# rsgba.f

          SUBROUTINE RSGBA (NM, N, A, B, W, MATZ, Z, FV1, FV2, IERR)
    C***BEGIN PROLOGUE  RSGBA
    C***PURPOSE  Compute the eigenvalues and, optionally, the eigenvectors
    C            of a symmetric generalized eigenproblem.
    C***LIBRARY   SLATEC (EISPACK)
    C***CATEGORY  D4B1
    C***TYPE      SINGLE PRECISION (RSGBA-S)
    C***KEYWORDS  EIGENVALUES, EIGENVECTORS, EISPACK
    C***AUTHOR  Smith, B. T., et al.
    C***DESCRIPTION
    C
    C     This subroutine calls the recommended sequence of
    C     subroutines from the eigensystem subroutine package (EISPACK)
    C     to find the eigenvalues and eigenvectors (if desired)
    C     for the REAL SYMMETRIC generalized eigenproblem  BAx = (LAMBDA)x.
    C
    C     On Input
    C
    C        NM must be set to the row dimension of the two-dimensional
    C          array parameters, A, B, and Z, as declared in the calling
    C          program dimension statement.  NM is an INTEGER variable.
    C
    C        N is the order of the matrices A and B.  N is an INTEGER
    C          variable.  N must be less than or equal to NM.
    C
    C        A contains a real symmetric matrix.  A is a two-dimensional
    C          REAL array, dimensioned A(NM,N).
    C
    C        B contains a positive definite real symmetric matrix.  B is a
    C          two-dimensional REAL array, dimensioned B(NM,N).
    C
    C        MATZ is an INTEGER variable set equal to zero if only
    C          eigenvalues are desired.  Otherwise, it is set to any
    C          non-zero integer for both eigenvalues and eigenvectors.
    C
    C     On Output
    C
    C        W contains the eigenvalues in ascending order.  W is a
    C          one-dimensional REAL array, dimensioned W(N).
    C
    C        Z contains the eigenvectors if MATZ is not zero.  Z is a
    C          two-dimensional REAL array, dimensioned Z(NM,N).
    C
    C        IERR is an INTEGER flag set to
    C          Zero       for normal return,
    C          10*N       if N is greater than NM,
    C          7*N+1      if B is not positive definite,
    C          J          if the J-th eigenvalue has not been
    C                     determined after 30 iterations.
    C                     The eigenvalues should be correct for indices
    C                     1, 2, ..., IERR-1, but no eigenvectors are
    C                     computed.
    C
    C        FV1 and FV2 are one-dimensional REAL arrays used for temporary
    C          storage, dimensioned FV1(N) and FV2(N).
    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  REBAKB, REDUC2, TQL2, TQLRAT, TRED1, TRED2
    C***REVISION HISTORY  (YYMMDD)
    C   760101  DATE WRITTEN
    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  RSGBA