C**********************************************************************
C
C     Copyright (C) 1991-1992  Roland W. Freund and Noel M. Nachtigal
C     All rights reserved.
C
C     This code is part of a copyrighted package.  For details, see the
C     file "cpyrit.doc" in the top-level directory.
C
C     *****************************************************************
C     ANY USE OF  THIS CODE CONSTITUTES ACCEPTANCE OF  THE TERMS OF THE
C                             COPYRIGHT NOTICE
C     *****************************************************************
C
C**********************************************************************
C
C     This file contains the routines for  the eigenvalue solver, using
C     the  three-term  recurrence  variant  of  the look-ahead  Lanczos
C     algorithm.
C
C**********************************************************************
C
      SUBROUTINE CSLAL (NDIM,NLEN,NLIM,MAXN,MAXVW,M,NORM,ZWK,DWK,IDX,
     $                  IWK,HWK,VECS,INFO)
C
C     Purpose:
C     This  subroutine uses  the Lanczos  algorithm  with look-ahead to
C     compute eigenvalue  estimates.  The algorithm was first described
C     in  the  RIACS Technical  Report 90.45, `An Implementation of the
C     Look-Ahead Lanczos Algorithm for Non-Hermitian Matrices, Part I`,
C     by R.W. Freund, M.H. Gutknecht and N.M. Nachtigal, November 1990.
C     The routine will first run the look-ahead Lanczos algorithm for a
C     number of steps.  It will then prompt the user  for the number of
C     eigenvalues to compute.  In addition, the routine will  also find
C     the common eigenvalues in two successive runs.
C
C     Parameters:
C     For a description of  the parameters, see the file "cslal.doc" in
C     the current directory.
C
C     External routines used:
C     subroutine saxpby(n,z,a,x,b,y)
C        Library routine, computes z = a * x + b * y.
C     real slamch(ch)
C        LAPACK routine, computes machine-related constants.
C     real scnrm2(n,dx,incx)
C        BLAS-1 routine, computes the 2-norm of x.
C     subroutine caxpby(n,z,a,x,b,y)
C        Library routine, computes z = a * x + b * y.
C     real cdotu(n,dx,incx,dy,incy)
C        BLAS-1 routine, computes y^H * x.
C     subroutine crandn(n,x,seed)
C        Library routine, fills x with random numbers.
C     subroutine cslal1(ndim,nlen,m,maxvw,numchk,n,l,lstar,nl,nlstar,vf,
C        ierr,adjust,norm1,norma,tmax,tnrm,zwk,dwk,iwk,idx,vecs)
C        Low-level routine, builds the vectors v_{n+1} and w_{n+1}.
C     subroutine cslalc(maxn,neig,nold,hwk,tf,vf)
C        Library routine, computes common eigenvalues.
C     subroutine cslale(maxn,neig,hwk,tf,vf)
C        Library routine, computes Lanczos eigenvalue approximations.
C
C     Noel M. Nachtigal
C     October 24, 1990
C
C**********************************************************************
C
      INTRINSIC ABS, AIMAG, REAL, SQRT, MAX0, MOD
      EXTERNAL SAXPBY, SLAMCH, SCNRM2, CAXPBY, CDOTU, CRANDN, CSLAL1
      EXTERNAL CSLALC, CSLALE
      COMPLEX CDOTU
      REAL SLAMCH, SCNRM2
C
      INTEGER INFO(4), M, MAXN, MAXVW, NDIM, NLEN, NLIM
      INTEGER IDX(3,NLIM+2), IWK(M,4)
      COMPLEX VECS(NDIM,1*MAXVW+2+1), ZWK(M,5*M+3)
      REAL DWK(M,4), HWK(MAXN,4*MAXN+8), NORM
C
C     Common block variables.
C
C
C     Common block CSLALX.
C
      REAL NORMA
      COMMON /CSLALX/NORMA
C
C     Miscellaneous parameters.
C
      COMPLEX CONE, CZERO
      PARAMETER (CONE = (1.0E0,0.0E0),CZERO = (0.0E0,0.0E0))
      REAL SONE, STEN, SZERO
      PARAMETER (SONE = 1.0E0,STEN = 1.0E1,SZERO = 0.0E0)
C
C     Local variables, permanent.
C
      INTEGER IERR, L, LSTAR, MVWBLT, N, NL, NLSTAR, NMAX, NUMCHK
      SAVE    IERR, L, LSTAR, MVWBLT, N, NL, NLSTAR, NMAX, NUMCHK
      INTEGER RETLBL, TF, VF
      SAVE    RETLBL, TF, VF
      REAL ADJUST, NORM1, TMAX, TMIN, TNRM
      SAVE             ADJUST, NORM1, TMAX, TMIN, TNRM
C
C     Local variables, transient.
C
      INTEGER I, J, K, NEIG, REVCOM
      COMPLEX CTMP
      REAL STMP1, STMP2
C
C     Local variables.
C
      INTEGER NLAL, NOLD
C
C     Initialize some of the permanent variables.
C
      DATA RETLBL /0/
C
C     Check the reverse communication flag to see where to branch.
C        REVCOM   RETLBL      Comment
C           0        0    first call, go to label 10
C           1       60    returning from AXB, go to label 60
C           2       70    returning from ATXB, go to label 70
C
      REVCOM  = INFO(2)
      INFO(2) = 0
      IF (REVCOM.EQ.0) THEN
         N      = 0
         NLAL   = 0
         MVWBLT = 0
         IF (RETLBL.EQ.0) GO TO 10
      ELSE IF (REVCOM.EQ.1) THEN
         IF (RETLBL.EQ.60) THEN
            GO TO 60
         END IF
      ELSE IF (REVCOM.EQ.2) THEN
         IF (RETLBL.EQ.70) GO TO 70
      END IF
      IERR = 1
      GO TO 110
C
C     Check whether the inputs are valid.
C
 10   IERR = 0
      IF (NDIM.LT.1)      IERR = 2
      IF (NLEN.LT.1)      IERR = 2
      IF (NLIM.LT.1)      IERR = 2
      IF (MAXVW.LT.1)     IERR = 2
      IF (NLEN.GT.NDIM)   IERR = 2
      IF (NLIM.GT.MAXN-2) IERR = 2
      IF (M.LT.2*MAXVW+2) IERR = 2
      IF (IERR.NE.0) GO TO 110
C
C     Extract from INFO the output units TF and VF,  and the starting
C     vector flags J and K.
C
      VF    = MAX0(INFO(1),0)
      J     = VF / 100000
      VF    = VF - J * 100000
      K     = VF / 10000
      VF    = VF - K * 10000
      TF    = VF / 100
      VF    = VF - TF * 100
C
C     Extract the norms.
C
      NORMA = SZERO
      NORM1 = ABS(NORM)
C
C     Set the adjustment parameters.
C
      NUMCHK = 25
      ADJUST = STEN
C
C     Extract and check the various tolerances and norm estimates.
C
      TNRM = SLAMCH('E') * STEN
      TMIN = SQRT(SQRT(SLAMCH('S')))
      TMAX = SONE / TMIN
C
C     Set up wrapped indices.  The following indices are used:
C        IDX(1,I) = indices used for IWK and DWK, row-dimensioned M;
C        IDX(2,I) = indices used for v_i;
C        IDX(3,I) = indices used for w_i.
C
      DO 20 I = 1, NLIM+2
         IDX(1,I) = MOD(I-1,M) + 1
         IDX(2,I) = 1 + 1 + 0*(MAXVW+2) + MOD(I-1,MAXVW+2)
         IDX(3,I) = IDX(2,I)
 20   CONTINUE
C
C     Check whether any starting vectors must be supplied.
C
      IF (K.EQ.0) CALL CRANDN (NLEN,VECS(1,1),1)
      CALL CAXPBY (NLEN,VECS(1,IDX(2,1)),CONE,VECS(1,1),CZERO,VECS(1,
     $IDX(2,1)))
CSYM  IF (J.EQ.0) CALL CRANDN (NLEN,VECS(1,1),1)
CSYM  CALL CAXPBY (NLEN,VECS(1,IDX(3,1)),CONE,VECS(1,1),CZERO,VECS(1,IDX(3,1)))
C
C     Zero out the Lanczos matrix.
C
      DO 40 I = 1, MAXN
         DO 30 J = 1, MAXN
            HWK(I,J) = SZERO
            HWK(I,MAXN+J) = SZERO
 30      CONTINUE
 40   CONTINUE
C
C     Scale the first pair of Lanczos vectors and check for invariant
C     subspaces.
C
      STMP1 = SCNRM2(NLEN,VECS(1,IDX(2,1)),1)
CSYM  STMP2 = SCNRM2(NLEN,VECS(1,IDX(3,1)),1)
      STMP2 = STMP1
      IF (STMP1.LT.TNRM) IERR = IERR + 16
      IF (STMP2.LT.TNRM) IERR = IERR + 32
      IF (IERR.NE.0) GO TO 110
      DWK(IDX(1,1),1)   = SONE
      ZWK(IDX(1,1),IDX(1,1)) = CDOTU(NLEN,VECS(1,IDX(2,1)),1,VECS(1,
     $IDX(3,1)),1) / ( STMP1 * STMP2 )
      IF ((STMP1.GE.TMAX).OR.(STMP1.LE.TMIN)) THEN
         CTMP = CMPLX(SONE / STMP1,SZERO)
         CALL CAXPBY (NLEN,VECS(1,IDX(2,1)),CTMP,VECS(1,IDX(2,1)),CZERO,
     $VECS(1,IDX(2,1)))
         STMP1 = SONE
      END IF
      IF ((STMP2.GE.TMAX).OR.(STMP2.LE.TMIN)) THEN
         CTMP = CMPLX(SONE / STMP2,SZERO)
CSYM     CALL CAXPBY (NLEN,VECS(1,IDX(3,1)),CTMP,VECS(1,IDX(3,1)),CZERO,VECS(1,IDX(3,1)))
         STMP2 = SONE
      END IF
      DWK(IDX(1,1),2) = SONE / STMP1
      DWK(IDX(1,1),3) = SONE / STMP2
C
C     Initialize the counters.
C
      L      = 1
      N      = 1
      NLAL   = 0
      NMAX   = 0
      IWK(IDX(1,0+1),1) = 1
      IWK(IDX(1,1+1),1) = 1
      MVWBLT = 1
      NL     = IWK(IDX(1,L+1),1)
C
C     This is one step of the coupled two-term Lanczos algorithm.
C     V_n, W_n, D_{n-1}, F_{n-1}, H_{n-1}, and D_{nn} are given.
C
C     Note that the previous step was  not necessarily step N-1,  as it
C     could have been a restart.
C     Except at the first step, the following hold:
C       NL.LE.N, N-NL.LE.MAXVW-1.
C
      IF (VF.NE.0) WRITE (VF,'(A29)') 'Running look-ahead Lanczos...'
 50   IWK(IDX(1,N),4) = L
      IWK(IDX(1,N),3) = N
C
C     Build v_{n+1} and w_{n+1}.
C     Have the caller carry out AXB, then return here.
C        CALL AXB (VECS(1,IDX(2,N)),VECS(1,1))
C
      INFO(2) = 1
      INFO(3) = IDX(2,N)
      INFO(4) = 1
      RETLBL  = 60
      RETURN
C
C     Have the caller carry out ATXB, then return here.
C        CALL ATXB (VECS(1,IDX(3,N)),VECS(1,1))
C
 60   INFO(2) = 2
      INFO(3) = IDX(3,N)
      INFO(4) = 2
      RETLBL  = 70
CSYM  RETURN
 70   IF ((VF.NE.0).AND.(N.LE.NMAX)) WRITE (VF,'(A11,I8)') 'Rebuilding:'
     $, N+1
      CALL CSLAL1 (NDIM,NLEN,M,MAXVW,NUMCHK,N,L,LSTAR,NL,NLSTAR,VF,IERR,
     $            ADJUST,NORM1,NORMA,TMAX,TMIN,TNRM,ZWK,DWK,IWK,IDX,VECS
     $)
      IF ((IERR.NE.0).AND.(IERR.NE.16).AND.(IERR.NE.32)
     $    .AND.(IERR.NE.48)) GO TO 110
      MVWBLT = MAX0(MVWBLT,NL-IWK(IDX(1,L-1+1),1))
      IWK(IDX(1,N),2) = NLSTAR
C
C     Update the counter for steps taken.
C
      NLAL = N
      NMAX = MAX0(NMAX,NLAL)
C
C     Extract the column of H.
C
      CALL SAXPBY (N+1,HWK(1,N),SZERO,HWK(1,N),SZERO,HWK(1,N))
      CALL SAXPBY (N+1,HWK(1,MAXN+N),SZERO,HWK(1,MAXN+N),SZERO,HWK(1,
     $MAXN+N))
      DO 80 I = NLSTAR, N+1
         CTMP       = ZWK(IDX(1,I),2*M+IDX(1,N))
         HWK(I,N) = REAL(CTMP)
         HWK(I,MAXN+N) = AIMAG(CTMP)
 80   CONTINUE
C
C     Do the next step.
C
      IF ((IERR.NE.0).OR.(N.GE.NLIM)) GO TO 90
      N = N + 1
      GO TO 50
C
C     The eigenvalue code starts here.
C
 90   NOLD = 0
 100  NEIG = 0
      WRITE (6,'()')
      WRITE (6,'(A43,I4)') 'Number of Lanczos steps completed        : '
     $, NLAL
      WRITE (6,'(A43,$)') 'Number of eigenvalues to compute (0=done): '
      READ (5,*) NEIG
      IF ((NEIG.GT.0).AND.(NEIG.LE.NLAL)) THEN
         CALL CSLALE (MAXN,NEIG,HWK,TF,VF)
         IF (NEIG.EQ.0) GO TO 100
         IF (NOLD.NE.0) CALL CSLALC (MAXN,NEIG,NOLD,HWK,TF,VF)
         NOLD = NEIG
         CALL SAXPBY (NOLD,HWK(1,4*MAXN+7),SONE,HWK(1,4*MAXN+4),SZERO,
     $HWK(1,4*MAXN+7))
         CALL SAXPBY (NOLD,HWK(1,4*MAXN+8),SONE,HWK(1,4*MAXN+5),SZERO,
     $HWK(1,4*MAXN+8))
      ELSE IF (NEIG.EQ.0) THEN
         GO TO 110
      END IF
      GO TO 100
C
C     Done.
C
 110  RETLBL  = 0
      NLIM    = NLAL
      INFO(1) = IERR
      NORM    = NORM1
      MAXVW   = MVWBLT
C
      RETURN
      END
C
C**********************************************************************
C
      SUBROUTINE CSLALC (MAXN,NEIG,NOLD,HWK,TF,VF)
C
C     Purpose:
C     This subroutine finds eigenvalues common  to the last two runs of
C     the eigenvalue routine.
C
C     Parameters:
C     MAXN  = the dimensioned size of the array HWK (input).
C     NEIG  = the number of eigs in the current run (input).
C     NOLD  = on entry, the number of eigs in the previous run; on exit
C             the number of common eigs (input/output).
C     HWK   = real work array (input/output).
C     TF    = if not 0, then the routine will output the common eigs to
C             this unit (input).
C     VF    = if not 0, then the routine will produce  verbose messages
C             on this unit (input).
C
C     External routines used:
C     subroutine dhpsrt(n,wr,wi,wm)
C        Library routine, sorts wr and wi and wm.
C
C     Noel M. Nachtigal
C     August 6, 1993
C
C**********************************************************************
C
      INTRINSIC ABS
      EXTERNAL DHPSRT
C
      INTEGER MAXN, NEIG, NOLD, TF, VF
      REAL HWK(MAXN,4*MAXN+8)
C
C     Local variables.
C
      INTEGER I, J, K
      REAL DISTM, EIMAG, EMAGN, EREAL, TOL, TOLM
C
C     Get the number of eigenvalues to find.
C
 10   WRITE (6,'()')
      WRITE (6,'(A43,$)') 'Find the common eigenvalues (1=Yes/0=No) ? '
      READ (5,*) I
      IF (I.NE.1) RETURN
      WRITE (6,'(A43,$)') 'Enter separation tolerance               : '
      READ (5,*) TOL
C
C     Check for common eigenvalues.
C
      K = 0
      DO 30 I = 1, NEIG
         EREAL = HWK(I,4*MAXN+4)
         EIMAG = HWK(I,4*MAXN+5)
         EMAGN = HWK(I,4*MAXN+6)
         DO 20 J = 1, NOLD
            DISTM = SQRT(HWK(J,4*MAXN+7)**2 + HWK(J,4*MAXN+8)**2)
            TOLM  = 0.5E0 * TOL * (EMAGN + DISTM)
            IF (ABS(EMAGN-DISTM).GE.TOLM) GO TO 20
            DISTM = SQRT((EREAL-HWK(J,4*MAXN+7))**2 + (EIMAG-HWK(J,
     $4*MAXN+8))**2)
            IF (DISTM.GE.TOLM) GO TO 20
            K        = K + 1
            HWK(K,4*MAXN+1) = EREAL
            HWK(K,4*MAXN+2) = EIMAG
            HWK(K,4*MAXN+3) = EMAGN
            GO TO 30
 20      CONTINUE
 30   CONTINUE
C
C     Sort the final eigenvalues by decreasing real part.
C
      CALL DHPSRT (K,HWK(1,4*MAXN+1),HWK(1,4*MAXN+2),HWK(1,4*MAXN+3))
C
C     Output the results.
C
      IF (VF.NE.0) WRITE (VF,'(A43,I4)')
     $             'Number of common eigenvalues found       : ', K
      IF (TF.NE.0) THEN
         WRITE (TF,'(A30,E12.7)') 'Common eigenvalues, tolerance: ', TOL
         WRITE (TF,'(2E25.17)') (HWK(I,4*MAXN+1),HWK(I,4*MAXN+2),I=1,K)
         WRITE (TF,'()')
      END IF
      GO TO 10
C
      END
C
C**********************************************************************
C
      SUBROUTINE CSLALE (MAXN,NEIG,HWK,TF,VF)
C
C     Purpose:
C     This subroutine computes the  eigenvalues estimates obtained from
C     the NEIG x NEIG upper left corner of the Lanczos matrix.  It uses
C     the heuristic proposed  by Cullum and Willoughby  to separate the
C     genuine eigenvalues from the spurious ones.
C
C     Parameters:
C     MAXN  = the dimensioned size of the array HWK (input).
C     NEIG  = the size of  the submatrix  whose eigs  are computed.  On
C             exit, it is the number of eigs found (input/output).
C     HWK   = real work array (input/output).
C     TF    = if not 0, then the routine  will output  the Lanczos eigs
C             to this unit (input).
C     VF    = if not 0, then the routine will produce  verbose messages
C             on this unit (input).
C
C     External routines used:
C     subroutine cbal(nm,n,ar,ai,low,igh,scale)
C        EISPACK routine, balances a matrix.
C     subroutine comqr(nm,n,low,igh,hr,hi,wr,wi,ierr)
C        EISPACK routine, computes eigenvalues of an upper Hessenberg
C        matrix.
C     subroutine saxpby(n,z,a,x,b,y)
C        Library routine, computes z = a * x + b * y.
C     subroutine dhpsrt(n,wr,wi,wm)
C        Library routine, sorts wr and wi and wm.
C     real slamch(ch)
C        LAPACK routine, computes machine-related constants.
C
C     Noel M. Nachtigal
C     August 6, 1993
C
C**********************************************************************
C
      INTRINSIC ABS, SQRT
      EXTERNAL CBAL, COMQR, SAXPBY, DHPSRT, SLAMCH
      REAL SLAMCH
C
      INTEGER MAXN, NEIG, TF, VF
      REAL HWK(MAXN,4*MAXN+8)
C
C     Miscellaneous parameters.
C
      REAL SONE, SZERO
      PARAMETER (SONE = 1.0E0,SZERO = 0.0E0)
C
C     Local variables.
C
      INTEGER I, IERR, J, K, NBEG, NCHK, NEND, NLAL
      REAL DISTM, EIMAG, EMAGN, EREAL, TOL, TOLM
      LOGICAL MULTIP
C
C     Compute the separation tolerance.
C
      TOL = SQRT(SLAMCH('E'))
C
C     Extract the NEIG x NEIG matrix.
C
      DO 10 I = 1, NEIG
         CALL SAXPBY (I+1,HWK(1,2*MAXN+I),SONE,HWK(1,I),SZERO,HWK(1,
     $2*MAXN+I))
         CALL SAXPBY (I+1,HWK(1,3*MAXN+I),SONE,HWK(1,MAXN+I),SZERO,HWK(1
     $,3*MAXN+I))
 10   CONTINUE
C
C     Balance it and compute its eigenvalues.
C
      IF (VF.NE.0) WRITE (VF,'(A24)') 'Computing eigenvalues...'
      CALL CBAL (MAXN,NEIG,HWK(1,2*MAXN+1),HWK(1,3*MAXN+1),I,J,HWK(1,
     $4*MAXN+1))
      CALL COMQR (MAXN,NEIG,I,J,HWK(1,2*MAXN+1),HWK(1,3*MAXN+1),HWK(1,
     $4*MAXN+1),HWK(1,4*MAXN+2),IERR)
      IF (IERR.NE.0) THEN
         WRITE (6,'(A25,I2)') 'Error return from COMQR: ', IERR
         RETURN
      END IF
C
C     Compute the magnitude of the eigenvalues.
C
      DO 20 I = 1, NEIG
         HWK(I,4*MAXN+3) = SQRT(HWK(I,4*MAXN+1)**2 + HWK(I,4*MAXN+2)**2)
 20   CONTINUE
C
C     Sort the eigenvalues in decreasing order of magnitude.
C
      CALL DHPSRT (NEIG,HWK(1,4*MAXN+3),HWK(1,4*MAXN+1),HWK(1,4*MAXN+2))
      IF (TF.NE.0) THEN
         WRITE (TF,'(A33,I4)') 'All Lanczos eigenvalues at step: ', NEIG
         WRITE (TF,'(2E25.17)') (HWK(I,4*MAXN+1),HWK(I,4*MAXN+2),I=1,
     $NEIG)
         WRITE (TF,'()')
      END IF
C
C     Separate the repeated eigenvalues from the simple ones.
C
      I    = 1
      NEND = 0
      NLAL = NEIG
      NBEG = NEIG + 1
 30   IF (I.GT.NLAL) GO TO 70
C
C     Outer loop, over all eigenvalues.
C
      J      = I + 1
      EREAL  = HWK(I,4*MAXN+1)
      EIMAG  = HWK(I,4*MAXN+2)
      EMAGN  = HWK(I,4*MAXN+3)
      MULTIP = .FALSE.
 40   IF (J.GT.NLAL) GO TO 60
C
C     Inner loop, find eigenvalues J close to eigenvalue I.  "Close" is
C     defined relative to the average of the two points,  so as to be a
C     symmetric relationship.
C
      TOLM = 0.5E0 * TOL * (EMAGN + HWK(J,4*MAXN+3))
C
C     If the difference  in magnitude  between I and J  is greater than
C     the tolerance, skip the remaining eigenvalues, they will  be even
C     further away (the eigenvalues are assumed sorted in some order of
C     magnitude).
C
      IF (EMAGN-HWK(J,4*MAXN+3).GE.TOLM) GO TO 60
C
C     Compute the distance between the two eigenvalues.
C
      DISTM = SQRT((EREAL-HWK(J,4*MAXN+1))**2 + (EIMAG-HWK(J,4*MAXN+2))
     $**2)
C
C     Check the eigenvalue J.
C
      IF (DISTM.GE.TOLM) THEN
         J = J + 1
      ELSE
         MULTIP = .TRUE.
         DO 50 K = J, NLAL-1
            HWK(K,4*MAXN+1) = HWK(K+1,4*MAXN+1)
            HWK(K,4*MAXN+2) = HWK(K+1,4*MAXN+2)
            HWK(K,4*MAXN+3) = HWK(K+1,4*MAXN+3)
 50      CONTINUE
         NLAL = NLAL - 1
      END IF
      GO TO 40
C
C     Collect the multiple eigenvalues in ELAL(1:NEND),  and the simple
C     ones in ELAL(NBEG:NEIG).
C
 60   IF (MULTIP) THEN
         NEND        = NEND + 1
         HWK(NEND,4*MAXN+4) = EREAL
         HWK(NEND,4*MAXN+5) = EIMAG
         HWK(NEND,4*MAXN+6) = EMAGN
      ELSE
         NBEG = NBEG - 1
         HWK(NBEG,4*MAXN+4) = EREAL
         HWK(NBEG,4*MAXN+5) = EIMAG
         HWK(NBEG,4*MAXN+6) = EMAGN
      END IF
      I = I + 1
      GO TO 30
 70   CONTINUE
C
C     Check whether they are all considered genuine.
C
      IF (NEND.EQ.NLAL) GO TO 120
C
C     Extract the (NEIG-1) x (NEIG-1) matrix.
C
      NCHK = NEIG - 1
      DO 80 I = 1, NCHK
         CALL SAXPBY (I+1,HWK(1,2*MAXN+I),SONE,HWK(2,I+1),SZERO,HWK(1,
     $2*MAXN+I))
         CALL SAXPBY (I+1,HWK(1,3*MAXN+I),SONE,HWK(2,MAXN+I+1),SZERO,
     $HWK(1,3*MAXN+I))
 80   CONTINUE
C
C     Balance it and compute its eigenvalues.
C
      IF (VF.NE.0) WRITE (VF,'(A30)') 'Computing check eigenvalues...'
      CALL CBAL (MAXN,NCHK,HWK(1,2*MAXN+1),HWK(1,3*MAXN+1),I,J,HWK(1,
     $4*MAXN+1))
      CALL COMQR (MAXN,NCHK,I,J,HWK(1,2*MAXN+1),HWK(1,3*MAXN+1),HWK(1,
     $4*MAXN+1),HWK(1,4*MAXN+2),IERR)
      IF (IERR.NE.0) THEN
         WRITE (6,'(A25,I2)') 'Error return from COMQR: ', IERR
         RETURN
      END IF
C
C     Compute the magnitude of the check eigenvalues.
C
      DO 90 I = 1, NCHK
         HWK(I,4*MAXN+3) = SQRT(HWK(I,4*MAXN+1)**2 + HWK(I,4*MAXN+2)**2)
 90   CONTINUE
C
C     Sort the eigenvalues in decreasing order of magnitude.
C
      CALL DHPSRT (NCHK,HWK(1,4*MAXN+3),HWK(1,4*MAXN+1),HWK(1,4*MAXN+2))
C
C     Check the  Lanczos eigenvalues that were simple;  keep those that
C     appear only in the Lanczos matrix.
C     The approach used is brute force; it could be more sophisticated.
C
      DO 110 I = NBEG, NEIG
         EREAL = HWK(I,4*MAXN+4)
         EIMAG = HWK(I,4*MAXN+5)
         EMAGN = HWK(I,4*MAXN+6)
         DO 100 J = 1, NCHK
            TOLM = 0.5E0 * TOL * (EMAGN + HWK(J,4*MAXN+3))
            IF (ABS(EMAGN-HWK(J,4*MAXN+3)).GE.TOLM) GO TO 100
            DISTM = SQRT((EREAL-HWK(J,4*MAXN+1))**2 + (EIMAG-HWK(J,
     $4*MAXN+2))**2)
            IF (DISTM.LT.TOLM) GO TO 110
 100     CONTINUE
C
C     It appears only in the Lanczos matrix, so it is good.
C
         NEND        = NEND + 1
         HWK(NEND,4*MAXN+4) = EREAL
         HWK(NEND,4*MAXN+5) = EIMAG
         HWK(NEND,4*MAXN+6) = EMAGN
 110  CONTINUE
C
C     Sort the final eigenvalues by decreasing real part.
C
 120  CALL DHPSRT (NEND,HWK(1,4*MAXN+4),HWK(1,4*MAXN+5),HWK(1,4*MAXN+6))
C
C     Output the results.
C
      IF (VF.NE.0) WRITE (VF,'(A43,I4)')
     $             'Number of Lanczos eigenvalues found      : ', NEND
      IF (TF.NE.0) THEN
         WRITE (TF,'(A30,I4)') 'Filtered eigenvalues at step: ', NEIG
         WRITE (TF,'(2E25.17)') (HWK(I,4*MAXN+4),HWK(I,4*MAXN+5),I=1,
     $NEND)
         WRITE (TF,'()')
      END IF
      NEIG = NEND
C
C     Done.
C
      RETURN
      END
C
C**********************************************************************
C
      COMPLEX FUNCTION CSLALH(I,J)
C
C     Purpose:
C     Returns the recurrence coefficients for inner vectors.
C
C     Parameters:
C     I = row index of the coefficient (input).
C     J = column index of the coefficient (input).
C
C     Noel M. Nachtigal
C     July 9, 1993
C
C**********************************************************************
C
C
C     Common block CSLALX.
C
      REAL NORMA
      COMMON /CSLALX/NORMA
C
      INTRINSIC CMPLX
C
      INTEGER I, J
C
      IF ((I.LT.1).OR.(J.LT.1)) THEN
         CSLALH = (0.0E0,0.0E0)
      ELSE IF (I.EQ.J) THEN
         CSLALH = CMPLX(NORMA,0.0E0)
      ELSE
         CSLALH = (0.0E0,0.0E0)
      END IF
C
      RETURN
      END
C
C**********************************************************************
C
      SUBROUTINE CSLAL1 (NDIM,NLEN,M,MAXVW,NUMCHK,N,L,LSTAR,NL,NLSTAR,
     $                  VF,IERR,ADJUST,NORM1,NORMA,TMAX,TMIN,TNRM,ZWK,
     $                  DWK,IWK,IDX,VECS)
C
C     Purpose:
C     This subroutine builds a new pair of vectors v_{n+1} and w_{n+1}.
C     It is called internally by  the Lanczos code, and is not meant to
C     to be called directly by the user code.
C
C     Parameters:
C        See descriptions in "cslal.doc" or "csqmr.doc".
C
C     External routines used:
C     real slamch(ch)
C        LAPACK routine, computes machine-related constants.
C     real scnrm2(n,x,incx)
C        BLAS-1 routine, computes the 2-norm of x.
C     subroutine caxpby(n,z,a,x,b,y)
C        Library routine, computes z = a * x + b * y.
C     real cdotu(n,x,incx,y,incy)
C        BLAS-1 routine, computes y^H * x.
C     subroutine cqrdc(x,ldx,n,p,qraux,jpvt,work,job)
C        LINPACK routine, computes the QR factorization of x.
C     subroutine cqrsl(x,ldx,n,k,qraux,y,qy,qty,b,rsd,xb,job,info)
C        LINPACK routine, applies the QR factorization of x.
C     subroutine csvdc(x,ldx,n,p,s,e,u,ldu,v,ldv,work,job,info)
C        LINPACK routine, computes the SVD of x.
C     subroutine cslal2 (ndim,nlen,m,zwk,dwk,iwk,idx,vecs)
C        Forces closure of an inner block.
C     real cslalh(i,n)
C        User-supplied routine, computes inner recurrence coefficients.
C
C     Noel M. Nachtigal
C     July 9, 1993
C
c**********************************************************************
C
      INTRINSIC CABS, ABS, CMPLX, AMAX1, REAL, MAX0
      EXTERNAL SLAMCH, SCNRM2, CAXPBY, CDOTU, CQRDC, CQRSL, CSVDC
      EXTERNAL CSLAL2, CSLALH
      COMPLEX CDOTU, CSLALH
      REAL SLAMCH, SCNRM2
C
      INTEGER IERR, L, LSTAR, M, MAXVW, N, NDIM, NL, NLEN, NLSTAR
      INTEGER IDX(3,3), IWK(M,4), NUMCHK, VF
      COMPLEX VECS(NDIM,1*MAXVW+2+1), ZWK(M,5*M+3)
      REAL ADJUST, NORM1, NORMA, TMAX, TMIN, TNRM
      REAL DWK(M,4)
C
C     Miscellaneous parameters.
C
      COMPLEX CONE, CZERO
      PARAMETER (CONE = (1.0E0,0.0E0),CZERO = (0.0E0,0.0E0))
      REAL SONE, SZERO
      PARAMETER (SONE = 1.0E0,SZERO = 0.0E0)
C
C     Local variables.
C
      INTEGER I, IJ, J, LBLKSZ, NP1
      COMPLEX CTMP, CTMP1, CTMP2
      REAL STMP, STMP1, STMP2, STMP3, STMP4
      REAL ISTMP1, ISTMP2, ISTMP3, ISTMP4
      LOGICAL IBUILT, INNER, RERUN
C
C     Initialize local variables.
C
      NP1        = N + 1
      DWK(IDX(1,N),4) = SZERO
      RERUN      = .FALSE.
      IBUILT     = .FALSE.
      IERR       = 0
      LBLKSZ     = N - NL + 1
C
C     Update the norm estimates.
C
      IF (N.LE.NUMCHK) THEN
         STMP1 = SCNRM2(NLEN,VECS(1,1),1) * DWK(IDX(1,N),2)
CSYM     STMP2 = SCNRM2(NLEN,VECS(1,1),1) * DWK(IDX(1,N),3)
         STMP2 = STMP1
         NORMA = AMAX1(STMP1,STMP2,NORMA)
      END IF
      NORM1 = AMAX1(ADJUST*NORMA,NORM1)
C
C     Clear current column of H.
C
      DO 100 I = 1, M
         ZWK(IDX(1,I),2*M+IDX(1,N)) = CZERO
 100  CONTINUE
C
C     Update D^{(n-1)} to D^{(n)}.
C
      DO 120 I = NL, N-1
         CTMP = CZERO
         DO 110 J = NL, N-1
            CTMP = CTMP + ZWK(IDX(1,I),IDX(1,J)) * ZWK(IDX(1,J),2*M+
     $IDX(1,N-1))
 110     CONTINUE
         CTMP     = ( ZWK(IDX(1,I),M+IDX(1,N-1)) - CTMP ) / ZWK(IDX(1,N)
     $,2*M+IDX(1,N-1))
         ZWK(IDX(1,I),IDX(1,N)) = CTMP
         ZWK(IDX(1,N),IDX(1,I)) = CTMP * DWK(IDX(1,N),1) / DWK(IDX(1,I),
     $1)
 120  CONTINUE
C
C     Compute l^\star.
C
      LSTAR  = MAX0(1,L-1)
      NLSTAR = IWK(IDX(1,LSTAR+1),1)
C
C     Compute F_{n,1:n-1} and F_{1:n-1,n}.  Delay computing F_{nn}.
C
      DO 140 I = MAX0(1,NL-1), N-1
         CTMP = CZERO
         DO 130 J = NL, I+1
            CTMP = CTMP + ZWK(IDX(1,N),IDX(1,J)) * ZWK(IDX(1,J),2*M+
     $IDX(1,I))
 130     CONTINUE
         ZWK(IDX(1,N),M+IDX(1,I)) = CTMP
         ZWK(IDX(1,I),M+IDX(1,N)) = CTMP * DWK(IDX(1,I),1) / DWK(IDX(1,N
     $),1)
         NORMA    = AMAX1(NORMA,CABS(ZWK(IDX(1,N),M+IDX(1,I))),
     $CABS(ZWK(IDX(1,I),M+IDX(1,N))))
         NORM1    = AMAX1(ADJUST*NORMA,NORM1)
 140  CONTINUE
C
C     Check whether D_l is nonsingular.
C
      IF (LBLKSZ.EQ.1) THEN
         INNER = CABS(ZWK(IDX(1,NL),IDX(1,NL))).EQ.SZERO
      ELSE
         DO 160 I = NL, N
            DO 150 J = NL, N
               ZWK(I-NL+1,4*M+J-NL+1) = ZWK(IDX(1,I),IDX(1,J))
 150        CONTINUE
 160     CONTINUE
         CALL CSVDC (ZWK(1,4*M+1),M,LBLKSZ,LBLKSZ,ZWK(1,5*M+1),ZWK(1,5*M
     $+3),CZERO,0,CZERO,0,ZWK(1,5*M+2),0,I)
         IF (I.NE.0) THEN
            IERR = -I
            GOTO 370
         END IF
         STMP = SZERO
         IF (REAL(ZWK(1,5*M+1)).NE.SZERO) THEN
            STMP = ABS( REAL(ZWK(LBLKSZ,5*M+1)) / REAL(ZWK(1,5*M+1)))
         END IF
         INNER = STMP.LT.(FLOAT(NLEN) * SLAMCH('E'))
      END IF
      IF ((VF.NE.0).AND.INNER)
     $    WRITE (VF,'(A31)') '... moment matrix D is singular'
C
C     Compute H_{n_{l-1}:n_l-1,n}, for n_l > 1.
C     Also, build the part common to both inner and regular vectors.
C     Assume that VECS(1,1) = A v_n and VECS(1,1) = A^T w_n.
C
      ZWK(IDX(1,NP1),2*M+IDX(1,N)) = CZERO
      IF (NL.EQ.1) GO TO 180
      IF (NL.EQ.NLSTAR+1) THEN
         ZWK(IDX(1,NLSTAR),2*M+IDX(1,N)) = ZWK(IDX(1,NLSTAR),M+IDX(1,N))
     $ / ZWK(IDX(1,NLSTAR),IDX(1,NLSTAR))
         CTMP = ZWK(IDX(1,NLSTAR),2*M+IDX(1,N)) * DWK(IDX(1,NLSTAR),2) /
     $ DWK(IDX(1,N),2)
         CALL CAXPBY (NLEN,VECS(1,1),CONE,VECS(1,1),-CTMP,VECS(1,IDX(2,
     $NLSTAR)))
         CTMP = ZWK(IDX(1,NLSTAR),2*M+IDX(1,N)) * DWK(IDX(1,NLSTAR),3) /
     $ DWK(IDX(1,N),3) * DWK(IDX(1,N),1) / DWK(IDX(1,NLSTAR),1)
CSYM     CALL CAXPBY (NLEN,VECS(1,1),CONE,VECS(1,1),-CTMP,VECS(1,IDX(3,NLSTAR)))
      ELSE IF (NL.GT.NLSTAR+1) THEN
C
C     If a block of size larger than 1 was just closed, combine all its
C     vectors into one.
C
         CTMP2 = CZERO
         DO 170 I = NL-1, NLSTAR, -1
            ZWK(IDX(1,I),2*M+IDX(1,N)) = ZWK(IDX(1,NL-1),M+IDX(1,N)) * 
     $ZWK(IDX(1,I),3*M+IDX(1,L-1))
            IF (N.NE.NL) GO TO 170
            CTMP1 = ZWK(IDX(1,I),3*M+IDX(1,L-1)) * DWK(IDX(1,I),2)
            CALL CAXPBY (NLEN,VECS(1,IDX(2,NL-1)),CTMP2,VECS(1,IDX(2,NL-
     $1)),CTMP1,VECS(1,IDX(2,I)))
            CTMP1 = ZWK(IDX(1,I),3*M+IDX(1,L-1)) * DWK(IDX(1,I),3) / 
     $DWK(IDX(1,I),1)
CSYM        CALL CAXPBY (NLEN,VECS(1,IDX(3,NL-1)),CTMP2,VECS(1,IDX(3,NL-1)),CTMP1,VECS(1,IDX(3,I)))
            CTMP2 = CONE
 170     CONTINUE
         CTMP1 = ZWK(IDX(1,NL-1),M+IDX(1,N)) / DWK(IDX(1,N),2)
         CALL CAXPBY (NLEN,VECS(1,1),CONE,VECS(1,1),-CTMP1,VECS(1,IDX(2,
     $NL-1)))
         CTMP1 = ZWK(IDX(1,NL-1),M+IDX(1,N)) * DWK(IDX(1,N),1) / 
     $DWK(IDX(1,N),3)
CSYM     CALL CAXPBY (NLEN,VECS(1,1),CONE,VECS(1,1),-CTMP1,VECS(1,IDX(3,NL-1)))
      END IF
C
C     Compute F_{nn}.
C
 180  ZWK(IDX(1,N),M+IDX(1,N)) = CDOTU(NLEN,VECS(1,IDX(3,N)),1,VECS(1,1)
     $,1) * DWK(IDX(1,N),2) * DWK(IDX(1,N),3)
      NORMA    = AMAX1(NORMA,CABS(ZWK(IDX(1,N),M+IDX(1,N))))
      NORM1    = AMAX1(ADJUST*NORMA,NORM1)
      IF (INNER) GO TO 320
C
C     Compute H_{n_l:n,n}.
C
      IWK(IDX(1,L+1+1),1) = NP1
      IF (LBLKSZ.EQ.1) THEN
         ZWK(IDX(1,NL),2*M+IDX(1,N)) = ZWK(IDX(1,NL),M+IDX(1,N)) / 
     $ZWK(IDX(1,NL),IDX(1,NL))
      ELSE
         DO 200 J = NL, N
            ZWK(J-NL+1,5*M+1) = ZWK(IDX(1,J),M+IDX(1,N))
            DO 190 IJ = NL, N
               ZWK(J-NL+1,4*M+IJ-NL+1) = ZWK(IDX(1,J),IDX(1,IJ))
 190        CONTINUE
 200     CONTINUE
         CALL CQRDC (ZWK(1,4*M+1),M,LBLKSZ,LBLKSZ,ZWK(1,5*M+3),0,CZERO,0
     $)
         CALL CQRSL (ZWK(1,4*M+1),M,LBLKSZ,LBLKSZ,ZWK(1,5*M+3),ZWK(1,5*M
     $+1),
     $               CZERO,ZWK(1,5*M+1),ZWK(1,5*M+2),ZWK(1,5*M+1),CZERO,
     $100,J)
         DO 210 J = NL, N
            ZWK(IDX(1,J),2*M+IDX(1,N)) = ZWK(J-NL+1,5*M+2)
 210     CONTINUE
      END IF
C
C     Either D_l is nonsingular, or VW is being rerun.  For the latter,
C     just finish building the vectors.  For the former,  the check for
C     H_{n_{l-1}:n,n} could be done.  However, the look-ahead  strategy
C     requires  the smaller of  the norm checks for H_{n_{l-1}:n,n} and
C     H_{n_l:n,n+1}, so both norms are computed first and then checked.
C
C     Build regular vectors.
C
      CALL CAXPBY (NLEN,VECS(1,IDX(2,NP1)),CONE,VECS(1,1),-ZWK(IDX(1,N),
     $2*M+IDX(1,N)),VECS(1,IDX(2,N)))
CSYM  CALL CAXPBY (NLEN,VECS(1,IDX(3,NP1)),CONE,VECS(1,1),-ZWK(IDX(1,N),2*M+IDX(1,N)),VECS(1,IDX(3,N)))
      DO 220 I = NL, N-1
         CTMP = ZWK(IDX(1,I),2*M+IDX(1,N)) * DWK(IDX(1,I),2) / DWK(IDX(1
     $,N),2)
         CALL CAXPBY (NLEN,VECS(1,IDX(2,NP1)),CONE,VECS(1,IDX(2,NP1)),-
     $CTMP,VECS(1,IDX(2,I)))
         CTMP = ZWK(IDX(1,I),2*M+IDX(1,N)) * DWK(IDX(1,I),3) / DWK(IDX(1
     $,N),3) * DWK(IDX(1,N),1) / DWK(IDX(1,I),1)
CSYM     CALL CAXPBY (NLEN,VECS(1,IDX(3,NP1)),CONE,VECS(1,IDX(3,NP1)),-CTMP,VECS(1,IDX(3,I)))
 220  CONTINUE
C
C     Compute scale factors for the new vectors.
C
 230  STMP3      = SCNRM2(NLEN,VECS(1,IDX(2,NP1)),1)
CSYM  STMP4      = SCNRM2(NLEN,VECS(1,IDX(3,NP1)),1)
      STMP4      = STMP3
      STMP1      = DWK(IDX(1,N),2) * STMP3
      STMP2      = DWK(IDX(1,N),3) * STMP4
      ZWK(IDX(1,NP1),2*M+IDX(1,N)) = CMPLX(STMP1,SZERO)
      IF (STMP1.LT.TNRM) IERR = IERR + 16
      IF (STMP2.LT.TNRM) IERR = IERR + 32
      IF (IERR.NE.0) GOTO 360
      DWK(IDX(1,NP1),1)     = DWK(IDX(1,N),1) * STMP1 / STMP2
      ZWK(IDX(1,NP1),IDX(1,NP1)) = CDOTU(NLEN,VECS(1,IDX(3,NP1)),1,
     $VECS(1,IDX(2,NP1)),1) / ( STMP3 * STMP4 )
      IF ((STMP3.GE.TMAX).OR.(STMP3.LE.TMIN)) THEN
         CTMP = CMPLX(SONE / STMP3,SZERO)
         CALL CAXPBY (NLEN,VECS(1,IDX(2,NP1)),CTMP,VECS(1,IDX(2,NP1)),
     $CZERO,VECS(1,IDX(2,NP1)))
         STMP3 = SONE
      END IF
      IF ((STMP4.GE.TMAX).OR.(STMP4.LE.TMIN)) THEN
         CTMP = CMPLX(SONE / STMP4,SZERO)
CSYM     CALL CAXPBY (NLEN,VECS(1,IDX(3,NP1)),CTMP,VECS(1,IDX(3,NP1)),CZERO,VECS(1,IDX(3,NP1)))
         STMP4 = SONE
      END IF
      DWK(IDX(1,NP1),2) = SONE / STMP3
      DWK(IDX(1,NP1),3) = SONE / STMP4
C
C     Compute the last column of D_l^{-1}.
C
      IF (LBLKSZ.EQ.1) THEN
         ZWK(IDX(1,NL),3*M+IDX(1,L)) = CONE / ZWK(IDX(1,NL),IDX(1,NL))
      ELSE
         DO 240 I = 1, LBLKSZ-1
            ZWK(I,5*M+1) = CZERO
 240     CONTINUE
         ZWK(LBLKSZ,5*M+1) = CONE
         CALL CQRSL (ZWK(1,4*M+1),M,LBLKSZ,LBLKSZ,ZWK(1,5*M+3),ZWK(1,5*M
     $+1),
     $               CZERO,ZWK(1,5*M+1),ZWK(1,5*M+2),ZWK(1,5*M+1),CZERO,
     $100,J)
         DO 250 I = NL, N
            ZWK(IDX(1,I),3*M+IDX(1,L)) = ZWK(I-NL+1,5*M+2)
 250     CONTINUE
      END IF
C
C     If VW is being rerun, then skip to the end.
C
      IF (RERUN) GO TO 360
C
C     Compute the norm of H_{n_{l-1}:n,n}.
C
      STMP1 = SZERO
      STMP2 = SZERO
      DO 260 I = IWK(IDX(1,L-1+1),1), N
         STMP  = CABS(ZWK(IDX(1,I),2*M+IDX(1,N)))
         STMP1 = STMP1 + STMP
         STMP2 = STMP2 + STMP / DWK(IDX(1,I),1)
 260  CONTINUE
      STMP2 = STMP2 * DWK(IDX(1,N),1)
C
C     Build the 2nd term for the next step, H_{n_l:n,n+1}, regular.
C     Compute the norm of H_{n_l:n,n+1}.
C
      STMP3 = SZERO
      STMP4 = SZERO
      CTMP  = ZWK(IDX(1,NP1),IDX(1,NP1)) * ZWK(IDX(1,NP1),2*M+IDX(1,N)) 
     $* DWK(IDX(1,N),1) / DWK(IDX(1,NP1),1)
      DO 270 I = NL, N
         STMP  = CABS(CTMP * ZWK(IDX(1,I),3*M+IDX(1,L)))
         STMP3 = STMP3 + STMP
         STMP4 = STMP4 + STMP / DWK(IDX(1,I),1)
 270  CONTINUE
      STMP4 = STMP4 * DWK(IDX(1,NP1),1)
C
C     Check H_{n_{l-1}:n,n} and H_{n_l:n-1,n+1}.
C
      STMP  = AMAX1(STMP1,STMP2,STMP3,STMP4)
      INNER = STMP.GT.NORM1
      IF (.NOT.INNER) GO TO 360
      DWK(IDX(1,N),4) = STMP
C
C     If H_{n_{l-1}:n,n} is bad, build inner vectors.
C
      IF (AMAX1(STMP1,STMP2).GT.NORM1) GO TO 320
C
C     If H_{n_l:n-1,n+1} is bad, check the inner vectors.
C     This only applies if n_l > 1.
C
      IF (NL.LE.1) GO TO 320
C
C     Build the inner vectors to compute the 2nd term at the next step.
C     Get the coefficients H_{n_l:n+1,n} in a temporary location.
C     Build inner vectors in VECS(1,1) and VECS(1,1).
C
      IBUILT = .TRUE.
      DO 280 I = NL, N
         ZWK(IDX(1,I),2*M+IDX(1,NP1)) = CSLALH(I,N)
         CTMP       = ZWK(IDX(1,I),2*M+IDX(1,NP1)) * DWK(IDX(1,I),2) / 
     $DWK(IDX(1,N),2)
         CALL CAXPBY (NLEN,VECS(1,1),CONE,VECS(1,1),-CTMP,VECS(1,IDX(2,I
     $)))
         CTMP       = ZWK(IDX(1,I),2*M+IDX(1,NP1)) * DWK(IDX(1,I),3) / 
     $DWK(IDX(1,N),3) * DWK(IDX(1,N),1) / DWK(IDX(1,I),1)
CSYM     CALL CAXPBY (NLEN,VECS(1,1),CONE,VECS(1,1),-CTMP,VECS(1,IDX(3,I)))
 280  CONTINUE
      ISTMP3       = SCNRM2(NLEN,VECS(1,1),1)
CSYM  ISTMP4       = SCNRM2(NLEN,VECS(1,1),1)
      ISTMP4       = ISTMP3
      ISTMP1       = DWK(IDX(1,N),2) * ISTMP3
      ISTMP2       = DWK(IDX(1,N),3) * ISTMP4
      ZWK(IDX(1,NP1),2*M+IDX(1,NP1)) = CMPLX(ISTMP1,SZERO)
      IF (ISTMP1.LT.TNRM) IERR = IERR + 16
      IF (ISTMP2.LT.TNRM) IERR = IERR + 32
      IF (IERR.NE.0) GOTO 330
C
C     Build the 2nd term for the next step, H_{n_{l-1}:n_l-1,n+1},
C     inner.  Compute the norm of H_{n_{l-1}:n_l-1,n+1}.
C
      CTMP = CZERO
      DO 290 J = NLSTAR, NL-1
         CTMP = CTMP + ZWK(IDX(1,NL),IDX(1,J)) * ZWK(IDX(1,I),2*M+IDX(1,
     $N))
 290  CONTINUE
      DO 300 J = NL, N
         CTMP = CTMP + ZWK(IDX(1,NL),IDX(1,J)) * ZWK(IDX(1,I),2*M+IDX(1,
     $NP1))
 300  CONTINUE
      STMP1 = SZERO
      STMP2 = SZERO
      STMP3 = AMAX1(STMP3,STMP4)
      CTMP  = ( ZWK(IDX(1,NL),M+IDX(1,N)) - CTMP ) / ZWK(IDX(1,NP1),2*M+
     $IDX(1,NP1))
      CTMP  = CTMP * ZWK(IDX(1,NL),2*M+IDX(1,NL-1)) * DWK(IDX(1,NL-1),1)
     $ / DWK(IDX(1,NL),1)
      DO 310 I = IWK(IDX(1,L-1+1),1), NL-1
         STMP  = CABS(ZWK(IDX(1,I),3*M+IDX(1,L-1)) * CTMP)
         STMP1 = STMP1 + STMP
         STMP2 = STMP2 + STMP / DWK(IDX(1,I),1)
 310  CONTINUE
      STMP2 = STMP2 * DWK(IDX(1,N),1)
C
C     Compare the inner and regular versions of the 2nd term at the next
C     step.  Build the vector corresponding to the smaller term.
C
      INNER = STMP3.GT.AMAX1(STMP1,STMP2)
      IF (.NOT.INNER) GO TO 360
C
C     Build inner vectors.
C     Check whether the block has to be forced to close.
C
 320  IF (VF.NE.0) WRITE (VF,'(A7,I5,A9)') 'Vector ',NP1,' is inner'
      IF (NP1-NL.EQ.MAXVW) THEN
         CALL CSLAL2 (NDIM,NLEN,M,N,L,LSTAR,NL,NLSTAR,VF,IERR,ADJUST,
     $               NORM1,ZWK,DWK,IWK,IDX,VECS)
         IF (IERR.NE.0) GO TO 370
         LBLKSZ = N - NL + 1
         INNER  = .FALSE.
         RERUN  = .TRUE.
         NP1    = N + 1
         GO TO 230
      END IF
C
C     The temporary vectors  contain either just partial inner vectors,
C     or the  completed ones,  depending on whether  IBUILT is  TRUE or
C     FALSE.  In either case, replace the regular vectors.
C
 330  CALL CAXPBY (NLEN,VECS(1,IDX(2,NP1)),CONE,VECS(1,1),CZERO,VECS(1,
     $IDX(2,NP1)))
CSYM  CALL CAXPBY (NLEN,VECS(1,IDX(3,NP1)),CONE,VECS(1,1),CZERO,VECS(1,IDX(3,NP1)))
C
C     Get the coefficients H_{n_l:n+1,n} and build inner vectors.
C
      IF (IBUILT) THEN
         DO 340 I = NL, NP1
            ZWK(IDX(1,I),2*M+IDX(1,N)) = ZWK(IDX(1,I),2*M+IDX(1,NP1))
 340     CONTINUE
         STMP1 = ISTMP1
         STMP2 = ISTMP2
         STMP3 = ISTMP3
         STMP4 = ISTMP4
      ELSE
         DO 350 I = NL, N
            ZWK(IDX(1,I),2*M+IDX(1,N)) = CSLALH(I,N)
            CTMP     = ZWK(IDX(1,I),2*M+IDX(1,N)) * DWK(IDX(1,I),2) / 
     $DWK(IDX(1,N),2)
            CALL CAXPBY (NLEN,VECS(1,IDX(2,NP1)),CONE,VECS(1,IDX(2,NP1))
     $,-CTMP,VECS(1,IDX(2,I)))
            CTMP     = ZWK(IDX(1,I),2*M+IDX(1,N)) * DWK(IDX(1,I),3) / 
     $DWK(IDX(1,N),3) * DWK(IDX(1,N),1) / DWK(IDX(1,I),1)
CSYM        CALL CAXPBY (NLEN,VECS(1,IDX(3,NP1)),CONE,VECS(1,IDX(3,NP1)),-CTMP,VECS(1,IDX(3,I)))
 350     CONTINUE
         STMP3 = SCNRM2(NLEN,VECS(1,IDX(2,NP1)),1)
CSYM     STMP4 = SCNRM2(NLEN,VECS(1,IDX(3,NP1)),1)
         STMP4 = STMP3
         STMP1 = DWK(IDX(1,N),2) * STMP3
         STMP2 = DWK(IDX(1,N),3) * STMP4
      END IF
      ZWK(IDX(1,NP1),2*M+IDX(1,N)) = CMPLX(STMP1,SZERO)
      IF (STMP1.LT.TNRM) IERR = IERR + 16
      IF (STMP2.LT.TNRM) IERR = IERR + 32
      IF (IERR.NE.0) GOTO 360
      DWK(IDX(1,NP1),1)     = DWK(IDX(1,N),1) * STMP1 / STMP2
      ZWK(IDX(1,NP1),IDX(1,NP1)) = CDOTU(NLEN,VECS(1,IDX(3,NP1)),1,
     $VECS(1,IDX(2,NP1)),1) / ( STMP3 * STMP4 )
      IF ((STMP3.GE.TMAX).OR.(STMP3.LE.TMIN)) THEN
         CTMP = CMPLX(SONE / STMP3,SZERO)
         CALL CAXPBY (NLEN,VECS(1,IDX(2,NP1)),CTMP,VECS(1,IDX(2,NP1)),
     $CZERO,VECS(1,IDX(2,NP1)))
         STMP3 = SONE
      END IF
      IF ((STMP4.GE.TMAX).OR.(STMP4.LE.TMIN)) THEN
         CTMP = CMPLX(SONE / STMP4,SZERO)
CSYM     CALL CAXPBY (NLEN,VECS(1,IDX(3,NP1)),CTMP,VECS(1,IDX(3,NP1)),CZERO,VECS(1,IDX(3,NP1)))
         STMP4 = SONE
      END IF
      DWK(IDX(1,NP1),2) = SONE / STMP3
      DWK(IDX(1,NP1),3) = SONE / STMP4
C
C     If regular vectors were built, update the counters.
C
 360  IF (.NOT.INNER) THEN
         L  = L + 1
         NL = IWK(IDX(1,L+1),1)
      END IF
C
 370  RETURN
      END
C
C**********************************************************************
C
      SUBROUTINE CSLAL2 (NDIM,NLEN,M,N,L,LSTAR,NL,NLSTAR,VF,IERR,
     $                  ADJUST,NORM1,ZWK,DWK,IWK,IDX,VECS)
C
C     Purpose:
C     This subroutine rebuilds the data for vectors v_{n+1} and w_{n+1}
C     at the point where a block  was forced  to close.  The routine is
C     called internally by the look-ahead Lanczos code and is not meant
C     to be called directly by the user code.
C
C     Parameters:
C        See descriptions in "cslal.doc" or "csqmr.doc".
C
C     External routines used:
C     subroutine caxpby(n,z,a,x,b,y)
C        Library routine, computes z = a * x + b * y.
C     subroutine cqrdc(x,ldx,n,p,qraux,jpvt,work,job)
C        LINPACK routine, computes the QR factorization of x.
C     subroutine cqrsl(x,ldx,n,k,qraux,y,qy,qty,b,rsd,xb,job,info)
C        LINPACK routine, applies the QR factorization of x.
C
C     Noel M. Nachtigal
C     May 31, 1993
C
C**********************************************************************
C
      EXTERNAL CAXPBY, CQRDC, CQRSL
C
      INTEGER IERR, L, LSTAR, M, N, NDIM, NL, NLEN, NLSTAR
      INTEGER IDX(3,3), IWK(M,4), VF
      COMPLEX VECS(NDIM,*), ZWK(M,5*M+3)
      REAL ADJUST, DWK(M,4), NORM1
C
C     Miscellaneous parameters.
C
      COMPLEX CONE, CZERO
      PARAMETER (CONE = (1.0E0,0.0E0),CZERO = (0.0E0,0.0E0))
      REAL SZERO
      PARAMETER (SZERO = 0.0E0)
C
C     Local variables.
C
      INTEGER I, IJ, J, LBLKSZ, NP1
      COMPLEX SCALV, SCALW, CTMP1, CTMP2
      REAL STMP1, STMP2
C
C     Find the index of the vector pair with the smallest pass value.
C
      IERR = 0
      IF (VF.NE.0) WRITE (VF,'(A20)') 'block did not close:'
      J     = NL
      STMP1 = DWK(IDX(1,J),4)
      DO 100 I = NL+1, N
         STMP2 = DWK(IDX(1,I),4)
         IF (STMP2.GT.SZERO) THEN
            IF ((STMP1.EQ.SZERO).OR.(STMP2.LT.STMP1)) THEN
               J     = I
               STMP1 = STMP2
            END IF
         END IF
 100  CONTINUE
      IF (STMP1.EQ.SZERO) THEN
         IF (VF.NE.0) WRITE (VF,'(A47)') 
     $'... no new norm estimates available (aborting).'
         IERR = 8
         RETURN
      END IF
      NORM1 = ADJUST * STMP1
      IF (VF.NE.0) WRITE (VF,'(A40,I5,E11.4)')
     $      '... updated norms, restarting from step:', IWK(IDX(1,J),3),
     $ NORM1
      IF (IWK(IDX(1,J),3).EQ.N) RETURN
      N  = IWK(IDX(1,J),3)
      L  = IWK(IDX(1,N),4)
      NL = IWK(IDX(1,L+1),1)
C
C     Initialize local variables.
C
      NP1        = N + 1
      DWK(IDX(1,N),4) = SZERO
      LBLKSZ     = N - NL + 1
C
C     Compute l^\star.
C
      LSTAR  = L - 1
      NLSTAR = IWK(IDX(1,LSTAR+1),1)
C
C     Compute H_{n_l:n,n}.  Save the old coefficients.
C
      IWK(IDX(1,L+1+1),1) = NP1
      IF (LBLKSZ.EQ.1) THEN
         ZWK(IDX(1,NL),2*M+IDX(1,NP1)) = ZWK(IDX(1,NL),2*M+IDX(1,N))
         ZWK(IDX(1,NL),2*M+IDX(1,N))   = ZWK(IDX(1,NL),M+IDX(1,N)) / 
     $ZWK(IDX(1,NL),IDX(1,NL))
      ELSE
         DO 120 J = NL, N
            ZWK(J-NL+1,5*M+1) = ZWK(IDX(1,J),M+IDX(1,N))
            DO 110 IJ = NL, N
               ZWK(J-NL+1,4*M+IJ-NL+1) = ZWK(IDX(1,J),IDX(1,IJ))
 110        CONTINUE
 120     CONTINUE
         CALL CQRDC (ZWK(1,4*M+1),M,LBLKSZ,LBLKSZ,ZWK(1,5*M+3),0,CZERO,0
     $)
         CALL CQRSL (ZWK(1,4*M+1),M,LBLKSZ,LBLKSZ,ZWK(1,5*M+3),ZWK(1,5*M
     $+1),
     $               CZERO,ZWK(1,5*M+1),ZWK(1,5*M+2),ZWK(1,5*M+1),CZERO,
     $100,J)
         DO 130 J = NL, N
            ZWK(IDX(1,J),2*M+IDX(1,NP1)) = ZWK(IDX(1,J),2*M+IDX(1,N))
            ZWK(IDX(1,J),2*M+IDX(1,N)) = ZWK(J-NL+1,5*M+2)
 130     CONTINUE
      END IF
C
C     Convert inner vectors to regular vectors.
C
      SCALV = ZWK(IDX(1,NP1),2*M+IDX(1,N)) * DWK(IDX(1,NP1),2)
      SCALW = ZWK(IDX(1,NP1),2*M+IDX(1,N)) * DWK(IDX(1,NP1),3) * 
     $DWK(IDX(1,N),1) / DWK(IDX(1,NP1),1)
      ZWK(IDX(1,NP1),2*M+IDX(1,N)) = CZERO
      DO 140 I = NL, N
         CTMP1 = ZWK(IDX(1,I),2*M+IDX(1,N)) - ZWK(IDX(1,I),2*M+IDX(1,NP1
     $))
         CTMP2 = CTMP1 * DWK(IDX(1,I),2) / SCALV
         CALL CAXPBY (NLEN,VECS(1,IDX(2,NP1)),CONE,VECS(1,IDX(2,NP1)),-
     $CTMP2,VECS(1,IDX(2,I)))
         CTMP2 = CTMP1 * DWK(IDX(1,I),3) / SCALW * DWK(IDX(1,N),1) / 
     $DWK(IDX(1,I),1)
CSYM     CALL CAXPBY (NLEN,VECS(1,IDX(3,NP1)),CONE,VECS(1,IDX(3,NP1)),-CTMP2,VECS(1,IDX(3,I)))
 140  CONTINUE
C
      RETURN
      END
C
C**********************************************************************