NESC0800 LINPACK.

1. NAME OR DESIGNATION OF PROGRAM:  LINPACK

3. DESCRIPTION OF PROBLEM OR FUNCTION

LINPACK is a collection of FORTRAN subroutines which analyze and solve  various classes of systems of simultaneous linear algebraic equations. The collection deals with general, banded, symmetric indefinite, symmetric positive definite, triangular, and tridiagonal square matrices, as well as with least squares problems and the QR and singular value decompositions of rectangular matrices. A subroutine-naming convention is employed in which each subroutine name consists of five letters which represent a coded specification (TXXYY) of the computation done by that subroutine. The first letter, T, indicates the matrix data type. Standard FORTRAN allows the use of three such types: S REAL, D DOUBLE PRECISION, and C COMPLEX. In addition, some FORTRAN systems allow a double-precision complex type: Z COMPLEX*16. The second and third letters of the subroutine name, XX, indicate the form of the matrix or its decomposition:

             GE  General              
             GB  General band
             PO  Positive definite
             PP  Positive definite packed
             PB  Positive definite band
             SI  Symmetric indefinite
             SP  Symmetric indefinite packed
             HI  Hermitian indefinite
             HP  Hermitian indefinite packed
             TR  Triangular
             GT  General tridiagonal
             PT  Positive definite tridiagonal
             CH  Cholesky decomposition
             QR  Orthogonal-triangular decomposition
             SV  Singular value decomposition

The final two letters, YY, indicate the computation done by the particular subroutine:
             FA  Factor
             CO  Factor and estimate condition
             SL  Solve
             DI  Determinant and/or inverse and/or inertia
             DC  Decompose
             UD  Update
             DD  Downdate
             EX  Exchange

The following chart shows all the LINPACK subroutines. The initial 'S' in the names may be replaced by D, C or Z and the initial 'C' in the complex-only names may be replaced by a Z.

                    FA    CO    SL    DI    DC    UD    DD    EX

             SGE     x     x     x     x
             SGB     x     x     x     x
             SPO     x     x     x     x
             SPP     x     x     x     x
             SPB     x     x     x     x
             SSI     x     x     x     x
             SSP     x     x     x     x
             CHI     x     x     x     x
             CHP     x     x     x     x
             STR           x     x
             SGT                 x
             SPT                 x
             SCH                             x     x     x     x
             SQR                 x           x
             SSV                             x

The LINPACK package also includes a set of routines to perform  basic vector operations called the Basic Linear Algebra Subprograms (BLAS).

4. METHOD OF SOLUTION

Gaussian elimination, Cholesky decomposition, QR, and singular value decomposition methods are used.

5. RESTRICTIONS ON THE COMPLEXITY OF THE PROBLEM

There are no subroutines for general sparse matrices or for iterative methods for very large problems.

6. TYPICAL RUNNING TIME

Running time varies with problem size. NESC executed each test case in about 8 seconds on Argonne's IBM370/195.

7. UNUSUAL FEATURES OF THE PROGRAM

The LINPACK subroutines contain no machine-dependent constants, input or output statements, character manipulations, COMMON or EQUIVALENCE statements, nor mixed-mode arithmetic. All subroutines except those with names beginning with Z use the portable subset of ANSI FORTRAN. The LINPACK project supports this software in the sense that detailed information on the testing procedures is available, and reports of poor or incorrect performance in conventional FORTRAN operating environments will gain immediate attention from the developers.

8. RELATED AND AUXILIARY PROGRAMS:

10. REFERENCES

- J.J. Dongarra, J.R. Bunch, C.B. Moler, G.W. Stewart:
LINPACK Users' Guide, Society  for Industrial and Applied Mathematics, Philadelphia, Pennsylvania, 1979.
- J.J. Dongarra and C.B. Moler:
LINPACK Working Note #13: Implementation Guide  for  LINPACK, ANL-80-105, October 1980.
- LINPACK, NESC No. 800, Description of "How to Bring up LINPACK on  a UNIX Version 7 System", National Energy Software Center Note 79-64, August 6, 1979.

- C.L. Lawson, R.J. Hanson, D.R. Kincaid and F.T. Krough:
Basic Linear Algebra Subprograms for FORTRAN Usage SAND77-0898  (October 1977)
- J.J. Dongarra and C.B. Moler:
LINPACK Working Note #13: Implementation Guide  for  LINPACK, Technical Memo
No. 330  (February 1979)
- Implementation and Testing of the Software Package LINPACK on DVA SIEMENS
7.80-S at the Computing Centre, University of Dusseldorf (in German) received
November 1989
- LINPACK User's Guide: This Guide is available at a cost of $17.00 per copy
with a 10% discount given for order of fifteen or more copies. If individuals
are SIAM members they can purchase personal copies at a 20% discount.

European requests are handled by:
HAYDEN & Son Ltd.
Spectrum House
Hillview Gardens
LONDON NW4 2JQ
United Kingdom

LINPACK User's Guide

11. MACHINE REQUIREMENTS

The entire coefficient matrix will usually be stored in the computer memory, although there are provisions for band  matrices and for row-by-row processing of large rectangular matrices. 240K bytes of storage are required for execution of a typical sample problem on the IBM360,370 system.

13. OPERATING SYSTEM UNDER WHICH PROGRAM IS EXECUTED:  OS/360,370 on the IBM360,370.

14. OTHER PROGRAMMING OR OPERATING INFORMATION OR RESTRICTIONS

The test drivers call a subroutine TRAPS to set the number of underflows permitted. The call is TRAPS(I1,I2,I3,I4,I5) where
I1 should be set to zero,
I2 is the number of floating-point overflows permitted,
I3 is the number of floating-point underflows permitted,
I4 is the number of fixed-point divides by zero permitted, and
I5 is the number of floating-point divides by zero permitted.

Each  installation will have to provide a subroutine TRAPS, which in turn, should call the local error handling routine which should be set to permit a large number of  underflows (5000). If the error-handling procedures are determined by the operating system control language this will have to be set appropriately and a dummy subroutine TRAPS supplied. TRAPS is the standard routine used in WATFIV. On the IBM360,370 the routine is ERRSET.

The sample problems, or testing aids, have been run at the computer installations listed below using a variety of compiler and operating systems.

       Test Site/Machine

Argonne National Laboratory / IBM370/195
Bell Laboratories at Murray Hill / Honeywell6080
College of William and Mary/IBM370 / 148
International Mathematical and Statistical Libraries (IMSL) / EclipseC330
Iowa State University / Itel-AS/5
Lawrence Livermore Laboratory / CDC7600
Los Alamos Scientific Laboratory / CDC7600, CRAY1
Monash University, Australia / Burroughs6700
NASA Langley Research Center / CDC Cyber175
National Center for Atmospheric Research / CDC7600, CRAY1
National Defense Research Institute, Tumba, Sweden / IBM360/75
Naval Weapons Center, China Lake / UNIVAC1110
Northwestern University / CDC6600
Oak Ridge National Laboratory / IBM360/91
Purdue University / CDC6500
Stanford University, SLAC / IBM370/168
University of California, San Diego / Burroughs6700
University of Kentucky / IBM370/158
University of Illinois, Chicago Circle / IBM370/168
University of Illinois at Urbana-Champaign / CDC Cyber175
The University of Michigan / Amdahl 470/V6
The University of Texas at Austin / CDC6600-6400
University of Toronto, Toronto, Canada / IBM370/165
The University of Wisconsin-Madison / UNIVAC1110
Yale University / DEC-KL-20, KA-10

15. NAME AND ESTABLISHMENT OF AUTHOR

   Contact       J. J. Dongarra
                 Mathematics and Computer Science Division
                 Argonne National Laboratory
                 9700 South Cass Avenue
                 Argonne, Illinois  60439

File name	File description	Records
NESC0800_01.001	SOURCE PROGRAM	6861
NESC0800_01.002	SOURCE PROGRAM	6867
NESC0800_01.003	SOURCE PROGRAM	8771
NESC0800_01.004	SOURCE PROGRAM	8935
NESC0800_01.005	SOURCE PROGRAM	562
NESC0800_01.006	SOURCE PROGRAM	560
NESC0800_01.007	SOURCE PROGRAM	575
NESC0800_01.008	SOURCE PROGRAM	580
NESC0800_01.009	SAMPLE PROBLEM INPUT	614
NESC0800_01.010	SAMPLE PROBLEM INPUT	612
NESC0800_01.011	SAMPLE PROBLEM INPUT	655
NESC0800_01.012	SAMPLE PROBLEM INPUT	545
NESC0800_01.013	SAMPLE PROBLEM INPUT	320
NESC0800_01.014	SAMPLE PROBLEM INPUT	413
NESC0800_01.015	SAMPLE PROBLEM INPUT	439
NESC0800_01.016	SAMPLE PROBLEM INPUT	394
NESC0800_01.017	SAMPLE PROBLEM INPUT	663
NESC0800_01.018	SAMPLE PROBLEM INPUT	457
NESC0800_01.019	SAMPLE PROBLEM INPUT	614
NESC0800_01.020	SAMPLE PROBLEM INPUT	616
NESC0800_01.021	SAMPLE PROBLEM INPUT	657
NESC0800_01.022	SAMPLE PROBLEM INPUT	548
NESC0800_01.023	SAMPLE PROBLEM INPUT	322
NESC0800_01.024	SAMPLE PROBLEM INPUT	414
NESC0800_01.025	SAMPLE PROBLEM INPUT	440
NESC0800_01.026	SAMPLE PROBLEM INPUT	394
NESC0800_01.027	SAMPLE PROBLEM INPUT	664
NESC0800_01.028	SAMPLE PROBLEM INPUT	459
NESC0800_01.029	SAMPLE PROBLEM INPUT	619
NESC0800_01.030	SAMPLE PROBLEM INPUT	620
NESC0800_01.031	SAMPLE PROBLEM INPUT	664
NESC0800_01.032	SAMPLE PROBLEM INPUT	666
NESC0800_01.033	SAMPLE PROBLEM INPUT	552
NESC0800_01.034	SAMPLE PROBLEM INPUT	325
NESC0800_01.035	SAMPLE PROBLEM INPUT	416
NESC0800_01.036	SAMPLE PROBLEM INPUT	440
NESC0800_01.037	SAMPLE PROBLEM INPUT	395
NESC0800_01.038	SAMPLE PROBLEM INPUT	666
NESC0800_01.039	SAMPLE PROBLEM INPUT	458
NESC0800_01.040	SAMPLE PROBLEM INPUT	636
NESC0800_01.041	SAMPLE PROBLEM INPUT	634
NESC0800_01.042	SAMPLE PROBLEM INPUT	680
NESC0800_01.043	SAMPLE PROBLEM INPUT	682
NESC0800_01.044	SAMPLE PROBLEM INPUT	564
NESC0800_01.045	SAMPLE PROBLEM INPUT	336
NESC0800_01.046	SAMPLE PROBLEM INPUT	433
NESC0800_01.047	SAMPLE PROBLEM INPUT	482
NESC0800_01.048	SAMPLE PROBLEM INPUT	433
NESC0800_01.049	SAMPLE PROBLEM INPUT	686
NESC0800_01.050	SAMPLE PROBLEM INPUT	477
NESC0800_01.051	SAMPLE PROBLEM INPUT	11800