elmhes.f
SUBROUTINE ELMHES (NM, N, LOW, IGH, A, INT)
C***BEGIN PROLOGUE ELMHES
C***PURPOSE Reduce a real general matrix to upper Hessenberg form
C using stabilized elementary similarity transformations.
C***LIBRARY SLATEC (EISPACK)
C***CATEGORY D4C1B2
C***TYPE SINGLE PRECISION (ELMHES-S, COMHES-C)
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 ELMHES,
C NUM. MATH. 12, 349-368(1968) by Martin and Wilkinson.
C HANDBOOK FOR AUTO. COMP., VOL.II-LINEAR ALGEBRA, 339-358(1971).
C
C Given a REAL GENERAL matrix, this subroutine
C reduces a submatrix situated in rows and columns
C LOW through IGH to upper Hessenberg form by
C stabilized elementary similarity transformations.
C
C On INPUT
C
C NM must be set to the row dimension of the two-dimensional
C array parameter, A, as declared in the calling program
C 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 the input matrix. A is a two-dimensional REAL
C array, dimensioned A(NM,N).
C
C On OUTPUT
C
C A contains the upper Hessenberg matrix. The multipliers which
C were used in the reduction are stored in the remaining
C triangle under the Hessenberg matrix.
C
C INT contains information on the rows and columns interchanged
C in the reduction. Only elements LOW through IGH are used.
C INT is a one-dimensional INTEGER array, dimensioned INT(IGH).
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 ELMHES