ELTRAN(3)

SYNOPSIS
SUBROUTINE ELTRAN (NM, N, LOW, IGH, A, INT, Z)

NAME
eltran - Accumulates the stabilized elementary similarity transformations used in the reduction of a real general matrix to upper Hessenberg form by ELMHES.

LIBRARY
SLATEC (EISPACK)

CATEGORY
D4C4

TYPE
SINGLE PRECISION (ELTRAN-S)

KEYWORDS
EIGENVALUES, EIGENVECTORS, EISPACK

AUTHOR
Smith, B. T., et al.

DESCRIPTION
This subroutine is a translation of the ALGOL procedure ELMTRANS, NUM. MATH. 16, 181-204(1970) by Peters and Wilkinson. HANDBOOK FOR AUTO. COMP., VOL.II-LINEAR ALGEBRA, 372-395(1971). This subroutine accumulates the stabilized elementary similarity transformations used in the reduction of a REAL GENERAL matrix to upper Hessenberg form by ELMHES. 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. LOW and IGH are two INTEGER variables determined by the balancing subroutine BALANC. If BALANC has not been used, set LOW=1 and IGH equal to the order of the matrix, N. A contains the multipliers which were used in the reduction by ELMHES in its lower triangle below the subdiagonal. A is a two-dimensional REAL array, dimensioned A(NM,IGH). INT contains information on the rows and columns interchanged in the reduction by ELMHES. Only elements LOW through IGH are used. INT is a one-dimensional INTEGER array, dimensioned INT(IGH). On OUTPUT Z contains the transformation matrix produced in the reduction by ELMHES. 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
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)