301 lines
10 KiB
FortranFixed
301 lines
10 KiB
FortranFixed
program znbdr3
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c
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c ... Construct matrices A and M in LAPACK-style band form.
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c Matrices A and M are derived from the finite
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c element discretization of the 1-dimensional
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c 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 boundary condition using
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c piecewise linear elements.
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c
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c ... Call ZNBAND to find eigenvalues LAMBDA such that
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c A*x = M*x*LAMBDA.
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c
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c ... Eigenvalues with largest real parts are sought.
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c
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c ... Use mode 2 of ZNAUPD .
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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 znband ARPACK banded eigenproblem solver.
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c dlapy2 LAPACK routine to compute sqrt(x**2+y**2) carefully.
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c zlaset LAPACK routine to initialize a matrix to zero.
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c zaxpy Level 1 BLAS that computes y <- alpha*x+y.
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c dznrm2 Level 1 BLAS that computes the norm of a vector.
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c zgbmv 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: nbdr3.F SID: 2.4 DATE OF SID: 10/20/00 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 %-------------------------------------%
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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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Complex*16
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& a(lda,maxn), m(lda,maxn), fac(lda,maxn),
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& workl(3*maxncv*maxncv+5*maxncv), workd(3*maxn),
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& workev(2*maxncv), v(ldv, maxncv),
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& resid(maxn), d(maxncv), ax(maxn), mx(maxn)
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Double precision
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& rwork(maxn), rd(maxncv,3)
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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, j,
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& n, idiag, isup, isub, maxitr,
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& mode, nconv
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logical rvec
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Double precision
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& tol
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Complex*16
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& rho, h, sigma
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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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Complex*16
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& one, zero, two
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parameter (one = (1.0D+0, 0.0D+0) ,
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& zero = (0.0D+0, 0.0D+0) ,
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& two = (2.0D+0, 0.0D+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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Double precision
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& dznrm2 , dlapy2
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external dznrm2 , zgbmv , zaxpy , dlapy2 , zlaset
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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 generalized eigenvalue problem is |
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c | solved (BMAT = 'G'). 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 and WHICH to solve problems |
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c | of different sizes, and to get different parts |
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c | the spectrum. However, The following |
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c | 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 = 10
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if ( n .gt. maxn ) then
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print *, ' ERROR with _NBDR3: 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 _NBDR3: 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 _NBDR3: NCV is greater than MAXNCV '
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go to 9000
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end if
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bmat = 'G'
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which = 'LM'
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sigma = zero
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c
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c %----------------------------------------------------%
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c | The work array WORKL is used in ZNAUPD as |
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c | workspace. Its dimension LWORKL has to be 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 machine |
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c | precision is used. Setting INFO=0 indicates that |
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c | using a randomly generated vector to start the |
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c | the ARNOLDI process. |
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c %----------------------------------------------------%
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c
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lworkl = 3*ncv**2+5*ncv
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info = 0
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tol = 0.0
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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 2 of ZNAUPD is used |
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c | (IPARAm(7) = 2). 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 znband . |
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c %---------------------------------------------------%
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c
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maxitr = 300
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mode = 2
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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 matrices A and M 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 zlaset ('A', lda, n, zero, zero, a, lda)
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call zlaset ('A', lda, n, zero, zero, m, lda)
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call zlaset ('A', lda, n, zero, zero, fac, 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 = 1
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ku = 1
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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 / dcmplx (n+1)
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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) = (2.0D+0, 0.0D+0) / h
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m(idiag,j) = (4.0D+0, 0.0D+0) * h
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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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isup = kl+ku
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isub = kl+ku+2
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rho = (1.0D+1, 0.0D+0)
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do 40 j = 1, n-1
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a(isup,j+1) = -one/h + rho/two
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a(isub,j) = -one/h - rho/two
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m(isup,j+1) = one*h
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m(isub,j) = one*h
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40 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. Eigenvalues are returned in |
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c | the one dimensional array D. Eigenvectors |
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c | are returned in the first NCONV (=IPARAM(5)) |
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c | columns of V. |
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c %-----------------------------------------------%
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c
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rvec = .true.
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call znband (rvec, 'A', select, d, v, ldv, sigma,
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& workev, n, a, m, lda, fac, kl, ku, which,
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& bmat, nev, tol, resid, ncv, v, ldv, iparam,
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& workd, workl, lworkl, rwork, 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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nconv = iparam(5)
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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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print *, ' '
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print *, '_NBDR3 '
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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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do 50 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 | || A*x - lambda*x || |
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c %----------------------------%
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c
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call zgbmv ('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 zgbmv ('Notranspose', n, n, kl, ku, one,
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& m(kl+1,1), lda, v(1,j), 1, zero,
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& mx, 1)
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call zaxpy (n, -d(j), mx, 1, ax, 1)
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rd(j,1) = dble (d(j))
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rd(j,2) = dimag (d(j))
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rd(j,3) = dznrm2 (n, ax, 1)
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rd(j,3) = rd(j,3) / dlapy2 (rd(j,1), rd(j,2))
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50 continue
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call dmout (6, nconv, 3, rd, 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 znband . |
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c %-------------------------------------%
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c
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print *, ' '
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print *, ' Error with _band, info= ', info
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print *, ' Check the documentation of _band '
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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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