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|
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subroutine lsline( |
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& simul |
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& , nn, ifail, lphprint |
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& , ifunc, nfunc |
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& , ff, dotdg |
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& , tmin, tmax, tact, epsx |
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& , dd, gg, xx, xdiff |
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& ) |
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|
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c ================================================================== |
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c SUBROUTINE lsline |
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c ================================================================== |
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c |
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c o line search algorithm for determining control vector update; |
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c After computing updated control vector from given gradient, |
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c a forward and adjoint model run are performed (simul.F) |
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c using the updated control vector. |
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c Tests are then applied to see whether solution has improved. |
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c |
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c o Reference: J.C. Gilbert & C. Lemarechal |
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c Some numerical experiments with variable-storage |
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c quasi-Newton algorithms |
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c Mathematical Programming 45 (1989), pp. 407-435 |
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c |
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c o started: ??? not reproducible |
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c |
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c o changed: Patrick Heimbach, MIT/EAPS |
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c |
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c o Version: 2.0, 24-Feb-2000: Patrick Heimbach, MIT/EAPS |
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c - severe changes in structure including various |
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c shifts of variables which are only used in this |
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c routine |
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c - number of 3 control flags for error handling |
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c (indic, moderl, ifail) reduced to 1 (ifail) |
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c and homogenized with routine lsoptv |
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c |
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c o Version: 2.1.0, 02-Mar-2000: Patrick Heimbach, MIT/EAPS |
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c - initial computation of tact and |
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c xdiff = xx + tact*dd |
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c moved to new routine lsupdxx |
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c tmin, tmax, tact needed as parameters |
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c |
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c ================================================================== |
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c SUBROUTINE lsline |
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c ================================================================== |
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|
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#include "blas1.h" |
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|
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implicit none |
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|
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c---------------------------------- |
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c declare arguments |
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c---------------------------------- |
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integer nn, ifail, ifunc, nfunc |
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double precision ff, dotdg, tmin, tmax, tact, epsx |
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double precision xx(nn), dd(nn), gg(nn), xdiff(nn) |
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|
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logical lphprint |
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|
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external simul |
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|
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c---------------------------------- |
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c declare local variables |
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c---------------------------------- |
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|
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double precision xpara1, xpara2 |
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parameter( xpara1 = 0.000001, xpara2=0.99999 ) |
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|
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double precision factor |
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parameter( factor = 0.2 ) |
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|
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double precision barmax |
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parameter( barmax = 0.3 ) |
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double precision barmul |
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parameter( barmul = 5.0 ) |
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double precision barmin |
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parameter( barmin = 0.01 ) |
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|
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integer i, indic |
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|
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double precision tg, fg, td, ta |
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double precision fa, fpa, fp |
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double precision fnew, fdiff |
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double precision z, test, barr |
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double precision left, right, told |
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|
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external DDOT |
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double precision DDOT |
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|
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c---------------------------------- |
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c check parameters |
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c---------------------------------- |
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|
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if ( (nn.le.0) |
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& .or. (dotdg.ge.0.0) |
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& .or. (xpara1.le.0.0) .or. (xpara1.ge.0.5) |
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& .or. (xpara2.le.xpara1) .or. (xpara2.ge.1.0) ) then |
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ifail = 9 |
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go to 999 |
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endif |
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|
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c---------------------------------- |
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c initialization |
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c---------------------------------- |
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indic = 0 |
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|
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barr = barmin |
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fg = ff |
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fa = ff |
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fpa = dotdg |
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|
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td = 0.0 |
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tg = 0.0 |
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ta = 0.0 |
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|
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c======================================================================= |
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c begin of simulation iter. |
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c======================================================================= |
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|
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do ifunc = 1, nfunc |
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|
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if (lphprint) |
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& print *, 'pathei-lsopt: ', ifunc, ' simul.' |
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|
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c------------------------------------ |
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cow( for offline mode (loffline.eq..TRUE.), simul reads |
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c in ecco_ctrl and ecco_cost from iteration optimcycle. |
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cow) There are no actual forward/adjoint runs in simul. |
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c------------------------------------ |
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call simul( indic, nn, xdiff, fnew, gg ) |
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|
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cow( compute tact (could be different from 1) |
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do i = 1, nn |
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if(dd(i) .ne. 0.and.(xdiff(i) - xx(i)).ne.0) then |
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tact = (xdiff(i) - xx(i))/ dd(i) |
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goto 301 |
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endif |
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end do |
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301 continue |
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c if tact is only slightly different from 1., then set it to 1. |
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c The difference is likely caused by trunction error. |
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if(abs(tact-1.).le.1.d-6) tact = 1. |
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write(*,'(a,e15.6)') |
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& ' pathei-lsopt: step size (tact) for the latest iteration |
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&: ',tact |
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cow) now we know tact (step size for the latest iteration). |
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|
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C compute fp = direction(dd) . gradient(gg) |
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fp = DDOT( nn, dd, 1, gg, 1 ) |
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fdiff = fnew - ff |
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|
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print*, 'pathei-lsopt: ' |
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cow( print out info related to Wolfe tests |
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print*,'==================================================' |
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print*, 'Wolfe test 1 (sufficient cost decrease condition):' |
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write(*,'(a,3e15.6)') ' Cost (iter i, iter i-1, reduction): ', |
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& fnew, ff, fdiff |
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write(*,'(a,a,3e15.6)')' alpha1, step size for iter i, ', |
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& '<dd(i-1).gg(i-1)> ', |
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& xpara1, tact, dotdg |
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if(fdiff .gt. tact*xpara1*dotdg) then |
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write(*,'(a,a,e15.6,a,e15.6)') |
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& ' cost reduction GT alpha1*step size', |
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& '*<dd(i-1).gg(i-1)> ', fdiff, ' > ', tact*xpara1*dotdg |
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print*, 'Wolfe test 1: failed' |
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else |
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write(*,'(a,a,e15.6,a,e15.6)') |
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& ' cost reduction LE alpha1*step size', |
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& '*<dd(i-1).gg(i-1)> ', fdiff, ' <= ', tact*xpara1*dotdg |
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print*, 'Wolfe test 1: passed' |
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endif |
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print*,'' |
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|
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print*, 'Wolfe test 2 (curvature condition):' |
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write(*,'(a,3e15.6)')' <dd(i-1).gg(i)>, <dd(i-1).gg(i-1)>: ', |
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& fp, dotdg |
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write(*,'(a,a,3e15.6)') |
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& ' alpha2,', 'alpha2*<dd(i-1).gg(i-1)>: ', |
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& xpara2, xpara2*dotdg |
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if (fp .gt. xpara2*dotdg) then |
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write(*,'(a,e15.6,a,e15.6)') |
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& ' <dd(i-1).gg(i)> GT alpha2* <dd(i-1).gg(i-1)>: ', |
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& fp, ' > ', xpara2*dotdg |
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print*, 'Wolfe test 2: passed' |
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else |
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write(*,'(a,e15.6,a,e15.6)') |
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& ' <dd(i-1).gg(i)> LE alpha2* <dd(i-1).gg(i-1)>: ', |
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& fp, ' <= ', xpara2*dotdg |
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print*, 'Wolfe test 2: failed' |
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endif |
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print*, '==================================================' |
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cow) |
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|
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c----------------------------------------- |
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c apply 1st Wolfe test |
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c----------------------------------------- |
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|
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if (fdiff .gt. tact*xpara1*dotdg) then |
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C if (lphprint) |
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C & print *, 'Wolfe test 1 (Armijo Rule) Failed' |
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if (lphprint) |
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& print *, 'pathei-lsopt: interpolate to get new step size' |
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td = tact |
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ifail = 0 |
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go to 500 |
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endif |
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|
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c----------------------------------------- |
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c 1st Wolfe test 1 ok, apply 2nd Wolf test |
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c----------------------------------------- |
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if (fp .gt. xpara2*dotdg) then |
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C if (lphprint) |
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C & print *, 'Pass Wolfe test 2 (Curvature condition)' |
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ifail = 0 |
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go to 320 |
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endif |
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|
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if (ifail.eq.0) go to 350 |
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|
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c----------------------------------------- |
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c 2nd Wolfe test 2 ok, donc pas serieux, on sort |
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c----------------------------------------- |
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|
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320 continue |
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|
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ff = fnew |
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do i = 1, nn |
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xx(i) = xdiff(i) |
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end do |
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cph( |
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if (lphprint) |
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& print *, 'pathei-lsopt: no inter-/extrapolation in lsline' |
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cph) |
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go to 888 |
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|
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|
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c----------------------------------------- |
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c extrapolation |
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c----------------------------------------- |
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|
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350 continue |
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|
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if (lphprint) |
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& print *, 'pathei-lsopt: extrapolate to get new step size' |
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tg = tact |
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fg = fnew |
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if (td .ne. 0.0) go to 500 |
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|
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told = tact |
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left = (1.0+barmin)*tact |
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right = 10.0*tact |
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call cubic( tact, fnew, fp, ta, fa, fpa, left, right ) |
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ta = told |
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if (tact.ge.tmax) then |
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ifail = 7 |
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tact = tmax |
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endif |
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|
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if (lphprint) |
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& print *, 'pathei-lsopt: extrapolation: ', |
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& 'td, tg, tact, ifail = ', td, tg, tact, ifail |
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|
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go to 900 |
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|
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c----------------------------------------- |
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c interpolation |
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c----------------------------------------- |
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|
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500 continue |
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|
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C td: tact (step size) |
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C tg: was set to zero |
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C So the limits are between 0.01 * tg and tact-0.01*tg (0 and tact for isuml = 1) |
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test = barr*(td-tg) |
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left = tg+test |
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right = td-test |
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told = tact |
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C input: |
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C tact: was set to 1 in input, but in output store the new step size |
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C fnew: the new cost function in input |
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C fp: new dotdg = dd . gg ( direction DOT gradient) |
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C ta: set to zero (namely set x0 = 0 so tact is distance between x1 and x0) |
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C fa: old cost function |
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C fpa: old dotdg = dd . gg (diretion DOT gradient) |
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call cubic( tact, fnew, fp, ta, fa, fpa, left, right ) |
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ta = told |
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if (tact.gt.left .and. tact.lt.right) then |
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C falling within left and right brackets. Keep the same barr |
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barr = dmax1( barmin, barr/barmul ) |
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else |
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C outside of the left and right brackets. Reduce barr by half |
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barr = dmin1( barmul*barr, barmax ) |
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endif |
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|
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if (lphprint) |
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& print *, 'pathei-lsopt: interpolation: ', |
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& 'td, tg, tact, ifail = ', td, tg, tact, ifail |
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|
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c----------------------------------------- |
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c end of iteration loop |
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c - tact peut etre bloque sur tmax |
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c (venant de lextrapolation avec ifail=7) |
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c----------------------------------------- |
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|
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900 continue |
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|
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fa = fnew |
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fpa = fp |
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|
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c----------------------------------------- |
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c --- faut-il continuer ? |
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c----------------------------------------- |
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if (td .eq. 0.0) go to 950 |
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if (td-tg .lt. tmin) go to 920 |
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|
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c----------------------------------------- |
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c limit due to machine precision |
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c----------------------------------------- |
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do i = 1, nn |
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z = xx(i) + tact*dd(i) |
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if ((z.ne.xx(i)) .and. (z.ne.xdiff(i))) go to 950 |
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end do |
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|
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c----------------------------------------- |
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c arret sur dxmin ou de secours |
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c----------------------------------------- |
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920 continue |
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ifail = 8 |
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|
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c----------------------------------------- |
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c si tg=0, xx = xx_depart, |
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c sinon on prend xx=x_left qui fait decroitre f |
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c----------------------------------------- |
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if (tg .ne. 0.0) then |
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ff = fg |
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do i = 1, nn |
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xx(i) = xx(i) + tg*dd(i) |
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end do |
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endif |
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|
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go to 999 |
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|
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c----------------------------------------- |
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c update vector for new simulation |
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c----------------------------------------- |
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950 continue |
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|
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do i = 1, nn |
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xdiff(i) = xx(i) + tact*dd(i) |
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end do |
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|
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c======================================================================= |
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c end of simulation iter. |
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c======================================================================= |
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if (lphprint) |
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& print *, 'pathei-lsopt: end of simulation iter: ', |
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& 'td, tg, tact, ifail = ', td, tg, tact, ifail |
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end do |
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|
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c----------------------------------------- |
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c too many function evaluations |
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c----------------------------------------- |
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ifail = 6 |
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ff = fg |
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do i = 1, nn |
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xx(i) = xx(i) + tg*dd(i) |
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end do |
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|
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|
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999 continue |
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C Set ifail=99 so we do not modify OPWARMD and OPWARMI |
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C We modify OPWARMD and OPWARMI Only if both Wolfe |
| 374 |
C conditions are satisfied. |
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|
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ifail = 99 |
| 377 |
|
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c----------------------------------------- |
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c end of routine |
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c----------------------------------------- |
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888 continue |
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|
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if (lphprint) |
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& print *, 'pathei-lsopt: end of lsline: ', |
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& 'td, tg, tact, ifail = ', td, tg, tact, ifail |
| 386 |
return |
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|
| 388 |
end |
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