352 lines
12 KiB
FortranFixed
352 lines
12 KiB
FortranFixed
program snbdr1
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c
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c ... Construct the matrix A in LAPACK-style band form.
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c The matrix A is derived from the discretization of
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c the 2-d convection-diffusion operator
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c
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c -Laplacian(u) + rho*partial(u)/partial(x).
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c
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c on the unit square with zero Dirichlet boundary condition
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c using standard central difference.
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c
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c ... Call SNBAND to find eigenvalues LAMBDA such that
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c A*x = LAMBDA*x.
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c
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c ... Use mode 1 of SNAUPD.
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c
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c\BeginLib
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c
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c snband ARPACK banded eigenproblem solver.
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c slapy2 LAPACK routine to compute sqrt(x**2+y**2) carefully.
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c slaset LAPACK routine to initialize a matrix to zero.
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c saxpy Level 1 BLAS that computes y <- alpha*x+y.
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c snrm2 Level 1 BLAS that computes the norm of a vector.
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c sgbmv Level 2 BLAS that computes the band matrix vector product
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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: nbdr1.F SID: 2.5 DATE OF SID: 08/26/96 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 %-------------------------------------%
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c | Define leading dimensions for all |
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c | arrays. |
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c | MAXN - Maximum size of the matrix |
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c | MAXNEV - Maximum number of |
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c | eigenvalues to be computed |
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c | MAXNCV - Maximum number of Arnoldi |
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c | vectors stored |
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c | MAXBDW - Maximum bandwidth |
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c %-------------------------------------%
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c
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integer maxn, maxnev, maxncv, maxbdw, lda,
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& lworkl, ldv
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parameter ( maxn = 1000, maxnev = 25, maxncv=50,
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& maxbdw=50, lda = maxbdw, 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), iwork(maxn)
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logical select(maxncv)
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Real
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& a(lda,maxn), m(lda,maxn), rfac(lda,maxn),
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& workl(3*maxncv*maxncv+6*maxncv), workd(3*maxn),
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& workev(3*maxncv), v(ldv, maxncv),
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& resid(maxn), d(maxncv, 3), ax(maxn)
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Complex
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& cfac(lda, maxn), workc(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 which*2, bmat
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integer nev, ncv, ku, kl, info, i, j, ido,
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& n, nx, lo, isub, isup, idiag, mode, maxitr,
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& nconv
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logical rvec, first
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Real
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& tol, rho, h, h2, sigmar, sigmai
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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
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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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& slapy2, snrm2
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external slapy2, snrm2, sgbmv, saxpy
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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 NX is the number of interior points |
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c | in the discretization of the 2-dimensional |
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c | convection-diffusion operator on the unit |
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c | square with zero Dirichlet boundary condition. |
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c | The number N(=NX*NX) is the dimension of the |
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c | matrix. A standard eigenvalue problem is |
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c | solved (BMAT = 'I'). NEV is the number of |
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c | eigenvalues to be approximated. The user can |
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c | modify NX, NEV, NCV, WHICH to solve problems of |
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c | different sizes, and to get different parts the |
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c | spectrum. However, The following conditions |
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c | 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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nx = 10
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n = nx*nx
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nev = 4
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ncv = 10
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if ( n .gt. maxn ) then
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print *, ' ERROR with _NBDR1: 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 _NBDR1: 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 _NBDR1: 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 = 'SM'
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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 | IPARAM(3) specifies the maximum number of Arnoldi |
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c | iterations allowed. Mode 1 of SNAUPD is used |
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c | (IPARAM(7) = 1). All these options can be changed |
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c | by the user. For details, see the documentation |
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c | in SNBAND. |
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c %---------------------------------------------------%
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c
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maxitr = 300
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mode = 1
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c
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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 | Construct the matrix A in LAPACK-style |
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c | banded form. |
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c %----------------------------------------%
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c
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c %---------------------------------------------%
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c | Zero out the workspace for banded matrices. |
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c %---------------------------------------------%
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c
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call slaset('A', lda, n, zero, zero, a, lda)
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call slaset('A', lda, n, zero, zero, m, lda)
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call slaset('A', lda, n, zero, zero, rfac, lda)
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c
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c %-------------------------------------%
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c | KU, KL are number of superdiagonals |
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c | and subdiagonals within the band of |
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c | matrices A and M. |
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c %-------------------------------------%
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c
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kl = nx
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ku = nx
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c
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c %---------------%
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c | Main diagonal |
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c %---------------%
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c
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h = one / real (nx+1)
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h2 = h*h
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c
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idiag = kl+ku+1
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do 30 j = 1, n
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a(idiag,j) = 4.0E+0 / h2
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30 continue
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c
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c %-------------------------------------%
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c | First subdiagonal and superdiagonal |
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c %-------------------------------------%
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c
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rho = 1.0E+2
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isup = kl+ku
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isub = kl+ku+2
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do 50 i = 1, nx
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lo = (i-1)*nx
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do 40 j = lo+1, lo+nx-1
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a(isup,j+1) = -one/h2 + rho/two/h
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a(isub,j) = -one/h2 - rho/two/h
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40 continue
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50 continue
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c
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c %------------------------------------%
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c | KL-th subdiagonal and KU-th super- |
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c | diagonal. |
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c %------------------------------------%
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c
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isup = kl+1
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isub = 2*kl+ku+1
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do 80 i = 1, nx-1
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lo = (i-1)*nx
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do 70 j = lo+1, lo+nx
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a(isup,nx+j) = -one / h2
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a(isub,j) = -one / h2
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70 continue
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80 continue
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c
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c %------------------------------------------------%
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c | Call ARPACK banded solver to find eigenvalues |
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c | and eigenvectors. The real parts of the |
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c | eigenvalues are returned in the first column |
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c | of D, the imaginary parts are returned in the |
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c | second column of D. Eigenvectors are returned |
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c | in the first NCONV (=IPARAM(5)) columns of V. |
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c %------------------------------------------------%
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c
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rvec = .true.
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call snband(rvec, 'A', select, d, d(1,2), v, ldv, sigmar, sigmai,
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& workev, n, a, m, lda, rfac, cfac, kl, ku, which,
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& bmat, nev, tol, resid, ncv, v, ldv, iparam, workd,
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& workl, lworkl, workc, iwork, info)
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c
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if ( info .eq. 0) then
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c
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c %-----------------------------------%
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c | Print out convergence information |
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c %-----------------------------------%
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c
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nconv = iparam(5)
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c
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print *, ' '
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print *, ' _NBDR1 '
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print *, ' ====== '
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print *, ' '
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print *, ' The size of the matrix is ', n
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print *, ' Number of eigenvalue 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 *, ' The number of converged Ritz values is ',
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& nconv
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print *, ' What portion of the spectrum ', which
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print *, ' The number of Implicit Arnoldi ',
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& ' update taken is ', iparam(3)
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print *, ' The number of OP*x is ', iparam(9)
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print *, ' The convergence tolerance is ', tol
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print *, ' '
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c
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c %----------------------------%
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c | Compute the residual norm. |
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c | || A*x - lambda*x || |
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c %----------------------------%
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c
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first = .true.
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do 90 j = 1, nconv
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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 sgbmv('Notranspose', n, n, kl, ku, one,
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& a(kl+1,1), lda, v(1,j), 1, zero,
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& ax, 1)
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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 sgbmv('Notranspose', n, n, kl, ku, one,
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& a(kl+1,1), lda, v(1,j), 1, zero,
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& ax, 1)
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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 sgbmv('Notranspose', n, n, kl, ku, one,
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& a(kl+1,1), lda, v(1,j+1), 1, zero,
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& ax, 1)
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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,3) = d(j,3) / slapy2(d(j,1),d(j,2))
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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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90 continue
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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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else
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c
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c %-------------------------------------%
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c | Either convergence failed, or there |
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c | is error. Check the documentation |
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c | for SNBAND. |
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c %-------------------------------------%
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c
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print *, ' '
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print *, ' Error with _nband, info= ', info
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print *, ' Check the documentation of _nband '
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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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9000 end
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