REBAKB(3)

SYNOPSIS
SUBROUTINE REBAKB (NM, N, B, DL, M, Z)

NAME
rebakb - Form the eigenvectors of a generalized symmetric eigensystem from the eigenvectors of derived matrix output from REDUC2.

LIBRARY
SLATEC (EISPACK)

CATEGORY
D4C4

TYPE
SINGLE PRECISION (REBAKB-S)

KEYWORDS
EIGENVALUES, EIGENVECTORS, EISPACK

AUTHOR
Smith, B. T., et al.

DESCRIPTION
This subroutine is a translation of the ALGOL procedure REBAKB, NUM. MATH. 11, 99-110(1968) by Martin and Wilkinson. HANDBOOK FOR AUTO. COMP., VOL.II-LINEAR ALGEBRA, 303-314(1971). This subroutine forms the eigenvectors of a generalized SYMMETRIC eigensystem by back transforming those of the derived symmetric matrix determined by REDUC2. On Input NM must be set to the row dimension of the two-dimensional array parameters, B and Z, as declared in the calling program dimension statement. NM is an INTEGER variable. N is the order of the matrix system. N is an INTEGER variable. N must be less than or equal to NM. B contains information about the similarity transformation (Cholesky decomposition) used in the reduction by REDUC2 in its strict lower triangle. B is a two-dimensional REAL array, dimensioned B(NM,N). DL contains further information about the transformation. DL is a one-dimensional REAL array, dimensioned DL(N). M is the number of eigenvectors to be back transformed. M is an INTEGER variable. Z contains 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 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)