SUBROUTINE CINVIT(NM,N,AR,AI,WR,WI,SELECT,MM,M,ZR,ZI,IERR,RM1,
     1   RM2,RV1,RV2)
C***BEGIN PROLOGUE  CINVIT
C***DATE WRITTEN   760101   (YYMMDD)
C***REVISION DATE  830518   (YYMMDD)
C***CATEGORY NO.  D4C2B
C***KEYWORDS  EIGENVALUES,EIGENVECTORS,EISPACK
C***AUTHOR  SMITH, B. T., ET AL.
C***PURPOSE  Computes eigenvectors of a complex upper Hessenberg
C            associated with specified eigenvalues using inverse
C            iteration.
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 two-dimensional
C          array parameters as declared in the calling program
C          dimension statement.
C
C        N is the order of the matrix.
C
C        AR and AI contain the real and imaginary parts,
C          respectively, of the Hessenberg matrix.
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.
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.
C
C        MM should be set to an upper bound for the number of
C          eigenvectors to be found.
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.
C
C        ZR and ZI contain the real and imaginary parts, respectively,
C          of the eigenvectors.  The eigenvectors are normalized
C          so that the component of largest magnitude is 1.
C          Any vector which fails the acceptance test is set to zero.
C
C        IERR is set to
C          Zero       for normal return,
C          -(2*N+1)   if more than MM eigenvectors have been specified,
C          -K         if the iteration corresponding to the K-th
C                     value fails,
C          -(N+K)     if both error situations occur.
C
C        RM1, RM2, RV1, and RV2 are temporary storage arrays.
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***REFERENCES  B. T. SMITH, J. M. BOYLE, J. J. DONGARRA, B. S. GARBOW,
C                 Y. IKEBE, V. C. KLEMA, C. B. MOLER, *MATRIX EIGEN-
C                 SYSTEM ROUTINES - EISPACK GUIDE*, SPRINGER-VERLAG,
C                 1976.
C***ROUTINES CALLED  CDIV,PYTHAG
C***END PROLOGUE  CINVIT