BALANC(3)

SYNOPSIS
SUBROUTINE BALANC (NM, N, A, LOW, IGH, SCALE)

NAME
balanc - Balance a real general matrix and isolate eigenvalues whenever possible.

LIBRARY
SLATEC (EISPACK)

CATEGORY
D4C1A

TYPE
SINGLE PRECISION (BALANC-S, CBAL-C)

KEYWORDS
EIGENVECTORS, EISPACK

AUTHOR
Smith, B. T., et al.

DESCRIPTION
This subroutine is a translation of the ALGOL procedure BALANCE, NUM. MATH. 13, 293-304(1969) by Parlett and Reinsch. HANDBOOK FOR AUTO. COMP., Vol.II-LINEAR ALGEBRA, 315-326(1971). This subroutine balances a REAL matrix and isolates eigenvalues whenever possible. On INPUT NM must be set to the row dimension of the two-dimensional array parameter, A, 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. A contains the input matrix to be balanced. A is a two-dimensional REAL array, dimensioned A(NM,N). On OUTPUT A contains the balanced matrix. LOW and IGH are two INTEGER variables such that A(I,J) is equal to zero if (1) I is greater than J and (2) J=1,...,LOW-1 or I=IGH+1,...,N. SCALE contains information determining the permutations and scaling factors used. SCALE is a one-dimensional REAL array, dimensioned SCALE(N). Suppose that the principal submatrix in rows LOW through IGH has been balanced, that P(J) denotes the index interchanged with J during the permutation step, and that the elements of the diagonal matrix used are denoted by D(I,J). Then SCALE(J) = P(J), for J = 1,...,LOW-1 = D(J,J), J = LOW,...,IGH = P(J) J = IGH+1,...,N. The order in which the interchanges are made is N to IGH+1, then 1 TO LOW-1. Note that 1 is returned for IGH if IGH is zero formally. The ALGOL procedure EXC contained in BALANCE appears in BALANC in line. (Note that the ALGOL roles of identifiers K,L have been reversed.) 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)