program ssbdr2 c c ... Construct the matrix A in LAPACK-style band form. c The matrix A is derived from the discretization of c the 2-dimensional Laplacian on the unit square c with zero Dirichlet boundary condition using standard c central difference. c c ... Call SSBAND to find eigenvalues LAMBDA closest to c SIGMA such that c A*x = x*LAMBDA. c c ... Use mode 3 of SSAUPD. c c\BeginLib c c\Routines called: c ssband ARPACK banded eigenproblem solver. c slapy2 LAPACK routine to compute sqrt(x**2+y**2) carefully. c slaset LAPACK routine to initialize a matrix to zero. c saxpy Level 1 BLAS that computes y <- alpha*x+y. c snrm2 Level 1 BLAS that computes the norm of a vector. c sgbmv Level 2 BLAS that computes the band matrix vector product. 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: sbdr2.F SID: 2.5 DATE OF SID: 08/26/96 RELEASE: 2 c c\Remarks c 1. None c c\EndLib c c---------------------------------------------------------------------- c c %-------------------------------------% c | Define leading dimensions for all | c | arrays. | c | MAXN - Maximum size of the matrix | c | MAXNEV - Maximum number of | c | eigenvalues to be computed | c | MAXNCV - Maximum number of Arnoldi | c | vectors stored | c | MAXBDW - Maximum bandwidth | c %-------------------------------------% c integer maxn, maxnev, maxncv, maxbdw, lda, & lworkl, ldv parameter ( maxn = 1000, maxnev = 25, maxncv=50, & maxbdw=50, lda = maxbdw, ldv = maxn ) c c %--------------% c | Local Arrays | c %--------------% c integer iparam(11), iwork(maxn) logical select(maxncv) Real & a(lda,maxn), m(lda,maxn), rfac(lda,maxn), & workl(3*maxncv*maxncv+6*maxncv), workd(3*maxn), & v(ldv, maxncv), resid(maxn), d(maxncv, 2), & ax(maxn) c c %---------------% c | Local Scalars | c %---------------% c character which*2, bmat integer nev, ncv, ku, kl, info, i, j, ido, & n, nx, lo, isub, isup, idiag, maxitr, mode, & nconv Real & tol, sigma, h2 logical rvec c c %------------% c | Parameters | c %------------% c Real & one, zero, two parameter (one = 1.0E+0 , zero = 0.0E+0 , two = 2.0E+0 ) c c %-----------------------------% c | BLAS & LAPACK routines used | c %-----------------------------% c Real & slapy2, snrm2 external slapy2, snrm2, saxpy, sgbmv 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 | Laplacian operator on the unit square with zero | c | Dirichlet boundary condition. The number | c | N(=NX*NX) is the dimension of the matrix. A | c | standard eigenvalue problem is solved | c | (BMAT = 'I'). NEV is the number of eigenvalues | c | (closest to the shift SIGMA) to be approximated. | c | Since the shift and invert mode is used, WHICH | c | is set to 'LM'. The user can modify NX, NEV, | c | NCV and SIGMA to solve problems of different | c | sizes, and to get different parts the spectrum. | c | However, the following conditions must be | c | satisfied: | c | N <= MAXN | c | NEV <= MAXNEV | c | NEV + 1 <= NCV <= MAXNCV | c %--------------------------------------------------% c nx = 10 n = nx*nx nev = 4 ncv = 10 if ( n .gt. maxn ) then print *, ' ERROR with _SBDR2: N is greater than MAXN ' go to 9000 else if ( nev .gt. maxnev ) then print *, ' ERROR with _SBDR2: NEV is greater than MAXNEV ' go to 9000 else if ( ncv .gt. maxncv ) then print *, ' ERROR with _SBDR2: NCV is greater than MAXNCV ' go to 9000 end if bmat = 'I' which = 'LM' sigma = zero c c %-----------------------------------------------------% c | The work array WORKL is used in SSAUPD as | c | workspace. Its dimension LWORKL is set as | c | illustrated below. The parameter TOL determines | c | the stopping criterion. If TOL<=0, machine | c | precision is used. The variable IDO is used for | c | reverse communication, and is initially set to 0. | c | Setting INFO=0 indicates that a random vector is | c | generated in SSAUPD to start the Arnoldi iteration. | c %-----------------------------------------------------% c lworkl = 3*ncv**2+6*ncv tol = zero ido = 0 info = 0 c c %---------------------------------------------------% c | IPARAM(3) specifies the maximum number of Arnoldi | c | iterations allowed. Mode 3 of SSAUPD is used | c | (IPARAM(7) = 3). All these options can be changed | c | by the user. For details see the documentation in | c | SSBAND. | c %---------------------------------------------------% c maxitr = 300 mode = 3 c iparam(3) = maxitr iparam(7) = mode c c %----------------------------------------% c | Construct the matrix A in LAPACK-style | c | banded form. | c %----------------------------------------% c c %---------------------------------------------% c | Zero out the workspace for banded matrices. | c %---------------------------------------------% c call slaset('A', lda, n, zero, zero, a, lda) call slaset('A', lda, n, zero, zero, m, lda) call slaset('A', lda, n, zero, zero, rfac, lda) c c %-------------------------------------% c | KU, KL are number of superdiagonals | c | and subdiagonals within the band of | c | matrices A and M. | c %-------------------------------------% c kl = nx ku = nx c c %---------------% c | Main diagonal | c %---------------% c h2 = one / ((nx+1)*(nx+1)) idiag = kl+ku+1 do 30 j = 1, n a(idiag,j) = 4.0E+0 / h2 30 continue c c %-------------------------------------% c | First subdiagonal and superdiagonal | c %-------------------------------------% c isup = kl+ku isub = kl+ku+2 do 50 i = 1, nx lo = (i-1)*nx do 40 j = lo+1, lo+nx-1 a(isup,j+1) = -one / h2 a(isub,j) = -one / h2 40 continue 50 continue c c %------------------------------------% c | KL-th subdiagonal and KU-th super- | c | diagonal. | c %------------------------------------% c isup = kl+1 isub = 2*kl+ku+1 do 80 i = 1, nx-1 lo = (i-1)*nx do 70 j = lo+1, lo+nx a(isup,nx+j) = -one / h2 a(isub,j) = -one / h2 70 continue 80 continue c c %-------------------------------------% c | Call SSBAND to find eigenvalues and | c | eigenvectors. Eigenvalues are | c | returned in the first column of D. | c | Eigenvectors are returned in the | c | first NCONV (=IPARAM(5)) columns of | c | V. | c %-------------------------------------% c rvec = .true. call ssband( rvec,'A', select, d, v, ldv, sigma, n, a, m, & lda, rfac, kl, ku, which, bmat, nev, tol, & resid, ncv, v, ldv, iparam, workd, workl, lworkl, & iwork, info) c if ( info .eq. 0) then c nconv = iparam(5) c c %-----------------------------------% c | Print out convergence information | c %-----------------------------------% c print *, ' ' print *, ' _SBDR2 ' print *, ' ====== ' print *, ' ' print *, ' The size of the matrix is ', n print *, ' Number of eigenvalue requested is ', nev print *, ' The number of Lanczos vectors generated', & ' (NCV) is ', ncv print *, ' The number of converged Ritz values is ', & nconv print *, ' What portion of the spectrum ', which print *, ' The number of Implicit Arnoldi', & ' update taken is ', iparam(3) print *, ' The number of OP*x is ', iparam(9) print *, ' The convergence tolerance is ', tol print *, ' ' c c %----------------------------% c | Compute the residual norm. | c | || A*x - lambda*x || | c %----------------------------% c do 90 j = 1, nconv call sgbmv('Notranspose', n, n, kl, ku, one, & a(kl+1,1), lda, v(1,j), 1, zero, & ax, 1) call saxpy(n, -d(j,1), v(1,j), 1, ax, 1) d(j,2) = snrm2(n, ax, 1) d(j,2) = d(j,2) / abs(d(j,1)) c 90 continue call smout(6, nconv, 2, d, maxncv, -6, & 'Ritz values and relative residuals') else c c %-------------------------------------% c | Either convergence failed, or there | c | is error. Check the documentation | c | for SSBAND. | c %-------------------------------------% c print *, ' ' print *, ' Error with _sband, info= ', info print *, ' Check the documentation of _sband ' print *, ' ' c end if c 9000 end