program dseupd_bug_2 c c dsdrv2 program modified to reveal the bug in 'dseupd()': c c * 'implicit none' added c * rvec = .false. (don't want the eigenvectors) c * computation of the norm residual has been commented out c * 5th and 6th original arguments (v and ldv) have been replaced by c others (z and ldz) c * z is an allocatable array -- it is claimed that it is not referenced c * ldz = ldv -- fulfill the requirement that ldz .ge. 1 c c the following error is expected: c c Program received signal SIGSEGV: Segmentation fault - invalid memory reference. c Backtrace for this error: c ... c #3 0x428E36 in dger_ at dger.f:199 c #4 0x4099ED in dseupd_ at dseupd.f:852 (discriminator 4) c #5 0x401A71 in dseupd_bug_2 at dseupd_bug_2.f:301 c c É. Canot -- IRISA/CNRS -- Edouard.Canot@irisa.fr c______________________________________________________________________________ c c Program to illustrate the idea of reverse communication c in shift and invert mode for a standard symmetric eigenvalue c problem. The following program uses the two LAPACK subroutines c dgttrf.f and dgttrs.f to factor and solve a tridiagonal system of c equations. c c We implement example two of ex-sym.doc in DOCUMENTS directory c c\Example-2 c ... Suppose we want to solve A*x = lambda*x in shift-invert mode, c where A is derived from the central difference discretization c of the 1-dimensional Laplacian on [0,1] with zero Dirichlet c boundary condition. c ... OP = (inv[A - sigma*I]) and B = I. c ... Use mode 3 of DSAUPD. c c\BeginLib c c\Routines called: c dsaupd ARPACK reverse communication interface routine. c dseupd ARPACK routine that returns Ritz values and (optionally) c Ritz vectors. c dgttrf LAPACK tridiagonal factorization routine. c dgttrs LAPACK tridiagonal solve routine. c daxpy daxpy Level 1 BLAS that computes y <- alpha*x+y. c dnrm2 Level 1 BLAS that computes the norm of a vector. c av Matrix vector multiplication routine that computes A*x. 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: sdrv2.F SID: 2.5 DATE OF SID: 10/17/00 RELEASE: 2 c c\Remarks c 1. None c c\EndLib c---------------------------------------------------------------------- c implicit none c c %-----------------------------% c | Define leading 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=10, maxncv=25, & ldv=maxn ) c c %--------------% c | Local Arrays | c %--------------% c Double precision & v(ldv,maxncv), workl(maxncv*(maxncv+8)), & workd(3*maxn), d(maxncv,2), resid(maxn), & ad(maxn), adl(maxn), adu(maxn), adu2(maxn), & ax(maxn) logical select(maxncv) integer iparam(11), ipntr(11), ipiv(maxn) double precision, allocatable :: z(:,:) integer :: ldz c c %---------------% c | Local Scalars | c %---------------% c character bmat*1, which*2 integer ido, n, nev, ncv, lworkl, info, j, ierr, & nconv, maxitr, ishfts, mode logical rvec Double precision & sigma, tol, h2 c c %------------% c | Parameters | c %------------% c Double precision & zero, one, two parameter (zero = 0.0D+0, one = 1.0D+0, & two = 2.0D+0) c c %-----------------------------% c | BLAS & LAPACK routines used | c %-----------------------------% c Double precision & dnrm2 external daxpy, dnrm2, dgttrf, dgttrs c c %--------------------% c | Intrinsic function | c %--------------------% c intrinsic abs c c %-----------------------% c | Executable Statements | c %-----------------------% c c %----------------------------------------------------% c | The number N is the dimension of the matrix. A | c | standard eigenvalue problem is solved (BMAT = 'I'. | c | NEV is the number of eigenvalues (closest to | c | SIGMA) to be approximated. Since the shift-invert | c | mode is used, WHICH is set to 'LM'. The user can | c | modify NEV, NCV, SIGMA to solve problems of | c | different sizes, and to get different parts of the | c | spectrum. However, The following conditions must | c | be satisfied: | c | N <= MAXN, | c | NEV <= MAXNEV, | c | NEV + 1 <= NCV <= MAXNCV | c %----------------------------------------------------% c n = 100 nev = 4 ncv = 10 if ( n .gt. maxn ) then print *, ' ERROR with _SDRV2: N is greater than MAXN ' go to 9000 else if ( nev .gt. maxnev ) then print *, ' ERROR with _SDRV2: NEV is greater than MAXNEV ' go to 9000 else if ( ncv .gt. maxncv ) then print *, ' ERROR with _SDRV2: NCV is greater than MAXNCV ' go to 9000 end if c bmat = 'I' which = 'LM' sigma = zero c c %--------------------------------------------------% c | The work array WORKL is used in DSAUPD 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 DSAUPD to start the Arnoldi | c | iteration. | c %--------------------------------------------------% c lworkl = ncv*(ncv+8) tol = zero ido = 0 info = 0 c c %---------------------------------------------------% c | This program uses exact shifts with respect to | c | the current Hessenberg matrix (IPARAM(1) = 1). | c | IPARAM(3) specifies the maximum number of Arnoldi | c | iterations allowed. Mode 3 of DSAUPD is used | c | (IPARAM(7) = 3). All these options may be | c | changed by the user. For details, see the | c | documentation in DSAUPD. | c %---------------------------------------------------% c ishfts = 1 maxitr = 300 mode = 3 c iparam(1) = ishfts iparam(3) = maxitr iparam(7) = mode c c %-----------------------------------------------------% c | Call LAPACK routine to factor (A-SIGMA*I), where A | c | is the 1-d Laplacian. | c %-----------------------------------------------------% c h2 = one / dble((n+1)*(n+1)) do 20 j=1,n ad(j) = two / h2 - sigma adl(j) = -one / h2 20 continue call dcopy (n, adl, 1, adu, 1) call dgttrf (n, adl, ad, adu, adu2, ipiv, ierr) if (ierr .ne. 0) then print *, ' ' print *, ' Error with _gttrf in SDRV2.' print *, ' ' go to 9000 end if c c %-------------------------------------------% c | M A I N L O O P (Reverse communication) | c %-------------------------------------------% c 10 continue c c %---------------------------------------------% c | Repeatedly call the routine DSAUPD and take | c | actions indicated by parameter IDO until | c | either convergence is indicated or maxitr | c | has been exceeded. | c %---------------------------------------------% c call dsaupd ( ido, bmat, n, which, nev, tol, resid, & ncv, v, ldv, iparam, ipntr, workd, workl, & lworkl, info ) c if (ido .eq. -1 .or. ido .eq. 1) then c c %----------------------------------------% c | Perform y <-- OP*x = inv[A-sigma*I]*x. | c | The user only need the linear system | c | solver here that takes workd(ipntr(1)) | c | as input, and returns the result to | c | workd(ipntr(2)). | c %----------------------------------------% c call dcopy (n, workd(ipntr(1)), 1, workd(ipntr(2)), 1) c call dgttrs ('Notranspose', n, 1, adl, ad, adu, adu2, ipiv, & workd(ipntr(2)), n, ierr) if (ierr .ne. 0) then print *, ' ' print *, ' Error with _gttrs in _SDRV2. ' print *, ' ' go to 9000 end if c c %-----------------------------------------% c | L O O P B A C K to call DSAUPD again. | c %-----------------------------------------% c go to 10 c end if c c %----------------------------------------% c | Either we have convergence or there is | c | an error. | c %----------------------------------------% c if ( info .lt. 0 ) then c c %----------------------------% c | Error message. Check the | c | documentation in DSAUPD | c %----------------------------% c print *, ' ' print *, ' Error with _saupd, info = ',info print *, ' Check documentation of _saupd ' print *, ' ' c else c c %-------------------------------------------% c | No fatal errors occurred. | c | Post-Process using DSEUPD. | c | | c | Computed eigenvalues may be extracted. | c | | c | Eigenvectors may also be computed now if | c | desired. (indicated by rvec = .true.) | c %-------------------------------------------% c rvec = .false. ldz = ldv c call dseupd ( rvec, 'All', select, d, z, ldz, sigma, & bmat, n, which, nev, tol, resid, ncv, v, ldv, & iparam, ipntr, workd, workl, lworkl, ierr ) c c %----------------------------------------------% c | Eigenvalues are returned in the first column | c | of the two dimensional array D and the | c | corresponding eigenvectors are returned in | c | the first NEV columns of the two dimensional | c | array V if requested. Otherwise, an | c | orthogonal basis for the invariant subspace | c | corresponding to the eigenvalues in D is | c | returned in V. | c %----------------------------------------------% if ( ierr .ne. 0 ) then c c %------------------------------------% c | Error condition: | c | Check the documentation of DSEUPD. | c %------------------------------------% c print *, ' ' print *, ' Error with _seupd, info = ', ierr print *, ' Check the documentation of _seupd ' print *, ' ' c else c nconv = iparam(5) CC do 30 j=1, nconv c c %---------------------------% c | Compute the residual norm | c | | c | || A*x - lambda*x || | c | | c | for the NCONV accurately | c | computed eigenvalues and | c | eigenvectors. (iparam(5) | c | indicates how many are | c | accurate to the requested | c | tolerance) | c %---------------------------% c CC call av(n, v(1,j), ax) CC call daxpy(n, -d(j,1), v(1,j), 1, ax, 1) CC d(j,2) = dnrm2(n, ax, 1) CC d(j,2) = d(j,2) / abs(d(j,1)) c CC 30 continue c c %-------------------------------% c | Display computed residuals | c %-------------------------------% c call dmout(6, nconv, 2, d, maxncv, -6, & 'Ritz values and relative residuals') end if c c %------------------------------------------% c | Print additional convergence information | c %------------------------------------------% c if ( info .eq. 1) then print *, ' ' print *, ' Maximum number of iterations reached.' print *, ' ' else if ( info .eq. 3) then print *, ' ' print *, ' No shifts could be applied during implicit', & ' Arnoldi update, try increasing NCV.' print *, ' ' end if c print *, ' ' print *, ' _SDRV2 ' print *, ' ====== ' print *, ' ' print *, ' Size of the matrix is ', n print *, ' The number of Ritz values requested is ', nev print *, ' The number of Arnoldi vectors generated', & ' (NCV) is ', ncv print *, ' What portion of the spectrum: ', which print *, ' The number of converged Ritz values is ', & nconv print *, ' The number of Implicit Arnoldi update', & ' iterations taken is ', iparam(3) print *, ' The number of OP*x is ', iparam(9) print *, ' The convergence criterion is ', tol print *, ' ' c end if c c %---------------------------% c | Done with program dsdrv2. | c %---------------------------% c 9000 continue c end c c------------------------------------------------------------------------ c Matrix vector subroutine c where the matrix is the 1 dimensional discrete Laplacian on c the interval [0,1] with zero Dirichlet boundary condition. c subroutine av (n, v, w) integer n, j Double precision & v(n), w(n), one, two, h2 parameter (one = 1.0D+0, two = 2.0D+0) c w(1) = two*v(1) - v(2) do 100 j = 2,n-1 w(j) = - v(j-1) + two*v(j) - v(j+1) 100 continue j = n w(j) = - v(j-1) + two*v(j) c c Scale the vector w by (1 / h^2). c h2 = one / dble((n+1)*(n+1)) call dscal(n, one/h2, w, 1) return end