CBABK2(3)

SYNOPSIS
SUBROUTINE CBABK2 (NM, N, LOW, IGH, SCALE, M, ZR, ZI)

NAME
cbabk2 - Form the eigenvectors of a complex general matrix from the eigenvectors of matrix output from CBAL.

LIBRARY
SLATEC (EISPACK)

CATEGORY
D4C4

TYPE
COMPLEX (BALBAK-S, CBABK2-C)

KEYWORDS
EIGENVECTORS, EISPACK

AUTHOR
Smith, B. T., et al.

DESCRIPTION
This subroutine is a translation of the ALGOL procedure CBABK2, which is a complex version of BALBAK, NUM. MATH. 13, 293-304(1969) by Parlett and Reinsch. HANDBOOK FOR AUTO. COMP., VOL.II-LINEAR ALGEBRA, 315-326(1971). This subroutine forms the eigenvectors of a COMPLEX GENERAL matrix by back transforming those of the corresponding balanced matrix determined by CBAL. On INPUT NM must be set to the row dimension of the two-dimensional array parameters, ZR and ZI, as declared in the calling program dimension statement. NM is an INTEGER variable. N is the order of the matrix Z=(ZR,ZI). N is an INTEGER variable. N must be less than or equal to NM. LOW and IGH are INTEGER variables determined by CBAL. SCALE contains information determining the permutations and scaling factors used by CBAL. SCALE is a one-dimensional REAL array, dimensioned SCALE(N). 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)