| 1 |
ou.wang |
1.1 |
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| 2 |
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subroutine lsline( |
| 3 |
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& simul |
| 4 |
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& , nn, ifail, lphprint |
| 5 |
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& , ifunc, nfunc |
| 6 |
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& , ff, dotdg |
| 7 |
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& , tmin, tmax, tact, epsx |
| 8 |
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& , dd, gg, xx, xdiff |
| 9 |
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& ) |
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| 11 |
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c ================================================================== |
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c SUBROUTINE lsline |
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c ================================================================== |
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c |
| 15 |
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c o line search algorithm for determining control vector update; |
| 16 |
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c After computing updated control vector from given gradient, |
| 17 |
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c a forward and adjoint model run are performed (simul.F) |
| 18 |
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c using the updated control vector. |
| 19 |
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c Tests are then applied to see whether solution has improved. |
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c |
| 21 |
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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 |
| 24 |
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c Mathematical Programming 45 (1989), pp. 407-435 |
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c |
| 26 |
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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 |
| 30 |
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c o Version: 2.0, 24-Feb-2000: Patrick Heimbach, MIT/EAPS |
| 31 |
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c - severe changes in structure including various |
| 32 |
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c shifts of variables which are only used in this |
| 33 |
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c routine |
| 34 |
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c - number of 3 control flags for error handling |
| 35 |
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c (indic, moderl, ifail) reduced to 1 (ifail) |
| 36 |
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c and homogenized with routine lsoptv |
| 37 |
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c |
| 38 |
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c o Version: 2.1.0, 02-Mar-2000: Patrick Heimbach, MIT/EAPS |
| 39 |
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c - initial computation of tact and |
| 40 |
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c xdiff = xx + tact*dd |
| 41 |
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c moved to new routine lsupdxx |
| 42 |
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c tmin, tmax, tact needed as parameters |
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c |
| 44 |
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c ================================================================== |
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c SUBROUTINE lsline |
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c ================================================================== |
| 47 |
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| 48 |
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#include "blas1.h" |
| 49 |
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| 50 |
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implicit none |
| 51 |
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| 52 |
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c---------------------------------- |
| 53 |
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c declare arguments |
| 54 |
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c---------------------------------- |
| 55 |
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integer nn, ifail, ifunc, nfunc |
| 56 |
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double precision ff, dotdg, tmin, tmax, tact, epsx |
| 57 |
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double precision xx(nn), dd(nn), gg(nn), xdiff(nn) |
| 58 |
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| 59 |
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logical lphprint |
| 60 |
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| 61 |
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external simul |
| 62 |
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| 63 |
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c---------------------------------- |
| 64 |
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c declare local variables |
| 65 |
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c---------------------------------- |
| 66 |
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| 67 |
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double precision xpara1, xpara2 |
| 68 |
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parameter( xpara1 = 0.000001, xpara2=0.99999 ) |
| 69 |
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| 70 |
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double precision factor |
| 71 |
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parameter( factor = 0.2 ) |
| 72 |
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| 73 |
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double precision barmax |
| 74 |
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parameter( barmax = 0.3 ) |
| 75 |
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double precision barmul |
| 76 |
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parameter( barmul = 5.0 ) |
| 77 |
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double precision barmin |
| 78 |
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parameter( barmin = 0.01 ) |
| 79 |
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| 80 |
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integer i, indic |
| 81 |
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| 82 |
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double precision tg, fg, td, ta |
| 83 |
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double precision fa, fpa, fp |
| 84 |
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double precision fnew, fdiff |
| 85 |
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double precision z, test, barr |
| 86 |
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double precision left, right, told |
| 87 |
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| 88 |
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external DDOT |
| 89 |
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double precision DDOT |
| 90 |
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| 91 |
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c---------------------------------- |
| 92 |
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c check parameters |
| 93 |
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c---------------------------------- |
| 94 |
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| 95 |
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if ( (nn.le.0) |
| 96 |
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& .or. (dotdg.ge.0.0) |
| 97 |
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& .or. (xpara1.le.0.0) .or. (xpara1.ge.0.5) |
| 98 |
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& .or. (xpara2.le.xpara1) .or. (xpara2.ge.1.0) ) then |
| 99 |
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ifail = 9 |
| 100 |
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go to 999 |
| 101 |
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endif |
| 102 |
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| 103 |
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c---------------------------------- |
| 104 |
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c initialization |
| 105 |
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c---------------------------------- |
| 106 |
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indic = 0 |
| 107 |
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| 108 |
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barr = barmin |
| 109 |
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fg = ff |
| 110 |
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fa = ff |
| 111 |
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fpa = dotdg |
| 112 |
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| 113 |
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td = 0.0 |
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tg = 0.0 |
| 115 |
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ta = 0.0 |
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| 117 |
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c======================================================================= |
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c begin of simulation iter. |
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c======================================================================= |
| 120 |
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| 121 |
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do ifunc = 1, nfunc |
| 122 |
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| 123 |
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if (lphprint) |
| 124 |
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& print *, 'pathei-lsopt: ', ifunc, ' simul.' |
| 125 |
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| 126 |
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c------------------------------------ |
| 127 |
ou.wang |
1.2 |
cow( for offline mode (loffline.eq..TRUE.), simul reads |
| 128 |
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c in ecco_ctrl and ecco_cost from iteration optimcycle. |
| 129 |
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cow) There are no actual forward/adjoint runs in simul. |
| 130 |
ou.wang |
1.1 |
c------------------------------------ |
| 131 |
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call simul( indic, nn, xdiff, fnew, gg ) |
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| 133 |
ou.wang |
1.2 |
cow( compute tact (could be different from 1) |
| 134 |
ou.wang |
1.1 |
do i = 1, nn |
| 135 |
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if(dd(i) .ne. 0.and.(xdiff(i) - xx(i)).ne.0) then |
| 136 |
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tact = (xdiff(i) - xx(i))/ dd(i) |
| 137 |
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goto 301 |
| 138 |
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endif |
| 139 |
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end do |
| 140 |
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301 continue |
| 141 |
ou.wang |
1.2 |
c if tact is only slightly different from 1., then set it to 1. |
| 142 |
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c The difference is likely caused by trunction error. |
| 143 |
ou.wang |
1.1 |
if(abs(tact-1.).le.1.d-6) tact = 1. |
| 144 |
ou.wang |
1.2 |
write(*,'(a,e15.6)') |
| 145 |
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& ' pathei-lsopt: step size (tact) for the latest iteration |
| 146 |
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&: ',tact |
| 147 |
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cow) now we know tact (step size for the latest iteration). |
| 148 |
ou.wang |
1.1 |
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| 149 |
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C compute fp = direction(dd) . gradient(gg) |
| 150 |
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fp = DDOT( nn, dd, 1, gg, 1 ) |
| 151 |
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fdiff = fnew - ff |
| 152 |
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| 153 |
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print*, 'pathei-lsopt: ' |
| 154 |
ou.wang |
1.2 |
cow( print out info related to Wolfe tests |
| 155 |
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print*,'==================================================' |
| 156 |
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print*, 'Wolfe test 1 (sufficient cost decrease condition):' |
| 157 |
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write(*,'(a,3e15.6)') ' Cost (iter i, iter i-1, reduction): ', |
| 158 |
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& fnew, ff, fdiff |
| 159 |
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write(*,'(a,a,3e15.6)')' alpha1, step size for iter i, ', |
| 160 |
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& '<dd(i-1).gg(i-1)> ', |
| 161 |
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& xpara1, tact, dotdg |
| 162 |
ou.wang |
1.1 |
if(fdiff .gt. tact*xpara1*dotdg) then |
| 163 |
ou.wang |
1.2 |
write(*,'(a,a,e15.6,a,e15.6)') |
| 164 |
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& ' cost reduction GT alpha1*step size', |
| 165 |
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& '*<dd(i-1).gg(i-1)> ', fdiff, ' > ', tact*xpara1*dotdg |
| 166 |
ou.wang |
1.1 |
print*, 'Wolfe test 1: failed' |
| 167 |
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else |
| 168 |
ou.wang |
1.2 |
write(*,'(a,a,e15.6,a,e15.6)') |
| 169 |
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& ' cost reduction LE alpha1*step size', |
| 170 |
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& '*<dd(i-1).gg(i-1)> ', fdiff, ' <= ', tact*xpara1*dotdg |
| 171 |
ou.wang |
1.1 |
print*, 'Wolfe test 1: passed' |
| 172 |
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endif |
| 173 |
ou.wang |
1.2 |
print*,'' |
| 174 |
ou.wang |
1.1 |
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| 175 |
ou.wang |
1.2 |
print*, 'Wolfe test 2 (curvature condition):' |
| 176 |
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write(*,'(a,3e15.6)')' <dd(i-1).gg(i)>, <dd(i-1).gg(i-1)>: ', |
| 177 |
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& fp, dotdg |
| 178 |
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write(*,'(a,a,3e15.6)') |
| 179 |
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& ' alpha2,', 'alpha2*<dd(i-1).gg(i-1)>: ', |
| 180 |
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& xpara2, xpara2*dotdg |
| 181 |
ou.wang |
1.1 |
if (fp .gt. xpara2*dotdg) then |
| 182 |
ou.wang |
1.2 |
write(*,'(a,e15.6,a,e15.6)') |
| 183 |
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& ' <dd(i-1).gg(i)> GT alpha2* <dd(i-1).gg(i-1)>: ', |
| 184 |
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& fp, ' > ', xpara2*dotdg |
| 185 |
ou.wang |
1.1 |
print*, 'Wolfe test 2: passed' |
| 186 |
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else |
| 187 |
ou.wang |
1.2 |
write(*,'(a,e15.6,a,e15.6)') |
| 188 |
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& ' <dd(i-1).gg(i)> LE alpha2* <dd(i-1).gg(i-1)>: ', |
| 189 |
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& fp, ' <= ', xpara2*dotdg |
| 190 |
ou.wang |
1.1 |
print*, 'Wolfe test 2: failed' |
| 191 |
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endif |
| 192 |
ou.wang |
1.2 |
print*, '==================================================' |
| 193 |
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cow) |
| 194 |
ou.wang |
1.1 |
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| 195 |
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c----------------------------------------- |
| 196 |
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c apply 1st Wolfe test |
| 197 |
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c----------------------------------------- |
| 198 |
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| 199 |
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if (fdiff .gt. tact*xpara1*dotdg) then |
| 200 |
ou.wang |
1.2 |
C if (lphprint) |
| 201 |
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C & print *, 'Wolfe test 1 (Armijo Rule) Failed' |
| 202 |
ou.wang |
1.1 |
if (lphprint) |
| 203 |
ou.wang |
1.2 |
& print *, 'pathei-lsopt: interpolate to get new step size' |
| 204 |
ou.wang |
1.1 |
td = tact |
| 205 |
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ifail = 0 |
| 206 |
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go to 500 |
| 207 |
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endif |
| 208 |
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| 209 |
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c----------------------------------------- |
| 210 |
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c 1st Wolfe test 1 ok, apply 2nd Wolf test |
| 211 |
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c----------------------------------------- |
| 212 |
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if (fp .gt. xpara2*dotdg) then |
| 213 |
ou.wang |
1.2 |
C if (lphprint) |
| 214 |
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C & print *, 'Pass Wolfe test 2 (Curvature condition)' |
| 215 |
ou.wang |
1.1 |
ifail = 0 |
| 216 |
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go to 320 |
| 217 |
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endif |
| 218 |
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| 219 |
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if (ifail.eq.0) go to 350 |
| 220 |
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| 221 |
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c----------------------------------------- |
| 222 |
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c 2nd Wolfe test 2 ok, donc pas serieux, on sort |
| 223 |
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c----------------------------------------- |
| 224 |
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| 225 |
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320 continue |
| 226 |
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| 227 |
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ff = fnew |
| 228 |
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do i = 1, nn |
| 229 |
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xx(i) = xdiff(i) |
| 230 |
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end do |
| 231 |
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cph( |
| 232 |
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if (lphprint) |
| 233 |
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& print *, 'pathei-lsopt: no inter-/extrapolation in lsline' |
| 234 |
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cph) |
| 235 |
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go to 888 |
| 236 |
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| 237 |
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| 238 |
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c----------------------------------------- |
| 239 |
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c extrapolation |
| 240 |
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c----------------------------------------- |
| 241 |
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| 242 |
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350 continue |
| 243 |
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| 244 |
ou.wang |
1.2 |
if (lphprint) |
| 245 |
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& print *, 'pathei-lsopt: extrapolate to get new step size' |
| 246 |
ou.wang |
1.1 |
tg = tact |
| 247 |
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fg = fnew |
| 248 |
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if (td .ne. 0.0) go to 500 |
| 249 |
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| 250 |
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told = tact |
| 251 |
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left = (1.0+barmin)*tact |
| 252 |
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right = 10.0*tact |
| 253 |
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call cubic( tact, fnew, fp, ta, fa, fpa, left, right ) |
| 254 |
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ta = told |
| 255 |
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if (tact.ge.tmax) then |
| 256 |
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ifail = 7 |
| 257 |
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tact = tmax |
| 258 |
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endif |
| 259 |
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| 260 |
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if (lphprint) |
| 261 |
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& print *, 'pathei-lsopt: extrapolation: ', |
| 262 |
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& 'td, tg, tact, ifail = ', td, tg, tact, ifail |
| 263 |
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| 264 |
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go to 900 |
| 265 |
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| 266 |
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c----------------------------------------- |
| 267 |
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c interpolation |
| 268 |
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c----------------------------------------- |
| 269 |
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| 270 |
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500 continue |
| 271 |
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| 272 |
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C td: tact (step size) |
| 273 |
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C tg: was set to zero |
| 274 |
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C So the limits are between 0.01 * tg and tact-0.01*tg (0 and tact for isuml = 1) |
| 275 |
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test = barr*(td-tg) |
| 276 |
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left = tg+test |
| 277 |
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right = td-test |
| 278 |
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told = tact |
| 279 |
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C input: |
| 280 |
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C tact: was set to 1 in input, but in output store the new step size |
| 281 |
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C fnew: the new cost function in input |
| 282 |
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C fp: new dotdg = dd . gg ( direction DOT gradient) |
| 283 |
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C ta: set to zero (namely set x0 = 0 so tact is distance between x1 and x0) |
| 284 |
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C fa: old cost function |
| 285 |
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C fpa: old dotdg = dd . gg (diretion DOT gradient) |
| 286 |
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call cubic( tact, fnew, fp, ta, fa, fpa, left, right ) |
| 287 |
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ta = told |
| 288 |
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if (tact.gt.left .and. tact.lt.right) then |
| 289 |
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C falling within left and right brackets. Keep the same barr |
| 290 |
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barr = dmax1( barmin, barr/barmul ) |
| 291 |
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else |
| 292 |
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C outside of the left and right brackets. Reduce barr by half |
| 293 |
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barr = dmin1( barmul*barr, barmax ) |
| 294 |
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endif |
| 295 |
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| 296 |
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if (lphprint) |
| 297 |
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& print *, 'pathei-lsopt: interpolation: ', |
| 298 |
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& 'td, tg, tact, ifail = ', td, tg, tact, ifail |
| 299 |
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| 300 |
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c----------------------------------------- |
| 301 |
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c end of iteration loop |
| 302 |
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c - tact peut etre bloque sur tmax |
| 303 |
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c (venant de lextrapolation avec ifail=7) |
| 304 |
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c----------------------------------------- |
| 305 |
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| 306 |
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900 continue |
| 307 |
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| 308 |
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fa = fnew |
| 309 |
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fpa = fp |
| 310 |
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| 311 |
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c----------------------------------------- |
| 312 |
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c --- faut-il continuer ? |
| 313 |
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c----------------------------------------- |
| 314 |
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if (td .eq. 0.0) go to 950 |
| 315 |
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if (td-tg .lt. tmin) go to 920 |
| 316 |
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| 317 |
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c----------------------------------------- |
| 318 |
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c limit due to machine precision |
| 319 |
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c----------------------------------------- |
| 320 |
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do i = 1, nn |
| 321 |
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z = xx(i) + tact*dd(i) |
| 322 |
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if ((z.ne.xx(i)) .and. (z.ne.xdiff(i))) go to 950 |
| 323 |
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end do |
| 324 |
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| 325 |
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c----------------------------------------- |
| 326 |
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c arret sur dxmin ou de secours |
| 327 |
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c----------------------------------------- |
| 328 |
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920 continue |
| 329 |
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ifail = 8 |
| 330 |
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| 331 |
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c----------------------------------------- |
| 332 |
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c si tg=0, xx = xx_depart, |
| 333 |
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c sinon on prend xx=x_left qui fait decroitre f |
| 334 |
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c----------------------------------------- |
| 335 |
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if (tg .ne. 0.0) then |
| 336 |
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ff = fg |
| 337 |
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do i = 1, nn |
| 338 |
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xx(i) = xx(i) + tg*dd(i) |
| 339 |
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end do |
| 340 |
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endif |
| 341 |
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| 342 |
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go to 999 |
| 343 |
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| 344 |
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c----------------------------------------- |
| 345 |
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c update vector for new simulation |
| 346 |
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c----------------------------------------- |
| 347 |
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950 continue |
| 348 |
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| 349 |
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do i = 1, nn |
| 350 |
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xdiff(i) = xx(i) + tact*dd(i) |
| 351 |
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end do |
| 352 |
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| 353 |
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c======================================================================= |
| 354 |
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c end of simulation iter. |
| 355 |
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c======================================================================= |
| 356 |
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if (lphprint) |
| 357 |
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& print *, 'pathei-lsopt: end of simulation iter: ', |
| 358 |
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& 'td, tg, tact, ifail = ', td, tg, tact, ifail |
| 359 |
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end do |
| 360 |
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| 361 |
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c----------------------------------------- |
| 362 |
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c too many function evaluations |
| 363 |
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c----------------------------------------- |
| 364 |
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ifail = 6 |
| 365 |
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ff = fg |
| 366 |
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do i = 1, nn |
| 367 |
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xx(i) = xx(i) + tg*dd(i) |
| 368 |
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end do |
| 369 |
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| 370 |
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| 371 |
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999 continue |
| 372 |
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C Set ifail=99 so we do not modify OPWARMD and OPWARMI |
| 373 |
ou.wang |
1.2 |
C We modify OPWARMD and OPWARMI Only if both Wolfe |
| 374 |
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C conditions are satisfied. |
| 375 |
ou.wang |
1.1 |
|
| 376 |
|
|
ifail = 99 |
| 377 |
|
|
|
| 378 |
|
|
c----------------------------------------- |
| 379 |
|
|
c end of routine |
| 380 |
|
|
c----------------------------------------- |
| 381 |
|
|
888 continue |
| 382 |
|
|
|
| 383 |
|
|
if (lphprint) |
| 384 |
|
|
& print *, 'pathei-lsopt: end of lsline: ', |
| 385 |
|
|
& 'td, tg, tact, ifail = ', td, tg, tact, ifail |
| 386 |
|
|
return |
| 387 |
|
|
|
| 388 |
|
|
end |
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