COMBAK(3)

SYNOPSIS
SUBROUTINE COMBAK (NM, LOW, IGH, AR, AI, INT, M, ZR, ZI)

NAME
combak - Form the eigenvectors of a complex general matrix from the eigenvectors of a upper Hessenberg matrix output from COMHES.

LIBRARY
SLATEC (EISPACK)

CATEGORY
D4C4

TYPE
COMPLEX (ELMBAK-S, COMBAK-C)

KEYWORDS
EIGENVALUES, EIGENVECTORS, EISPACK

AUTHOR
Smith, B. T., et al.

DESCRIPTION
This subroutine is a translation of the ALGOL procedure COMBAK, NUM. MATH. 12, 349-368(1968) by Martin and Wilkinson. HANDBOOK FOR AUTO. COMP., VOL.II-LINEAR ALGEBRA, 339-358(1971). This subroutine forms the eigenvectors of a COMPLEX GENERAL matrix by back transforming those of the corresponding upper Hessenberg matrix determined by COMHES. On INPUT NM must be set to the row dimension of the two-dimensional array parameters, AR, AI, ZR and ZI, as declared in the calling program dimension statement. NM is an INTEGER variable. LOW and IGH are two INTEGER variables determined by the balancing subroutine CBAL. If CBAL has not been used, set LOW=1 and IGH equal to the order of the matrix. AR and AI contain the multipliers which were used in the reduction by COMHES in their lower triangles below the subdiagonal. AR and AI are two-dimensional REAL arrays, dimensioned AR(NM,IGH) and AI(NM,IGH). INT contains information on the rows and columns interchanged in the reduction by COMHES. Only elements LOW through IGH are used. INT is a one-dimensional INTEGER array, dimensioned INT(IGH). M is the number of eigenvectors to be back transformed. M is an INTEGER variable. ZR and ZI contain the real and imaginary parts, respectively, of the eigenvectors to be back transformed in their first M columns. ZR and ZI are two-dimensional REAL arrays, dimensioned ZR(NM,M) and ZI(NM,M). On OUTPUT ZR and ZI contain the real and imaginary parts, respectively, of the transformed eigenvectors in their first M columns. Questions and comments should be directed to B. S. Garbow, APPLIED MATHEMATICS DIVISION, ARGONNE NATIONAL LABORATORY ------------------------------------------------------------------

REFERENCES
B. T. Smith, J. M. Boyle, J. J. Dongarra, B. S. Garbow, Y. Ikebe, V. C. Klema and C. B. Moler, Matrix Eigen- system Routines - EISPACK Guide, Springer-Verlag, 1976.

ROUTINES CALLED
(NONE)

REVISION HISTORY (YYMMDD)
760101 DATE WRITTEN
890831 Modified array declarations. (WRB)
890831 REVISION DATE from Version 3.2
891214 Prologue converted to Version 4.0 format. (BAB)
920501 Reformatted the REFERENCES section. (WRB)