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NESC0918 LASO, LASO-2

LASO, Subroutine Library for Matrix Manipulation, Eigenvalues and Eigenvectors

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1. NAME OR DESIGNATION OF PROGRAM:  LASO2. LASO2, block Lanczos
symetric eigenvalue code.
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2. COMPUTERS
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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.
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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.
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5. RESTRICTIONS ON THE COMPLEXITY OF THE PROBLEM:
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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.
NESC0918/02
NEA-DB ran the test case included in this package on a  DEC VAX 8810 computer in 13 seconds of CPU time.
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7. UNUSUAL FEATURES OF THE PROGRAM:
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8. RELATED AND AUXILIARY PROGRAMS

The primary difference between the  original LASO and LASO2 is that LASO2 does not use EISPACK to compute the eigenvalues of the band matrix generated by the Lanczos  algorithm. The Basic Linear Algebra Subroutines (BLAS) used are taken from LINPACK (NESC 800).
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9. STATUS
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.
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.
NESC0918/02
About 400K bytes of VAX 8810 main storage are required  to run the test case included in this package.
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12. PROGRAMMING LANGUAGE(S) USED
Package ID Computer language
NESC0918/01 FORTRAN-IV
NESC0918/02 FORTRAN-IV
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13. OPERATING SYSTEM UNDER WHICH PROGRAM IS EXECUTED:
VMS 5.0 (DEC VAX6220), VM/CMS (IBM4331).
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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.
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15. NAME AND ESTABLISHMENT OF AUTHORS

- D. S. Scott
  Computer Science Department
  The University of Texas at Austin, U. S. A.
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16. MATERIAL AVAILABLE
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
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17. CATEGORIES
  • P. General Mathematical and Computing System Routines

Keywords: eigenvalues, eigenvectors, matrices, numerical solution.