program bug_79_double_complex c c The initial vector should be in the range of OP (#79) c c We implement example one of ex-complex.doc in DOCUMENTS directory c c\Example-1 c ... Suppose we want to solve A*x = lambda*x in regular mode, c where A is obtained from the standard central difference c discretization of the convection-diffusion operator c (Laplacian u) + rho*(du / dx) c on the unit squre [0,1]x[0,1] with zero Dirichlet boundary c condition. c c ... OP = A and B = I. c c ... Assume "call av (nx,x,y)" computes y = A*x c c ... Use mode 1 of ZNAUPD . c c\BeginLib c c\Routines called c znaupd ARPACK reverse communication interface routine. c zneupd ARPACK routine that returns Ritz values and (optionally) c Ritz vectors. c dlapy2 LAPACK routine to compute sqrt(x**2+y**2) carefully. c dznrm2 Level 1 BLAS that computes the norm of a complex vector. c zaxpy Level 1 BLAS that computes y <- alpha*x+y. c av Matrix vector multiplication routine that computes A*x. c tv Matrix vector multiplication routine that computes T*x, c where T is a tridiagonal matrix. It is used in routine c av. 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\SCCS Information: @(#) c FILE: ndrv1.F SID: 2.4 DATE OF SID: 10/17/00 RELEASE: 2 c c\Remarks c 1. None c c\EndLib c--------------------------------------------------------------------------- c c %-----------------------------% c | Define maximum 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=12, maxncv=30, ldv=maxn) c c %--------------% c | Local Arrays | c %--------------% c integer iparam(11), ipntr(14) logical select(maxncv) Complex*16 & ax(maxn), d(maxncv), & v(ldv,maxncv), workd(3*maxn), & workev(3*maxncv), resid(maxn), & workl(3*maxncv*maxncv+5*maxncv) Double precision & rwork(maxncv), rd(maxncv,3) c c %---------------% c | Local Scalars | c %---------------% c character bmat*1, which*2 integer ido, n, nx, nev, ncv, lworkl, info, j, & ierr, nconv, maxitr, ishfts, mode Complex*16 & sigma Double precision & tol,res1,res2 logical rvec c c %-----------------------------% c | BLAS & LAPACK routines used | c %-----------------------------% c Double precision & dznrm2 , dlapy2 external dznrm2 , zaxpy , dlapy2 c c %-----------------------% c | Executable Statements | c %-----------------------% c c %--------------------------------------------------% c | The number NX is the number of interior points | c | in the discretization of the 2-dimensional | c | convection-diffusion operator on the unit | c | square with zero Dirichlet boundary condition. | c | The number N(=NX*NX) is the dimension of the | c | matrix. A standard eigenvalue problem is | c | solved (BMAT = 'I'). NEV is the number of | c | eigenvalues to be approximated. The user can | c | modify NX, NEV, NCV, WHICH to solve problems of | c | different sizes, and to get different parts of | c | the spectrum. However, The following | c | conditions must be satisfied: | c | N <= MAXN | c | NEV <= MAXNEV | c | NEV + 2 <= NCV <= MAXNCV | c %--------------------------------------------------% c nx = 10 n = nx*nx nev = 4 ncv = 20 if ( n .gt. maxn ) then print *, ' ERROR with _NDRV1: N is greater than MAXN ' go to 9000 else if ( nev .gt. maxnev ) then print *, ' ERROR with _NDRV1: NEV is greater than MAXNEV ' go to 9000 else if ( ncv .gt. maxncv ) then print *, ' ERROR with _NDRV1: NCV is greater than MAXNCV ' go to 9000 end if bmat = 'I' which = 'LM' c c %---------------------------------------------------% c | The work array WORKL is used in ZNAUPD 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 to start the ARNOLDI iteration. | c %---------------------------------------------------% c lworkl = 3*ncv**2+5*ncv tol = 0.0 ido = 0 info = 1 do 5, i = 1, n resid(i) = (1.0d0, 0.0d0) 5 continue c %---------------------------% c | compute A * resid by hand | c %---------------------------% call av (nx, resid, workd) res1 = dznrm2 (n, workd, 1) c c %---------------------------------------------------% c | This program uses exact shift with respect to | c | the current Hessenberg matrix (IPARAM(1) = 1). | c | IPARAM(3) specifies the maximum number of Arnoldi | c | iterations allowed. Mode 1 of ZNAUPD is used | c | (IPARAM(7) = 1). All these options can be changed | c | by the user. For details see the documentation in | c | ZNAUPD . | c %---------------------------------------------------% c ishfts = 1 maxitr = 300 mode = 1 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 ZNAUPD and take | c | actions indicated by parameter IDO until | c | either convergence is indicated or maxitr | c | has been exceeded. | c %---------------------------------------------% c call znaupd ( ido, bmat, n, which, nev, tol, resid, ncv, & v, ldv, iparam, ipntr, workd, workl, lworkl, & rwork,info ) c if (ido .eq. -1 .or. ido .eq. 1) then c c %-------------------------------------------% c | Perform matrix vector multiplication | c | y <--- OP*x | c | The user should supply his/her own | c | matrix vector multiplication routine here | c | that takes workd(ipntr(1)) as the input | c | vector, and return the matrix vector | c | product to workd(ipntr(2)). | c %-------------------------------------------% c call av (nx, workd(ipntr(1)), workd(ipntr(2))) res2 = dznrm2 (n, workd(ipntr(2)), 1) c %----------------------------------% c | res2 should contain the norm of | c | initial vector that is A * resid | c %----------------------------------% go to 9000 end if 9000 continue if (res1 .ne. res2) then stop 1 end if end c c========================================================================== c c matrix vector subroutine c c The matrix used is the convection-diffusion operator c discretized using centered difference. c subroutine av (nx, v, w) integer nx, j, lo Complex*16 & v(nx*nx), w(nx*nx), one, h2 parameter (one = (1.0D+0, 0.0D+0) ) external zaxpy , tv c c Computes w <--- OP*v, where OP is the nx*nx by nx*nx block c tridiagonal matrix c c | T -I | c |-I T -I | c OP = | -I T | c | ... -I| c | -I T| c c derived from the standard central difference discretization c of the convection-diffusion operator (Laplacian u) + rho*(du/dx) c with zero boundary condition. c c The subroutine TV is called to computed y<---T*x. c c h2 = one / dcmplx ((nx+1)*(nx+1)) c call tv(nx,v(1),w(1)) call zaxpy (nx, -one/h2, v(nx+1), 1, w(1), 1) c do 10 j = 2, nx-1 lo = (j-1)*nx call tv(nx, v(lo+1), w(lo+1)) call zaxpy (nx, -one/h2, v(lo-nx+1), 1, w(lo+1), 1) call zaxpy (nx, -one/h2, v(lo+nx+1), 1, w(lo+1), 1) 10 continue c lo = (nx-1)*nx call tv(nx, v(lo+1), w(lo+1)) call zaxpy (nx, -one/h2, v(lo-nx+1), 1, w(lo+1), 1) c return end c========================================================================= subroutine tv (nx, x, y) c integer nx, j Complex*16 & x(nx), y(nx), h, h2, dd, dl, du c Complex*16 & one, rho parameter (one = (1.0D+0, 0.0D+0) , & rho = (1.0D+2, 0.0D+0) ) c c Compute the matrix vector multiplication y<---T*x c where T is a nx by nx tridiagonal matrix with DD on the c diagonal, DL on the subdiagonal, and DU on the superdiagonal c h = one / dcmplx (nx+1) h2 = h*h dd = (4.0D+0, 0.0D+0) / h2 dl = -one/h2 - (5.0D-1, 0.0D+0) *rho/h du = -one/h2 + (5.0D-1, 0.0D+0) *rho/h c y(1) = dd*x(1) + du*x(2) do 10 j = 2,nx-1 y(j) = dl*x(j-1) + dd*x(j) + du*x(j+1) 10 continue y(nx) = dl*x(nx-1) + dd*x(nx) return end