NESC0918 LASO, LASO-2
LASO, Subroutine Library for Matrix Manipulation, Eigenvalues and Eigenvectors
NAME OR DESIGNATION OF PROGRAM, COMPUTER, DESCRIPTION OF PROGRAM OR FUNCTION, METHOD OF SOLUTION, RESTRICTIONS ON THE COMPLEXITY OF THE PROBLEM, TYPICAL RUNNING TIME, UNUSUAL FEATURES OF THE PROGRAM, RELATED AND AUXILIARY PROGRAMS, STATUS, REFERENCES, MACHINE REQUIREMENTS, LANGUAGE, OPERATING SYSTEM UNDER WHICH PROGRAM IS EXECUTED, OTHER PROGRAMMING OR OPERATING INFORMATION OR RESTRICTIONS, NAME AND ESTABLISHMENT OF AUTHORS, MATERIAL, CATEGORIES
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| Program name | Package id | Status | Status date |
|---|---|---|---|
| LASO | NESC0918/01 | Tested | 11-JUN-1982 |
| LASO2 | NESC0918/02 | Tested | 12-MAR-1990 |
Machines used:
| Package ID | Orig. computer | Test computer |
|---|---|---|
| NESC0918/01 | IBM 3033 | IBM 3033 |
| NESC0918/02 | Many Computers | DEC VAX 8810 |
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3. DESCRIPTION OF PROGRAM OR FUNCTION
LASO2 is a package of subroutines developed for solving large sparse symmetric eigenvalue problems. There are two driver subroutines, one to determine a fixed number of eigenvalues and eigenvectors at one end of the spectrum of a large sparse symmetric matrix and other to determine all the eigenvalues and eigenvectors of a large sparse symmetric matrix outside a user-defined excluded interval. Both a single-precision for long word-length (60-bit) machines and a double-precision version for short word-length (32-bit) machines are included.
LASO2 is a package of subroutines developed for solving large sparse symmetric eigenvalue problems. There are two driver subroutines, one to determine a fixed number of eigenvalues and eigenvectors at one end of the spectrum of a large sparse symmetric matrix and other to determine all the eigenvalues and eigenvectors of a large sparse symmetric matrix outside a user-defined excluded interval. Both a single-precision for long word-length (60-bit) machines and a double-precision version for short word-length (32-bit) machines are included.
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4. METHOD OF SOLUTION
LASO2 uses a block Lanczos algorithm with selective orthogonalization to maintain the stability of the algorithm. To compute the eigenvalues of the band matrix generated by the Lanczos algorithm LASO2 uses SLAEIG, a specialized version of the subroutine SBPRQS, which takes advantage of known approximations to eigenvectors. LASO2 monitors all the eigenvalues of interest at every Lanczos step.
LASO2 uses a block Lanczos algorithm with selective orthogonalization to maintain the stability of the algorithm. To compute the eigenvalues of the band matrix generated by the Lanczos algorithm LASO2 uses SLAEIG, a specialized version of the subroutine SBPRQS, which takes advantage of known approximations to eigenvectors. LASO2 monitors all the eigenvalues of interest at every Lanczos step.
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6. TYPICAL RUNNING TIME
Running time varies depending on the problem and the computer used. NESC compiled and executed the sample problem in 5.2 CPU minutes on an IBM4331 and 1.1 minutes on an DEC VAX6220.
Running time varies depending on the problem and the computer used. NESC compiled and executed the sample problem in 5.2 CPU minutes on an IBM4331 and 1.1 minutes on an DEC VAX6220.
NESC0918/02
NEA-DB ran the test case included in this package on a DEC VAX 8810 computer in 13 seconds of CPU time.[ top ]
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| Package ID | Status date | Status |
|---|---|---|
| NESC0918/01 | 11-JUN-1982 | Tested at NEADB |
| NESC0918/02 | 12-MAR-1990 | Tested at NEADB |
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10. REFERENCES
- J. J. Dongarra, J. R. Bunch, C. B. Moler, and G. W. Stewart
LINPACK User's Guide, Society for Industrial and Applied
Mathmatics, Philadelphia, Pennsylvania, 1979.
- G. E. Forsythe, M. A. Malcolm, and C. B. Moler
Computer Methods for Mathematical Computations,
Series in Automatic Computing,
Prentice-Hall, Englewood Cliffs, New Jersey, 1977.
- J. J. Dongarra, J. R. Bunch, C. B. Moler, and G. W. Stewart
LINPACK User's Guide, Society for Industrial and Applied
Mathmatics, Philadelphia, Pennsylvania, 1979.
- G. E. Forsythe, M. A. Malcolm, and C. B. Moler
Computer Methods for Mathematical Computations,
Series in Automatic Computing,
Prentice-Hall, Englewood Cliffs, New Jersey, 1977.
NESC0918/01, included references:
- D.S. Scott:LASO - Block Lanczos Software for Symmetric Eigenvalue Problems
ORNL/CSD-48 (November 1979).
- LASO, NESC No. 918, Tape Description,
National Energy Software Center Note 81-57, May 7, 1981.
NESC0918/02, included references:
- D.S. Scott:LASO - Block Lanczos Software for Symmetric Eigenvalue Problems
ORNL/CSD-48 (November 1979)
- M. Birgersson:
LASO2, Tape Description, Sample Problem Output, and Replacement
Random Number Generator Function for the VAX,
NESC Note 89-32, (February 20, 1989).
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11. MACHINE REQUIREMENTS
1252 Kbytes of memory are needed for compilation, and 942 Kbytes are used for the double-precision execution of the sample problem on an IBM4331. 1.2 Mbytes are used to load LASO2 on a DEC VAX6220.
1252 Kbytes of memory are needed for compilation, and 942 Kbytes are used for the double-precision execution of the sample problem on an IBM4331. 1.2 Mbytes are used to load LASO2 on a DEC VAX6220.
NESC0918/02
About 400K bytes of VAX 8810 main storage are required to run the test case included in this package.[ top ]
| Package ID | Computer language |
|---|---|
| NESC0918/01 | FORTRAN-IV |
| NESC0918/02 | FORTRAN-IV |
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14. OTHER PROGRAMMING OR OPERATING INFORMATION OR RESTRICTIONS
Only a single-precision URAND function is provided for generating uniform random numbers on the interval (0,1). Use on other than DEC20 and IBM-compatible hardware may require modification. The NESC Note includes a listing of a replacement function for use on a DEC VAX6220.
Only a single-precision URAND function is provided for generating uniform random numbers on the interval (0,1). Use on other than DEC20 and IBM-compatible hardware may require modification. The NESC Note includes a listing of a replacement function for use on a DEC VAX6220.
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NESC0918/01
| File name | File description | Records |
|---|---|---|
| NESC0918_01.003 | LASO INFORMATION FILE | 108 |
| NESC0918_01.004 | LASO, DOUBLE PRECISION SOURCE (FORTRAN-4) | 3211 |
| NESC0918_01.006 | TEST DRIVER, DOUBLE PRECISION SOURCE | 248 |
| NESC0918_01.007 | EISPACK ROUTINES, DOUBLE PRECISION SOURCE | 2022 |
| NESC0918_01.008 | LASO, SINGLE PRECISION SOURCE (FORTRAN-4) | 3205 |
| NESC0918_01.010 | TEST DRIVER, SINGLE PRECISION SOURCE | 248 |
| NESC0918_01.011 | LASO DOUBLE PRECISION, OUTPUT OF TEST CASE | 69 |
| NESC0918_01.012 | LASO, JCL TO RUN THE TEST CASE | 66 |
NESC0918/02
| File name | File description | Records |
|---|---|---|
| NESC0918_02.001 | LASO2 information file | 107 |
| NESC0918_02.002 | FORTRAN routines for single precision | 1043 |
| NESC0918_02.003 | FORTRAN routines for single precision | 1085 |
| NESC0918_02.004 | FORTRAN routines for single precision | 1052 |
| NESC0918_02.005 | FORTRAN routines for double precision | 1036 |
| NESC0918_02.006 | FORTRAN routines for double precision | 1083 |
| NESC0918_02.007 | FORTRAN routines for double precision | 1037 |
| NESC0918_02.008 | FORTRAN double prec. driver routine | 244 |
| NESC0918_02.009 | Output of double prec. sample probl.,VAX8810 | 69 |
| NESC0918_02.010 | Changes to LASO,user guide SNLASO and SILASO | 1455 |
Keywords: eigenvalues, eigenvectors, matrices, numerical solution.