BANDR(3)

SYNOPSIS
SUBROUTINE BANDR (NM, N, MB, A, D, E, E2, MATZ, Z)

NAME
bandr - Reduce a real symmetric band matrix to symmetric tridiagonal matrix and, optionally, accumulate orthogonal similarity transformations.

LIBRARY
SLATEC (EISPACK)

CATEGORY
D4C1B1

TYPE
SINGLE PRECISION (BANDR-S)

KEYWORDS
EIGENVALUES, EIGENVECTORS, EISPACK

AUTHOR
Smith, B. T., et al.

DESCRIPTION
This subroutine is a translation of the ALGOL procedure BANDRD, NUM. MATH. 12, 231-241(1968) by Schwarz. HANDBOOK FOR AUTO. COMP., VOL.II-LINEAR ALGEBRA, 273-283(1971). This subroutine reduces a REAL SYMMETRIC BAND matrix to a symmetric tridiagonal matrix using and optionally accumulating orthogonal similarity transformations. 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 is 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 should be set to .TRUE. if the transformation matrix is to be accumulated, and to .FALSE. otherwise. MATZ is a LOGICAL variable. On OUTPUT A has been destroyed, except for its last two columns which contain a copy of the tridiagonal matrix. D contains the diagonal elements of the tridiagonal matrix. D is a one-dimensional REAL array, dimensioned D(N). E contains the subdiagonal elements of the tridiagonal matrix in its last N-1 positions. E(1) is set to zero. E is a one-dimensional REAL array, dimensioned E(N). E2 contains the squares of the corresponding elements of E. E2 may coincide with E if the squares are not needed. E2 is a one-dimensional REAL array, dimensioned E2(N). Z contains the orthogonal transformation matrix produced in the reduction if MATZ has been set to .TRUE. Otherwise, Z is not referenced. Z is a two-dimensional REAL array, dimensioned Z(NM,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
(NONE)

REVISION HISTORY (YYMMDD)
760101 DATE WRITTEN
890531 Changed all specific intrinsics to generic. (WRB)
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)