464 lines
16 KiB
FortranFixed
464 lines
16 KiB
FortranFixed
program sndrv2
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c
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c Simple program to illustrate the idea of reverse communication
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c in shift-invert mode for a standard nonsymmetric eigenvalue problem.
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c
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c We implement example two of ex-nonsym.doc in DOCUMENTS directory
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c
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c\Example-2
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c ... Suppose we want to solve A*x = lambda*x in shift-invert mode,
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c where A is derived from the centered difference discretization
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c of the 1-dimensional convection-diffusion operator
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c (d^2u / dx^2) + rho*(du/dx)
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c on the interval [0,1] with zero Dirichlet boundary condition.
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c
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c ... The shift sigma is a real number.
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c
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c ... OP = inv[A-sigma*I] and B = I.
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c
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c ... Use mode 3 of SNAUPD.
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c
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c\BeginLib
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c
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c\Routines called:
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c snaupd ARPACK reverse communication interface routine.
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c sneupd ARPACK routine that returns Ritz values and (optionally)
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c Ritz vectors.
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c sgttrf LAPACK tridiagonal factorization routine.
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c sgttrs LAPACK tridiagonal solve routine.
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c slapy2 LAPACK routine to compute sqrt(x**2+y**2) carefully.
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c saxpy Level 1 BLAS that computes y <- alpha*x+y.
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c scopy Level 1 BLAS that copies one vector to another.
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c sdot Level 1 BLAS that computes the dot product of two vectors.
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c snrm2 Level 1 BLAS that computes the norm of a vector.
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c av Matrix vector multiplication routine that computes A*x.
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c
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c\Author
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c Richard Lehoucq
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c Danny Sorensen
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c Chao Yang
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c Dept. of Computational &
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c Applied Mathematics
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c Rice University
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c Houston, Texas
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c
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c\SCCS Information: @(#)
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c FILE: ndrv2.F SID: 2.5 DATE OF SID: 10/17/00 RELEASE: 2
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c
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c\Remarks
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c 1. None
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c
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c\EndLib
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c--------------------------------------------------------------------------
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c
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c %-----------------------------%
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c | Define leading dimensions |
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c | for all arrays. |
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c | MAXN: Maximum dimension |
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c | of the A allowed. |
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c | MAXNEV: Maximum NEV allowed |
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c | MAXNCV: Maximum NCV allowed |
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c %-----------------------------%
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c
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integer maxn, maxnev, maxncv, ldv
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parameter (maxn=256, maxnev=10, maxncv=25,
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& ldv=maxn )
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c
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c %--------------%
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c | Local Arrays |
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c %--------------%
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c
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integer iparam(11), ipntr(14), ipiv(maxn)
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logical select(maxncv)
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Real
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& ax(maxn), d(maxncv,3), resid(maxn),
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& v(ldv, maxncv), workd(3*maxn),
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& workev(3*maxncv),
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& workl(3*maxncv*maxncv+6*maxncv),
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& dd(maxn), dl(maxn), du(maxn),
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& du2(maxn)
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c
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c %---------------%
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c | Local Scalars |
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c %---------------%
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c
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character bmat*1, which*2
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integer ido, n, nev, ncv, lworkl, info, j,
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& ierr, nconv, maxitr, ishfts, mode
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Real
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& tol, h, s,
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& sigmar, sigmai, s1, s2, s3
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logical first, rvec
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c
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c %------------%
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c | Parameters |
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c %------------%
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c
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Real
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& one, zero, two, rho
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common /convct/ rho
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parameter (one = 1.0E+0, zero = 0.0E+0,
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& two = 2.0E+0)
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c
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c %-----------------------------%
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c | BLAS & LAPACK routines used |
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c %-----------------------------%
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c
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Real
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& sdot, snrm2, slapy2
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external sgttrf, sgttrs, sdot, snrm2, slapy2
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c
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c %--------------------%
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c | Intrinsic function |
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c %--------------------%
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c
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intrinsic abs
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c
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c %-----------------------%
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c | Executable statements |
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c %-----------------------%
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c
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c %--------------------------------------------------%
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c | The number N is the dimension of the matrix. A |
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c | standard eigenvalue problem is solved (BMAT = |
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c | 'I'). NEV is the number of eigenvalues (closest |
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c | to the shift SIGMAR) to be approximated. Since |
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c | the shift-invert mode is used, WHICH is set to |
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c | 'LM'. The user can modify NEV, NCV, SIGMAR to |
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c | solve problems of different sizes, and to get |
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c | different parts of the spectrum. However, The |
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c | following conditions must be satisfied: |
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c | N <= MAXN, |
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c | NEV <= MAXNEV, |
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c | NEV + 2 <= NCV <= MAXNCV |
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c %--------------------------------------------------%
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c
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n = 100
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nev = 4
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ncv = 20
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if ( n .gt. maxn ) then
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print *, ' ERROR with _NDRV2: N is greater than MAXN '
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go to 9000
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else if ( nev .gt. maxnev ) then
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print *, ' ERROR with _NDRV2: NEV is greater than MAXNEV '
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go to 9000
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else if ( ncv .gt. maxncv ) then
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print *, ' ERROR with _NDRV2: NCV is greater than MAXNCV '
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go to 9000
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end if
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bmat = 'I'
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which = 'LM'
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sigmar = 1.0E+0
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sigmai = 0.0E+0
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c
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c %----------------------------------------------------%
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c | Construct C = A - SIGMA*I in real arithmetic, and |
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c | factor C in real arithmetic using LAPACK |
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c | subroutine sgttrf. The matrix A is chosen to be |
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c | the tridiagonal matrix derived from standard |
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c | central difference of the 1-d convection diffusion |
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c | operator u" + rho*u' on the interval [0, 1] with |
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c | zero Dirichlet boundary condition. |
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c %----------------------------------------------------%
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c
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rho = 1.0E+1
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h = one / real(n+1)
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s = rho*h / two
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c
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s1 = -one-s
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s2 = two - sigmar
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s3 = -one+s
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c
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do 10 j = 1, n-1
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dl(j) = s1
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dd(j) = s2
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du(j) = s3
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10 continue
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dd(n) = s2
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c
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call sgttrf(n, dl, dd, du, du2, ipiv, ierr)
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if ( ierr .ne. 0 ) then
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print*, ' '
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print*, ' ERROR with _gttrf in _NDRV2.'
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print*, ' '
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go to 9000
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end if
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c
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c %-----------------------------------------------------%
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c | The work array WORKL is used in SNAUPD as |
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c | workspace. Its dimension LWORKL is set as |
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c | illustrated below. The parameter TOL determines |
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c | the stopping criterion. If TOL<=0, machine |
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c | precision is used. The variable IDO is used for |
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c | reverse communication, and is initially set to 0. |
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c | Setting INFO=0 indicates that a random vector is |
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c | generated in SNAUPD to start the Arnoldi iteration. |
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c %-----------------------------------------------------%
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c
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lworkl = 3*ncv**2+6*ncv
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tol = zero
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ido = 0
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info = 0
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c
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c %---------------------------------------------------%
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c | This program uses exact shifts with respect to |
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c | the current Hessenberg matrix (IPARAM(1) = 1). |
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c | IPARAM(3) specifies the maximum number of Arnoldi |
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c | iterations allowed. Mode 3 of SNAUPD is used |
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c | (IPARAM(7) = 3). All these options can be |
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c | changed by the user. For details see the |
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c | documentation in SNAUPD. |
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c %---------------------------------------------------%
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c
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ishfts = 1
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maxitr = 300
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mode = 3
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iparam(1) = ishfts
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iparam(3) = maxitr
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iparam(7) = mode
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c
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c %-------------------------------------------%
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c | M A I N L O O P (Reverse communication) |
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c %-------------------------------------------%
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c
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20 continue
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c
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c %---------------------------------------------%
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c | Repeatedly call the routine SNAUPD and take |
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c | actions indicated by parameter IDO until |
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c | either convergence is indicated or maxitr |
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c | has been exceeded. |
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c %---------------------------------------------%
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c
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call snaupd ( ido, bmat, n, which, nev, tol, resid,
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& ncv, v, ldv, iparam, ipntr, workd, workl, lworkl,
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& info )
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c
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if ( ido .eq. -1 .or. ido .eq. 1) then
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c
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c %-------------------------------------------%
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c | Perform y <--- OP*x = inv[A-SIGMA*I]*x |
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c | The user should supply his/her own linear |
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c | system solver here that takes |
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c | workd(ipntr(1)) as the input, and returns |
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c | the result to workd(ipntr(2)). |
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c %-------------------------------------------%
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c
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call scopy( n, workd(ipntr(1)), 1, workd(ipntr(2)), 1)
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c
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call sgttrs('N', n, 1, dl, dd, du, du2, ipiv,
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& workd(ipntr(2)), n, ierr)
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if ( ierr .ne. 0 ) then
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print*, ' '
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print*, ' ERROR with _gttrs in _NDRV2.'
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print*, ' '
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go to 9000
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end if
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c
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c %-----------------------------------------%
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c | L O O P B A C K to call SNAUPD again. |
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c %-----------------------------------------%
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c
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go to 20
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c
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end if
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c
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c %-----------------------------------------%
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c | Either we have convergence, or there is |
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c | an error. |
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c %-----------------------------------------%
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c
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if ( info .lt. 0 ) then
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c
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c %--------------------------%
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c | Error message, check the |
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c | documentation in SNAUPD. |
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c %--------------------------%
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c
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print *, ' '
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print *, ' Error with _naupd, info = ', info
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print *, ' Check the documentation in _naupd.'
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print *, ' '
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c
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else
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c
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c %-------------------------------------------%
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c | No fatal errors occurred. |
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c | Post-Process using SNEUPD. |
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c | |
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c | Computed eigenvalues may be extracted. |
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c | |
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c | Eigenvectors may also be computed now if |
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c | desired. (indicated by rvec = .true.) |
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c %-------------------------------------------%
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c
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rvec = .true.
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c
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call sneupd ( rvec, 'A', select, d, d(1,2), v, ldv,
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& sigmar, sigmai, workev, bmat, n, which, nev, tol,
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& resid, ncv, v, ldv, iparam, ipntr, workd,
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& workl, lworkl, ierr )
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c
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c %-----------------------------------------------%
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c | The real part of the eigenvalue is returned |
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c | in the first column of the two dimensional |
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c | array D, and the imaginary part is returned |
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c | in the second column of D. The corresponding |
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c | eigenvectors are returned in the first NEV |
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c | columns of the two dimensional array V if |
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c | requested. Otherwise, an orthogonal basis |
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c | for the invariant subspace corresponding to |
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c | the eigenvalues in D is returned in V. |
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c %-----------------------------------------------%
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c
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if ( ierr .ne. 0 ) then
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c
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c %------------------------------------%
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c | Error condition: |
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c | Check the documentation of SNEUPD. |
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c %------------------------------------%
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c
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print *, ' '
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print *, ' Error with _neupd, info = ', ierr
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print *, ' Check the documentation of _neupd. '
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print *, ' '
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c
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else
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c
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first = .true.
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nconv = iparam(5)
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do 30 j=1, nconv
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c
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c %---------------------------%
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c | Compute the residual norm |
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c | |
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c | || A*x - lambda*x || |
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c | |
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c | for the NCONV accurately |
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c | computed eigenvalues and |
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c | eigenvectors. (iparam(5) |
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c | indicates how many are |
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c | accurate to the requested |
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c | tolerance) |
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c %---------------------------%
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c
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if (d(j,2) .eq. zero) then
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c
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c %--------------------%
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c | Ritz value is real |
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c %--------------------%
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c
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call av(n, v(1,j), ax)
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call saxpy(n, -d(j,1), v(1,j), 1, ax, 1)
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d(j,3) = snrm2(n, ax, 1)
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d(j,3) = d(j,3) / abs(d(j,1))
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c
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else if (first) then
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c
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c %------------------------%
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c | Ritz value is complex |
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c | Residual of one Ritz |
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c | value of the conjugate |
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c | pair is computed. |
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c %------------------------%
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c
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call av(n, v(1,j), ax)
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call saxpy(n, -d(j,1), v(1,j), 1, ax, 1)
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call saxpy(n, d(j,2), v(1,j+1), 1, ax, 1)
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d(j,3) = snrm2(n, ax, 1)
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call av(n, v(1,j+1), ax)
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call saxpy(n, -d(j,2), v(1,j), 1, ax, 1)
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call saxpy(n, -d(j,1), v(1,j+1), 1, ax, 1)
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d(j,3) = slapy2( d(j,3), snrm2(n, ax, 1) )
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d(j+1,3) = d(j,3)
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first = .false.
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else
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first = .true.
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end if
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c
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30 continue
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c
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c %-----------------------------%
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c | Display computed residuals. |
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c %-----------------------------%
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c
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call smout(6, nconv, 3, d, maxncv, -6,
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& 'Ritz values (Real,Imag) and relative residuals')
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c
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end if
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c
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c %-------------------------------------------%
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c | Print additional convergence information. |
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c %-------------------------------------------%
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c
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if ( info .eq. 1) then
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print *, ' '
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print *, ' Maximum number of iterations reached.'
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print *, ' '
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else if ( info .eq. 3) then
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print *, ' '
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print *, ' No shifts could be applied during implicit',
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& ' Arnoldi update, try increasing NCV.'
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print *, ' '
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end if
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c
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print *, ' '
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print *, ' _NDRV2 '
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print *, ' ====== '
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print *, ' '
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print *, ' Size of the matrix is ', n
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print *, ' The number of Ritz values requested is ', nev
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print *, ' The number of Arnoldi vectors generated',
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& ' (NCV) is ', ncv
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print *, ' What portion of the spectrum: ', which
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print *, ' The number of converged Ritz values is ',
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& nconv
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print *, ' The number of Implicit Arnoldi update',
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& ' iterations taken is ', iparam(3)
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print *, ' The number of OP*x is ', iparam(9)
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print *, ' The convergence criterion is ', tol
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print *, ' '
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c
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end if
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c
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c %---------------------------%
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c | Done with program sndrv2. |
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c %---------------------------%
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c
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9000 continue
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c
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end
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c
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c-------------------------------------------------------------------
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c
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c matrix vector multiplication subroutine
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c
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subroutine av (n, v, w)
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integer n, j
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Real
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& v(n), w(n), rho, two, one, dd, dl, du, s, h
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common /convct/ rho
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parameter (one = 1.0E+0, two = 2.0E+0 )
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c
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c Compute the matrix vector multiplication y<---A*x
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c where A is a n by n nonsymmetric tridiagonal matrix derived from
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c the central difference discretization of the 1-dimensional
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c convection diffusion operator on the interval [0,1] with
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c zero Dirichlet boundary condition.
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c
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c
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h = one / real(n+1)
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s = rho *h / two
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dd = two
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dl = -one - s
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du = -one + s
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c
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w(1) = dd*v(1) + du*v(2)
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do 10 j = 2,n-1
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w(j) = dl*v(j-1) + dd*v(j) + du*v(j+1)
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10 continue
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w(n) = dl*v(n-1) + dd*v(n)
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return
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end
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