Re: porting arapck code to octave

[Jaroslav Hajek]

On Sat, Dec 20, 2008 at 12:27 AM, David Bateman <address@hidden> wrote:
> I've been looking at porting the eigs function to octave and basically have
> it finished.. However I have a bizarre issue in that
>
> eigs (diag(1:100),4,'LM')
>
> doesn't work due to an internal error in an ARPACK function.. I'd remember
> something like this and that I'd patch arpack to avoid it on my machine in
> the past. However, I thought I'd investigate the issue further and modified
> an ARPACK example function "dssimp" to treat the exact same case as above
> and no bug manifested..
>
> I then tried reimplementing dssimp  as an oct-file, trying to keep it close
> to the same functionality as the fortran code (ie arrays initialized to
> zero, etc), and the result was I saw the same bug in the DSAUPD function as
> previously. I've been staring at this code for hours and don't see what the
> issue is. I attach my modified dssimp.f and the code that duplicates it in
> octave with "dssimp(diag(1:100))"... Anyone want to confirm that
>
> gfortran -o dssimp dssimp.f -larpack -lblas -llapack
> ./dssimp
>
> works and gives the 4 largest eigenvalues [100, 99, 98, 97] as expected.
> whereas
>
> mkoctfile dssimp.cc -larpack
> octave --eval "dssimp(diag(1:100))"
>
> doesn't... Anyone want to look at the code and see if they can see an issue
> that I missed?
>
> Regards
> David
>
>
>
>
> --
> David Bateman                                address@hidden
> 35 rue Gambetta                              +33 1 46 04 02 18 (Home)
> 92100 Boulogne-Billancourt FRANCE            +33 6 72 01 06 33 (Mob)
>
>
>      program dssimp
> c
> c     This example program is intended to illustrate the
> c     simplest case of using ARPACK in considerable detail.
> c     This code may be used to understand basic usage of ARPACK
> c     and as a template for creating an interface to ARPACK.
> c
> c     This code shows how to use ARPACK to find a few eigenvalues
> c     (lambda) and corresponding eigenvectors (x) for the standard
> c     eigenvalue problem:
> c
> c                        A*x = lambda*x
> c
> c     where A is an n by n real symmetric matrix.
> c
> c     The main points illustrated here are
> c
> c        1) How to declare sufficient memory to find NEV
> c           eigenvalues of largest magnitude.  Other options
> c           are available.
> c
> c        2) Illustration of the reverse communication interface
> c           needed to utilize the top level ARPACK routine DSAUPD
> c           that computes the quantities needed to construct
> c           the desired eigenvalues and eigenvectors(if requested).
> c
> c        3) How to extract the desired eigenvalues and eigenvectors
> c           using the ARPACK routine DSEUPD.
> c
> c     The only thing that must be supplied in order to use this
> c     routine on your problem is to change the array dimensions
> c     appropriately, to specify WHICH eigenvalues you want to compute
> c     and to supply a matrix-vector product
> c
> c                         w <-  Av
> c
> c     in place of the call to AV( ) below.
> c
> c     Once usage of this routine is understood, you may wish to explore
> c     the other available options to improve convergence, to solve
> generalized
> c     problems, etc.  Look at the file ex-sym.doc in DOCUMENTS directory.
> c     This codes implements
> c
> c\Example-1
> c     ... Suppose we want to solve A*x = lambda*x in regular mode,
> c         where A is derived from the central difference discretization
> c         of the 2-dimensional Laplacian on the unit square with
> c         zero Dirichlet boundary condition.
> c     ... OP = A  and  B = I.
> c     ... Assume "call av (n,x,y)" computes y = A*x
> c     ... Use mode 1 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     dnrm2   Level 1 BLAS that computes the norm of a vector.
> c     daxpy   Level 1 BLAS that computes y <- alpha*x+y.
> 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: ssimp.F   SID: 2.6   DATE OF SID: 10/17/00   RELEASE: 2
> c
> c\Remarks
> c     1. None
> c
> c\EndLib
> c
> c-----------------------------------------------------------------------
> c
> c     %------------------------------------------------------%
> c     | Storage Declarations:                                |
> c     |                                                      |
> c     | The maximum dimensions for all arrays are            |
> c     | set here to accommodate a problem size of            |
> c     | N .le. MAXN                                          |
> c     |                                                      |
> c     | NEV is the number of eigenvalues requested.          |
> c     |     See specifications for ARPACK usage below.       |
> c     |                                                      |
> c     | NCV is the largest number of basis vectors that will |
> c     |     be used in the Implicitly Restarted Arnoldi      |
> c     |     Process.  Work per major iteration is            |
> c     |     proportional to N*NCV*NCV.                       |
> c     |                                                      |
> c     | You must set:                                        |
> c     |                                                      |
> c     | MAXN:   Maximum dimension 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),
>     &                 ax(maxn)
>      logical          select(maxncv)
>      integer          iparam(11), ipntr(11)
> c
> c     %---------------%
> c     | Local Scalars |
> c     %---------------%
> c
>      character        bmat*1, which*2
>      integer          ido, n, nev, ncv, lworkl, info, ierr,
>     &                 j, nx, ishfts, maxitr, mode1, nconv
>      logical          rvec
>      Double precision
>     &                 tol, sigma
> c
> c     %------------%
> c     | Parameters |
> c     %------------%
> c
>      Double precision
>     &                 zero
>      parameter        (zero = 0.0D+0)
> c
> c     %-----------------------------%
> c     | BLAS & LAPACK routines used |
> c     %-----------------------------%
> c
>      Double precision
>     &                 dnrm2
>      external         dnrm2, daxpy
> c
> c     %--------------------%
> c     | Intrinsic function |
> c     %--------------------%
> c
>      intrinsic        abs
> c
> c     %-----------------------%
> c     | Executable Statements |
> c     %-----------------------%
> c
> c     %-------------------------------------------------%
> c     | The following include statement and assignments |
> c     | initiate trace output from the internal         |
> c     | actions of ARPACK.  See debug.doc in the        |
> c     | DOCUMENTS directory for usage.  Initially, the  |
> c     | most useful information will be a breakdown of  |
> c     | time spent in the various stages of computation |
> c     | given by setting msaupd = 1.                    |
> c     %-------------------------------------------------%
> c
>      include 'debug.h'
>      ndigit = -3
>      logfil = 6
>      msgets = 0
>      msaitr = 0
>      msapps = 0
>      msaupd = 1
>      msaup2 = 0
>      mseigt = 0
>      mseupd = 0
> c
> c     %-------------------------------------------------%
> c     | The following sets dimensions for this problem. |
> c     %-------------------------------------------------%
> c
>      nx = 10
>      n = nx*nx
> c
> c     %-----------------------------------------------%
> c     |                                               |
> c     | Specifications for ARPACK usage are set       |
> c     | below:                                        |
> c     |                                               |
> c     |    1) NEV = 4  asks for 4 eigenvalues to be   |
> c     |       computed.                               |
> c     |                                               |
> c     |    2) NCV = 20 sets the length of the Arnoldi |
> c     |       factorization                           |
> c     |                                               |
> c     |    3) This is a standard problem              |
> c     |         (indicated by bmat  = 'I')            |
> c     |                                               |
> c     |    4) Ask for the NEV eigenvalues of          |
> c     |       largest magnitude                       |
> c     |         (indicated by which = 'LM')           |
> c     |       See documentation in DSAUPD for the     |
> c     |       other options SM, LA, SA, LI, SI.       |
> c     |                                               |
> c     | Note: NEV and NCV must satisfy the following  |
> c     | conditions:                                   |
> c     |              NEV <= MAXNEV                    |
> c     |          NEV + 1 <= NCV <= MAXNCV             |
> c     %-----------------------------------------------%
> c
>      nev   = 4
>      ncv   = 20
>      bmat  = 'I'
>      which = 'LM'
> c
>      if ( n .gt. maxn ) then
>         print *, ' ERROR with _SSIMP: N is greater than MAXN '
>         go to 9000
>      else if ( nev .gt. maxnev ) then
>         print *, ' ERROR with _SSIMP: NEV is greater than MAXNEV '
>         go to 9000
>      else if ( ncv .gt. maxncv ) then
>         print *, ' ERROR with _SSIMP: NCV is greater than MAXNCV '
>         go to 9000
>      end if
> c
> c     %-----------------------------------------------------%
> c     |                                                     |
> c     | Specification of stopping rules and initial         |
> c     | conditions before calling DSAUPD                    |
> c     |                                                     |
> c     | TOL  determines the stopping criterion.             |
> c     |                                                     |
> c     |      Expect                                         |
> c     |           abs(lambdaC - lambdaT) < TOL*abs(lambdaC) |
> c     |               computed   true                       |
> c     |                                                     |
> c     |      If TOL .le. 0,  then TOL <- macheps            |
> c     |           (machine precision) is used.              |
> c     |                                                     |
> c     | IDO  is the REVERSE COMMUNICATION parameter         |
> c     |      used to specify actions to be taken on return  |
> c     |      from DSAUPD. (See usage below.)                |
> c     |                                                     |
> c     |      It MUST initially be set to 0 before the first |
> c     |      call to DSAUPD.                                |
> c     |                                                     |
> c     | INFO on entry specifies starting vector information |
> c     |      and on return indicates error codes            |
> c     |                                                     |
> c     |      Initially, setting INFO=0 indicates that a     |
> c     |      random starting vector is requested to         |
> c     |      start the ARNOLDI iteration.  Setting INFO to  |
> c     |      a nonzero value on the initial call is used    |
> c     |      if you want to specify your own starting       |
> c     |      vector (This vector must be placed in RESID.)  |
> c     |                                                     |
> c     | The work array WORKL is used in DSAUPD as           |
> c     | workspace.  Its dimension LWORKL is set as          |
> c     | illustrated below.                                  |
> c     |                                                     |
> c     %-----------------------------------------------------%
> c
>      lworkl = ncv*(ncv+8)
>      tol = zero
>      info = 0
>      ido = 0
> c
> c     %---------------------------------------------------%
> c     | Specification of Algorithm Mode:                  |
> c     |                                                   |
> c     | This program uses the exact shift strategy        |
> c     | (indicated by setting PARAM(1) = 1).              |
> c     | IPARAM(3) specifies the maximum number of Arnoldi |
> c     | iterations allowed.  Mode 1 of DSAUPD is used     |
> c     | (IPARAM(7) = 1). All these options can be changed |
> c     | by the user. For details see the documentation in |
> c     | DSAUPD.                                           |
> c     %---------------------------------------------------%
> c
>      ishfts = 1
>      maxitr = 300
>      mode1 = 1
> c
>      iparam(1) = ishfts
> c
>      iparam(3) = maxitr
> c
>      iparam(7) = mode1
> c
> c     %------------------------------------------------%
> c     | M A I N   L O O P (Reverse communication loop) |
> 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 matrix vector multiplication |
> c           |              y <--- OP*x             |
> c           | The user should supply his/her own   |
> c           | matrix vector multiplication routine |
> c           | here that takes workd(ipntr(1)) as   |
> c           | the input, and return the result to  |
> c           | workd(ipntr(2)).                     |
> c           %--------------------------------------%
> c
>            call av2 (nx, workd(ipntr(1)), workd(ipntr(2)))
> 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 in _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 be also computed now if  |
> c        | desired.  (indicated by rvec = .true.)    |
> c        |                                           |
> c        | The routine DSEUPD now called to do this  |
> c        | post processing (Other modes may require  |
> c        | more complicated post processing than     |
> c        | mode1.)                                   |
> c        |                                           |
> c        %-------------------------------------------%
> c
>          rvec = .true.
> c
>          call dseupd ( rvec, 'All', select, d, v, ldv, 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 NCONV (=IPARAM(5)) columns of the  |
> c         | two dimensional array V if requested.        |
> c         | Otherwise, an orthogonal basis for the       |
> c         | invariant subspace corresponding to the      |
> c         | eigenvalues in D is returned in V.           |
> c         %----------------------------------------------%
> 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)
>             do 20 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
>                call av2(nx, v(1,j), ax)
>                call daxpy(n, -d(j,1), v(1,j), 1, ax, 1)
>                d(j,2) = dnrm2(n, ax, 1)
>                d(j,2) = d(j,2) / abs(d(j,1))
> c
>  20          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 *, ' _SSIMP '
>          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 dssimp. |
> c     %---------------------------%
> c
>  9000 continue
> c
>      end
> c
>      subroutine av2 (nx, v, w)
>      integer nx, j
>      double precision  v(nx*nx), w(nx*nx)
>      do 10 j = 1, nx * nx
>         w(j) = dble(j) * v(j)
>  10   continue
>
>      end
>
> c
> c ------------------------------------------------------------------
> c     matrix vector subroutine
> c
> c     The matrix used is the 2 dimensional discrete Laplacian on unit
> c     square with zero Dirichlet boundary condition.
> 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     The subroutine TV is called to computed y<---T*x.
> c
>      subroutine av (nx, v, w)
>      integer           nx, j, lo, n2
>      Double precision
>     &                  v(nx*nx), w(nx*nx), one, h2
>      parameter         ( one = 1.0D+0 )
> c
>      call tv(nx,v(1),w(1))
>      call daxpy(nx, -one, 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 daxpy(nx, -one, v(lo-nx+1), 1, w(lo+1), 1)
>         call daxpy(nx, -one, 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 daxpy(nx, -one, v(lo-nx+1), 1, w(lo+1), 1)
> c
> c     Scale the vector w by (1/h^2), where h is the mesh size
> c
>      n2 = nx*nx
>      h2 = one / dble((nx+1)*(nx+1))
>      call dscal(n2, one/h2, w, 1)
>      return
>      end
> c
> c-------------------------------------------------------------------
>      subroutine tv (nx, x, y)
> c
>      integer           nx, j
>      Double precision
>     &                  x(nx), y(nx), dd, dl, du
> c
>      Double precision
>     &                  one, four
>      parameter         (one = 1.0D+0, four = 4.0D+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
> c
>      dd  = four
>      dl  = -one
>      du  = -one
> 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
>
>
>

1. rather than your MY_LOCAL_BUFFER, you can use the pre-defined
OCTAVE_LOCAL_BUFFER_INIT.

2. the following snippet:
                  for (octave_idx_type i = 0; i < n; i++)
                    workd[i+ipntr[1]-1] = static_cast<double>(i) * 
workd[i+ipntr[0]-1];
is obviously not multiplying by diag(1:100), but by diag(0:99).

3.
              retval(1) = eig_val;
              retval(2) = eig_vec;

should read

              retval(0) = eig_val;
              retval(1) = eig_vec;

after correcting these problems, I get the correct answer:
ans =

    97.000
    98.000
    99.000
   100.000

regards


-- 
RNDr. Jaroslav Hajek
computing expert
Aeronautical Research and Test Institute (VZLU)
Prague, Czech Republic
url: www.highegg.matfyz.cz