c\BeginDoc
c
c\Name: cnaupd
c
c\Description:
c Reverse communication interface for the Implicitly Restarted Arnoldi
c iteration. This is intended to be used to find a few eigenpairs of a
c complex linear operator OP with respect to a semi-inner product defined
c by a hermitian positive semi-definite real matrix B. B may be the identity
c matrix. NOTE: if both OP and B are real, then ssaupd or snaupd should
c be used.
c
c
c The computed approximate eigenvalues are called Ritz values and
c the corresponding approximate eigenvectors are called Ritz vectors.
c
c cnaupd is usually called iteratively to solve one of the
c following problems:
c
c Mode 1: A*x = lambda*x.
c ===> OP = A and B = I.
c
c Mode 2: A*x = lambda*M*x, M hermitian positive definite
c ===> OP = inv[M]*A and B = M.
c ===> (If M can be factored see remark 3 below)
c
c Mode 3: A*x = lambda*M*x, M hermitian semi-definite
c ===> OP = inv[A - sigma*M]*M and B = M.
c ===> shift-and-invert mode
c If OP*x = amu*x, then lambda = sigma + 1/amu.
c
c
c NOTE: The action of w <- inv[A - sigma*M]*v or w <- inv[M]*v
c should be accomplished either by a direct method
c using a sparse matrix factorization and solving
c
c [A - sigma*M]*w = v or M*w = v,
c
c or through an iterative method for solving these
c systems. If an iterative method is used, the
c convergence test must be more stringent than
c the accuracy requirements for the eigenvalue
c approximations.
c
c\Usage:
c call cnaupd
c ( IDO, BMAT, N, WHICH, NEV, TOL, RESID, NCV, V, LDV, IPARAM,
c IPNTR, WORKD, WORKL, LWORKL, RWORK, INFO )
c
c\Arguments
c IDO Integer. (INPUT/OUTPUT)
c Reverse communication flag. IDO must be zero on the first
c call to cnaupd. IDO will be set internally to
c indicate the type of operation to be performed. Control is
c then given back to the calling routine which has the
c responsibility to carry out the requested operation and call
c cnaupd with the result. The operand is given in
c WORKD(IPNTR(1)), the result must be put in WORKD(IPNTR(2)).
c -------------------------------------------------------------
c IDO = 0: first call to the reverse communication interface
c IDO = -1: compute Y = OP * X where
c IPNTR(1) is the pointer into WORKD for X,
c IPNTR(2) is the pointer into WORKD for Y.
c This is for the initialization phase to force the
c starting vector into the range of OP.
c IDO = 1: compute Y = OP * X where
c IPNTR(1) is the pointer into WORKD for X,
c IPNTR(2) is the pointer into WORKD for Y.
c In mode 3, the vector B * X is already
c available in WORKD(ipntr(3)). It does not
c need to be recomputed in forming OP * X.
c IDO = 2: compute Y = M * X where
c IPNTR(1) is the pointer into WORKD for X,
c IPNTR(2) is the pointer into WORKD for Y.
c IDO = 3: compute and return the shifts in the first
c NP locations of WORKL.
c IDO = 99: done
c -------------------------------------------------------------
c After the initialization phase, when the routine is used in
c the "shift-and-invert" mode, the vector M * X is already
c available and does not need to be recomputed in forming OP*X.
c
c BMAT Character*1. (INPUT)
c BMAT specifies the type of the matrix B that defines the
c semi-inner product for the operator OP.
c BMAT = 'I' -> standard eigenvalue problem A*x = lambda*x
c BMAT = 'G' -> generalized eigenvalue problem A*x = lambda*M*x
c
c N Integer. (INPUT)
c Dimension of the eigenproblem.
c
c WHICH Character*2. (INPUT)
c 'LM' -> want the NEV eigenvalues of largest magnitude.
c 'SM' -> want the NEV eigenvalues of smallest magnitude.
c 'LR' -> want the NEV eigenvalues of largest real part.
c 'SR' -> want the NEV eigenvalues of smallest real part.
c 'LI' -> want the NEV eigenvalues of largest imaginary part.
c 'SI' -> want the NEV eigenvalues of smallest imaginary part.
c
c NEV Integer. (INPUT)
c Number of eigenvalues of OP to be computed. 0 < NEV < N-1.
c
c TOL Real scalar. (INPUT)
c Stopping criteria: the relative accuracy of the Ritz value
c is considered acceptable if BOUNDS(I) .LE. TOL*ABS(RITZ(I))
c where ABS(RITZ(I)) is the magnitude when RITZ(I) is complex.
c DEFAULT = slamch('EPS') (machine precision as computed
c by the LAPACK auxiliary subroutine slamch).
c
c RESID Complex array of length N. (INPUT/OUTPUT)
c On INPUT:
c If INFO .EQ. 0, a random initial residual vector is used.
c If INFO .NE. 0, RESID contains the initial residual vector,
c possibly from a previous run.
c On OUTPUT:
c RESID contains the final residual vector.
c
c NCV Integer. (INPUT)
c Number of columns of the matrix V. NCV must satisfy the two
c inequalities 1 <= NCV-NEV and NCV <= N.
c This will indicate how many Arnoldi vectors are generated
c at each iteration. After the startup phase in which NEV
c Arnoldi vectors are generated, the algorithm generates
c approximately NCV-NEV Arnoldi vectors at each subsequent update
c iteration. Most of the cost in generating each Arnoldi vector is
c in the matrix-vector operation OP*x. (See remark 4 below.)
c
c V Complex array N by NCV. (OUTPUT)
c Contains the final set of Arnoldi basis vectors.
c
c LDV Integer. (INPUT)
c Leading dimension of V exactly as declared in the calling program.
c
c IPARAM Integer array of length 11. (INPUT/OUTPUT)
c IPARAM(1) = ISHIFT: method for selecting the implicit shifts.
c The shifts selected at each iteration are used to filter out
c the components of the unwanted eigenvector.
c -------------------------------------------------------------
c ISHIFT = 0: the shifts are to be provided by the user via
c reverse communication. The NCV eigenvalues of
c the Hessenberg matrix H are returned in the part
c of WORKL array corresponding to RITZ.
c ISHIFT = 1: exact shifts with respect to the current
c Hessenberg matrix H. This is equivalent to
c restarting the iteration from the beginning
c after updating the starting vector with a linear
c combination of Ritz vectors associated with the
c "wanted" eigenvalues.
c ISHIFT = 2: other choice of internal shift to be defined.
c -------------------------------------------------------------
c
c IPARAM(2) = No longer referenced
c
c IPARAM(3) = MXITER
c On INPUT: maximum number of Arnoldi update iterations allowed.
c On OUTPUT: actual number of Arnoldi update iterations taken.
c
c IPARAM(4) = NB: blocksize to be used in the recurrence.
c The code currently works only for NB = 1.
c
c IPARAM(5) = NCONV: number of "converged" Ritz values.
c This represents the number of Ritz values that satisfy
c the convergence criterion.
c
c IPARAM(6) = IUPD
c No longer referenced. Implicit restarting is ALWAYS used.
c
c IPARAM(7) = MODE
c On INPUT determines what type of eigenproblem is being solved.
c Must be 1,2,3; See under \Description of cnaupd for the
c four modes available.
c
c IPARAM(8) = NP
c When ido = 3 and the user provides shifts through reverse
c communication (IPARAM(1)=0), _naupd returns NP, the number
c of shifts the user is to provide. 0 < NP < NCV-NEV.
c
c IPARAM(9) = NUMOP, IPARAM(10) = NUMOPB, IPARAM(11) = NUMREO,
c OUTPUT: NUMOP = total number of OP*x operations,
c NUMOPB = total number of B*x operations if BMAT='G',
c NUMREO = total number of steps of re-orthogonalization.
c
c IPNTR Integer array of length 14. (OUTPUT)
c Pointer to mark the starting locations in the WORKD and WORKL
c arrays for matrices/vectors used by the Arnoldi iteration.
c -------------------------------------------------------------
c IPNTR(1): pointer to the current operand vector X in WORKD.
c IPNTR(2): pointer to the current result vector Y in WORKD.
c IPNTR(3): pointer to the vector B * X in WORKD when used in
c the shift-and-invert mode.
c IPNTR(4): pointer to the next available location in WORKL
c that is untouched by the program.
c IPNTR(5): pointer to the NCV by NCV upper Hessenberg
c matrix H in WORKL.
c IPNTR(6): pointer to the ritz value array RITZ
c IPNTR(7): pointer to the (projected) ritz vector array Q
c IPNTR(8): pointer to the error BOUNDS array in WORKL.
c IPNTR(14): pointer to the NP shifts in WORKL. See Remark 5 below.
c
c Note: IPNTR(9:13) is only referenced by cneupd. See Remark 2 below.
c
c IPNTR(9): pointer to the NCV RITZ values of the
c original system.
c IPNTR(10): Not Used
c IPNTR(11): pointer to the NCV corresponding error bounds.
c IPNTR(12): pointer to the NCV by NCV upper triangular
c Schur matrix for H.
c IPNTR(13): pointer to the NCV by NCV matrix of eigenvectors
c of the upper Hessenberg matrix H. Only referenced by
c cneupd if RVEC = .TRUE. See Remark 2 below.
c
c -------------------------------------------------------------
c
c WORKD Complex work array of length 3*N. (REVERSE COMMUNICATION)
c Distributed array to be used in the basic Arnoldi iteration
c for reverse communication. The user should not use WORKD
c as temporary workspace during the iteration !!!!!!!!!!
c See Data Distribution Note below.
c
c WORKL Complex work array of length LWORKL. (OUTPUT/WORKSPACE)
c Private (replicated) array on each PE or array allocated on
c the front end. See Data Distribution Note below.
c
c LWORKL Integer. (INPUT)
c LWORKL must be at least 3*NCV**2 + 5*NCV.
c
c RWORK Real work array of length NCV (WORKSPACE)
c Private (replicated) array on each PE or array allocated on
c the front end.
c
c
c INFO Integer. (INPUT/OUTPUT)
c If INFO .EQ. 0, a randomly initial residual vector is used.
c If INFO .NE. 0, RESID contains the initial residual vector,
c possibly from a previous run.
c Error flag on output.
c = 0: Normal exit.
c = 1: Maximum number of iterations taken.
c All possible eigenvalues of OP has been found. IPARAM(5)
c returns the number of wanted converged Ritz values.
c = 2: No longer an informational error. Deprecated starting
c with release 2 of ARPACK.
c = 3: No shifts could be applied during a cycle of the
c Implicitly restarted Arnoldi iteration. One possibility
c is to increase the size of NCV relative to NEV.
c See remark 4 below.
c = -1: N must be positive.
c = -2: NEV must be positive.
c = -3: NCV-NEV >= 1 and less than or equal to N.
c = -4: The maximum number of Arnoldi update iteration
c must be greater than zero.
c = -5: WHICH must be one of 'LM', 'SM', 'LR', 'SR', 'LI', 'SI'
c = -6: BMAT must be one of 'I' or 'G'.
c = -7: Length of private work array is not sufficient.
c = -8: Error return from LAPACK eigenvalue calculation;
c = -9: Starting vector is zero.
c = -10: IPARAM(7) must be 1,2,3.
c = -11: IPARAM(7) = 1 and BMAT = 'G' are incompatible.
c = -12: IPARAM(1) must be equal to 0 or 1.
c = -9999: Could not build an Arnoldi factorization.
c User input error highly likely. Please
c check actual array dimensions and layout.
c IPARAM(5) returns the size of the current Arnoldi
c factorization.
c
c\Remarks
c 1. The computed Ritz values are approximate eigenvalues of OP. The
c selection of WHICH should be made with this in mind when using
c Mode = 3. When operating in Mode = 3 setting WHICH = 'LM' will
c compute the NEV eigenvalues of the original problem that are
c closest to the shift SIGMA . After convergence, approximate eigenvalues
c of the original problem may be obtained with the ARPACK subroutine cneupd.
c
c 2. If a basis for the invariant subspace corresponding to the converged Ritz
c values is needed, the user must call cneupd immediately following
c completion of cnaupd. This is new starting with release 2 of ARPACK.
c
c 3. If M can be factored into a Cholesky factorization M = LL`
c then Mode = 2 should not be selected. Instead one should use
c Mode = 1 with OP = inv(L)*A*inv(L`). Appropriate triangular
c linear systems should be solved with L and L` rather
c than computing inverses. After convergence, an approximate
c eigenvector z of the original problem is recovered by solving
c L`z = x where x is a Ritz vector of OP.
c
c 4. At present there is no a-priori analysis to guide the selection
c of NCV relative to NEV. The only formal requirement is that NCV > NEV + 1.
c However, it is recommended that NCV .ge. 2*NEV. If many problems of
c the same type are to be solved, one should experiment with increasing
c NCV while keeping NEV fixed for a given test problem. This will
c usually decrease the required number of OP*x operations but it
c also increases the work and storage required to maintain the orthogonal
c basis vectors. The optimal "cross-over" with respect to CPU time
c is problem dependent and must be determined empirically.
c See Chapter 8 of Reference 2 for further information.
c
c 5. When IPARAM(1) = 0, and IDO = 3, the user needs to provide the
c NP = IPARAM(8) complex shifts in locations
c WORKL(IPNTR(14)), WORKL(IPNTR(14)+1), ... , WORKL(IPNTR(14)+NP).
c Eigenvalues of the current upper Hessenberg matrix are located in
c WORKL(IPNTR(6)) through WORKL(IPNTR(6)+NCV-1). They are ordered
c according to the order defined by WHICH. The associated Ritz estimates
c are located in WORKL(IPNTR(8)), WORKL(IPNTR(8)+1), ... ,
c WORKL(IPNTR(8)+NCV-1).
c
c-----------------------------------------------------------------------
c
c\Data Distribution Note:
c
c Fortran-D syntax:
c ================
c Complex resid(n), v(ldv,ncv), workd(3*n), workl(lworkl)
c decompose d1(n), d2(n,ncv)
c align resid(i) with d1(i)
c align v(i,j) with d2(i,j)
c align workd(i) with d1(i) range (1:n)
c align workd(i) with d1(i-n) range (n+1:2*n)
c align workd(i) with d1(i-2*n) range (2*n+1:3*n)
c distribute d1(block), d2(block,:)
c replicated workl(lworkl)
c
c Cray MPP syntax:
c ===============
c Complex resid(n), v(ldv,ncv), workd(n,3), workl(lworkl)
c shared resid(block), v(block,:), workd(block,:)
c replicated workl(lworkl)
c
c CM2/CM5 syntax:
c ==============
c
c-----------------------------------------------------------------------
c
c include 'ex-nonsym.doc'
c
c-----------------------------------------------------------------------
c
c\BeginLib
c
c\Local variables:
c xxxxxx Complex
c
c\References:
c 1. D.C. Sorensen, "Implicit Application of Polynomial Filters in
c a k-Step Arnoldi Method", SIAM J. Matr. Anal. Apps., 13 (1992),
c pp 357-385.
c 2. R.B. Lehoucq, "Analysis and Implementation of an Implicitly
c Restarted Arnoldi Iteration", Rice University Technical Report
c TR95-13, Department of Computational and Applied Mathematics.
c 3. B.N. Parlett & Y. Saad, "_Complex_ Shift and Invert Strategies for
c Real Matrices", Linear Algebra and its Applications, vol 88/89,
c pp 575-595, (1987).
c
c\Routines called:
c cnaup2 ARPACK routine that implements the Implicitly Restarted
c Arnoldi Iteration.
c cstatn ARPACK routine that initializes the timing variables.
c ivout ARPACK utility routine that prints integers.
c cvout ARPACK utility routine that prints vectors.
c second ARPACK utility routine for timing.
c slamch LAPACK routine that determines machine constants.
c
c\Author
c Danny Sorensen Phuong Vu
c Richard Lehoucq CRPC / Rice University
c Dept. of Computational & Houston, Texas
c Applied Mathematics
c Rice University
c Houston, Texas
c
c\SCCS Information: @(#)
c FILE: naupd.F SID: 2.9 DATE OF SID: 07/21/02 RELEASE: 2
c
c\Remarks
c
c\EndLib
c
c-----------------------------------------------------------------------
c
subroutine cnaupd
& ( ido, bmat, n, which, nev, tol, resid, ncv, v, ldv, iparam,
& ipntr, workd, workl, lworkl, rwork, info )
c
c %----------------------------------------------------%
c | Include files for debugging and timing information |
c %----------------------------------------------------%
c
include 'debug.h'
include 'stat.h'
c
c %------------------%
c | Scalar Arguments |
c %------------------%
c
character bmat*1, which*2
integer ido, info, ldv, lworkl, n, ncv, nev
Real
& tol
c
c %-----------------%
c | Array Arguments |
c %-----------------%
c
integer iparam(11), ipntr(14)
Complex
& resid(n), v(ldv,ncv), workd(3*n), workl(lworkl)
Real
& rwork(ncv)
c
c %------------%
c | Parameters |
c %------------%
c
Complex
& one, zero
parameter (one = (1.0E+0, 0.0E+0), zero = (0.0E+0, 0.0E+0))
c
c %---------------%
c | Local Scalars |
c %---------------%
c
integer bounds, ierr, ih, iq, ishift, iupd, iw,
& ldh, ldq, levec, mode, msglvl, mxiter, nb,
& nev0, next, np, ritz, j
save bounds, ih, iq, ishift, iupd, iw,
& ldh, ldq, levec, mode, msglvl, mxiter, nb,
& nev0, next, np, ritz
c
c %----------------------%
c | External Subroutines |
c %----------------------%
c
external cnaup2, cvout, ivout, second, cstatn
c
c %--------------------%
c | External Functions |
c %--------------------%
c
Real
& slamch
external slamch
c
c %-----------------------%
c | Executable Statements |
c %-----------------------%
c
if (ido .eq. 0) then
c
c %-------------------------------%
c | Initialize timing statistics |
c | & message level for debugging |
c %-------------------------------%
c
call cstatn
call second (t0)
msglvl = mcaupd
c
c %----------------%
c | Error checking |
c %----------------%
c
ierr = 0
ishift = iparam(1)
c levec = iparam(2)
mxiter = iparam(3)
c nb = iparam(4)
nb = 1
c
c %--------------------------------------------%
c | Revision 2 performs only implicit restart. |
c %--------------------------------------------%
c
iupd = 1
mode = iparam(7)
c
if (n .le. 0) then
ierr = -1
else if (nev .le. 0) then
ierr = -2
else if (ncv .le. nev .or. ncv .gt. n) then
ierr = -3
else if (mxiter .le. 0) then
ierr = -4
else if (which .ne. 'LM' .and.
& which .ne. 'SM' .and.
& which .ne. 'LR' .and.
& which .ne. 'SR' .and.
& which .ne. 'LI' .and.
& which .ne. 'SI') then
ierr = -5
else if (bmat .ne. 'I' .and. bmat .ne. 'G') then
ierr = -6
else if (lworkl .lt. 3*ncv**2 + 5*ncv) then
ierr = -7
else if (mode .lt. 1 .or. mode .gt. 3) then
ierr = -10
else if (mode .eq. 1 .and. bmat .eq. 'G') then
ierr = -11
end if
c
c %------------%
c | Error Exit |
c %------------%
c
if (ierr .ne. 0) then
info = ierr
ido = 99
go to 9000
end if
c
c %------------------------%
c | Set default parameters |
c %------------------------%
c
if (nb .le. 0) nb = 1
if (tol .le. 0.0E+0 ) tol = slamch('EpsMach')
if (ishift .ne. 0 .and.
& ishift .ne. 1 .and.
& ishift .ne. 2) ishift = 1
c
c %----------------------------------------------%
c | NP is the number of additional steps to |
c | extend the length NEV Lanczos factorization. |
c | NEV0 is the local variable designating the |
c | size of the invariant subspace desired. |
c %----------------------------------------------%
c
np = ncv - nev
nev0 = nev
c
c %-----------------------------%
c | Zero out internal workspace |
c %-----------------------------%
c
do 10 j = 1, 3*ncv**2 + 5*ncv
workl(j) = zero
10 continue
c
c %-------------------------------------------------------------%
c | Pointer into WORKL for address of H, RITZ, BOUNDS, Q |
c | etc... and the remaining workspace. |
c | Also update pointer to be used on output. |
c | Memory is laid out as follows: |
c | workl(1:ncv*ncv) := generated Hessenberg matrix |
c | workl(ncv*ncv+1:ncv*ncv+ncv) := the ritz values |
c | workl(ncv*ncv+ncv+1:ncv*ncv+2*ncv) := error bounds |
c | workl(ncv*ncv+2*ncv+1:2*ncv*ncv+2*ncv) := rotation matrix Q |
c | workl(2*ncv*ncv+2*ncv+1:3*ncv*ncv+5*ncv) := workspace |
c | The final workspace is needed by subroutine cneigh called |
c | by cnaup2. Subroutine cneigh calls LAPACK routines for |
c | calculating eigenvalues and the last row of the eigenvector |
c | matrix. |
c %-------------------------------------------------------------%
c
ldh = ncv
ldq = ncv
ih = 1
ritz = ih + ldh*ncv
bounds = ritz + ncv
iq = bounds + ncv
iw = iq + ldq*ncv
next = iw + ncv**2 + 3*ncv
c
ipntr(4) = next
ipntr(5) = ih
ipntr(6) = ritz
ipntr(7) = iq
ipntr(8) = bounds
ipntr(14) = iw
end if
c
c %-------------------------------------------------------%
c | Carry out the Implicitly restarted Arnoldi Iteration. |
c %-------------------------------------------------------%
c
call cnaup2
& ( ido, bmat, n, which, nev0, np, tol, resid, mode, iupd,
& ishift, mxiter, v, ldv, workl(ih), ldh, workl(ritz),
& workl(bounds), workl(iq), ldq, workl(iw),
& ipntr, workd, rwork, info )
c
c %--------------------------------------------------%
c | ido .ne. 99 implies use of reverse communication |
c | to compute operations involving OP. |
c %--------------------------------------------------%
c
if (ido .eq. 3) iparam(8) = np
if (ido .ne. 99) go to 9000
c
iparam(3) = mxiter
iparam(5) = np
iparam(9) = nopx
iparam(10) = nbx
iparam(11) = nrorth
c
c %------------------------------------%
c | Exit if there was an informational |
c | error within cnaup2. |
c %------------------------------------%
c
if (info .lt. 0) go to 9000
if (info .eq. 2) info = 3
c
if (msglvl .gt. 0) then
call ivout (logfil, 1, mxiter, ndigit,
& '_naupd: Number of update iterations taken')
call ivout (logfil, 1, np, ndigit,
& '_naupd: Number of wanted "converged" Ritz values')
call cvout (logfil, np, workl(ritz), ndigit,
& '_naupd: The final Ritz values')
call cvout (logfil, np, workl(bounds), ndigit,
& '_naupd: Associated Ritz estimates')
end if
c
call second (t1)
tcaupd = t1 - t0
c
if (msglvl .gt. 0) then
c
c %--------------------------------------------------------%
c | Version Number & Version Date are defined in version.h |
c %--------------------------------------------------------%
c
write (6,1000)
write (6,1100) mxiter, nopx, nbx, nrorth, nitref, nrstrt,
& tmvopx, tmvbx, tcaupd, tcaup2, tcaitr, titref,
& tgetv0, tceigh, tcgets, tcapps, tcconv, trvec
1000 format (//,
& 5x, '=============================================',/
& 5x, '= Complex implicit Arnoldi update code =',/
& 5x, '= Version Number: ', ' 2.3', 21x, ' =',/
& 5x, '= Version Date: ', ' 07/31/96', 16x, ' =',/
& 5x, '=============================================',/
& 5x, '= Summary of timing statistics =',/
& 5x, '=============================================',//)
1100 format (
& 5x, 'Total number update iterations = ', i5,/
& 5x, 'Total number of OP*x operations = ', i5,/
& 5x, 'Total number of B*x operations = ', i5,/
& 5x, 'Total number of reorthogonalization steps = ', i5,/
& 5x, 'Total number of iterative refinement steps = ', i5,/
& 5x, 'Total number of restart steps = ', i5,/
& 5x, 'Total time in user OP*x operation = ', f12.6,/
& 5x, 'Total time in user B*x operation = ', f12.6,/
& 5x, 'Total time in Arnoldi update routine = ', f12.6,/
& 5x, 'Total time in naup2 routine = ', f12.6,/
& 5x, 'Total time in basic Arnoldi iteration loop = ', f12.6,/
& 5x, 'Total time in reorthogonalization phase = ', f12.6,/
& 5x, 'Total time in (re)start vector generation = ', f12.6,/
& 5x, 'Total time in Hessenberg eig. subproblem = ', f12.6,/
& 5x, 'Total time in getting the shifts = ', f12.6,/
& 5x, 'Total time in applying the shifts = ', f12.6,/
& 5x, 'Total time in convergence testing = ', f12.6,/
& 5x, 'Total time in computing final Ritz vectors = ', f12.6/)
end if
c
9000 continue
c
return
c
c %---------------%
c | End of cnaupd |
c %---------------%
c
end