BALBAK(3)

SYNOPSIS
SUBROUTINE BALBAK (NM, N, LOW, IGH, SCALE, M, Z)

NAME
balbak - Form the eigenvectors of a real general matrix from the eigenvectors of matrix output from BALANC.

LIBRARY
SLATEC (EISPACK)

CATEGORY
D4C4

TYPE
SINGLE PRECISION (BALBAK-S, CBABK2-C)

KEYWORDS
EIGENVECTORS, EISPACK

AUTHOR
Smith, B. T., et al.

DESCRIPTION
This subroutine is a translation of the ALGOL procedure 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 REAL GENERAL matrix by back transforming those of the corresponding balanced matrix determined by BALANC. On INPUT NM must be set to the row dimension of the two-dimensional array parameter, Z, as declared in the calling program dimension statement. NM is an INTEGER variable. N is the number of components of the vectors in matrix Z. N is an INTEGER variable. N must be less than or equal to NM. LOW and IGH are INTEGER variables determined by BALANC. SCALE contains information determining the permutations and scaling factors used by BALANC. SCALE is a one-dimensional REAL array, dimensioned SCALE(N). M is the number of columns of Z to be back transformed. M is an INTEGER variable. Z contains the real and imaginary parts of the eigen- vectors to be back transformed in its first M columns. Z is a two-dimensional REAL array, dimensioned Z(NM,M). On OUTPUT Z contains the real and imaginary parts of the transformed eigenvectors in its 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)