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C DNAUPD    SOURCE    BP208322  20/02/06    21:15:21     10512          c\BeginDoccc\Name: dnaupdcc\Description:c  Reverse communication interface for the Implicitly Restarted Arnoldic  iteration. This subroutine computes approximations to a few eigenpairsc  of a linear operator "OP" with respect to a semi-inner product defined byc  a symmetric positive semi-definite real matrix B. B may be the identityc  matrix. NOTE: If the linear operator "OP" is real and symmetricc  with respect to the real positive semi-definite symmetric matrix B,c  i.e. B*OP = (OP)*B, then subroutine dsaupd  should be used instead.cc  The computed approximate eigenvalues are called Ritz values andc  the corresponding approximate eigenvectors are called Ritz vectors.cc  dnaupd  is usually called iteratively to solve one of thec  following problems:cc  Mode 1:  A*x = lambda*x.c           ===> OP = A  and  B = I.cc  Mode 2:  A*x = lambda*M*x, M symmetric positive definitec           ===> OP = inv[M]*A  and  B = M.c           ===> (If M can be factored see remark 3 below)cc  Mode 3:  A*x = lambda*M*x, M symmetric semi-definitec           ===> OP = Real_Part{ inv[A - sigma*M]*M }  and  B = M.c           ===> shift-and-invert mode (in real arithmetic)c           If OP*x = amu*x, thenc           amu = 1/2 * [ 1/(lambda-sigma) + 1/(lambda-conjg(sigma)) ].c           Note: If sigma is real, i.e. imaginary part of sigma is zero;c                 Real_Part{ inv[A - sigma*M]*M } == inv[A - sigma*M]*Mc                 amu == 1/(lambda-sigma).cc  Mode 4:  A*x = lambda*M*x, M symmetric semi-definitec           ===> OP = Imaginary_Part{ inv[A - sigma*M]*M }  and  B = M.c           ===> shift-and-invert mode (in real arithmetic)c           If OP*x = amu*x, thenc           amu = 1/2i * [ 1/(lambda-sigma) - 1/(lambda-conjg(sigma)) ].cc  Both mode 3 and 4 give the same enhancement to eigenvalues close toc  the (complex) shift sigma.  However, as lambda goes to infinity,c  the operator OP in mode 4 dampens the eigenvalues more strongly thanc  does OP defined in mode 3.cc  NOTE: The action of w &lt;- inv[A - sigma*M]*v or w &lt;- inv[M]*vc        should be accomplished either by a direct methodc        using a sparse matrix factorization and solvingcc           [A - sigma*M]*w = v  or M*w = v,cc        or through an iterative method for solving thesec        systems.  If an iterative method is used, thec        convergence test must be more stringent thanc        the accuracy requirements for the eigenvaluec        approximations.cc\Usage:c  call dnaupdc     ( IDO, BMAT, N, WHICH, NEV, TOL, RESID, NCV, V, LDV, IPARAM,c       IPNTR, WORKD, WORKL, LWORKL, INFO )cc\Argumentsc  IDO     Integer.  (INPUT/OUTPUT)c          Reverse communication flag.  IDO must be zero on the firstc          call to dnaupd .  IDO will be set internally toc          indicate the type of operation to be performed.  Control isc          then given back to the calling routine which has thec          responsibility to carry out the requested operation and callc          dnaupd  with the result.  The operand is given inc          WORKD(IPNTR(1)), the result must be put in WORKD(IPNTR(2)).c          -------------------------------------------------------------c          IDO =  0: first call to the reverse communication interfacec          IDO = -1: compute  Y = OP * X  wherec                    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 thec                    starting vector into the range of OP.c          IDO =  1: compute  Y = OP * X  wherec                    IPNTR(1) is the pointer into WORKD for X,c                    IPNTR(2) is the pointer into WORKD for Y.c                    In mode 3 and 4, the vector B * X is alreadyc                    available in WORKD(ipntr(3)).  It does notc                    need to be recomputed in forming OP * X.c          IDO =  2: compute  Y = B * X  wherec                    IPNTR(1) is the pointer into WORKD for X,c                    IPNTR(2) is the pointer into WORKD for Y.c          IDO =  3: compute the IPARAM(8) real and imaginary partsc                    of the shifts where INPTR(14) is the pointerc                    into WORKL for placing the shifts. See Remarkc                    5 below.c          IDO = 99: donec          -------------------------------------------------------------cc  BMAT    Character*1.  (INPUT)c          BMAT specifies the type of the matrix B that defines thec          semi-inner product for the operator OP.c          BMAT = 'I' -> standard eigenvalue problem A*x = lambda*xc          BMAT = 'G' -> generalized eigenvalue problem A*x = lambda*B*xcc  N       Integer.  (INPUT)c          Dimension of the eigenproblem.cc  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.cc  NEV     Integer.  (INPUT)c          Number of eigenvalues of OP to be computed. 0 &lt; NEV &lt; N-1.cc  TOL     Double precision  scalar.  (INPUT/OUTPUT)c          Stopping criterion: the relative accuracy of the Ritz valuec          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 = DLAMCH ('EPS')  (machine precision as computedc                    by the LAPACK auxiliary subroutine DLAMCH ).cc  RESID   Double precision  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.cc  NCV     Integer.  (INPUT)c          Number of columns of the matrix V. NCV must satisfy the twoc          inequalities 2 &lt;= NCV-NEV and NCV &lt;= N.c          This will indicate how many Arnoldi vectors are generatedc          at each iteration.  After the startup phase in which NEVc          Arnoldi vectors are generated, the algorithm generatesc          approximately NCV-NEV Arnoldi vectors at each subsequent updatec          iteration. Most of the cost in generating each Arnoldi vector isc          in the matrix-vector operation OP*x.c          NOTE: 2 &lt;= NCV-NEV in order that complex conjugate pairs of Ritzc          values are kept together. (See remark 4 below)cc  V       REAL*8  array N by NCV.  (OUTPUT)c          Contains the final set of Arnoldi basis vectors.cc  LDV     Integer.  (INPUT)c          Leading dimension of V exactly as declared in the calling program.cc  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 restartc          the Arnoldi iteration in an implicit fashion.c          -------------------------------------------------------------c          ISHIFT = 0: the shifts are provided by the user viac                      reverse communication.  The real and imaginaryc                      parts of the NCV eigenvalues of the Hessenbergc                      matrix H are returned in the part of the WORKLc                      array corresponding to RITZR and RITZI. See remarkc                      5 below.c          ISHIFT = 1: exact shifts with respect to the currentc                      Hessenberg matrix H.  This is equivalent toc                      restarting the iteration with a starting vectorc                      that is a linear combination of approximate Schurc                      vectors associated with the "wanted" Ritz values.c          -------------------------------------------------------------cc          IPARAM(2) = No longer referenced.cc          IPARAM(3) = MXITERc          On INPUT:  maximum number of Arnoldi update iterations allowed.c          On OUTPUT: actual number of Arnoldi update iterations taken.cc          IPARAM(4) = NB: blocksize to be used in the recurrence.c          The code currently works only for NB = 1.cc          IPARAM(5) = NCONV: number of "converged" Ritz values.c          This represents the number of Ritz values that satisfyc          the convergence criterion.cc          IPARAM(6) = IUPDc          No longer referenced. Implicit restarting is ALWAYS used.cc          IPARAM(7) = MODEc          On INPUT determines what type of eigenproblem is being solved.c          Must be 1,2,3,4; See under \Description of dnaupd  for thec          four modes available.cc          IPARAM(8) = NPc          When ido = 3 and the user provides shifts through reversec          communication (IPARAM(1)=0), dnaupd  returns NP, the numberc          of shifts the user is to provide. 0 &lt; NP &lt;=NCV-NEV. See Remarkc          5 below.cc          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.cc  IPNTR   Integer array of length 14.  (OUTPUT)c          Pointer to mark the starting locations in the WORKD and WORKLc          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 inc                    the shift-and-invert mode.c          IPNTR(4): pointer to the next available location in WORKLc                    that is untouched by the program.c          IPNTR(5): pointer to the NCV by NCV upper Hessenberg matrixc                    H in WORKL.c          IPNTR(6): pointer to the real part of the ritz value arrayc                    RITZR in WORKL.c          IPNTR(7): pointer to the imaginary part of the ritz value arrayc                    RITZI in WORKL.c          IPNTR(8): pointer to the Ritz estimates in array WORKL associatedc                    with the Ritz values located in RITZR and RITZI in WORKL.cc          IPNTR(14): pointer to the NP shifts in WORKL. See Remark 5 below.cc          Note: IPNTR(9:13) is only referenced by dneupd . See Remark 2 below.cc          IPNTR(9):  pointer to the real part of the NCV RITZ values of thec                     original system.c          IPNTR(10): pointer to the imaginary part of the NCV RITZ values ofc                     the original system.c          IPNTR(11): pointer to the NCV corresponding error bounds.c          IPNTR(12): pointer to the NCV by NCV upper quasi-triangularc                     Schur matrix for H.c          IPNTR(13): pointer to the NCV by NCV matrix of eigenvectorsc                     of the upper Hessenberg matrix H. Only referenced byc                     dneupd  if RVEC = .TRUE. See Remark 2 below.c          -------------------------------------------------------------cc  WORKD   Double precision  work array of length 3*N.  (REVERSE COMMUNICATION)c          Distributed array to be used in the basic Arnoldi iterationc          for reverse communication.  The user should not use WORKDc          as temporary workspace during the iteration. Upon terminationc          WORKD(1:N) contains B*RESID(1:N). If an invariant subspacec          associated with the converged Ritz values is desired, see remarkc          2 below, subroutine dneupd  uses this output.c          See Data Distribution Note below.cc  WORKL   Double precision  work array of length LWORKL.  (OUTPUT/WORKSPACE)c          Private (replicated) array on each PE or array allocated onc          the front end.  See Data Distribution Note below.cc  LWORKL  Integer.  (INPUT)c          LWORKL must be at least 3*NCV**2 + 6*NCV.cc  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 startingc                with release 2 of ARPACK.c          =  3: No shifts could be applied during a cycle of thec                Implicitly restarted Arnoldi iteration. One possibilityc                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 >= 2 and less than or equal to N.c          = -4: The maximum number of Arnoldi update iterationc                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 1,2,3,4.c          = -11: IPARAM(7) = 1 and BMAT = 'G' are incompatable.c          = -12: IPARAM(1) must be equal to 0 or 1.c          = -9999: Could not build an Arnoldi factorization.c                   IPARAM(5) returns the size of the current Arnoldic                   factorization.cc\Remarksc  1. The computed Ritz values are approximate eigenvalues of OP. Thec     selection of WHICH should be made with this in mind whenc     Mode = 3 and 4.  After convergence, approximate eigenvalues of thec     original problem may be obtained with the ARPACK subroutine dneupd .cc  2. If a basis for the invariant subspace corresponding to the converged Ritzc     values is needed, the user must call dneupd  immediately followingc     completion of dnaupd . This is new starting with release 2 of ARPACK.cc  3. If M can be factored into a Cholesky factorization M = LLc     then Mode = 2 should not be selected.  Instead one should usec     Mode = 1 with  OP = inv(L)*A*inv(L).  Appropriate triangularc     linear systems should be solved with L and L ratherc     than computing inverses.  After convergence, an approximatec     eigenvector z of the original problem is recovered by solvingc     Lz = x  where x is a Ritz vector of OP.cc  4. At present there is no a-priori analysis to guide the selectionc     of NCV relative to NEV.  The only formal requrement is that NCV > NEV + 2.c     However, it is recommended that NCV .ge. 2*NEV+1.  If many problems ofc     the same type are to be solved, one should experiment with increasingc     NCV while keeping NEV fixed for a given test problem.  This willc     usually decrease the required number of OP*x operations but itc     also increases the work and storage required to maintain the orthogonalc     basis vectors.  The optimal "cross-over" with respect to CPU timec     is problem dependent and must be determined empirically.c     See Chapter 8 of Reference 2 for further information.cc  5. When IPARAM(1) = 0, and IDO = 3, the user needs to provide thec     NP = IPARAM(8) real and imaginary parts of the shifts in locationsc         real part                  imaginary partc         -----------------------    --------------c     1   WORKL(IPNTR(14))           WORKL(IPNTR(14)+NP)c     2   WORKL(IPNTR(14)+1)         WORKL(IPNTR(14)+NP+1)c                        .                          .c                        .                          .c                        .                          .c     NP  WORKL(IPNTR(14)+NP-1)      WORKL(IPNTR(14)+2*NP-1).cc     Only complex conjugate pairs of shifts may be applied and the pairsc     must be placed in consecutive locations. The real part of thec     eigenvalues of the current upper Hessenberg matrix are located inc     WORKL(IPNTR(6)) through WORKL(IPNTR(6)+NCV-1) and the imaginary partc     in WORKL(IPNTR(7)) through WORKL(IPNTR(7)+NCV-1). They are orderedc     according to the order defined by WHICH. The complex conjugatec     pairs are kept together and the associated Ritz estimates are located inc     WORKL(IPNTR(8)), WORKL(IPNTR(8)+1), ... , WORKL(IPNTR(8)+NCV-1).cc-----------------------------------------------------------------------cc\Data Distribution Note:cc  Fortran-D syntax:c  ================c  Double precision  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)cc  Cray MPP syntax:c  ===============c  Double precision   resid(n), v(ldv,ncv), workd(n,3), workl(lworkl)c  shared     resid(block), v(block,:), workd(block,:)c  replicated workl(lworkl)cc  CM2/CM5 syntax:c  ==============cc-----------------------------------------------------------------------cc     include   'ex-nonsym.doc'cc-----------------------------------------------------------------------cc\BeginLibcc\Local variables:c     xxxxxx  realcc\References:c  1. D.C. Sorensen, "Implicit Application of Polynomial Filters inc     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 Implicitlyc     Restarted Arnoldi Iteration", Rice University Technical Reportc     TR95-13, Department of Computational and Applied Mathematics.c  3. B.N. Parlett & Y. Saad, "Complex Shift and Invert Strategies forc     Real Matrices", Linear Algebra and its Applications, vol 88/89,c     pp 575-595, (1987).cc\Routines called:c     dnaup2   ARPACK routine that implements the Implicitly Restartedc             Arnoldi Iteration.c     ivout   ARPACK utility routine that prints integers.c     arscnd  ARPACK utility routine for timing. -> deleted by BP in 2020c     dvout    ARPACK utility routine that prints vectors.c     dlamch   LAPACK routine that determines machine constants.cc\Authorc     Danny Sorensen               Phuong Vuc     Richard Lehoucq              CRPC / Rice Universityc     Dept. of Computational &     Houston, Texasc     Applied Mathematicsc     Rice Universityc     Houston, Texascc\Revision history:c     12/16/93: Version '1.1'cc\SCCS Information: @(#)c FILE: naupd.F   SID: 2.8   DATE OF SID: 04/10/01   RELEASE: 2cc\Remarkscc\EndLibcc-----------------------------------------------------------------------c      subroutine dnaupd     &   ( ido, bmat, n, which, nev, tol, resid, ncv, v, ldv, iparam,     &     ipntr, workd, workl, lworkl, ITRAK, info )cc     %----------------------------------------------------%c     | Include files for debugging and timing information |c -INC TARTRAKc     %----------------------------------------------------%ccc     %------------------%c     | Scalar Arguments |c     %------------------%c      character  bmat*1, which*2      integer    ido, info, ldv, lworkl, n, ncv, nev      REAL*8     &           tolcc     %-----------------%c     | Array Arguments |c     %-----------------%c      integer    iparam(11), ipntr(14)      INTEGER    ITRAK(5)      REAL*8     &           resid(n), v(ldv,ncv), workd(3*n), workl(lworkl)cc     %------------%c     | Parameters |c     %------------%c      REAL*8     &           one, zero      parameter (one = 1.0D+0 , zero = 0.0D+0 )cc     %---------------%c     | Local Scalars |c     %---------------%c      integer    bounds, ierr, ih, iq, ishift, iupd, iw,     &           ldh, ldq, levec, mode, msglvl, mxiter, nb,     &           nev0, next, np, ritzi, ritzr, j      save       bounds, ih, iq, ishift, iupd, iw, ldh, ldq,c      &           levec, mode, msglvl, mxiter, nb, nev0, next,     &           levec, mode, mxiter, nb, nev0, next,     &           np, ritzi, ritzr      parameter (msglvl=0)cc     %----------------------%c     | External Subroutines |c     %----------------------%c      external   dnaup2 , dvout , ivout,  dstatncc     %--------------------%c     | External Functions |c     %--------------------%c      REAL*8     &           dlamch      external   dlamchcc     %-----------------------%c     | Executable Statements |c     %-----------------------%        nopx  =ITRAK(1)        nbx   =ITRAK(2)        nrorth=ITRAK(3)        nitref=ITRAK(4)        nrstrt=ITRAK(5)c      if (ido .eq. 0) thencc        %-------------------------------%c        | Initialize timing statistics  |c        | & message level for debugging |c        %-------------------------------%c         call dstatn(nopx,nbx,nrorth,nitref,nrstrt)*         call arscnd (t0)c          msglvl = mnaupdcc        %----------------%c        | Error checking |c        %----------------%c         ierr   = 0         ishift = iparam(1)c         levec  = iparam(2)         mxiter = iparam(3)c         nb     = iparam(4)         nb     = 1cc        %--------------------------------------------%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+1 .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 + 6*ncv) then            ierr = -7         else if (mode .lt. 1 .or. mode .gt. 4) then                                                ierr = -10         else if (mode .eq. 1 .and. bmat .eq. 'G') then                                                ierr = -11         else if (ishift .lt. 0 .or. ishift .gt. 1) then                                                ierr = -12         end ifcc        %------------%c        | Error Exit |c        %------------%c         if (ierr .ne. 0) then            info = ierr            ido  = 99            go to 9000         end ifcc        %------------------------%c        | Set default parameters |c        %------------------------%c         if (nb .le. 0)                         nb = 1         if (tol .le. zero)                     tol = dlamch ('EpsMach')cc        %----------------------------------------------%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   = nevcc        %-----------------------------%c        | Zero out internal workspace |c        %-----------------------------%c         do 10 j = 1, 3*ncv**2 + 6*ncv            workl(j) = zero  10     continuecc        %-------------------------------------------------------------%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+2*ncv) := real and imaginary        |c        |                                   parts of ritz values      |c        | workl(ncv*ncv+2*ncv+1:ncv*ncv+3*ncv) := error bounds        |c        | workl(ncv*ncv+3*ncv+1:2*ncv*ncv+3*ncv) := rotation matrix Q |c        | workl(2*ncv*ncv+3*ncv+1:3*ncv*ncv+6*ncv) := workspace       |c        | The final workspace is needed by subroutine dneigh  called   |c        | by dnaup2 . Subroutine dneigh  calls LAPACK routines for      |c        | calculating eigenvalues and the last row of the eigenvector |c        | matrix.                                                     |c        %-------------------------------------------------------------%c         ldh    = ncv         ldq    = ncv         ih     = 1         ritzr  = ih     + ldh*ncv         ritzi  = ritzr  + ncv         bounds = ritzi  + ncv         iq     = bounds + ncv         iw     = iq     + ldq*ncv         next   = iw     + ncv**2 + 3*ncvc         ipntr(4) = next         ipntr(5) = ih         ipntr(6) = ritzr         ipntr(7) = ritzi         ipntr(8) = bounds         ipntr(14) = iwc      end ifcc     %-------------------------------------------------------%c     | Carry out the Implicitly restarted Arnoldi Iteration. |c     %-------------------------------------------------------%c      call dnaup2     &   ( ido, bmat, n, which, nev0, np, tol, resid, mode, iupd,     &     ishift, mxiter, v, ldv, workl(ih), ldh, workl(ritzr),     &     workl(ritzi), workl(bounds), workl(iq), ldq, workl(iw),     &     ipntr, workd, ITRAK, info )c       recup        nopx  =ITRAK(1)        nbx   =ITRAK(2)        nrorth=ITRAK(3)        nitref=ITRAK(4)        nrstrt=ITRAK(5)cc     %--------------------------------------------------%c     | ido .ne. 99 implies use of reverse communication |c     | to compute operations involving OP or shifts.    |c     %--------------------------------------------------%c      if (ido .eq. 3) iparam(8) = np      if (ido .ne. 99) go to 9000c      iparam(3)  = mxiter      iparam(5)  = np      iparam(9)  = nopx      iparam(10) = nbx      iparam(11) = nrorthcc     %------------------------------------%c     | Exit if there was an informational |c     | error within dnaup2 .               |c     %------------------------------------%c      if (info .lt. 0) go to 9000      if (info .eq. 2) info = 3c      if (msglvl .gt. 0) then         call ivout ( 1, mxiter, ndigit,     &               '_naupd: Number of update iterations taken')         call ivout ( 1, np, ndigit,     &               '_naupd: Number of wanted "converged" Ritz values')         call dvout ( np, workl(ritzr), ndigit,     &               '_naupd: Real part of the final Ritz values')         call dvout ( np, workl(ritzi), ndigit,     &               '_naupd: Imaginary part of the final Ritz values')         call dvout ( np, workl(bounds), ndigit,     &               '_naupd: Associated Ritz estimates')      end ifc*      call arscnd (t1)c       tnaupd = t1 - t0c      if (msglvl .gt. 0) thencc        %--------------------------------------------------------%c        | Version Number & Version Date are defined in version.h |c        %--------------------------------------------------------%c         write (6,1000)         write (6,1100) mxiter, nopx, nbx, nrorth, nitref, nrstrtc      &                 ,tmvopx, tmvbx, tnaupd, tnaup2, tnaitr, titref,c      &                  tgetv0, tneigh, tngets, tnapps, tnconv, trvec 1000    format (//,     &      5x, '=============================================',/     &      5x, '= Nonsymmetric implicit Arnoldi update code =',/     &      5x, '= Version Number: ', ' 2.4' , 21x, ' =',/     &      5x, '= Version Date:   ', ' 07/31/96' , 16x,   ' =',/     &      5x, '=============================================',//)c      &      5x, '= Summary of timing statistics              =',/c      &      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,/)c      &      5x, 'Total time in user OP*x operation          = ', f12.6,/c      &      5x, 'Total time in user B*x operation           = ', f12.6,/c      &      5x, 'Total time in Arnoldi update routine       = ', f12.6,/c      &      5x, 'Total time in naup2 routine                = ', f12.6,/c      &      5x, 'Total time in basic Arnoldi iteration loop = ', f12.6,/c      &      5x, 'Total time in reorthogonalization phase    = ', f12.6,/c      &      5x, 'Total time in (re)start vector generation  = ', f12.6,/c      &      5x, 'Total time in Hessenberg eig. subproblem   = ', f12.6,/c      &      5x, 'Total time in getting the shifts           = ', f12.6,/c      &      5x, 'Total time in applying the shifts          = ', f12.6,/c      &      5x, 'Total time in convergence testing          = ', f12.6,/c      &      5x, 'Total time in computing final Ritz vectors = ', f12.6/)      end ifc 9000 continuecc     ITRAK(..)=...  inutile car ITRAK fourni a dsaup2 par ex et pas modifie iciccc     %---------------%c     | End of dnaupd  |c     %---------------%c      end   `

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