RSB(3)

SYNOPSIS
SUBROUTINE RSB (NM, N, MB, A, W, MATZ, Z, FV1, FV2, IERR)

NAME
rsb - Compute the eigenvalues and, optionally, the eigenvectors of a symmetric band matrix.

LIBRARY
SLATEC (EISPACK)

CATEGORY
D4A6

TYPE
SINGLE PRECISION (RSB-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 BAND matrix. 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. N is the order of the matrix A. N is an INTEGER variable. N must be less than or equal to NM. MB is the half band width of the matrix, defined as the number of adjacent diagonals, including the principal diagonal, required to specify the non-zero portion of the lower triangle of the matrix. MB must be less than or equal to N. MB is an INTEGER variable. A contains the lower triangle of the real symmetric band matrix. Its lowest subdiagonal is stored in the last N+1-MB positions of the first column, its next subdiagonal in the last N+2-MB positions of the second column, further subdiagonals similarly, and finally its principal diagonal in the N positions of the last column. Contents of storage locations not part of the matrix are arbitrary. A is a two-dimensional REAL array, dimensioned A(NM,MB). 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 A has been destroyed. W contains the eigenvalues in ascending order. W is a one- dimensional REAL array, dimensioned W(N). Z contains the eigenvectors if MATZ is not zero. The eigenvectors 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, 12*N if MB is either non-positive or greater than N, J if the J-th eigenvalue has not been determined after 30 iterations. The eigenvalues and eigenvectors, if requested, should be correct for indices 1, 2, ..., IERR-1. FV1 and FV2 are one-dimensional REAL arrays used for temporary storage, dimensioned FV1(N) and FV2(N). 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
BANDR, TQL2, TQLRAT

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)