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 implicit none ! LOCAL SCALARS integer :: allocerr,fcnt,i,inform,iprint,iter,itrial,j,maxfc,maxit,maxnv,n, & nsites,ntrials,spginfo, nsegs 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),vxb(64),vyb(64) 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 nsegs = 4 iter = 1 vxb(1:nsegs) = (/0.0d0, 1.0d0, 1.0d0, 0.0d0 /) vxb(5:64) = 0.0d0 vyb(1:nsegs) = (/ 0.0d0, 0.0d0, 1.0d0, 1.0d0 /) vyb(5:64) = 0.0d0 call includes_triang_segs(vxb,vyb,nsegs,iter) ! Set disjoint convex polygons Aj whose union define A pdata%npols = 21 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, 6, 5, 7, 6, 6, 6, 5, 7, 6, 6, 6, 5, 7, 6, 6, 6, 5, 7, 5 /) 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)) = (/ vxb(1), vxb(2), vxb(3), vxb(63), vxb(64), vxb(1) /) pdata%ypol( 1,1:pdata%nvpols(1)) = (/ vyb(1), vyb(2), vyb(3), vyb(63), vyb(64), vyb(1) /) pdata%xpol( 2,1:pdata%nvpols(2)) = (/ vxb(3), vxb(4), vxb(5), vxb(6), vxb(7), vxb(3) /) pdata%ypol( 2,1:pdata%nvpols(2)) = (/ vyb(3), vyb(4), vyb(5), vyb(6), vyb(7), vyb(3) /) pdata%xpol( 3,1:pdata%nvpols(3)) = (/ vxb(59), vxb(60), vxb(61), vxb(62), vxb(63), vxb(59) /) pdata%ypol( 3,1:pdata%nvpols(3)) = (/ vyb(59), vyb(60), vyb(61), vyb(62), vyb(63), vyb(59) /) pdata%xpol( 4,1:pdata%nvpols(4)) = (/ vxb(63), vxb(3), vxb(7), vxb(59), vxb(63) /) pdata%ypol( 4,1:pdata%nvpols(4)) = (/ vyb(63), vyb(3), vyb(7), vyb(59), vyb(63) /) pdata%xpol( 5,1:pdata%nvpols(5)) = (/ vxb(59), vxb(7), vxb(8), vxb(9), vxb(57), vxb(58), vxb(59) /) pdata%ypol( 5,1:pdata%nvpols(5)) = (/ vyb(59), vyb(7), vyb(8), vyb(9), vyb(57), vyb(58), vyb(59) /) pdata%xpol( 6,1:pdata%nvpols(6)) = (/ vxb(11), vxb(12), vxb(13), vxb(14), vxb(15), vxb(11) /) pdata%ypol( 6,1:pdata%nvpols(6)) = (/ vyb(11), vyb(12), vyb(13), vyb(14), vyb(15), vyb(11) /) pdata%xpol( 7,1:pdata%nvpols(7)) = (/ vxb(15), vxb(16), vxb(17), vxb(18), vxb(19), vxb(15) /) pdata%ypol( 7,1:pdata%nvpols(7)) = (/ vyb(15), vyb(16), vyb(17), vyb(18), vyb(19), vyb(15) /) pdata%xpol( 8,1:pdata%nvpols(8)) = (/ vxb(19), vxb(20), vxb(21), vxb(22), vxb(23), vxb(19) /) pdata%ypol( 8,1:pdata%nvpols(8)) = (/ vyb(19), vyb(20), vyb(21), vyb(22), vyb(23), vyb(19) /) pdata%xpol( 9,1:pdata%nvpols(9)) = (/ vxb(19), vxb(23), vxb(11), vxb(15), vxb(19) /) pdata%ypol( 9,1:pdata%nvpols(9)) = (/ vyb(19), vyb(23), vyb(11), vyb(15), vyb(19) /) pdata%xpol(10,1:pdata%nvpols(10)) = (/ vxb(9), vxb(10), vxb(11), vxb(23), vxb(24), vxb(25), vxb(9) /) pdata%ypol(10,1:pdata%nvpols(10)) = (/ vyb(9), vyb(10), vyb(11), vyb(23), vyb(24), vyb(25), vyb(9) /) pdata%xpol(11,1:pdata%nvpols(11)) = (/ vxb(27), vxb(28), vxb(29), vxb(30), vxb(31), vxb(27) /) pdata%ypol(11,1:pdata%nvpols(11)) = (/ vyb(27), vyb(28), vyb(29), vyb(30), vyb(31), vyb(27) /) pdata%xpol(12,1:pdata%nvpols(12)) = (/ vxb(31), vxb(32), vxb(33), vxb(34), vxb(35), vxb(31) /) pdata%ypol(12,1:pdata%nvpols(12)) = (/ vyb(31), vyb(32), vyb(33), vyb(34), vyb(35), vyb(31) /) pdata%xpol(13,1:pdata%nvpols(13)) = (/ vxb(35), vxb(36), vxb(37), vxb(38), vxb(39), vxb(35) /) pdata%ypol(13,1:pdata%nvpols(13)) = (/ vyb(35), vyb(36), vyb(37), vyb(38), vyb(39), vyb(35) /) pdata%xpol(14,1:pdata%nvpols(14)) = (/ vxb(35), vxb(39), vxb(27), vxb(31), vxb(35) /) pdata%ypol(14,1:pdata%nvpols(14)) = (/ vyb(35), vyb(39), vyb(27), vyb(31), vyb(35) /) pdata%xpol(15,1:pdata%nvpols(15)) = (/ vxb(27), vxb(39), vxb(40), vxb(41), vxb(25), vxb(26), vxb(27) /) pdata%ypol(15,1:pdata%nvpols(15)) = (/ vyb(27), vyb(39), vyb(40), vyb(41), vyb(25), vyb(26), vyb(27) /) pdata%xpol(16,1:pdata%nvpols(16)) = (/ vxb(43), vxb(44), vxb(45), vxb(46), vxb(47), vxb(43) /) pdata%ypol(16,1:pdata%nvpols(16)) = (/ vyb(43), vyb(44), vyb(45), vyb(46), vyb(47), vyb(43) /) pdata%xpol(17,1:pdata%nvpols(17)) = (/ vxb(47), vxb(48), vxb(49), vxb(50), vxb(51), vxb(47) /) pdata%ypol(17,1:pdata%nvpols(17)) = (/ vyb(47), vyb(48), vyb(49), vyb(50), vyb(51), vyb(47) /) pdata%xpol(18,1:pdata%nvpols(18)) = (/ vxb(51), vxb(52), vxb(53), vxb(54), vxb(55), vxb(51) /) pdata%ypol(18,1:pdata%nvpols(18)) = (/ vyb(51), vyb(52), vyb(53), vyb(54), vyb(55), vyb(51) /) pdata%xpol(19,1:pdata%nvpols(19)) = (/ vxb(51), vxb(55), vxb(43), vxb(47), vxb(51) /) pdata%ypol(19,1:pdata%nvpols(19)) = (/ vyb(51), vyb(55), vyb(43), vyb(47), vyb(51) /) pdata%xpol(20,1:pdata%nvpols(20)) = (/ vxb(43), vxb(55), vxb(56), vxb(57), vxb(41), vxb(42), vxb(43) /) pdata%ypol(20,1:pdata%nvpols(20)) = (/ vyb(43), vyb(55), vyb(56), vyb(57), vyb(41), vyb(42), vyb(43) /) pdata%xpol(21,1:pdata%nvpols(21)) = (/ vxb(41), vxb(57), vxb(9), vxb(25), vxb(41) /) pdata%ypol(21,1:pdata%nvpols(21)) = (/ vyb(41), vyb(57), vyb(9), vyb(25), vyb(41) /) pdata%poledges( 1,1:pdata%nvpols(1)-1) = (/ 0, 0, 1, 0, 0 /) pdata%poledges( 2,1:pdata%nvpols(2)-1) = (/ 0, 0, 0, 0, 1 /) pdata%poledges( 3,1:pdata%nvpols(3)-1) = (/ 0, 0, 0, 0, 1 /) pdata%poledges( 4,1:pdata%nvpols(4)-1) = (/ 1, 1, 1, 1 /) pdata%poledges( 5,1:pdata%nvpols(5)-1) = (/ 1, 0, 0, 1, 0, 0 /) pdata%poledges( 6,1:pdata%nvpols(6)-1) = (/ 0, 0, 0, 0, 1 /) pdata%poledges( 7,1:pdata%nvpols(7)-1) = (/ 0, 0, 0, 0, 1 /) pdata%poledges( 8,1:pdata%nvpols(8)-1) = (/ 0, 0, 0, 0, 1 /) pdata%poledges( 9,1:pdata%nvpols(9)-1) = (/ 1, 1, 1, 1 /) pdata%poledges(10,1:pdata%nvpols(10)-1) = (/ 0, 0, 1, 0, 0, 1 /) pdata%poledges(11,1:pdata%nvpols(11)-1) = (/ 0, 0, 0, 0, 1 /) pdata%poledges(12,1:pdata%nvpols(12)-1) = (/ 0, 0, 0, 0, 1 /) pdata%poledges(13,1:pdata%nvpols(13)-1) = (/ 0, 0, 0, 0, 1 /) pdata%poledges(14,1:pdata%nvpols(14)-1) = (/ 1, 1, 1, 1 /) pdata%poledges(15,1:pdata%nvpols(15)-1) = (/ 1, 0, 0, 1, 0, 0 /) pdata%poledges(16,1:pdata%nvpols(16)-1) = (/ 0, 0, 0, 0, 1 /) pdata%poledges(17,1:pdata%nvpols(17)-1) = (/ 0, 0, 0, 0, 1 /) pdata%poledges(18,1:pdata%nvpols(18)-1) = (/ 0, 0, 0, 0, 1 /) pdata%poledges(19,1:pdata%nvpols(19)-1) = (/ 1, 1, 1, 1 /) pdata%poledges(20,1:pdata%nvpols(20)-1) = (/ 1, 0, 0, 1, 0, 0 /) pdata%poledges(21,1:pdata%nvpols(21)-1) = (/ 1, 1, 1, 1 /) ! 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 = 5.0d0 / scale ! Goal function data pdata%Jweight(0:5) = 0.0d0 pdata%Jweight(0) = 10.0d0 pdata%Jweight(1) = 1.0d0 pdata%J0delta = 0.1d0 ! 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,"(A15,I0,A3)") 'fig-cesaro-ini-',nsites,'.mp' call drawsol(n,x0,filename,c_loc(pdata)) write(filename,"(A15,I0,A3)") 'fig-cesaro-end-',nsites,'.mp' call drawsol(n,x,filename,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 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) contains ! ****************************************************************** ! ****************************************************************** recursive subroutine includes_triang_segs(vxb,vyb,nsegs,iter) implicit none ! PARAMETERS real(kind=8), parameter :: PI = dacos( - 1.0d0 ) ! SCALAR ARGUMENTS integer, intent(in) :: iter,nsegs ! ARRAY ARGUMENTS real(kind=8), intent(inout) :: vxb(64),vyb(64) ! LOCAL SCALARS integer :: i,ind real(kind=8) :: rotv(2) ! LOCAL ARRAYS real(kind=8) :: mthirdx(2),mthirdy(2),auxvxb(64),auxvyb(64) auxvxb(1:64) = vxb(1:64) auxvyb(1:64) = vyb(1:64) ind = 1 do i = 1,nsegs if ( i .lt. nsegs ) then mthirdx(1) = auxvxb(i) + (1.0d0/3.0d0)*(auxvxb(i+1) - auxvxb(i)) mthirdx(2) = auxvxb(i) + (2.0d0/3.0d0)*(auxvxb(i+1) - auxvxb(i)) mthirdy(1) = auxvyb(i) + (1.0d0/3.0d0)*(auxvyb(i+1) - auxvyb(i)) mthirdy(2) = auxvyb(i) + (2.0d0/3.0d0)*(auxvyb(i+1) - auxvyb(i)) call vector_rotate_base_2d( (/ mthirdx(2), mthirdy(2) /), (/ mthirdx(1), mthirdy(1) /), PI / 3.0d0, rotv ) else mthirdx(1) = auxvxb(i) + (1.0d0/3.0d0)*(auxvxb(1) - auxvxb(i)) mthirdx(2) = auxvxb(i) + (2.0d0/3.0d0)*(auxvxb(1) - auxvxb(i)) mthirdy(1) = auxvyb(i) + (1.0d0/3.0d0)*(auxvyb(1) - auxvyb(i)) mthirdy(2) = auxvyb(i) + (2.0d0/3.0d0)*(auxvyb(1) - auxvyb(i)) call vector_rotate_base_2d( (/ mthirdx(2), mthirdy(2) /), (/ mthirdx(1), mthirdy(1) /), PI / 3.0d0, rotv ) end if vxb(ind) = auxvxb(i) vyb(ind) = auxvyb(i) ind = ind + 1 vxb(ind) = mthirdx(1) vyb(ind) = mthirdy(1) ind = ind + 1 vxb(ind) = rotv(1) vyb(ind) = rotv(2) ind = ind + 1 vxb(ind) = mthirdx(2) vyb(ind) = mthirdy(2) ind = ind + 1 end do if ( iter .lt. 2 ) then call includes_triang_segs(vxb,vyb,nsegs*4,iter+1) end if end subroutine includes_triang_segs end program optvorma