ORTRAN(3)

SYNOPSIS
SUBROUTINE ORTRAN (NM, N, LOW, IGH, A, ORT, Z)

NAME
ortran - Accumulate orthogonal similarity transformations in the reduction of real general matrix by ORTHES.

LIBRARY
SLATEC (EISPACK)

CATEGORY
D4C4

TYPE
SINGLE PRECISION (ORTRAN-S)

KEYWORDS
EIGENVALUES, EIGENVECTORS, EISPACK

AUTHOR
Smith, B. T., et al.

DESCRIPTION
This subroutine is a translation of the ALGOL procedure ORTRANS, 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 orthogonal similarity transformations used in the reduction of a REAL GENERAL matrix to upper Hessenberg form by ORTHES. 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 some information about the orthogonal trans- formations used in the reduction to Hessenberg form by ORTHES in its strict lower triangle. A is a two-dimensional REAL array, dimensioned A(NM,IGH). ORT contains further information about the orthogonal trans- formations used in the reduction by ORTHES. Only elements LOW through IGH are used. ORT is a one-dimensional REAL array, dimensioned ORT(IGH). On OUTPUT Z contains the transformation matrix produced in the reduction by ORTHES to the upper Hessenberg form. Z is a two- dimensional REAL array, dimensioned Z(NM,N). ORT has been used for temporary storage as is not restored. 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)