SLATEC Routines --- CINVIT ---

*DECK CINVIT
      SUBROUTINE CINVIT (NM, N, AR, AI, WR, WI, SELECT, MM, M, ZR, ZI,
     +   IERR, RM1, RM2, RV1, RV2)
C***BEGIN PROLOGUE  CINVIT
C***PURPOSE  Compute the eigenvectors of a complex upper Hessenberg
C            associated with specified eigenvalues using inverse
C            iteration.
C***LIBRARY   SLATEC (EISPACK)
C***CATEGORY  D4C2B
C***TYPE      COMPLEX (INVIT-S, CINVIT-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 CXINVIT
C     by Peters and Wilkinson.
C     HANDBOOK FOR AUTO. COMP. VOL.II-LINEAR ALGEBRA, 418-439(1971).
C
C     This subroutine finds those eigenvectors of A COMPLEX UPPER
C     Hessenberg matrix corresponding to specified eigenvalues,
C     using inverse iteration.
C
C     On INPUT
C
C        NM must be set to the row dimension of the two-dimensional
C          array parameters, AR, AI, 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 A=(AR,AI).  N is an INTEGER
C          variable.  N must be less than or equal to NM.
C
C        AR and AI contain the real and imaginary parts, respectively,
C          of the complex upper Hessenberg matrix.  AR and AI are
C          two-dimensional REAL arrays, dimensioned AR(NM,N)
C          and AI(NM,N).
C
C        WR and WI contain the real and imaginary parts, respectively,
C          of the eigenvalues of the matrix.  The eigenvalues must be
C          stored in a manner identical to that of subroutine  COMLR,
C          which recognizes possible splitting of the matrix.  WR and
C          WI are one-dimensional REAL arrays, dimensioned WR(N) and
C          WI(N).
C
C        SELECT specifies the eigenvectors to be found.  The
C          eigenvector corresponding to the J-th eigenvalue is
C          specified by setting SELECT(J) to .TRUE.  SELECT is a
C          one-dimensional LOGICAL array, dimensioned SELECT(N).
C
C        MM should be set to an upper bound for the number of
C          eigenvectors to be found.  MM is an INTEGER variable.
C
C     On OUTPUT
C
C        AR, AI, WI, and SELECT are unaltered.
C
C        WR may have been altered since close eigenvalues are perturbed
C          slightly in searching for independent eigenvectors.
C
C        M is the number of eigenvectors actually found.  M is an
C          INTEGER variable.
C
C        ZR and ZI contain the real and imaginary parts, respectively,
C          of the eigenvectors corresponding to the flagged eigenvalues.
C          The eigenvectors are normalized so that the component of
C          largest magnitude is 1.  Any vector which fails the
C          acceptance test is set to zero.  ZR and ZI are
C          two-dimensional REAL arrays, dimensioned ZR(NM,MM) and
C          ZI(NM,MM).
C
C        IERR is an INTEGER flag set to
C          Zero       for normal return,
C          -(2*N+1)   if more than MM eigenvectors have been requested
C                     (the MM eigenvectors calculated to this point are
C                     in ZR and ZI),
C          -K         if the iteration corresponding to the K-th
C                     value fails (if this occurs more than once, K
C                     is the index of the last occurrence); the
C                     corresponding columns of ZR and ZI are set to
C                     zero vectors,
C          -(N+K)     if both error situations occur.
C
C        RV1 and RV2 are one-dimensional REAL arrays used for
C          temporary storage, dimensioned RV1(N) and RV2(N).
C          They hold the approximate eigenvectors during the inverse
C          iteration process.
C
C        RM1 and RM2 are two-dimensional REAL arrays used for
C          temporary storage, dimensioned RM1(N,N) and RM2(N,N).
C          These arrays hold the triangularized form of the upper
C          Hessenberg matrix used in the inverse iteration process.
C
C     The ALGOL procedure GUESSVEC appears in CINVIT in-line.
C
C     Calls PYTHAG(A,B) for sqrt(A**2 + B**2).
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, PYTHAG
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  CINVIT