ORTBAK(3)

SYNOPSIS
SUBROUTINE ORTBAK (NM, LOW, IGH, A, ORT, M, Z)

NAME
ortbak - Form the eigenvectors of a general real matrix from the eigenvectors of the upper Hessenberg matrix output from ORTHES.

LIBRARY
SLATEC (EISPACK)

CATEGORY
D4C4

TYPE
SINGLE PRECISION (ORTBAK-S, CORTB-C)

KEYWORDS
EIGENVALUES, EIGENVECTORS, EISPACK

AUTHOR
Smith, B. T., et al.

DESCRIPTION
This subroutine is a translation of the ALGOL procedure ORTBAK, 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 REAL GENERAL matrix by back transforming those of the corresponding upper Hessenberg matrix determined by ORTHES. On INPUT NM must be set to the row dimension of the two-dimensional array parameters, A and Z, 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 BALANC. If BALANC has not been used, set LOW=1 and IGH equal to the order of the matrix. A contains some information about the orthogonal trans- formations used in the reduction to Hessenberg form by ORTHES in its strict lower triangle. A is a two-dimensional REAL array, dimensioned A(NM,IGH). ORT contains further information about the orthogonal trans- formations used in the reduction by ORTHES. Only elements LOW through IGH are used. ORT is a one-dimensional REAL array, dimensioned ORT(IGH). 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 eigenvectors 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. ORT has been used for temporary storage as is not restored. NOTE that ORTBAK preserves vector Euclidean norms. 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)