CORTH(3)

SYNOPSIS
SUBROUTINE CORTH (NM, N, LOW, IGH, AR, AI, ORTR, ORTI)

NAME
corth - Reduce a complex general matrix to complex upper Hessenberg form using unitary similarity transformations.

LIBRARY
SLATEC (EISPACK)

CATEGORY
D4C1B2

TYPE
COMPLEX (ORTHES-S, CORTH-C)

KEYWORDS
EIGENVALUES, EIGENVECTORS, EISPACK

AUTHOR
Smith, B. T., et al.

DESCRIPTION
This subroutine is a translation of a complex analogue of the ALGOL procedure ORTHES, NUM. MATH. 12, 349-368(1968) by Martin and Wilkinson. HANDBOOK FOR AUTO. COMP., VOL.II-LINEAR ALGEBRA, 339-358(1971). Given a COMPLEX GENERAL matrix, this subroutine reduces a submatrix situated in rows and columns LOW through IGH to upper Hessenberg form by unitary similarity transformations. On INPUT NM must be set to the row dimension of the two-dimensional array parameters, AR and AI, as declared in the calling program dimension statement. NM is an INTEGER variable. N is the order of the matrix A=(AR,AI). 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 CBAL. If CBAL has not been used, set LOW=1 and IGH equal to the order of the matrix, N. AR and AI contain the real and imaginary parts, respectively, of the complex input matrix. AR and AI are two-dimensional REAL arrays, dimensioned AR(NM,N) and AI(NM,N). On OUTPUT AR and AI contain the real and imaginary parts, respectively, of the Hessenberg matrix. Information about the unitary transformations used in the reduction is stored in the remaining triangles under the Hessenberg matrix. ORTR and ORTI contain further information about the unitary transformations. Only elements LOW through IGH are used. ORTR and ORTI are one-dimensional REAL arrays, dimensioned ORTR(IGH) and ORTI(IGH). Calls PYTHAG(A,B) for sqrt(A**2 + B**2). 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
PYTHAG

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)