SLATEC Routines --- ORTRAN ---

*DECK ORTRAN
      SUBROUTINE ORTRAN (NM, N, LOW, IGH, A, ORT, Z)
C***BEGIN PROLOGUE  ORTRAN
C***PURPOSE  Accumulate orthogonal similarity transformations in the
C            reduction of real general matrix by ORTHES.
C***LIBRARY   SLATEC (EISPACK)
C***CATEGORY  D4C4
C***TYPE      SINGLE PRECISION (ORTRAN-S)
C***KEYWORDS  EIGENVALUES, EIGENVECTORS, EISPACK
C***AUTHOR  Smith, B. T., et al.
C***DESCRIPTION
C
C     This subroutine is a translation of the ALGOL procedure ORTRANS,
C     NUM. MATH. 16, 181-204(1970) by Peters and Wilkinson.
C     HANDBOOK FOR AUTO. COMP., VOL.II-LINEAR ALGEBRA, 372-395(1971).
C
C     This subroutine accumulates the orthogonal similarity
C     transformations used in the reduction of a REAL GENERAL
C     matrix to upper Hessenberg form by  ORTHES.
C
C     On INPUT
C
C        NM must be set to the row dimension of the two-dimensional
C          array parameters, A and Z, as declared in the calling
C          program dimension statement.  NM is an INTEGER variable.
C
C        N is the order of the matrix A.  N is an INTEGER variable.
C          N must be less than or equal to NM.
C
C        LOW and IGH are two INTEGER variables determined by the
C          balancing subroutine  BALANC.  If  BALANC  has not been
C          used, set LOW=1 and IGH equal to the order of the matrix, N.
C
C        A contains some information about the orthogonal trans-
C          formations used in the reduction to Hessenberg form by
C          ORTHES  in its strict lower triangle.  A is a two-dimensional
C          REAL array, dimensioned A(NM,IGH).
C
C        ORT contains further information about the orthogonal trans-
C          formations used in the reduction by  ORTHES.  Only elements
C          LOW through IGH are used.  ORT is a one-dimensional REAL
C          array, dimensioned ORT(IGH).
C
C     On OUTPUT
C
C        Z contains the transformation matrix produced in the reduction
C          by  ORTHES  to the upper Hessenberg form.  Z is a two-
C          dimensional REAL array, dimensioned Z(NM,N).
C
C        ORT has been used for temporary storage as is not restored.
C
C     Questions and comments should be directed to B. S. Garbow,
C     APPLIED MATHEMATICS DIVISION, ARGONNE NATIONAL LABORATORY
C     ------------------------------------------------------------------
C
C***REFERENCES  B. T. Smith, J. M. Boyle, J. J. Dongarra, B. S. Garbow,
C                 Y. Ikebe, V. C. Klema and C. B. Moler, Matrix Eigen-
C                 system Routines - EISPACK Guide, Springer-Verlag,
C                 1976.
C***ROUTINES CALLED  (NONE)
C***REVISION HISTORY  (YYMMDD)
C   760101  DATE WRITTEN
C   890831  Modified array declarations.  (WRB)
C   890831  REVISION DATE from Version 3.2
C   891214  Prologue converted to Version 4.0 format.  (BAB)
C   920501  Reformatted the REFERENCES section.  (WRB)
C***END PROLOGUE  ORTRAN