program optvorma use iso_c_binding, only: c_ptr,c_loc,c_f_pointer use optvor, only: pdata_type,evalfg,proj,approxg,drawsol,InA,compscale,compvols implicit none ! LOCAL SCALARS integer :: allocerr,fcnt,i,inform,iprint,iter,itrial,j,maxfc,maxit,maxnv,n, & nsites,ntrials,spginfo real(kind=8) :: area,epsopt,f,fbest,finish,ftarget,gpsupn,marg,scale,seed,start type(pdata_type), target :: pdata ! LOCAL ARRAYS real(kind=8) :: p(2) real(kind=8), allocatable :: g(:),x(:),x0(:),vol(:) character(len=80) :: filename ! FUNCTIONS real(kind=8) :: drand ! Problem data ! Set sites write(*,*) 'Enter nsites>0: ' read(*,*) nsites ! Set disjoint convex polygons Aj whose union define A pdata%npols = 22 allocate(pdata%nvpols(pdata%npols),stat=allocerr) if ( allocerr .ne. 0 ) then write(*,*) 'Allocation error.' stop end if pdata%nvpols(1:pdata%npols) = (/ 6, 6, 5, 7, 5, 7, 5, 7, 5, 7, 5, 7, 7, 6, 8, 5, 4, 8, 6, 5, 5, 6 /) maxnv = maxval( pdata%nvpols(1:pdata%npols) ) allocate(pdata%poledges(pdata%npols,maxnv),pdata%xpol(pdata%npols,maxnv), & pdata%ypol(pdata%npols,maxnv),stat=allocerr) if ( allocerr .ne. 0 ) then write(*,*) 'Allocation error.' stop end if pdata%xpol( 1,1:pdata%nvpols(1)) = (/ 0.0d0, 0.0d0, 2.49d0, 3.0d0, 3.0d0, 0.0d0 /) pdata%ypol( 1,1:pdata%nvpols(1)) = (/ 0.0d0, -3.44d0, -3.44d0, -3.0d0, 0.0d0, 0.0d0 /) pdata%xpol( 2,1:pdata%nvpols(2)) = (/ 0.0d0, 0.0d0, 1.58d0, 2.49d0, 2.49d0, 0.0d0 /) pdata%ypol( 2,1:pdata%nvpols(2)) = (/ -3.44d0, -4.5d0, -4.5d0, -3.74d0, -3.44d0, -3.44d0 /) pdata%xpol( 3,1:pdata%nvpols(3)) = (/ 0.0d0, 0.0d0, 1.58d0, 1.58d0, 0.0d0 /) pdata%ypol( 3,1:pdata%nvpols(3)) = (/ -4.5d0, -4.79d0, -4.79d0, -4.5d0, -4.5d0 /) pdata%xpol( 4,1:pdata%nvpols(4)) = (/ 0.0d0, 0.0d0, 1.87d0, 2.0d0, 2.0d0, 1.58d0, 0.0d0 /) pdata%ypol( 4,1:pdata%nvpols(4)) = (/ -4.79d0, -5.48d0, -5.48d0, -5.4d0, -5.14d0, -4.79d0, -4.79d0 /) pdata%xpol( 5,1:pdata%nvpols(5)) = (/ 0.0d0, 0.0d0, 1.87d0, 1.87d0, 0.0d0 /) pdata%ypol( 5,1:pdata%nvpols(5)) = (/ -5.48d0, -5.86d0, -5.86d0, -5.48d0, -5.48d0 /) pdata%xpol( 6,1:pdata%nvpols(6)) = (/ 0.0d0, 0.0d0, 2.26d0, 2.42d0, 2.42d0, 1.87d0, 0.0d0 /) pdata%ypol( 6,1:pdata%nvpols(6)) = (/ -5.86d0, -6.9d0, -6.9d0, -6.76d0, -6.51d0, -5.86d0, -5.86d0 /) pdata%xpol( 7,1:pdata%nvpols(7)) = (/ 0.0d0, 0.0d0, 2.26d0, 2.26d0, 0.0d0 /) pdata%ypol( 7,1:pdata%nvpols(7)) = (/ -6.9d0, -7.22d0, -7.22d0, -6.9d0, -6.9d0 /) pdata%xpol( 8,1:pdata%nvpols(8)) = (/ 0.0d0, 0.0d0, 2.1d0, 2.43d0, 2.43d0, 2.26d0, 0.0d0 /) pdata%ypol( 8,1:pdata%nvpols(8)) = (/ -7.22d0, -7.98d0, -7.98d0, -7.65d0, -7.4d0, -7.22d0, -7.22d0 /) pdata%xpol( 9,1:pdata%nvpols(9)) = (/ 0.0d0, 0.0d0, 2.1d0, 2.1d0, 0.0d0 /) pdata%ypol( 9,1:pdata%nvpols(9)) = (/ -7.98d0, -8.2d0, -8.2d0, -7.98d0, -7.98d0 /) pdata%xpol(10,1:pdata%nvpols(10)) = (/ 0.0d0, 0.0d0, 2.26d0, 2.43d0, 2.43d0, 2.1d0, 0.0d0 /) pdata%ypol(10,1:pdata%nvpols(10)) = (/ -8.2d0, -8.87d0, -8.87d0, -8.74d0, -8.49d0, -8.2d0, -8.2d0 /) pdata%xpol(11,1:pdata%nvpols(11)) = (/ 0.0d0, 0.0d0, 2.26d0, 2.26d0, 0.0d0 /) pdata%ypol(11,1:pdata%nvpols(11)) = (/ -8.87d0, -9.17d0, -9.17d0, -8.87d0, -8.87d0 /) pdata%xpol(12,1:pdata%nvpols(12)) = (/ 0.0d0, 0.0d0, 1.87d0, 2.43d0, 2.43d0, 2.26d0, 0.0d0 /) pdata%ypol(12,1:pdata%nvpols(12)) = (/ -9.17d0, -10.15d0, -10.15d0, -9.62d0, -9.28d0, -9.17d0, -9.17d0 /) pdata%xpol(13,1:pdata%nvpols(13)) = (/ 0.0d0, 0.0d0, 0.37d0, 0.94d0, 1.87d0, 1.87d0, 0.0d0 /) pdata%ypol(13,1:pdata%nvpols(13)) = (/ -10.15d0, -10.5d0, -10.9d0, -10.9d0, -10.35d0, -10.15d0, -10.15d0 /) pdata%xpol(14,1:pdata%nvpols(14)) = (/ 0.94d0, 1.29d0, 1.86d0, 2.26d0, 1.87d0, 0.94d0 /) pdata%ypol(14,1:pdata%nvpols(14)) = (/ -10.9d0, -11.35d0, -11.12d0, -10.7d0, -10.35d0, -10.9d0 /) pdata%xpol(15,1:pdata%nvpols(15)) = (/ 0.85d0, 0.58d0, -0.51d0, -3.0d0, -3.6d0, -3.0d0, 0.0d0, 0.85d0 /) pdata%ypol(15,1:pdata%nvpols(15)) = (/ 6.06d0, 6.68d0, 6.53d0, 6.0d0, 3.5d0, 0.7d0, 0.0d0, 6.06d0 /) pdata%xpol(16,1:pdata%nvpols(16)) = (/ 1.5d0, 0.85d0, 0.0d0, 3.0d0, 1.5d0 /) pdata%ypol(16,1:pdata%nvpols(16)) = (/ 5.86d0, 6.06d0, 0.0d0, 0.0d0, 5.86d0 /) pdata%xpol(17,1:pdata%nvpols(17)) = (/ 1.5d0, 3.0d0, 2.15d0, 1.5d0 /) pdata%ypol(17,1:pdata%nvpols(17)) = (/ 5.86d0, 0.0d0, 6.06d0, 5.86d0 /) pdata%xpol(18,1:pdata%nvpols(18)) = (/ 2.15d0, 3.0d0, 6.0d0, 6.6d0, 6.0d0, 3.51d0, 2.42d0, 2.15d0 /) pdata%ypol(18,1:pdata%nvpols(18)) = (/ 6.06d0, 0.0d0, 0.7d0, 3.35d0, 6.0d0, 6.53d0, 6.68d0, 6.06d0 /) pdata%xpol(19,1:pdata%nvpols(19)) = (/ 0.58d0, 0.85d0, 0.69d0, 0.0d0, -0.51d0, 0.58d0 /) pdata%ypol(19,1:pdata%nvpols(19)) = (/ 6.68d0, 7.3d0, 8.16d0, 7.62d0, 6.53d0, 6.68d0 /) pdata%xpol(20,1:pdata%nvpols(20)) = (/ 0.85d0, 1.5d0, 1.5d0, 0.69d0, 0.85d0 /) pdata%ypol(20,1:pdata%nvpols(20)) = (/ 7.3d0, 7.5d0, 8.5d0, 8.16d0, 7.3d0 /) pdata%xpol(21,1:pdata%nvpols(21)) = (/ 1.5d0, 2.15d0, 2.31d0, 1.5d0, 1.5d0 /) pdata%ypol(21,1:pdata%nvpols(21)) = (/ 7.5d0, 7.3d0, 8.16d0, 8.5d0, 7.5d0 /) pdata%xpol(22,1:pdata%nvpols(22)) = (/ 2.42d0, 3.51d0, 3.0d0, 2.31d0, 2.15d0, 2.42d0 /) pdata%ypol(22,1:pdata%nvpols(22)) = (/ 6.68d0, 6.53d0, 7.62d0, 8.16d0, 7.3d0, 6.68d0 /) pdata%poledges( 1,1:pdata%nvpols(1)-1) = (/ 0, 1, 0, 0, 1 /) pdata%poledges( 2,1:pdata%nvpols(2)-1) = (/ 0, 1, 0, 0, 1 /) pdata%poledges( 3,1:pdata%nvpols(3)-1) = (/ 0, 1, 0, 1 /) pdata%poledges( 4,1:pdata%nvpols(4)-1) = (/ 0, 1, 0, 0, 0, 1 /) pdata%poledges( 5,1:pdata%nvpols(5)-1) = (/ 0, 1, 0, 1 /) pdata%poledges( 6,1:pdata%nvpols(6)-1) = (/ 0, 1, 0, 0, 0, 1 /) pdata%poledges( 7,1:pdata%nvpols(7)-1) = (/ 0, 1, 0, 1 /) pdata%poledges( 8,1:pdata%nvpols(8)-1) = (/ 0, 1, 0, 0, 0, 1 /) pdata%poledges( 9,1:pdata%nvpols(9)-1) = (/ 0, 1, 0, 1 /) pdata%poledges(10,1:pdata%nvpols(10)-1) = (/ 0, 1, 0, 0, 0, 1 /) pdata%poledges(11,1:pdata%nvpols(11)-1) = (/ 0, 1, 0, 1 /) pdata%poledges(12,1:pdata%nvpols(12)-1) = (/ 0, 1, 0, 0, 0, 1 /) pdata%poledges(13,1:pdata%nvpols(13)-1) = (/ 0, 0, 0, 1, 0, 1 /) pdata%poledges(14,1:pdata%nvpols(14)-1) = (/ 0, 0, 0, 0, 1 /) pdata%poledges(15,1:pdata%nvpols(15)-1) = (/ 0, 1, 0, 0, 0, 0, 1 /) pdata%poledges(16,1:pdata%nvpols(16)-1) = (/ 0, 1, 1, 1 /) pdata%poledges(17,1:pdata%nvpols(17)-1) = (/ 1, 1, 0 /) pdata%poledges(18,1:pdata%nvpols(18)-1) = (/ 1, 0, 0, 0, 0, 1, 0 /) pdata%poledges(19,1:pdata%nvpols(19)-1) = (/ 0, 1, 0, 0, 1 /) pdata%poledges(20,1:pdata%nvpols(20)-1) = (/ 0, 1, 0, 1 /) pdata%poledges(21,1:pdata%nvpols(21)-1) = (/ 0, 1, 0, 1 /) pdata%poledges(22,1:pdata%nvpols(22)-1) = (/ 1, 0, 0, 1, 0 /) ! Scale A so cells have ideal area near unity call compscale(nsites,scale,area,c_loc(pdata)) pdata%volA = area do j = 1,pdata%npols pdata%xpol(j,1:pdata%nvpols(j)) = scale * pdata%xpol(j,1:pdata%nvpols(j)) pdata%ypol(j,1:pdata%nvpols(j)) = scale * pdata%ypol(j,1:pdata%nvpols(j)) end do pdata%xmin = minval( pdata%xpol(1,1:pdata%nvpols(1)) ) pdata%xmax = maxval( pdata%xpol(1,1:pdata%nvpols(1)) ) pdata%ymin = minval( pdata%ypol(1,1:pdata%nvpols(1)) ) pdata%ymax = maxval( pdata%ypol(1,1:pdata%nvpols(1)) ) do j = 2,pdata%npols pdata%xmin = min( pdata%xmin, minval( pdata%xpol(j,1:pdata%nvpols(j)) ) ) pdata%xmax = max( pdata%xmax, maxval( pdata%xpol(j,1:pdata%nvpols(j)) ) ) pdata%ymin = min( pdata%ymin, minval( pdata%ypol(j,1:pdata%nvpols(j)) ) ) pdata%ymax = max( pdata%ymax, maxval( pdata%ypol(j,1:pdata%nvpols(j)) ) ) end do marg = 0.1d0 * max( 1.0d0, abs( pdata%xmin ), abs( pdata%xmax ), abs( pdata%ymin), abs( pdata%ymax ) ) pdata%xmin = pdata%xmin - marg pdata%xmax = pdata%xmax + marg pdata%ymin = pdata%ymin - marg pdata%ymax = pdata%ymax + marg pdata%c(1:2) = 0.5d0 * (/ pdata%xmax + pdata%xmin, pdata%ymax + pdata%ymin /) pdata%rmax = norm2(pdata%c - (/ pdata%xmin, pdata%ymin /)) pdata%drawscale = 0.35d0 / scale ! Optimize write(*,*) 'Enter ntrials>0: ' read(*,*) ntrials n = 2 * nsites allocate(x(n),x0(n),g(n),vol(nsites),stat=allocerr) if ( allocerr .ne. 0 ) then write(*,*) 'Allocation error.' stop end if fbest = huge( 1.0d0 ) do itrial = 1,ntrials seed = 123456.0d0 * itrial write(*,*) 'Processing trial itrial = ',itrial do i = 1,nsites p(1) = pdata%xmin + ( pdata%xmax - pdata%xmin ) * drand(seed) p(2) = pdata%ymin + ( pdata%ymax - pdata%ymin ) * drand(seed) do while ( .not. InA(p,c_loc(pdata)) ) p(1) = pdata%xmin + ( pdata%xmax - pdata%xmin ) * drand(seed) p(2) = pdata%ymin + ( pdata%ymax - pdata%ymin ) * drand(seed) end do x(2*i-1) = p(1) x(2*i) = p(2) end do x0(1:n) = x(1:n) epsopt = 1.0d-08 ftarget = 1.0d-08 maxit = 10000 maxfc = 10000 iprint = 0 call cpu_time(start) call spg(n,x,epsopt,ftarget,maxit,maxfc,iprint,f,gpsupn,iter,fcnt,spginfo,inform, & evalfg,proj,c_loc(pdata)) call cpu_time(finish) write(*,*) 'Statistics: f = ',f,' gpsupn = ',gpsupn,' it = ',iter,' fcnt = ',fcnt, & ' spginfo = ',spginfo,' time = ',finish-start if ( f .lt. fbest ) then fbest = f write(*,*) 'Solution was improved. New best f = ',fbest write(filename,"(A12,I0,A3)") 'fig-key-ini-',nsites,'.mp' call drawsol(n,x0,filename,c_loc(pdata)) write(filename,"(A12,I0,A3)") 'fig-key-end-',nsites,'.mp' call drawsol(n,x,filename,c_loc(pdata)) call compvols(n,x,vol,c_loc(pdata)) open(unit=10,file='tabline.txt') write(10,1000) scale,pdata%volA,pdata%npols,nsites,itrial,f,gpsupn,iter,fcnt,spginfo,finish-start, & pdata%volA / nsites, & count( vol(1:nsites) .lt. sqrt( epsilon( 1.0d0 ) ) ), & maxval( abs( vol(1:nsites) * nsites / pdata%volA - 1.0d0 ), vol(1:nsites) .ge. sqrt( epsilon( 1.0d0 ) ) ) close(10) if ( fbest .le. ftarget ) then write(*,*) 'A global minimizer has been found!' exit end if end if end do deallocate(x,x0,g,vol,stat=allocerr) if ( allocerr .ne. 0 ) then write(*,*) 'Deallocation error.' stop end if stop 1000 format(1P,E12.5,1X,1P,E12.5,1X,I3,1X,I6,1X,I6,1X,1P,E12.5,1X,1P,E7.1,2(1X,I6),1X,I2,0P,F14.6,1X,1P,E12.5,1X,I6,1X,1P,E12.5) end program optvorma