corth.f
SUBROUTINE CORTH (NM, N, LOW, IGH, AR, AI, ORTR, ORTI)
C***BEGIN PROLOGUE CORTH
C***PURPOSE Reduce a complex general matrix to complex upper Hessenberg
C form using unitary similarity transformations.
C***LIBRARY SLATEC (EISPACK)
C***CATEGORY D4C1B2
C***TYPE COMPLEX (ORTHES-S, CORTH-C)
C***KEYWORDS EIGENVALUES, EIGENVECTORS, EISPACK
C***AUTHOR Smith, B. T., et al.
C***DESCRIPTION
C
C This subroutine is a translation of a complex analogue of
C the ALGOL procedure ORTHES, NUM. MATH. 12, 349-368(1968)
C by Martin and Wilkinson.
C HANDBOOK FOR AUTO. COMP., VOL.II-LINEAR ALGEBRA, 339-358(1971).
C
C Given a COMPLEX GENERAL matrix, this subroutine
C reduces a submatrix situated in rows and columns
C LOW through IGH to upper Hessenberg form by
C unitary similarity transformations.
C
C On INPUT
C
C NM must be set to the row dimension of the two-dimensional
C array parameters, AR and AI, as declared in the calling
C program dimension statement. NM is an INTEGER variable.
C
C N is the order of the matrix A=(AR,AI). N is an INTEGER
C variable. N must be less than or equal to NM.
C
C LOW and IGH are two INTEGER variables determined by the
C balancing subroutine CBAL. If CBAL has not been used,
C set LOW=1 and IGH equal to the order of the matrix, N.
C
C AR and AI contain the real and imaginary parts, respectively,
C of the complex input matrix. AR and AI are two-dimensional
C REAL arrays, dimensioned AR(NM,N) and AI(NM,N).
C
C On OUTPUT
C
C AR and AI contain the real and imaginary parts, respectively,
C of the Hessenberg matrix. Information about the unitary
C transformations used in the reduction is stored in the
C remaining triangles under the Hessenberg matrix.
C
C ORTR and ORTI contain further information about the unitary
C transformations. Only elements LOW through IGH are used.
C ORTR and ORTI are one-dimensional REAL arrays, dimensioned
C ORTR(IGH) and ORTI(IGH).
C
C Calls PYTHAG(A,B) for sqrt(A**2 + B**2).
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 PYTHAG
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 CORTH