Sophie

arpack-3.3.0-3.mga6.x86_64.rpm

program snbdr2
c
c     ... Construct matrices A in LAPACK-style band form.
c         The matrix A is derived from the discretization of
c         the 2-d convection-diffusion operator
c
c               -Laplacian(u) + rho*partial(u)/partial(x).
c
c         on the unit square with zero Dirichlet boundary condition
c         using standard central difference.
c
c     ... Define the shift SIGMA = (SIGMAR, SIGMAI).
c
c     ... Call SNBAND to find eigenvalues LAMBDA closest to SIGMA
c         such that
c                       A*x = LAMBDA*x.
c
c     ... Use mode 3 of SNAUPD.
c
c\BeginLib
c
c\Routines called:
c     snband  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: nbdr2.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),
&                 workev(3*maxncv), v(ldv, maxncv),
&                 resid(maxn), d(maxncv, 3), ax(maxn)
Complex
&                 cfac(lda, maxn), workc(maxn)
c
c     %---------------%
c     | Local Scalars |
c     %---------------%
c
character        which*2, bmat
integer          nev, ncv, ku, kl, info, i, j, ido,
&                 n, nx, lo, idiag, isub, isup, mode, maxitr,
&                 nconv
logical          rvec, first
Real
&                 tol, rho, h2, h, sigmar, sigmai
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     | Intrinsic function |
c     %--------------------%
c
intrinsic         abs
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 (closest to (SIGMAR,SIGMAI)) to be  |
c     | approximated. Since the shift-invert moded is   |
c     | used, WHICH is set to 'LM'. The user can modify |
c     | NX, NEV, NCV, SIGMAR, SIGMAI to solve problems  |
c     | of different sizes, and to get different parts  |
c     | the spectrum. However, The following conditions |
c     | 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 _NBDR2: N is greater than MAXN '
go to 9000
else if ( nev .gt. maxnev ) then
print *, ' ERROR with _NBDR2: NEV is greater than MAXNEV '
go to 9000
else if ( ncv .gt. maxncv ) then
print *, ' ERROR with _NBDR2: NCV is greater than MAXNCV '
go to 9000
end if
bmat = 'I'
which = 'LM'
sigmar = 1.0E+4
sigmai = 0.0E+0
c
c     %-----------------------------------------------------%
c     | The work array WORKL is used in SNAUPD 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 SNAUPD 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 SNAUPD is used     |
c     | (IPARAM(7) = 3). All these options can be changed |
c     | by the user. For details, see the documentation   |
c     | in SNBAND.                                        |
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.                   |
c     %-------------------------------------%
c
kl   = nx
ku   = nx
c
c     %---------------%
c     | Main diagonal |
c     %---------------%
c
h  = one / real (nx+1)
h2 = h*h
c
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
rho = 1.0E+1
do 50 i = 1, nx
lo = (i-1)*nx
do 40 j = lo+1, lo+nx-1
a(isub,j+1) = -one/h2 + rho/two/h
a(isup,j) = -one/h2 - rho/two/h
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 ARPACK banded solver to find eigenvalues  |
c     | and eigenvectors. The real parts of the        |
c     | eigenvalues are returned in the first column   |
c     | of D, the imaginary parts are returned in the  |
c     | second column of D.  Eigenvectors are returned |
c     | in the first NCONV (=IPARAM(5)) columns of V.  |
c     %------------------------------------------------%
c
rvec = .true.
call snband(rvec, 'A', select, d, d(1,2), v, ldv, sigmar,
&     sigmai, workev, n, a, m, lda, rfac, cfac, kl, ku,
&     which, bmat, nev, tol, resid, ncv, v, ldv, iparam,
&     workd, workl, lworkl, workc, iwork, info)
c
if ( info .eq. 0) then
c
c        %-----------------------------------%
c        | Print out convergence information |
c        %-----------------------------------%
c
nconv = iparam(5)
c
print *, ' '
print *, ' _NBDR2 '
print *, ' ====== '
print *, ' '
print *, ' The size of the matrix is ', n
print *, ' Number of eigenvalue requested is ', nev
print *, ' The number of Arnoldi 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
first = .true.
do 90 j = 1, nconv
c
if ( d(j,2) .eq. zero ) then
c
c              %--------------------%
c              | Ritz value is real |
c              %--------------------%
c
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,3) = snrm2(n, ax, 1)
d(j,3) = d(j,3) / abs(d(j,1))
c
else if ( first ) then
c
c              %------------------------%
c              | Ritz value is complex  |
c              | Residual of one Ritz   |
c              | value of the conjugate |
c              | pair is computed.      |
c              %------------------------%
c
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)
call saxpy(n, d(j,2), v(1,j+1), 1, ax, 1)
d(j,3) = snrm2(n, ax, 1)
call sgbmv('Notranspose', n, n, kl, ku, one,
&                    a(kl+1,1), lda, v(1,j+1), 1, zero,
&                    ax, 1)
call saxpy(n, -d(j,1), v(1,j+1), 1, ax, 1)
call saxpy(n, -d(j,2), v(1,j), 1, ax, 1)
d(j,3) = slapy2( d(j,3), snrm2(n, ax, 1) )
d(j,3) = d(j,3) / slapy2(d(j,1),d(j,2))
d(j+1,3) = d(j,3)
first = .false.
else
first = .true.
end if
c
90      continue

call smout(6, nconv, 3, d, maxncv, -6,
&             'Ritz values (Real,Imag) and relative residuals')
else
c
c        %-------------------------------------%
c        | Either convergence failed, or there |
c        | is error.  Check the documentation  |
c        | for SNBAND.                         |
c        %-------------------------------------%
c
print *, ' '
print *, ' Error with _nband, info= ', info
print *, ' Check the documentation of _nband '
print *, ' '
c
end if
c
9000 end