cinvit.f
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