CORTB(3)

SYNOPSIS
SUBROUTINE CORTB (NM, LOW, IGH, AR, AI, ORTR, ORTI, M, ZR, ZI)

NAME
cortb - Form the eigenvectors of a complex general matrix from eigenvectors of upper Hessenberg matrix output from CORTH.

LIBRARY
SLATEC (EISPACK)

CATEGORY
D4C4

TYPE
COMPLEX (ORTBAK-S, CORTB-C)

KEYWORDS
EIGENVALUES, EIGENVECTORS, EISPACK

AUTHOR
Smith, B. T., et al.

DESCRIPTION
This subroutine is a translation of a complex analogue 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 COMPLEX GENERAL matrix by back transforming those of the corresponding upper Hessenberg matrix determined by CORTH. 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 information about the unitary trans- formations used in the reduction by CORTH in their strict lower triangles. AR and AI are two-dimensional REAL arrays, dimensioned AR(NM,IGH) and AI(NM,IGH). ORTR and ORTI contain further information about the unitary transformations used in the reduction by CORTH. Only elements LOW through IGH are used. ORTR and ORTI are one-dimensional REAL arrays, dimensioned ORTR(IGH) and ORTI(IGH). M is the number of columns of Z=(ZR,ZI) 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. ORTR and ORTI have been altered. Note that CORTB 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)