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congrad.F
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congrad.F
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subroutine congr (npt, variable, bc_symm
&, guess, dpsi, forc, res
&, cf
&, max_iterations, iterations, epsilon
&, imask, iperm, jperm, iofs, nisle, nippts
&, converged
&, estimated_error
& )
c
c=======================================================================
c
c C O N G R A D
c
c solve:
c
c A * dpsi = forc
c
c for "dpsi" with dirichlet boundary conditions (dpsi=const on
c each component of the boundary) by a preconditioned conjugate
c gradient algorithm.
c
c inputs:
c npt = 5 or 9 (active coefficients)
c variable = character string identifying solution variable
c bc_symm = equatorial symmetry type (used only when the
c symmetry option is on. otherwise ignore it)
c guess = initial approximation to solution
c A = linear operator (assumed symmetric)
c typically A is grad{(1/h)*grad(dpsi)} -
c 2dt*acor*{grad(f/h) x grad(dpsi)}
c using 5 or 9 pt discretizations
c cf = imt x jmt x 3 x 3 array of coefficients of A
c forc = the sum of all terms evaluated at times tau
c or tau-1
c epsilon = convergence criterion
c max_iterations = maximum number of iterations
c imask = shows which land masses have perimeter equations
c iperm = i coordinate of island perimeter points
c jperm = j coordinate of island perimeter points
c iofs = offset in iperm, jperm for start of perimeter
c of land_mass(isle)
c nisle = actual number of land_masses
c nippts = number of perimeter ocean points for a land_mass
c output:
c dpsi = answer
c iterations = actual number of iterations performed
c converged = logical value
c estimated_error = estimated maximum error in solution
c based on step sizes and convergence rate
c
c
c author: Charles Goldberg e-mail: [email protected]
c
c based on the preconditioned conjugate gradient algorithm given
c in:
c
c A Reformulation and Implementation of the Bryan-Cox-Semtner
c Ocean Model on the Connection Machine
c J.K. Dukowicz, R.D. Smith, and R.C. Malone
c Journal of Atmospheric and Oceanic Technology
c Vol 10. No. 2 April 1993
c
c=======================================================================
c
c more specifically, the equations to be solved are
c
c sum (A(ij,i'j') * dpsi(i'j')) = forc(ij)
c
c where the subscripts ij and i'j' range over all "free ocean"
c T cells ij=(i,j) that are not adjacent to land T cells,
c and one ij=isle for each boundary component of the ocean.
c
c with this choice of variables, in the absence of coriolis terms
c (acor=0), the operator A is symmetric, i.e.,
c
c A(ij,i'j') = A(i'j',ij)
c
c
c the algorithm (essentially executable in Fortran 90) is...
c
c subroutine congrad (A, guess, forc, dpsi, iterations)
c
c use matrix_module
c
c intent (in) :: A, guess, forc
c intent (out) :: dpsi, iterations
c
c type(dpsi_type) :: guess, dpsi, Zres, s
c type(res_type) :: res, As, forc
c type(operator) :: A
c type(inv_op) :: Z
c dimension (0:max_iterations) :: dpsi, res, s, As, beta, alpha
c
c dpsi(0) = guess
c res(0) = forc - A * dpsi(0)
c beta(0) = 1
c s(0) = zerovector()
c do k = 1 to max_iterations
c Zres(k-1) = Z * res(k-1)
c beta(k) = res(k-1) * Zres(k-1)
c s(k) = Zres(k-1) + (beta(k)/beta(k-1)) * s(k-1)
c As(k) = A * s(k)
c alpha(k) = beta(k) / (s(k) * As(k))
c dpsi(k) = dpsi(k-1) + alpha(k) * s(k)
c res(k) = res(k-1) - alpha(k) * As(k)
c estimated_error = err_est(k, alpha(k), s(k))
c if (estimated_error) < epsilon) exit
c end do
c if (k > max_iterations) then
c print *, 'did not converge in ',k,' iterations'
c stop '=>congrad'
c end if
c
c iterations = k
c dpsi = dpsi(k)
c
c end
c
c where...
c
c the "vector" and "operator" types used in conjugate gradient
c are mapped to ordinary 2-dimensional fortran arrays as follows:
c
c type(dpsi_type) :: guess, dpsi, Zres, s
c if ij=(i,j) is a mid-ocean point, map dpsi(ij)-->dpsi(i,j)
c if ij=isle is an ocean boundary subscript, replicate the
c value dpsi(isle) in dpsi(i,j) for each (i,j) in the ocean
c perimeter of land_mass(isle). the arrays iperm(isle) and
c jperm(isle), along with iofs(isle) locate these ocean
c perimeter T cells.
c type(res_type) :: res, As, forc
c if ij=(i,j) is a mid-ocean point, res(ij)-->res(i,j)
c if ij=isle is an ocean boundary subscript, the value of
c res(isle) = sum (res(i,j))
c where the sum is taken over all (i,j) in the ocean perimeter
c of land_mass(isle). sometimes, the computed values
c res(i,j) represent contributions of T cell (i,j) to the
c component res(isle), and sometimes the values are balanced
c so that res(i,j)=res(isle)/nippts(isle). note that, even
c when balanced, the relation between type(res_type) variables
c res(isle) and res(i,j) differs from that of type(dpsi_type)
c variables dpsi(isle) and dpsi(i,j) on T cells in the ocean
c perimeter.
c type(operator) :: A
c the nearly diagonal quality of the operators used
c permits a representation as a small collection of
c 2-dimensional arrays.
c the diagonal, A(ij,ij), is stored in an array cfdiag(i,j)
c as follows:
c if ij=(i,j) is a mid-ocean point, A(ij,ij) = cfdiag(i,j)
c if ij=isle is an ocean boundary subscript,
c A(isle, isle) = sum (cfdiag(i,j))
c where the sum is taken over all (i,j) in the ocean perimeter
c of land_mass(isle). each cfdiag(i,j) represents the contribution
c of T cell (i,j) to the island variable diagonal coefficient.
c the off-diagonal terms A(ij,i`j`) are stored in 4 arrays
c cfn, cfs, cfe, and cfw if A is a 5-point operator, and in
c these and 4 additional arrays, cfne, cfnw, cfse, cfsw, if
c A is a 9-point operator. For example, if i`=i and j`=j+1,
c then A(ij,i`j`) is stored in cfn(i,j).
c if ij=(i,j) is a mid-ocean point and i`j`=isle` is and ocean
c perimeter subscript, with i`=i and j`=j+1, then
c cfn(i,j)=A(ij,isle`) is the coefficient of the island
c variable dpsi(isle`) in the equation for mid-ocean point
c dpsi(ij)=dpsi(i,j).
c if ij=isle is an ocean perimeter point and i`j`=(i`,j`) is
c a mid-ocean point, with i`=i and j`=j-1, then
c cfs(i,j)=A(isle,i`j`) is the coefficient of the mid-ocean
c variable dpsi(i`j`)=dpsi(i,j) in the equation for the island
c variable dpsi(isle). note that equations for island
c variables dpsi(isle) are "non-local" in the sense that
c they usually contain more than 5 or 9 terms, some of which
c involve values dpsi(i`j`) outside of a compact 5-point
c or 9-point neighborhood.
c type(inv_op) :: Z
c the approximate inverse operator Z used at present is a
c diagonal operator Z(ij,ij) = 1/A(ij,ij).
c if ij=(i,j) is a mid-ocean point,
c then Z(i,j)=Z(ij)=1/A(ij)=1/cfdiag(i,j)
c if ij=isle is an ocean perimeter point, then
c Z(isle) is replicated at each ocean perimeter T cell
c bordering land_mass(isle).
c Z(i,j)=Z(isle)=1/A(isle)=1/sum(A(i,j))
c
c=======================================================================
c
#include "size.h"
c
logical imask, converged
character * 16 variable
character *(*) bc_symm
dimension guess(imt,jmt), dpsi(imt,jmt), Zres(imt,jmt)
dimension s(imt,jmt)
dimension res(imt,jmt), As(imt,jmt), forc(imt,jmt)
dimension cf(imt,jmt,-1:1,-1:1)
dimension Z(imt,jmt)
dimension imask(-mnisle:mnisle)
dimension iperm(maxipp), jperm(maxipp), iofs(mnisle)
dimension nippts(mnisle)
c
#ifdef debug_congrad
c
c-----------------------------------------------------------------------
c verify that domain(forc) is a subset of domain(A)
c-----------------------------------------------------------------------
c
call subset (forc, cf(1,1,0,0), nerror)
if (nerror .ne. 0) then
print '(a,a,a,i5,a,a)'
&, 'fatal error: ',variable(1:len_trim(variable))
&, ' forcing is nonzero at ',nerror,' points '
&, ' with no equation, i.e., cf(i,j,0,0)=0.'
c stop '=>congr'
end if
#endif
c
#ifdef symmetry
c
c-----------------------------------------------------------------------
c check for allowable symmetry conditions at equator
c-----------------------------------------------------------------------
c
if (bc_symm .ne. 't even' .and. bc_symm .ne. 't odd') then
write (*,*)
&'=>Error: type of bc_symm is ',bc_symm,' in congrad.F'
&, '... Only allowed type is "t even" or "t odd"'
stop
endif
#endif
c
c-----------------------------------------------------------------------
c impose boundary conditions on guess
c dpsi(0) = guess
c-----------------------------------------------------------------------
c
call border(guess, bc_symm)
c
do i=1,imt
do j=1,jmt
dpsi(i,j) = guess(i,j)
end do
end do
c
c-----------------------------------------------------------------------
c make approximate inverse operator Z (always even symmetry)
c-----------------------------------------------------------------------
c
call make_inv (cf, Z,
& imask, iperm, jperm, iofs, nisle, nippts)
call border(Z, 't even')
c
c-----------------------------------------------------------------------
c res(0) = forc - A * dpsi(0)
c impose cyclic and/or symmetry conditions on res(i,j)
c-----------------------------------------------------------------------
c
if (npt .eq. 5) then
call op5_vec(cf, dpsi, res)
else
call op9_vec(cf, dpsi, res)
end if
do i=2,imt-1
do j=2,jmt-1
res(i,j) = forc(i,j) - res(i,j)
end do
end do
c
call border(res, bc_symm)
c
c-----------------------------------------------------------------------
c Zres(k-1) = Z * res(k-1)
c see if guess is a solution, bail out to avoid division by zero
c-----------------------------------------------------------------------
c
k = 0
call inv_op(Z, res, Zres,
& imask, iperm, jperm, iofs, nisle, nippts)
c
c set borders of Zres using cyclic/symmetry, if defined.
c
call border(Zres, bc_symm)
c
#ifdef debug_congrad
Zresmax = absvecmax(Zres,imax,jmax)
print '(a,a,i5,a,e14.7,a,i3,a,i3,a)'
&, variable(1:len_trim(variable))
&, ' iteration',k,' max Zres = ',Zresmax
&, ' at (',imax,',',jmax,')'
#else
Zresmax = absmax(Zres)
#endif
c
c Assume convergence rate of 0.99 to extrapolate error
c
if (100.0 * Zresmax .lt. epsilon) then
estimated_error = 100.0 * Zresmax
goto 101
endif
c
c-----------------------------------------------------------------------
c beta(0) = 1
c s(0) = zerovector()
c-----------------------------------------------------------------------
c
betakm1 = 1.0
call zero_vec(s)
c
c-----------------------------------------------------------------------
c begin iteration loop
c-----------------------------------------------------------------------
c
do k = 1,max_iterations
c
c-----------------------------------------------------------------------
c Zres(k-1) = Z * res(k-1)
c-----------------------------------------------------------------------
c
call inv_op(Z, res, Zres,
& imask, iperm, jperm, iofs, nisle, nippts)
c
c set borders of Zres using cyclic/symmetry, if defined.
c
call border(Zres, bc_symm)
c
c-----------------------------------------------------------------------
c beta(k) = res(k-1) * Zres(k-1)
c-----------------------------------------------------------------------
c
betak = dot2(Zres, res)
if (k .eq. 1) then
betak_min = abs(betak)
elseif (k .gt. 2) then
betak_min = min(betak_min, abs(betak))
if (abs(betak) .gt. 100.0*betak_min) then
write (*,'(/a/a/)')
& 'WARNING: conjugate gradient terminated because correction'
&, ' steps are diverging. Probable cause...roundoff'
smax = absmax(s)
step = abs(alpha) * smax
estimated_error=step*convergence_rate/(1.0-convergence_rate)
go to 101
endif
endif
c
c-----------------------------------------------------------------------
c s(k) = Zres(k-1) + (beta(k)/beta(k-1)) * s(k-1)
c-----------------------------------------------------------------------
c
betaquot = betak/betakm1
do i=1,imt
do j=1,jmt
s(i,j) = Zres(i,j) + betaquot * s(i,j)
end do
end do
c
c-----------------------------------------------------------------------
c As(k) = A * s(k)
c-----------------------------------------------------------------------
c
if (npt .eq. 5) then
call op5_vec(cf, s, As)
else
call op9_vec(cf, s, As)
end if
c
call border(As, bc_symm)
c
c-----------------------------------------------------------------------
c If s=0 then the division for alpha(k) gives a float exception.
c Assume convergence rate of 0.99 to extrapolate error.
c Also assume alpha(k) ~ 1.
c-----------------------------------------------------------------------
c
s_dot_As = dot2(s, As)
if (abs(s_dot_As) .lt. abs(betak)*1.e-10) then
smax = absmax(s)
#ifdef debug_congrad
print *, 'Congrad exited on smax=',smax
#endif
estimated_error = 100.0 * smax
goto 101
endif
c
c-----------------------------------------------------------------------
c alpha(k) = beta(k) / (s(k) * As(k))
c-----------------------------------------------------------------------
c
alpha = betak / s_dot_As
#ifdef debug_congrad
print *, 'alpha=',alpha,' beta(k)=',betak
#endif
c
c-----------------------------------------------------------------------
c update values:
c dpsi(k) = dpsi(k-1) + alpha(k) * s(k)
c res(k) = res(k-1) - alpha(k) * As(k)
c-----------------------------------------------------------------------
c
do i=1,imt
do j=1,jmt
dpsi (i,j) = dpsi(i,j) + alpha * s(i,j)
res (i,j) = res (i,j) - alpha * As(i,j)
end do
end do
call avg_dist (res,
& imask, iperm, jperm, iofs, nisle, nippts)
c
call border(res, bc_symm)
c
#ifdef debug_congrad
smax = absvecmax(s, imax, jmax)
print '(a,i5,a,e14.7,a,i3,a,i3,a)',
& 'iteration',k,' max correct = ',alpha*smax,
& ' at (',imax,',',jmax,')'
#else
smax = absmax(s)
#endif
c
c-----------------------------------------------------------------------
c test for convergence
c if (estimated_error) < epsilon) exit
c-----------------------------------------------------------------------
c
step = abs(alpha) * smax
if (k .eq. 1) then
step1 = step
estimated_error = step
if (step .lt. epsilon) goto 101
else if (step .lt. epsilon) then
cfactor = log(step/step1)
convergence_rate = exp(cfactor/(k-1))
estimated_error = step*convergence_rate/(1.0-convergence_rate)
#ifdef debug_congrad
print '(a,i6,4(a,e13.4))'
&, 'iteration=', k, ', correction=', step
&, ', convergence rate=', convergence_rate
&, ', estimated error=', estimated_error
#endif
if (estimated_error .lt. epsilon) goto 101
end if
c
betakm1 = betak
c
end do
c
c-----------------------------------------------------------------------
c end of iteration loop
c-----------------------------------------------------------------------
c
101 continue
if (k .gt. max_iterations) then
cfactor = log(step/step1)
convergence_rate = exp(cfactor/(k-1))
estimated_error = step*convergence_rate/(1.0-convergence_rate)
#ifdef debug_congrad
print '(a,i4,a,a,e10.3,a,e10.3)',
& '****> congrad did not converge in ',k,' iterations.'
&,' maximum dpsi is ',absmax(dpsi)
&,' estimated error is ',estimated_error
#endif
converged = .false.
else
converged = .true.
end if
iterations = k
c
c-----------------------------------------------------------------------
c return the last increment of dpsi in the argument res
c-----------------------------------------------------------------------
c
if (iterations .eq. 0) then
do i=1,imt
do j=1,jmt
res(i,j) = Zres(i,j)
end do
end do
else
do i=1,imt
do j=1,jmt
res(i,j) = alpha * s(i,j)
end do
end do
endif
#ifdef debug_congrad
c
c print out convergence information each call
c
print '(a,l1,a,i4,a,a,a,a,e10.3,a,e10.3)',
& ' congrad converged = ',converged,' in ',k,' iterations.'
&,' maximum ',variable(1:len_trim(variable)),' is ',absmax(dpsi)
&,' estimated error is ',estimated_error
#endif
c
return
end
c
c=======================================================================
c
c M A T R I X M O D U L E F O R C O N G R A D
c
c=======================================================================
c
subroutine zero_vec (v)
#include "size.h"
dimension v(imt,jmt)
do i=1,imt
do j=1,jmt
v(i,j) = 0.0
end do
end do
return
end
subroutine add_vec (v,w,vpw)
#include "size.h"
dimension v(imt,jmt), w(imt,jmt), vpw(imt,jmt)
do i=1,imt
do j=1,jmt
vpw(i,j) = v(i,j) + w(i,j)
end do
end do
return
end
subroutine sub_vec (v,w,vmw)
#include "size.h"
dimension v(imt,jmt), w(imt,jmt), vmw(imt,jmt)
do i=1,imt
do j=1,jmt
vmw(i,j) = v(i,j) - w(i,j)
end do
end do
return
end
subroutine mult_vec(v,w,vtw)
#include "size.h"
dimension v(imt,jmt), w(imt,jmt), vtw(imt,jmt)
do i=1,imt
do j=1,jmt
vtw(i,j) = v(i,j) * w(i,j)
end do
end do
return
end
subroutine div_vec(v,w,vdw)
#include "size.h"
dimension v(imt,jmt), w(imt,jmt), vdw(imt,jmt)
do i=1,imt
do j=1,jmt
if (w(i,j) .ne. 0) then
vdw(i,j) = v(i,j) / w(i,j)
else
vdw(i,j) = 0.0
end if
end do
end do
return
end
subroutine scalar_vec (scalar,w,sw)
#include "size.h"
dimension w(imt,jmt), sw(imt,jmt)
do i=1,imt
do j=1,jmt
sw(i,j) = scalar * w(i,j)
end do
end do
return
end
subroutine neg_vec (v)
#include "size.h"
dimension v(imt,jmt)
do i=1,imt
do j=1,jmt
v(i,j) = -v(i,j)
end do
end do
return
end
function dot2 (dp_vec, res_vec)
c
c this dot product produces the correct answers because for
c ocean perimeter subscripts, ij=isle, the value on a
c type(dpsi_type) vector, dp_vec(isle)=dp_vec(i,j), i.e., the true
c value is replicated, and for a type(res_type) vector,
c res_vec(isle) = sum (res_vec(i,j)), i.e., the true value is the
c accumulation of the distributed values.
c
#include "size.h"
dimension dp_vec(imt,jmt), res_vec(imt,jmt)
dimension rowsum (jmt)
c
do j=2,jmt-1
rowsum(j) = 0.0
do i=2,imt-1
rowsum(j) = rowsum(j) + dp_vec(i,j) * res_vec(i,j)
end do
end do
c
dot2 = 0.0
do j=2,jmt-1
dot2 = dot2 + rowsum(j)
end do
c
return
end
subroutine op5_vec(cf, dpsi, res)
c
c res = A * dpsi
c
c this subroutine does not collect the terms of the true value
c of res(isle) = sum (res(i,j)). the contributions to the sum
c remain distributed among the T cells (i,j) that form the
c ocean perimeter of land_mass(isle).
c
c at present, borders are not computed [i=1 or imt] [j=1 or jmt]
c
#include "size.h"
dimension cf(imt,jmt,-1:1,-1:1)
dimension dpsi(imt,jmt)
dimension res(imt,jmt)
c
do j=2,jmt-1
do i=2,imt-1
res(i,j) = cf(i,j, 0, 0) * dpsi(i,j) +
& cf(i,j, 0, 1) * dpsi(i,j+1) +
& cf(i,j, 0,-1) * dpsi(i,j-1) +
& cf(i,j, 1, 0) * dpsi(i+1,j) +
& cf(i,j,-1, 0) * dpsi(i-1,j)
end do
end do
c
return
end
subroutine op9_vec(cf, dpsi, res)
c
c res = A * dpsi
c
c this subroutine does not collect the terms of the true value
c of res(isle) = sum (res(i,j)). the contributions to the sum
c remain distributed among the T cells (i,j) that form the
c ocean perimeter of land_mass(isle).
c
c at present, borders are not computed [i=1 or imt] [j=1 or jmt]
c
#include "size.h"
dimension cf(imt,jmt,-1:1,-1:1)
dimension dpsi(imt,jmt)
dimension res(imt,jmt)
c
do j=2,jmt-1
do i=2,imt-1
res(i,j) = cf(i,j, 0, 0) * dpsi(i ,j ) +
& cf(i,j, 0, 1) * dpsi(i ,j+1) +
& cf(i,j, 0,-1) * dpsi(i ,j-1) +
& cf(i,j, 1, 0) * dpsi(i+1,j ) +
& cf(i,j,-1, 0) * dpsi(i-1,j ) +
& cf(i,j, 1, 1) * dpsi(i+1,j+1) +
& cf(i,j,-1, 1) * dpsi(i-1,j+1) +
& cf(i,j, 1,-1) * dpsi(i+1,j-1) +
& cf(i,j,-1,-1) * dpsi(i-1,j-1)
end do
end do
c
return
end
subroutine subset (a, b, nerror)
c
c verifies that the set of subscripts for which a(i,j) .ne. 0.0
c is a subset of the set of subscripts for which b(i,j) .ne. 0.0
c
#include "size.h"
dimension a(imt,jmt), b(imt,jmt)
c
nerror = 0
do i=2,imt-1
do j=2,jmt-1
if (a(i,j) .ne. 0.0 .and. b(i,j) .eq. 0.0) then
nerror = nerror + 1
print '(a,i3,a,i3,a,a)', '(',i,',',j,')'
& ,' forcing is reset to zero'
c set forcing (i.e., a(i,j)) to zero
a(i,j) = 0.0
end if
end do
end do
c
return
end
subroutine inv_op(Z, res, Zres,
& imask, iperm, jperm, iofs, nisle, nippts)
c
c
c apply and approximate inverse Z or the operator A
c
c res is type(res_type), i.e., perimeter values res(isle)
c are the sum of the distributed contributions res(i,j)
c Zres is type(dpsi_type), i.e., perimeter values Zres(isle)
c must be replicated at each perimeter point Zres(i,j)
c
c borders of Zres [i=1 or imt] [j=1 or jmt] must be defined
c and must satisfy cyclic and/or symmetry, if defined.
c
c currently, Z is diagonal: Z(ij) = 1/A(ij)
c and is stored in type(dpsi_type) format, i.e., Z(isle) is
c replicated and stored in each Z(i,j) in the perimeter of
c land_mass(isle).
c
#include "size.h"
c
logical imask
dimension imask (-mnisle:mnisle)
dimension iperm(maxipp), jperm(maxipp)
dimension iofs (mnisle)
dimension nippts(mnisle)
c
dimension Z(imt,jmt)
dimension res(imt,jmt)
dimension Zres(imt,jmt)
c
do i=1,imt
do j=1,jmt
Zres(i,j) = Z(i,j) * res(i,j)
end do
end do
c
c sum contributions to Zres(isle)
c distribute Zres(isle) to all perimeter points
c
call sum_dist (Zres,
& imask, iperm, jperm, iofs, nisle, nippts)
c
return
end
function absvecmax(res, imax, jmax)
c
#include "size.h"
dimension res(imt,jmt)
c
absvecmax = 0.0
do i=2,imt-1
do j=2,jmt-1
if (abs(res(i,j)) .gt. absvecmax) then
absvecmax = abs(res(i,j))
imax = i
jmax = j
end if
end do
end do
return
end
function absmax (f)
c
#include "size.h"
dimension f(imt,jmt)
c
amax = 0.0
do i=1,imt
do j=1,jmt
amax = max(amax, abs(f(i,j)))
end do
end do
absmax = amax
return
end
function absmin (f)
c
#include "size.h"
dimension f(imt,jmt)
c
amin = 1.0e37
do i=1,imt
do j=1,jmt
if (f(i,j) .ne. 0 .and. abs(f(i,j)) .lt. amin) then
amin = abs(f(i,j))
end if
end do
end do
absmin = amin
return
end
subroutine make_inv (cf, Z,
& imask, iperm, jperm, iofs, nisle, nippts)
c
c construct an approximate inverse Z to A
c
c Z will be diagonal: Z(ij) = 1/A(ij)
c and values for ocean perimeter entries Z(isle) will be replicated
c at all T cells Z(i,j) in the ocean perimeter of land_mass(isle).
c
c T cells (i,j) for which there is no diagonal coefficient
c i.e., A(ij)=A(i,j)=0, are masked off by assigning Z(i,j)=0.
c there are effectively no equations and no variables dpsi(i,j)
c at these points.
c
#include "size.h"
logical imask
dimension imask (-mnisle:mnisle)
dimension iperm(maxipp), jperm(maxipp)
dimension iofs (mnisle)
dimension nippts(mnisle)
c
dimension cf(imt,jmt,-1:1,-1:1)
dimension Z(imt,jmt)
c
c copy diagonal coefficients of A to Z
c
do i=2,imt-1
do j=2,jmt-1
Z(i,j) = cf(i,j,0,0)
end do
end do
c
c for each land_mass(isle),
c sum the contributions to cfdiag(isle)=A(isle,isle)
c now stored in Z(i,j) at ocean perimeter T cells and replicate
c the sum in all Z(i,j) for which (i,j) is in ocean perimeter
c of land_mass(isle).
c
call sum_dist (Z,
& imask, iperm, jperm, iofs, nisle, nippts)
c
c now invert Z
c
do i=2,imt-1
do j=2,jmt-1
if (Z(i,j) .ne. 0.0) then
Z(i,j) = 1/Z(i,j)
else
Z(i,j) = 0.0
end if
end do
end do
c
c make inverse zero on island perimeters that are not integrated
c
do isle=1,nisle
if (.not. imask(isle)) then
do n=1,nippts(isle)
i = iperm(iofs(isle)+n)
j = jperm(iofs(isle)+n)
Z(i,j) = 0.0
end do
end if
end do
c
return
end
subroutine sum_dist (Zres,
& imask, iperm, jperm, iofs, nisle, nippts)
c
c
c sum contributions to Zres(isle)
c distribute Zres(isle) to all perimeter points
c
c this subroutine converts a type(res_type) vector with
c distributed contributions to perimeter values
c Zres(isle) = sum (Zres(i,j))
c into a type (dpsi_type) vector with replicated values
c for land_mass perimeters
c Zres(isle) = Zres(i,j)
c for all (i,j) in the ocean perimeter of land_mass(isle).
c
#include "size.h"
logical imask
dimension imask (-mnisle:mnisle)
dimension iperm(maxipp), jperm(maxipp)
dimension iofs (mnisle)
dimension nippts(mnisle)
c
dimension Zres(imt,jmt)
dimension Zresisle(mnisle)
c
c sum contributions to Zres(isle)
c
#ifdef timing
call tic ('isle','loop1')
#endif
do isle=1,nisle
if (imask(isle)) then
Zresisle(isle) = 0.0
do n=1,nippts(isle)
i = iperm(iofs(isle)+n)
j = jperm(iofs(isle)+n)
Zresisle(isle) = Zresisle(isle) + Zres(i,j)
end do
end if
end do
#ifdef timing
call toc ('isle','loop1')
#endif
c
c distribute Zres(isle) to all perimeter points
c
#ifdef timing
call tic ('isle','loop2')
#endif
do isle=1,nisle
if (imask(isle)) then
do n=1,nippts(isle)
i = iperm(iofs(isle)+n)
j = jperm(iofs(isle)+n)
Zres(i,j) = Zresisle(isle)
end do
end if
end do
#ifdef timing
call toc ('isle','loop2')
#endif
c
return
end
#ifdef debug_congrad
subroutine examine_isles (cf,forc,dpsi,res,
& imask, iperm, jperm, iofs, nisle, nippts)
c
c sum contributions to res(isle)
c distribute res(isle) to all perimeter points
c
c this subroutine is for debugging printouts of
c island values.
c
#include "size.h"
logical imask
dimension imask (-mnisle:mnisle)
dimension iperm(maxipp), jperm(maxipp)
dimension iofs (mnisle)
dimension nippts(mnisle)
c
dimension res(imt,jmt)
dimension resisle(mnisle)
c
dimension cf(imt,jmt,-1:1,-1:1)
dimension forc (imt,jmt)
dimension dpsi (imt,jmt)
c
c sum contributions to res(isle)
c
#ifdef timing
call tic ('isle','loop5')
#endif
do isle=1,nisle
if (imask(isle)) then
print *,'examine: isle=',isle,' nisle=',nisle
resisle(isle) = 0.0
do n=1,nippts(isle)
i = iperm(iofs(isle)+n)
j = jperm(iofs(isle)+n)
resisle(isle) = resisle(isle) + res(i,j)
if (1 .ne. 1) then
print '(2i3,a,e12.5)',i,j,' res =',res(i,j)
print '(2i3,a,e12.5)',i,j,' forc =',forc(i,j)
print '(2i3,a,e12.5)',i,j,' dpsi =',dpsi(i,j)
print '(2i3,a,e12.5)',i,j,' cfdiag=',cf(i,j,0,0)
print '(2i3,a,e12.5)',i,j,' cfn =',cf(i,j,0,1)
print '(2i3,a,e12.5)',i,j,' cfs =',cf(i,j,0,-1)
print '(2i3,a,e12.5)',i,j,' cfe =',cf(i,j,1,0)
print '(2i3,a,e12.5)',i,j,' cfw =',cf(i,j,-1,0)
print *,' '
end if
end do
print *, 'resisle = ', resisle(isle)
print *,' '