.
To link into a program prog.c, compile it using
cc -o prog_name prog.c ....(source files).... meschach.a -lm
This code has been mostly developed on the University of Queensland, Australia's Pyramid 9810 running BSD4.3. Initial development was on a Zilog Zeus Z8000 machine running Zeus, a Unix workalike operating system. Versions have also been successfully used on various Unix machines including Sun 3's, IBM RT's, SPARC's and an IBM RS/6000 running AIX. It has also been compiled on an IBM AT clone using Quick C. It has been designed to compile under either Kernighan and Richie, (Edition 1) C and under ANSI C. (And, indeed, it has been compiled in both ANSI C and non-ANSI C environments.)
b) On non-Unix machines
First look in the machines directory for your system type. If it is there, then copy the machine dependent files machine.h, makefile (and possibly machine.c) to the Meschach directory.
If your machine type is not there, then you will need to either compile
by hand'', or construct your own makefile and possibly machine.h as well. The machine-dependent files for various systems should be used as a starting point, and the vanilla'' version of machine.h should be used.
Information on the machine-dependent files follows in the next three
subsections.
On an IBM PC clone, the source code would be on a floppy disk. Use
xcopy a:* meschach
to copy it to the meschach directory. Then cd meschach'', and then compile the source code. Different compilers on MSDOS machines will require different installation procedures. Check the directory meschach for the appropriate makefile'' for your compiler. If your compiler is
not listed, then you should try compiling it ``by hand'', modifying the
machine-dependent files as necessary.
Worst come to worst, for a given C compiler, execute *.c on MS-DOS machines. For example, tcc *.c for Turbo C, and msc *.c for Microsoft C, or if you are using Quick C, qcl *.c and of course cc *.c for the standard Unix compiler.
Once the object files have been generated, you will need to combine them into a library. Consult your local compiler's manual for details of how to do this.
When compiling programs/routines that use Meschach, you will need to have access the the header files in the INCLUDE directory. The INCLUDE directory's contents can be copied to the directory where the programs/routines are compiled.
The files in the DOC directory form a very brief form of documentation on the the library routines in Meschach. See the printed documentation for more comprehensive documentation of the Meschach routines. This can be obtained from the authors via email.
The files and directories created by the machines.shar shell archive contain the files machine.c machine.h and makefile for a particular machine/operating system/compiler where they need to be different. Copy the files in the appropriate directory for your machine/operating system/compiler to the directory with the Meschach source before compiling.
c) makefile
This is setup by using the configure script on a Unix system, based on the makefile.in file. However, if you want to modify how the library is compiled, you are free to change the makefile.
The most likely change that you would want to make to this file is to change the line
CFLAGS = -O
to suit your particular compiler.
The code is intended to be compilable by both ANSI and non-ANSI compilers.
To achieve this portability without sacrificing the ANSI function prototypes (which are very useful for avoiding problems with passing parameters) there is a token ANSI_C which must be #define'd in order to take full advantage of ANSI C. To do this you should do all compilations with
#define ANSI_C 1
This can also be done at the compilation stage with a -DANSI_C flag. Again, you will have to use the -DANSI_C flag or its equivalent whenever you compile, or insert the line
#define ANSI_C 1
in machine.h, to make full use of ANSI C with this matrix library.
d) machine.h
Like makefile this is normally set up by the configure script on Unix machines. However, for non-Unix systems, or if you need to set some things ``by hand'', change machine.h.
There are a few quantities in here that should be modified to suit your particular compiler. Firstly, the macros MEM_COPY() and MEM_ZERO() need to be correctly defined here. The original library was compiled on BSD systems, and so it originally relied on bcopy() and bzero().
In machine.h you will find the definitions for using the standard ANSI C library routines:
/--------------------ANSI C--------------------/ #include <stddef.h> #include <string.h> #define MEM_COPY(from,to,size) memmove((to),(from),(size)) #define MEM_ZERO(where,size) memset((where),'\0',(size))
Delete or comment out the alternative definitions and it should compile correctly. The source files containing memmove() and/or memset() are available by anonymous ftp from some ftp sites (try archie to discover them). The files are usually called memmove.c or memset.c. Some ftp sites which currently (Jan '94) have a version of these files are munnari.oz.au (in Australia), ftp.uu.net, gatekeeper.dec.com (USA), and unix.hensa.ac.uk (in the UK). The directory in which you will find memmove.c and memset.c typically looks like .../bsd-sources/lib/libc/...
There are two further machine-dependent quantities that should be set. These are machine epsilon or the unit roundoff for double precision arithmetic, and the maximum value produced by the rand() routine, which is used in rand_vec() and rand_mat().
The current definitions of these are
#define MACHEPS 2.2e-16 #define MAX_RAND 2.147483648e9
The value of MACHEPS should be correct for all IEEE standard double precision arithmetic.
However, ANSI C's <float.h> contains #define'd quantities DBL_EPSILON and RAND_MAX, so if you have an ANSI C compiler and headers, replace the above two lines of machine.h with
#include <float.h> /* for Real == float */ #define MACHEPS DBL_EPSILON #define MAX_RAND RAND_MAX
The default value given for MAX_RAND is 2^31 , as the Pyramid 9810 and the SPARC 2's both have 32 bit words. There is a program macheps.c which is included in your source files which computes and prints out the value of MACHEPS for your machine.
Some other macros control some aspects of Meschach. One of these is SEGMENTED which should be #define'd if you are working with a machine or compiler that does not allow large arrays to be allocated. For example, the most common memory models for MS-DOS compilers do not allow more than 64Kbyte to be allocated in one block. This limits square matrices to be no more than 9090 . Inserting #define SEGMENTED 1 into machine.h will mean that matrices are allocated a row at a time.
4. SAMPLE TESTS
There are several programs for checking Meschach called torture
(source: torture.c) for the dense routines, sptort (source: sptort.c) for the sparse routines, ztorture (source ztorture.c) for a complex version of torture, memtort (source memtort.c) for memory allocation/deallocation, itertort (source itertort.c) for iterative methods, mfuntort (source mfuntort.c) for computing powers of dense matrices, iotort (source iotort.c) for I/O routines. These can be compiled using make by "make torture", "make sptort", etc. The programs are part of meschach0.shar.
5. OTHER PROBLEMS
Meschach is not a commercial package, so we do not guarantee that everything will be perfect or will install smoothly. Inevitably there will be unforeseen problems. If you come across any bugs or inconsistencies, please let us know. If you need to modify the results of the configure script, or need to construct your own machine.h and makefile's, please send them to us. A number of people sent us the machine dependent files for Meschach 1.1, but with the use of configure, and the new information needed for version 1.2, these machine dependent files don't have quite the right information. Hopefully, though, they are redundant. Non-Unix platforms at present require ``manual'' installation. Because of the variety of platforms (MS-DOS, Macintosh, VAX/VMS, Prime, Amiga, Atari, ....) this is left up to the users of these platforms. We hope that you can use the distibutable machine-dependent files as a starting point for this task.
If you have programs or routines written using Meschach v.1.1x, you should put the statement
#include "oldnames.h"
at the beginning of your files. This is because a large number of the names of the routines have been changed (e.g. "get_vec()" has become "v_get()"). This will enable you to use the old names, although all of the error messages etc., will use the new names. Also note that the new iterative routines have a very different calling sequence. If you need the old iterative routines, they are in oldmeschach.shar.
If you wish to let us know what you have done, etc., our email addresses are
[email protected]
[email protected]
Good luck!
ACKNOWLEDGMENTS
Many people have helped in various ways with ideas and suggestions.
Needless to say, the bugs are all ours! But these people should be thanked for their encouragement etc. These include a number of people at University of Queensland: Graeme Chandler, David De Wit, Martin Sharry, Michael Forbes, Phil Kilby, John Holt, Phil Pollett and Tony Watts. At the Australian National University: Mike Osborne, Steve Roberts, Margaret Kahn and Teresa Leyk. Karen George of the University of Canberra has been a source of both ideas and encouragement. Email has become significant part of work, and many people have pointed out bugs, inconsistencies and improvements to Meschach by email. These people include Ajay Shah of the University of Southern California, Dov Grobgeld of the Weizmann Institute, John Edstrom of the University of Calgary, Eric Grosse, one of the netlib organisers, Ole Saether of Oslo, Norway, Alfred Thiele and Pierre Asselin of Carnegie-Mellon Univeristy, Daniel Polani of the University of Mainz, Marian Slodicka of Slovakia, Kaifu Wu of Pomona, Hidetoshi Shimodaira of the University of Tokyo, Eng Siong of Edinburgh, Hirokawa Rui of the University of Tokyo, Marko Slyz of the University of Michigan, and Brook Milligan of the University of Texas. This list is only partial, and there are many others who have corresponded with us on details about Meschach and the like. Finally our thanks go to all those that have had to struggle with compilers and other things to get Meschach to work.