HTRIB3(3)

SYNOPSIS
SUBROUTINE HTRIB3 (NM, N, A, TAU, M, ZR, ZI)

NAME
htrib3 - Compute the eigenvectors of a complex Hermitian matrix from the eigenvectors of a real symmetric tridiagonal matrix output from HTRID3.

LIBRARY
SLATEC (EISPACK)

CATEGORY
D4C4

TYPE
SINGLE PRECISION (HTRIB3-S)

KEYWORDS
EIGENVALUES, EIGENVECTORS, EISPACK

AUTHOR
Smith, B. T., et al.

DESCRIPTION
This subroutine is a translation of a complex analogue of the ALGOL procedure TRBAK3, NUM. MATH. 11, 181-195(1968) by Martin, Reinsch, and Wilkinson. HANDBOOK FOR AUTO. COMP., VOL.II-LINEAR ALGEBRA, 212-226(1971). This subroutine forms the eigenvectors of a COMPLEX HERMITIAN matrix by back transforming those of the corresponding real symmetric tridiagonal matrix determined by HTRID3. On INPUT NM must be set to the row dimension of the two-dimensional array parameters, A, ZR, and ZI, as declared in the calling program dimension statement. NM is an INTEGER variable. N is the order of the matrix. N is an INTEGER variable. N must be less than or equal to NM. A contains some information about the unitary transformations used in the reduction by HTRID3. A is a two-dimensional REAL array, dimensioned A(NM,N). TAU contains further information about the transformations. TAU is a one-dimensional REAL array, dimensioned TAU(2,N). M is the number of eigenvectors to be back transformed. M is an INTEGER variable. ZR contains the eigenvectors to be back transformed in its first M columns. The contents of ZI are immaterial. 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. NOTE that the last component of each returned vector is real and that vector Euclidean norms are preserved. 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)