Sophie

arpack-3.3.0-3.mga6.x86_64.rpm

```      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

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