c-----------------------------------------------------------------------
c\BeginDoc
c
c\Name: sgetv0
c
c\Description:
c  Generate a random initial residual vector for the Arnoldi process.
c  Force the residual vector to be in the range of the operator OP.
c
c\Usage:
c  call sgetv0
c     ( IDO, BMAT, ITRY, INITV, N, J, V, LDV, RESID, RNORM,
c       IPNTR, WORKD, IERR )
c
c\Arguments
c  IDO     Integer.  (INPUT/OUTPUT)
c          Reverse communication flag.  IDO must be zero on the first
c          call to sgetv0.
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 =  2: compute  Y = B * X  where
c                    IPNTR(1) is the pointer into WORKD for X,
c                    IPNTR(2) is the pointer into WORKD for Y.
c          IDO = 99: done
c          -------------------------------------------------------------
c
c  BMAT    Character*1.  (INPUT)
c          BMAT specifies the type of the matrix B in the (generalized)
c          eigenvalue problem A*x = lambda*B*x.
c          B = 'I' -> standard eigenvalue problem A*x = lambda*x
c          B = 'G' -> generalized eigenvalue problem A*x = lambda*B*x
c
c  ITRY    Integer.  (INPUT)
c          ITRY counts the number of times that sgetv0 is called.
c          It should be set to 1 on the initial call to sgetv0.
c
c  INITV   Logical variable.  (INPUT)
c          .TRUE.  => the initial residual vector is given in RESID.
c          .FALSE. => generate a random initial residual vector.
c
c  N       Integer.  (INPUT)
c          Dimension of the problem.
c
c  J       Integer.  (INPUT)
c          Index of the residual vector to be generated, with respect to
c          the Arnoldi process.  J > 1 in case of a "restart".
c
c  V       Real N by J array.  (INPUT)
c          The first J-1 columns of V contain the current Arnoldi basis
c          if this is a "restart".
c
c  LDV     Integer.  (INPUT)
c          Leading dimension of V exactly as declared in the calling
c          program.
c
c  RESID   Real array of length N.  (INPUT/OUTPUT)
c          Initial residual vector to be generated.  If RESID is
c          provided, force RESID into the range of the operator OP.
c
c  RNORM   Real scalar.  (OUTPUT)
c          B-norm of the generated residual.
c
c  IPNTR   Integer array of length 3.  (OUTPUT)
c
c  WORKD   Real work array of length 2*N.  (REVERSE COMMUNICATION).
c          On exit, WORK(1:N) = B*RESID to be used in SSAITR.
c
c  IERR    Integer.  (OUTPUT)
c          =  0: Normal exit.
c          = -1: Cannot generate a nontrivial restarted residual vector
c                in the range of the operator OP.
c
c\EndDoc
c
c-----------------------------------------------------------------------
c
c\BeginLib
c
c\Local variables:
c     xxxxxx  real
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
c\Routines called:
c     second  ARPACK utility routine for timing.
c     svout   ARPACK utility routine for vector output.
c     slarnv  LAPACK routine for generating a random vector.
c     sgemv   Level 2 BLAS routine for matrix vector multiplication.
c     scopy   Level 1 BLAS that copies one vector to another.
c     sdot    Level 1 BLAS that computes the scalar product of two vectors.
c     snrm2   Level 1 BLAS that computes the norm of a vector.
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: getv0.F   SID: 2.6   DATE OF SID: 8/27/96   RELEASE: 2
c
c\EndLib
c
c-----------------------------------------------------------------------
c
      subroutine sgetv0
     &   ( ido, bmat, itry, initv, n, j, v, ldv, resid, rnorm,
     &     ipntr, workd, ierr )
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
      logical    initv
      integer    ido, ierr, itry, j, ldv, n
      Real
     &           rnorm
c
c     %-----------------%
c     | Array Arguments |
c     %-----------------%
c
      integer    ipntr(3)
      Real
     &           resid(n), v(ldv,j), workd(2*n)
c
c     %------------%
c     | Parameters |
c     %------------%
c
      Real
     &           one, zero
      parameter (one = 1.0E+0, zero = 0.0E+0)
c
c     %------------------------%
c     | Local Scalars & Arrays |
c     %------------------------%
c
      logical    first, inits, orth
      integer    idist, iseed(4), iter, msglvl, jj
      Real
     &           rnorm0
      save       first, iseed, inits, iter, msglvl, orth, rnorm0
c
c     %----------------------%
c     | External Subroutines |
c     %----------------------%
c
      external   slarnv, svout, scopy, sgemv, second
c
c     %--------------------%
c     | External Functions |
c     %--------------------%
c
      Real
     &           sdot, snrm2
      external   sdot, snrm2
c
c     %---------------------%
c     | Intrinsic Functions |
c     %---------------------%
c
      intrinsic    abs, sqrt
c
c     %-----------------%
c     | Data Statements |
c     %-----------------%
c
      data       inits /.true./
c
c     %-----------------------%
c     | Executable Statements |
c     %-----------------------%
c
c
c     %-----------------------------------%
c     | Initialize the seed of the LAPACK |
c     | random number generator           |
c     %-----------------------------------%
c
      if (inits) then
          iseed(1) = 1
          iseed(2) = 3
          iseed(3) = 5
          iseed(4) = 7
          inits = .false.
      end if
c
      if (ido .eq.  0) then
c
c        %-------------------------------%
c        | Initialize timing statistics  |
c        | & message level for debugging |
c        %-------------------------------%
c
         call second (t0)
         msglvl = mgetv0
c
         ierr   = 0
         iter   = 0
         first  = .FALSE.
         orth   = .FALSE.
c
c        %-----------------------------------------------------%
c        | Possibly generate a random starting vector in RESID |
c        | Use a LAPACK random number generator used by the    |
c        | matrix generation routines.                         |
c        |    idist = 1: uniform (0,1)  distribution;          |
c        |    idist = 2: uniform (-1,1) distribution;          |
c        |    idist = 3: normal  (0,1)  distribution;          |
c        %-----------------------------------------------------%
c
         if (.not.initv) then
            idist = 2
            call slarnv (idist, iseed, n, resid)
         end if
c
c        %----------------------------------------------------------%
c        | Force the starting vector into the range of OP to handle |
c        | the generalized problem when B is possibly (singular).   |
c        %----------------------------------------------------------%
c
         call second (t2)
         if (bmat .eq. 'G') then
            nopx = nopx + 1
            ipntr(1) = 1
            ipntr(2) = n + 1
            call scopy (n, resid, 1, workd, 1)
            ido = -1
            go to 9000
         end if
      end if
c
c     %-----------------------------------------%
c     | Back from computing OP*(initial-vector) |
c     %-----------------------------------------%
c
      if (first) go to 20
c
c     %-----------------------------------------------%
c     | Back from computing B*(orthogonalized-vector) |
c     %-----------------------------------------------%
c
      if (orth)  go to 40
c
      if (bmat .eq. 'G') then
         call second (t3)
         tmvopx = tmvopx + (t3 - t2)
      end if
c
c     %------------------------------------------------------%
c     | Starting vector is now in the range of OP; r = OP*r; |
c     | Compute B-norm of starting vector.                   |
c     %------------------------------------------------------%
c
      call second (t2)
      first = .TRUE.
      if (bmat .eq. 'G') then
         nbx = nbx + 1
         call scopy (n, workd(n+1), 1, resid, 1)
         ipntr(1) = n + 1
         ipntr(2) = 1
         ido = 2
         go to 9000
      else if (bmat .eq. 'I') then
         call scopy (n, resid, 1, workd, 1)
      end if
c
   20 continue
c
      if (bmat .eq. 'G') then
         call second (t3)
         tmvbx = tmvbx + (t3 - t2)
      end if
c
      first = .FALSE.
      if (bmat .eq. 'G') then
          rnorm0 = sdot (n, resid, 1, workd, 1)
          rnorm0 = sqrt(abs(rnorm0))
      else if (bmat .eq. 'I') then
           rnorm0 = snrm2(n, resid, 1)
      end if
      rnorm  = rnorm0
c
c     %---------------------------------------------%
c     | Exit if this is the very first Arnoldi step |
c     %---------------------------------------------%
c
      if (j .eq. 1) go to 50
c
c     %----------------------------------------------------------------
c     | Otherwise need to B-orthogonalize the starting vector against |
c     | the current Arnoldi basis using Gram-Schmidt with iter. ref.  |
c     | This is the case where an invariant subspace is encountered   |
c     | in the middle of the Arnoldi factorization.                   |
c     |                                                               |
c     |       s = V^{T}*B*r;   r = r - V*s;                           |
c     |                                                               |
c     | Stopping criteria used for iter. ref. is discussed in         |
c     | Parlett's book, page 107 and in Gragg & Reichel TOMS paper.   |
c     %---------------------------------------------------------------%
c
      orth = .TRUE.
   30 continue
c
      call sgemv ('T', n, j-1, one, v, ldv, workd, 1,
     &            zero, workd(n+1), 1)
      call sgemv ('N', n, j-1, -one, v, ldv, workd(n+1), 1,
     &            one, resid, 1)
c
c     %----------------------------------------------------------%
c     | Compute the B-norm of the orthogonalized starting vector |
c     %----------------------------------------------------------%
c
      call second (t2)
      if (bmat .eq. 'G') then
         nbx = nbx + 1
         call scopy (n, resid, 1, workd(n+1), 1)
         ipntr(1) = n + 1
         ipntr(2) = 1
         ido = 2
         go to 9000
      else if (bmat .eq. 'I') then
         call scopy (n, resid, 1, workd, 1)
      end if
c
   40 continue
c
      if (bmat .eq. 'G') then
         call second (t3)
         tmvbx = tmvbx + (t3 - t2)
      end if
c
      if (bmat .eq. 'G') then
         rnorm = sdot (n, resid, 1, workd, 1)
         rnorm = sqrt(abs(rnorm))
      else if (bmat .eq. 'I') then
         rnorm = snrm2(n, resid, 1)
      end if
c
c     %--------------------------------------%
c     | Check for further orthogonalization. |
c     %--------------------------------------%
c
      if (msglvl .gt. 2) then
          call svout (logfil, 1, [rnorm0], ndigit,
     &                '_getv0: re-orthonalization ; rnorm0 is')
          call svout (logfil, 1, [rnorm], ndigit,
     &                '_getv0: re-orthonalization ; rnorm is')
      end if
c
      if (rnorm .gt. 0.717*rnorm0) go to 50
c
      iter = iter + 1
      if (iter .le. 1) then
c
c        %-----------------------------------%
c        | Perform iterative refinement step |
c        %-----------------------------------%
c
         rnorm0 = rnorm
         go to 30
      else
c
c        %------------------------------------%
c        | Iterative refinement step "failed" |
c        %------------------------------------%
c
         do 45 jj = 1, n
            resid(jj) = zero
   45    continue
         rnorm = zero
         ierr = -1
      end if
c
   50 continue
c
      if (msglvl .gt. 0) then
         call svout (logfil, 1, [rnorm], ndigit,
     &        '_getv0: B-norm of initial / restarted starting vector')
      end if
      if (msglvl .gt. 2) then
         call svout (logfil, n, resid, ndigit,
     &        '_getv0: initial / restarted starting vector')
      end if
      ido = 99
c
      call second (t1)
      tgetv0 = tgetv0 + (t1 - t0)
c
 9000 continue
      return
c
c     %---------------%
c     | End of sgetv0 |
c     %---------------%
c
      end
