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|
program psndrv3
c
c Message Passing Layer: BLACS
c
c Simple program to illustrate the idea of reverse communication
c in inverse mode for a generalized nonsymmetric eigenvalue problem.
c
c We implement example three of ex-nonsym.doc in DOCUMENTS directory
c
c\Example-3
c ... Suppose we want to solve A*x = lambda*B*x in inverse mode,
c where A is derived from the 1-dimensional convection-diffusion
c operator on the interval [0,1] with zero boundary condition,
c and M is the tridiagonal matrix with 4 on the diagonal and 1
c on the subdiagonals.
c ... So OP = inv[M]*A and B = M.
c ... Use mode 2 of PSNAUPD.
c
c\BeginLib
c
c\Routines called:
c psnaupd Parallel ARPACK reverse communication interface routine.
c psneupd Parallel ARPACK routine that returns Ritz values and (optionally)
c Ritz vectors.
c spttrf LAPACK symmetric positive definite tridiagonal factorization
c routine.
c spttrs LAPACK symmetric positive definite tridiagonal solve routine.
c slapy2 LAPACK routine to compute sqrt(x**2+y**2) carefully.
c saxpy Level 1 BLAS that computes y <- alpha*x+y.
c psnorm2 Parallel version of Level 1 BLAS that computes the norm of a vector.
c av Parallel Matrix vector multiplication routine that computes A*x.
c mv Matrix vector multiplication routine that computes M*x.
c
c\Author
c Richard Lehoucq
c Danny Sorensen
c Chao Yang
c Dept. of Computational &
c Applied Mathematics
c Rice University
c Houston, Texas
c
c\Parallel Modifications
c Kristi Maschhoff
c
c\Revision history:
c Starting Point: Serial Code FILE: ndrv3.F SID: 2.2
c
c\SCCS Information:
c FILE: ndrv3.F SID: 1.2 DATE OF SID: 09/14/98 RELEASE: 1
c
c\Remarks
c 1. None
c
c\EndLib
c--------------------------------------------------------------------------
c
include 'debug.h'
include 'stat.h'
c %-----------------%
c | BLACS INTERFACE |
c %-----------------%
c
integer comm, iam, nprocs, nloc,
& nprow, npcol, myprow, mypcol
c
external BLACS_PINFO, BLACS_SETUP, BLACS_GET,
& BLACS_GRIDINIT, BLACS_GRIDINFO
c
c %-----------------------------%
c | Define leading dimensions |
c | for all arrays. |
c | MAXN: Maximum dimension |
c | of the A allowed. |
c | MAXNEV: Maximum NEV allowed |
c | MAXNCV: Maximum NCV allowed |
c %-----------------------------%
c
integer maxn, maxnev, maxncv, ldv
parameter (maxn=256, maxnev=10, maxncv=25,
& ldv=maxn )
c
c %--------------%
c | Local Arrays |
c %--------------%
c
integer iparam(11), ipntr(14)
logical select(maxncv)
Real
& ax(maxn), mx(maxn), d(maxncv, 3), resid(maxn),
& v(ldv,maxncv), workd(3*maxn),
& workev(3*maxncv),
& workl(3*maxncv*maxncv+6*maxncv),
& md(maxn), me(maxn-1), temp(maxn), temp_buf(maxn)
c
c %---------------%
c | Local Scalars |
c %---------------%
c
character bmat*1, which*2
integer ido, n, nev, ncv, lworkl, info, ierr, j,
& nconv, maxitr, ishfts, mode, blk
Real
& tol, sigmar, sigmai
logical first, rvec
c
c %------------%
c | Parameters |
c %------------%
c
Real
& zero, one
parameter (zero = 0.0, one = 1.0)
c
c %-----------------------------%
c | BLAS & LAPACK routines used |
c %-----------------------------%
Real
& psnorm2, slapy2
external saxpy, psnorm2, spttrf, spttrs, slapy2
c
c %-----------------------%
c | Executable Statements |
c %-----------------------%
c
call BLACS_PINFO( iam, nprocs )
c
c If in PVM, create virtual machine if it doesn't exist
c
if (nprocs .lt. 1) then
if (iam .eq. 0) then
write(*,1000)
read(*, 2000) nprocs
endif
call BLACS_SETUP( iam, nprocs )
endif
c
1000 format('How many processes in machine?')
2000 format(I3)
c
c Set up processors in 1D Grid
c
nprow = nprocs
npcol = 1
c
c Get default system context, and define grid
c
call BLACS_GET( 0, 0, comm )
call BLACS_GRIDINIT( comm, 'Row', nprow, npcol )
call BLACS_GRIDINFO( comm, nprow, npcol, myprow, mypcol )
c
c If I'm not in grid, go to end of program
c
if ( (myprow .ge. nprow) .or. (mypcol .ge. npcol) ) goto 9000
c
ndigit = -3
logfil = 6
mnaupd = 1
c
c %----------------------------------------------------%
c | The number N is the dimension of the matrix. A |
c | generalized eigenvalue problem is solved (BMAT = |
c | 'G'). NEV is the number of eigenvalues to be |
c | approximated. The user can modify NEV, NCV, WHICH |
c | to solve problems of different sizes, and to get |
c | different parts of the spectrum. However, The |
c | following conditions must be satisfied: |
c | N <= MAXN, |
c | NEV <= MAXNEV, |
c | NEV + 2 <= NCV <= MAXNCV |
c %----------------------------------------------------%
c
n = 100
nev = 4
ncv = 20
c
c %--------------------------------------%
c | Set up distribution of data to nodes |
c %--------------------------------------%
c
nloc = (n / nprocs )
blk = nloc
if ( mod(n, nprocs) .gt. 0 ) then
if ( myprow .eq. nprow-1 ) nloc = nloc + mod(n, nprocs)
* if ( mod(n, nprocs) .gt. myprow ) nloc = nloc + 1
endif
c
if ( nloc .gt. maxn ) then
print *, ' ERROR with _NDRV3: NLOC is greater than MAXN '
go to 9000
else if ( nev .gt. maxnev ) then
print *, ' ERROR with _NDRV3: NEV is greater than MAXNEV '
go to 9000
else if ( ncv .gt. maxncv ) then
print *, ' ERROR with _NDRV3: NCV is greater than MAXNCV '
go to 9000
end if
bmat = 'G'
which = 'LM'
c
c %-----------------------------------------------------%
c | The matrix M is chosen to be the symmetric tri- |
c | diagonal matrix with 4 on the diagonal and 1 on the |
c | off diagonals. It is factored by LAPACK subroutine |
c | spttrf. |
c %-----------------------------------------------------%
c
do 20 j = 1, n-1
md(j) = 4.0
me(j) = one
20 continue
md(n) = 4.0*one
c
call spttrf(n, md, me, ierr)
if ( ierr .ne. 0 ) then
print*, ' '
print*, ' ERROR with _pttrf. '
print*, ' '
go to 9000
end if
c
c %-----------------------------------------------------%
c | The work array WORKL is used in SNAUPD as |
c | workspace. Its dimension LWORKL is set as |
c | illustrated below. The parameter TOL determines |
c | the stopping criterion. If TOL<=0, machine |
c | precision is used. The variable IDO is used for |
c | reverse communication, and is initially set to 0. |
c | Setting INFO=0 indicates that a random vector is |
c | generated in SNAUPD to start the Arnoldi iteration. |
c %-----------------------------------------------------%
c
lworkl = 3*ncv**2+6*ncv
tol = 0.0
ido = 0
info = 0
c
c %---------------------------------------------------%
c | This program uses exact shifts with respect to |
c | the current Hessenberg matrix (IPARAM(1) = 1). |
c | IPARAM(3) specifies the maximum number of Arnoldi |
c | iterations allowed. Mode 2 of SNAUPD is used |
c | (IPARAM(7) = 2). All these options can be |
c | changed by the user. For details, see the |
c | documentation in SNAUPD. |
c %---------------------------------------------------%
c
ishfts = 1
maxitr = 300
mode = 2
c
iparam(1) = ishfts
iparam(3) = maxitr
iparam(7) = mode
c
c %-------------------------------------------%
c | M A I N L O O P (Reverse communication) |
c %-------------------------------------------%
c
10 continue
c
c %---------------------------------------------%
c | Repeatedly call the routine SNAUPD and take |
c | actions indicated by parameter IDO until |
c | either convergence is indicated or maxitr |
c | has been exceeded. |
c %---------------------------------------------%
c
call psnaupd( comm, ido, bmat, nloc, which, nev, tol, resid,
& ncv, v, ldv, iparam, ipntr, workd,
& workl, lworkl, info )
c
if (ido .eq. -1 .or. ido .eq. 1) then
c
c %----------------------------------------%
c | Perform y <--- OP*x = inv[M]*A*x |
c | The user should supply his/her own |
c | matrix vector routine and a linear |
c | system solver. The matrix-vector |
c | subroutine should take workd(ipntr(1)) |
c | as input, and the final result should |
c | be returned to workd(ipntr(2)). |
c %----------------------------------------%
c
call av (comm, nloc, n, workd(ipntr(1)), workd(ipntr(2)))
c======== Hack for Linear system ======= ccc
call sscal(n, zero, temp, 1)
do 15 j=1,nloc
temp(myprow*blk + j) = workd(ipntr(2) + j - 1)
15 continue
call sgsum2d( comm, 'All', ' ', n, 1, temp, n, -1, -1 )
call spttrs(n, 1, md, me, temp, n,
& ierr)
if ( ierr .ne. 0 ) then
print*, ' '
print*, ' ERROR with _pttrs. '
print*, ' '
go to 9000
end if
do 16 j=1,nloc
workd(ipntr(2) + j - 1 ) = temp(myprow*blk + j)
16 continue
c
c %-----------------------------------------%
c | L O O P B A C K to call SNAUPD again. |
c %-----------------------------------------%
c
go to 10
c
else if ( ido .eq. 2) then
c
c %-------------------------------------%
c | Perform y <--- M*x |
c | The matrix vector multiplication |
c | routine should take workd(ipntr(1)) |
c | as input and return the result to |
c | workd(ipntr(2)). |
c %-------------------------------------%
c
call mv (comm, nloc, workd(ipntr(1)), workd(ipntr(2)))
c
c %-----------------------------------------%
c | L O O P B A C K to call SNAUPD again. |
c %-----------------------------------------%
c
go to 10
c
end if
c
c
c %-----------------------------------------%
c | Either we have convergence, or there is |
c | an error. |
c %-----------------------------------------%
c
if ( info .lt. 0 ) then
c
c %---------------------------%
c | Error message. Check the |
c | documentation in PSNAUPD. |
c %---------------------------%
c
if ( myprow .eq. 0 ) then
print *, ' '
print *, ' Error with _naupd, info = ', info
print *, ' Check the documentation of _naupd.'
print *, ' '
endif
c
else
c
c %-------------------------------------------%
c | No fatal errors occurred. |
c | Post-Process using SNEUPD. |
c | |
c | Computed eigenvalues may be extracted. |
c | |
c | Eigenvectors may also be computed now if |
c | desired. (indicated by rvec = .true.) |
c %-------------------------------------------%
c
rvec = .true.
call psneupd ( comm, rvec, 'A', select, d, d(1,2), v, ldv,
& sigmar, sigmai, workev, bmat, nloc, which, nev, tol,
& resid, ncv, v, ldv, iparam, ipntr, workd,
& workl, lworkl, ierr )
c
c %-----------------------------------------------%
c | The real part of the eigenvalue is returned |
c | in the first column of the two dimensional |
c | array D, and the IMAGINARY part is returned |
c | in the second column of D. The corresponding |
c | eigenvectors are returned in the first NEV |
c | columns of the two dimensional array V if |
c | requested. Otherwise, an orthogonal basis |
c | for the invariant subspace corresponding to |
c | the eigenvalues in D is returned in V. |
c %-----------------------------------------------%
c
if ( ierr .ne. 0 ) then
c
c %------------------------------------%
c | Error condition: |
c | Check the documentation of SNEUPD. |
c %------------------------------------%
c
if ( myprow .eq. 0 ) then
print *, ' '
print *, ' Error with _neupd, info = ', ierr
print *, ' Check the documentation of _neupd'
print *, ' '
endif
c
else
c
first = .true.
nconv = iparam(5)
do 30 j=1, iparam(5)
c
c %---------------------------%
c | Compute the residual norm |
c | |
c | || A*x - lambda*M*x || |
c | |
c | for the NCONV accurately |
c | computed eigenvalues and |
c | eigenvectors. (iparam(5) |
c | indicates how many are |
c | accurate to the requested |
c | tolerance) |
c %---------------------------%
c
if (d(j,2) .eq. zero) then
c
c %--------------------%
c | Ritz value is real |
c %--------------------%
c
call av(comm, nloc, n, v(1,j), ax)
call mv(comm, nloc, v(1,j), mx)
call saxpy(nloc, -d(j,1), mx, 1, ax, 1)
d(j,3) = psnorm2(comm, nloc, ax, 1)
c
else if (first) then
c
c %------------------------%
c | Ritz value is complex |
c | Residual of one Ritz |
c | value of the conjugate |
c | pair is computed. |
c %------------------------%
c
call av(comm, nloc, n, v(1,j), ax)
call mv(comm, nloc, v(1,j), mx)
call saxpy(nloc, -d(j,1), mx, 1, ax, 1)
call mv(comm, nloc, v(1,j+1), mx)
call saxpy(nloc, d(j,2), mx, 1, ax, 1)
d(j,3) = psnorm2(comm, nloc, ax, 1)**2
call av(comm, nloc, n, v(1,j+1), ax)
call mv(comm, nloc, v(1,j+1), mx)
call saxpy(nloc, -d(j,1), mx, 1, ax, 1)
call mv(comm, nloc, v(1,j), mx)
call saxpy(nloc, -d(j,2), mx, 1, ax, 1)
d(j,3) = slapy2( d(j,3), psnorm2(comm,nloc,ax,1) )
d(j+1,3) = d(j,3)
first = .false.
else
first = .true.
end if
c
30 continue
c
c %-----------------------------%
c | Display computed residuals. |
c %-----------------------------%
c
call psmout(comm, 6, nconv, 3, d, maxncv, -6,
& 'Ritz values (Real,Imag) and direct residuals')
c
end if
c
c %------------------------------------------%
c | Print additional convergence information |
c %------------------------------------------%
c
if (myprow .eq. 0)then
if ( info .eq. 1) then
print *, ' '
print *, ' Maximum number of iterations reached.'
print *, ' '
else if ( info .eq. 3) then
print *, ' '
print *, ' No shifts could be applied during implicit
& Arnoldi update, try increasing NCV.'
print *, ' '
end if
c
print *, ' '
print *, '_NDRV3 '
print *, '====== '
print *, ' '
print *, ' Size of the matrix is ', n
print *, ' The number of processors is ', nprocs
print *, ' The number of Ritz values requested is ', nev
print *, ' The number of Arnoldi vectors generated',
& ' (NCV) is ', ncv
print *, ' What portion of the spectrum: ', which
print *, ' The number of converged Ritz values is ',
& nconv
print *, ' The number of Implicit Arnoldi update',
& ' iterations taken is ', iparam(3)
print *, ' The number of OP*x is ', iparam(9)
print *, ' The convergence criterion is ', tol
print *, ' '
c
endif
end if
c
c %----------------------------%
c | Done with program psndrv3. |
c %----------------------------%
c
9000 continue
c
c %-------------------------%
c | Release resources BLACS |
c %-------------------------%
c
call BLACS_GRIDEXIT ( comm )
call BLACS_EXIT(0)
c
end
c
c==========================================================================
c
c parallel matrix vector multiplication subroutine
c
c Compute the matrix vector multiplication y<---A*x
c where A is a n by n nonsymmetric tridiagonal matrix derived
c from the central difference discretization of the 1-dimensional
c convection diffusion operator on the interval [0,1] with
c zero Dirichlet boundary condition.
c
subroutine av (comm, nloc, n, v, w)
c
c .. BLACS Declarations ...
integer comm, nprow, npcol, myprow, mypcol
external BLACS_GRIDINFO, sgesd2d, sgerv2d
c
integer nloc, n, j, next, prev
Real
& v(nloc), w(nloc), one, two, dd, dl, du,
& s, h, rho, mv_buf
parameter ( rho = 10.0, one = 1.0,
& two = 2.0)
c
call BLACS_GRIDINFO( comm, nprow, npcol, myprow, mypcol )
h = one / real(n+1)
s = rho*h / two
dd = two
dl = -one - s
du = -one + s
c
w(1) = dd*v(1) + du*v(2)
do 10 j = 2,nloc-1
w(j) = dl*v(j-1) + dd*v(j) + du*v(j+1)
10 continue
w(nloc) = dl*v(nloc-1) + dd*v(nloc)
c
next = myprow + 1
prev = myprow - 1
if ( myprow .lt. nprow-1 ) then
call sgesd2d( comm, 1, 1, v(nloc), 1, next, mypcol)
endif
if ( myprow .gt. 0 ) then
call sgerv2d( comm, 1, 1, mv_buf, 1, prev, mypcol )
w(1) = w(1) + dl*mv_buf
endif
c
if ( myprow .gt. 0 ) then
call sgesd2d( comm, 1, 1, v(1), 1, prev, mypcol)
endif
if ( myprow .lt. nprow-1 ) then
call sgerv2d( comm, 1, 1, mv_buf, 1, next, mypcol )
w(nloc) = w(nloc) + du*mv_buf
endif
c
return
end
c------------------------------------------------------------------------
c
c Compute the matrix vector multiplication y<---M*x
c where M is a n by n tridiagonal matrix with 4 on the
c diagonal, 1 on the subdiagonal and the superdiagonal.
c
subroutine mv (comm, nloc, v, w)
c
c .. BLACS Declarations ...
integer comm, nprow, npcol, myprow, mypcol
external BLACS_GRIDINFO, sgesd2d, sgerv2d
c
integer nloc, j, next, prev
Real
& v(nloc), w(nloc), one, four, mv_buf
parameter ( one = 1.0, four = 4.0)
c
call BLACS_GRIDINFO( comm, nprow, npcol, myprow, mypcol )
c
w(1) = four*v(1) + one*v(2)
do 10 j = 2,nloc-1
w(j) = one*v(j-1) + four*v(j) + one*v(j+1)
10 continue
w(nloc) = one*v(nloc-1) + four*v(nloc)
c
next = myprow + 1
prev = myprow - 1
if ( myprow .lt. nprow-1 ) then
call sgesd2d( comm, 1, 1, v(nloc), 1, next, mypcol)
endif
if ( myprow .gt. 0 ) then
call sgerv2d( comm, 1, 1, mv_buf, 1, prev, mypcol )
w(1) = w(1) + mv_buf
endif
c
if ( myprow .gt. 0 ) then
call sgesd2d( comm, 1, 1, v(1), 1, prev, mypcol)
endif
if ( myprow .lt. nprow-1 ) then
call sgerv2d( comm, 1, 1, mv_buf, 1, next, mypcol )
w(nloc) = w(nloc) + mv_buf
endif
c
return
end
c------------------------------------------------------------
subroutine mv2 (comm, n, v, w)
integer n, j, comm
Real
& v(n), w(n)
do 10 j=1,n
w(j) = v(j)
10 continue
c
return
end
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