# ortran.f

          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