*     F08TQF Example Program Text
*     Mark 21.  NAG Copyright 2004.
*     .. Parameters ..
      INTEGER          NIN, NOUT
      PARAMETER        (NIN=5,NOUT=6)
      INTEGER          NMAX
      PARAMETER        (NMAX=10)
      INTEGER          LIWORK, LRWORK, LWORK
      PARAMETER        (LIWORK=1,LRWORK=NMAX,LWORK=2*NMAX)
      CHARACTER        UPLO
      PARAMETER        (UPLO='U')
*     .. Local Scalars ..
      DOUBLE PRECISION ANORM, BNORM, EPS, RCOND, RCONDB, T1
      INTEGER          I, INFO, J, LIWOPT, LRWOPT, LWOPT, N
*     .. Local Arrays ..
      COMPLEX *16      AP((NMAX*(NMAX+1))/2), BP((NMAX*(NMAX+1))/2),
     +                 DUMMY(1,1), WORK(LWORK)
      DOUBLE PRECISION EERBND(NMAX), RWORK(LRWORK), W(NMAX)
      INTEGER          IWORK(LIWORK)
*     .. External Functions ..
      DOUBLE PRECISION F06UDF, X02AJF
      EXTERNAL         F06UDF, X02AJF
*     .. External Subroutines ..
      EXTERNAL         ZHPGVD, ZTPCON
*     .. Intrinsic Functions ..
      INTRINSIC        ABS
*     .. Executable Statements ..
      WRITE (NOUT,*) 'F08TQF Example Program Results'
      WRITE (NOUT,*)
*     Skip heading in data file
      READ (NIN,*)
      READ (NIN,*) N
      IF (N.LE.NMAX) THEN
*
*        Read the upper or lower triangular parts of the matrices A and
*        B from data file
*
         IF (UPLO.EQ.'U') THEN
            READ (NIN,*) ((AP(I+(J*(J-1))/2),J=I,N),I=1,N)
            READ (NIN,*) ((BP(I+(J*(J-1))/2),J=I,N),I=1,N)
         ELSE IF (UPLO.EQ.'L') THEN
            READ (NIN,*) ((AP(I+((2*N-J)*(J-1))/2),J=1,I),I=1,N)
            READ (NIN,*) ((BP(I+((2*N-J)*(J-1))/2),J=1,I),I=1,N)
         END IF
*
*        Compute the one-norms of the symmetric matrices A and B
*
         ANORM = F06UDF('One norm',UPLO,N,AP,RWORK)
         BNORM = F06UDF('One norm',UPLO,N,BP,RWORK)
*
*        Solve the generalized symmetric eigenvalue problem
*        A*B*x = lambda*x (ITYPE = 2)
*
         CALL ZHPGVD(2,'No vectors',UPLO,N,AP,BP,W,DUMMY,1,WORK,LWORK,
     +               RWORK,LRWORK,IWORK,LIWORK,INFO)
         LWOPT = WORK(1)
         LRWOPT = RWORK(1)
         LIWOPT = IWORK(1)
*
         IF (INFO.EQ.0) THEN
*
*           Print solution
*
            WRITE (NOUT,*) 'Eigenvalues'
            WRITE (NOUT,99999) (W(J),J=1,N)
*
*           Call ZTPCON (F07UUF) to estimate the reciprocal condition
*           number of the Cholesky factor of B.  Note that:
*           cond(B) = 1/RCOND**2.  ZTPCON requires WORK and RWORK to be
*           of length at least 2*N and N respectively
*
            CALL ZTPCON('One norm',UPLO,'Non-unit',N,BP,RCOND,WORK,
     +                  RWORK,INFO)
*
*           Print the reciprocal condition number of B
*
            RCONDB = RCOND**2
            WRITE (NOUT,*)
            WRITE (NOUT,*)
     +        'Estimate of reciprocal condition number for B'
            WRITE (NOUT,99998) RCONDB
*
*           Get the machine precision, EPS, and if RCONDB is not less
*           than EPS**2, compute error estimates for the eigenvalues
*
            EPS = X02AJF()
            IF (RCOND.GE.EPS) THEN
               T1 = ANORM*BNORM
               DO 20 I = 1, N
                  EERBND(I) = EPS*(T1+ABS(W(I))/RCONDB)
   20          CONTINUE
*
*              Print the approximate error bounds for the eigenvalues
*
               WRITE (NOUT,*)
               WRITE (NOUT,*) 'Error estimates for the eigenvalues'
               WRITE (NOUT,99998) (EERBND(I),I=1,N)
            ELSE
               WRITE (NOUT,*)
               WRITE (NOUT,*) 'B is very ill-conditioned, error ',
     +           'estimates have not been computed'
            END IF
         ELSE IF (INFO.GT.N .AND. INFO.LE.2*N) THEN
            I = INFO - N
            WRITE (NOUT,99997) 'The leading minor of order ', I,
     +        ' of B is not positive definite'
         ELSE
            WRITE (NOUT,99996) 'Failure in ZHPGVD. INFO =', INFO
         END IF
*
*        Print workspace information
*
         IF (LWORK.LT.LWOPT) THEN
            WRITE (NOUT,*)
            WRITE (NOUT,99995) 'Optimum workspace required = ', LWOPT,
     +        'Workspace provided         = ', LWORK
         END IF
         IF (LRWORK.LT.LRWOPT) THEN
            WRITE (NOUT,*)
            WRITE (NOUT,99995) 'Real workspace required = ', LRWOPT,
     +        'Real workspace provided = ', LRWORK
         END IF
         IF (LIWORK.LT.LIWOPT) THEN
            WRITE (NOUT,*)
            WRITE (NOUT,99995) 'Integer workspace required = ', LIWOPT,
     +        'Integer workspace provided = ', LIWORK
         END IF
      ELSE
         WRITE (NOUT,*) 'NMAX too small'
      END IF
      STOP
*
99999 FORMAT (3X,(6F11.4))
99998 FORMAT (4X,1P,6E11.1)
99997 FORMAT (1X,A,I4,A)
99996 FORMAT (1X,A,I4)
99995 FORMAT (1X,A,I5,/1X,A,I5)
      END