comlr2.f
SUBROUTINE COMLR2 (NM, N, LOW, IGH, INT, HR, HI, WR, WI, ZR, ZI,
+ IERR)
C***BEGIN PROLOGUE COMLR2
C***PURPOSE Compute the eigenvalues and eigenvectors of a complex upper
C Hessenberg matrix using the modified LR method.
C***LIBRARY SLATEC (EISPACK)
C***CATEGORY D4C2B
C***TYPE COMPLEX (COMLR2-C)
C***KEYWORDS EIGENVALUES, EIGENVECTORS, EISPACK, LR METHOD
C***AUTHOR Smith, B. T., et al.
C***DESCRIPTION
C
C This subroutine is a translation of the ALGOL procedure COMLR2,
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 finds the eigenvalues and eigenvectors
C of a COMPLEX UPPER Hessenberg matrix by the modified LR
C method. The eigenvectors of a COMPLEX GENERAL matrix
C can also be found if COMHES has been used to reduce
C this general matrix to Hessenberg form.
C
C On INPUT
C
C NM must be set to the row dimension of the two-dimensional
C array parameters, HR, HI, ZR and ZI, as declared in the
C calling program dimension statement. NM is an INTEGER
C variable.
C
C N is the order of the matrix H=(HR,HI). 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 INT contains information on the rows and columns
C interchanged in the reduction by COMHES, if performed.
C Only elements LOW through IGH are used. If you want the
C eigenvectors of a complex general matrix, leave INT as it
C came from COMHES. If the eigenvectors of the Hessenberg
C matrix are desired, set INT(J)=J for these elements. INT
C is a one-dimensional INTEGER array, dimensioned INT(IGH).
C
C HR and HI contain the real and imaginary parts, respectively,
C of the complex upper Hessenberg matrix. Their lower
C triangles below the subdiagonal contain the multipliers
C which were used in the reduction by COMHES, if performed.
C If the eigenvectors of a complex general matrix are
C desired, leave these multipliers in the lower triangles.
C If the eigenvectors of the Hessenberg matrix are desired,
C these elements must be set to zero. HR and HI are
C two-dimensional REAL arrays, dimensioned HR(NM,N) and
C HI(NM,N).
C
C On OUTPUT
C
C The upper Hessenberg portions of HR and HI have been
C destroyed, but the location HR(1,1) contains the norm
C of the triangularized matrix.
C
C WR and WI contain the real and imaginary parts, respectively,
C of the eigenvalues of the upper Hessenberg matrix. If an
C error exit is made, the eigenvalues should be correct for
C indices IERR+1, IERR+2, ..., N. WR and WI are one-
C dimensional REAL arrays, dimensioned WR(N) and WI(N).
C
C ZR and ZI contain the real and imaginary parts, respectively,
C of the eigenvectors. The eigenvectors are unnormalized.
C If an error exit is made, none of the eigenvectors has been
C found. ZR and ZI are two-dimensional REAL arrays,
C dimensioned ZR(NM,N) and ZI(NM,N).
C
C IERR is an INTEGER flag set to
C Zero for normal return,
C J if the J-th eigenvalue has not been
C determined after a total of 30*N iterations.
C The eigenvalues should be correct for indices
C IERR+1, IERR+2, ..., N, but no eigenvectors are
C computed.
C
C Calls CSROOT for complex square root.
C Calls CDIV for complex division.
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 CDIV, CSROOT
C***REVISION HISTORY (YYMMDD)
C 760101 DATE WRITTEN
C 890531 Changed all specific intrinsics to generic. (WRB)
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 COMLR2