RST(3)

SYNOPSIS
SUBROUTINE RST (NM, N, W, E, MATZ, Z, IERR)

NAME
rst - Compute the eigenvalues and, optionally, the eigenvectors of a real symmetric tridiagonal matrix.

LIBRARY
SLATEC (EISPACK)

CATEGORY
D4A5

TYPE
SINGLE PRECISION (RST-S)

KEYWORDS
EIGENVALUES, EIGENVECTORS, EISPACK

AUTHOR
Smith, B. T., et al.

DESCRIPTION
This subroutine calls the recommended sequence of subroutines from the eigensystem subroutine package (EISPACK) to find the eigenvalues and eigenvectors (if desired) of a REAL SYMMETRIC TRIDIAGONAL matrix. 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 order of the matrix. N is an INTEGER variable. N must be less than or equal to NM. W contains the diagonal elements of the real symmetric tridiagonal matrix. W is a one-dimensional REAL array, dimensioned W(N). E contains the subdiagonal elements of the matrix in its last N-1 positions. E(1) is arbitrary. E is a one-dimensional REAL array, dimensioned E(N). MATZ is an INTEGER variable set equal to zero if only eigenvalues are desired. Otherwise, it is set to any non-zero integer for both eigenvalues and eigenvectors. On Output W contains the eigenvalues in ascending order. Z contains the eigenvectors if MATZ is not zero. The eigen- vectors are orthonormal. Z is a two-dimensional REAL array, dimensioned Z(NM,N). IERR is an INTEGER flag set to Zero for normal return, 10*N if N is greater than NM, J if the J-th eigenvalue has not been determined after 30 iterations. The eigenvalues and eigenvectors in the W and Z arrays should be correct for indices 1, 2, ..., IERR-1. 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
IMTQL1, IMTQL2

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)