| 1 |
C $Header: $ |
| 2 |
C $Name: $ |
| 3 |
subroutine m1qn3 (simul,prosca,ctonb,ctcab,n,x,f,g,dxmin,df1, |
| 4 |
& epsg,normtype,impres,io,imode,omode,niter,nsim, |
| 5 |
& iz,dz,ndz,reverse,indic,izs,rzs,dzs) |
| 6 |
c |
| 7 |
c----------------------------------------------------------------------- |
| 8 |
c |
| 9 |
c M1QN3, Version 3.3, October 2009 |
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c |
| 11 |
c M1qn3 has two running modes: the SID (Scalar Initial Scaling) mode |
| 12 |
c and the DIS (Diagonal Initial Scaling) mode. Both do not require |
| 13 |
c the same amount of storage, the same subroutines, ... |
| 14 |
c In the description below, items that differ in the DIS mode with |
| 15 |
c respect to the SIS mode are given in brakets. |
| 16 |
c |
| 17 |
c Use the following subroutines: |
| 18 |
c M1QN3A |
| 19 |
c DDD, DDDS |
| 20 |
c NLIS0 + DCUBE (Dec 88) |
| 21 |
c MUPDTS, DYSTBL. |
| 22 |
c |
| 23 |
c The following routines are proposed to the user in case the |
| 24 |
c Euclidean scalar product is used: |
| 25 |
c DUCLID, DTONBE, DTCABE. |
| 26 |
c |
| 27 |
c La sous-routine M1QN3 est une interface entre le programme |
| 28 |
c appelant et la sous-routine M1QN3A, le minimiseur proprement dit. |
| 29 |
c |
| 30 |
c Le module PROSCA est sense realiser le produit scalaire de deux |
| 31 |
c vecteurs de Rn; le module DTONB est sense realiser le changement |
| 32 |
c de coordonnees correspondant au changement de bases: base |
| 33 |
c euclidienne -> base orthonormale (pour le produit scalaire |
| 34 |
c PROSCA); le module CTBAB fait la transformation inverse: base |
| 35 |
c orthonormale -> base euclidienne. |
| 36 |
c |
| 37 |
c Iz is an integer working zone for M1QN3A, its dimension is 5. |
| 38 |
c It is formed of 5 scalars that are set by the optimizer: |
| 39 |
c - the dimension of the problem, |
| 40 |
c - an identifier of the scaling mode, |
| 41 |
c - the number of updates, |
| 42 |
c - two pointers. |
| 43 |
c |
| 44 |
c Dz est la zone de travail pour M1QN3A, de dimension ndz. |
| 45 |
c Elle est subdivisee en |
| 46 |
c 3 [ou 4] vecteurs de dimension n: d,gg,[diag,]aux |
| 47 |
c m scalaires: alpha |
| 48 |
c m vecteurs de dimension n: ybar |
| 49 |
c m vecteurs de dimension n: sbar |
| 50 |
c |
| 51 |
c m est alors le plus grand entier tel que |
| 52 |
c m*(2*n+1)+3*n .le. ndz [m*(2*n+1)+4*n .le. ndz)] |
| 53 |
c soit m := (ndz-3*n) / (2*n+1) [m := (ndz-4*n) / (2*n+1)]. |
| 54 |
c Il faut avoir m >= 1, donc ndz >= 5n+1 [ndz >= 6n+1]. |
| 55 |
c |
| 56 |
c A chaque iteration la metrique est formee a partir d un multiple |
| 57 |
c de l'identite [d'une matrice diagonale] D qui est mise a jour m |
| 58 |
c fois par la formule de BFGS en utilisant les m couples {y,s} les |
| 59 |
c plus recents. |
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c |
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c----------------------------------------------------------------------- |
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c |
| 63 |
c Authors: Jean Charles Gilbert, Claude Lemarechal, INRIA. |
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c |
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c Copyright 2008, 2009, INRIA. |
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c |
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c M1QN3 is distributed under the terms of the GNU General Public |
| 68 |
c License. |
| 69 |
c |
| 70 |
c----------------------------------------------------------------------- |
| 71 |
c |
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c This program is free software: you can redistribute it and/or |
| 73 |
c modify it under the terms of the GNU General Public License as |
| 74 |
c published by the Free Software Foundation, either version 3 of |
| 75 |
c the License, or (at your option) any later version. |
| 76 |
c |
| 77 |
c This program is distributed in the hope that it will be useful, |
| 78 |
c but WITHOUT ANY WARRANTY; without even the implied warranty of |
| 79 |
c MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU |
| 80 |
c General Public License for more details. |
| 81 |
c |
| 82 |
c You should have received a copy of the GNU General Public License |
| 83 |
c along with this program. If not, see |
| 84 |
c <http://www.gnu.org/licenses/>. |
| 85 |
c |
| 86 |
c----------------------------------------------------------------------- |
| 87 |
c |
| 88 |
implicit none |
| 89 |
c |
| 90 |
c arguments |
| 91 |
c |
| 92 |
character*3 normtype |
| 93 |
integer n,impres,io,imode(3),omode,niter,nsim,iz(5),ndz,indic, |
| 94 |
& reverse,izs(*) |
| 95 |
real rzs(*) |
| 96 |
double precision x(n),f,g(n),dxmin,df1,epsg,dz(ndz),dzs(*) |
| 97 |
external simul,prosca,ctonb,ctcab |
| 98 |
c |
| 99 |
c --- local variables |
| 100 |
c |
| 101 |
c The variable 'reentry' is used to know where to jump when entering |
| 102 |
c the subroutine in reverse commnunication (it is better than using |
| 103 |
c 'reverse', which is known outside m1qn3 and could be changed by |
| 104 |
c the user): |
| 105 |
c = 0: no jump, start at the begining of the subroutine |
| 106 |
c = 1: jump inside m1qn3a, where the simulator was called with |
| 107 |
c indic=1 |
| 108 |
c = 2: jump inside m1qn3a/mlis3, where the simulator was called with |
| 109 |
c indic=4 |
| 110 |
c The variable 'reentry' is set to 0 by the compiler and when m1qn3 |
| 111 |
c has completed its job (see below); since the value is saved, it |
| 112 |
c has always the value 0 when entering the solver for the first |
| 113 |
c time when solving a new problem, even if it is in the same |
| 114 |
c program. |
| 115 |
c |
| 116 |
logical inmemo,sscale |
| 117 |
integer ntravu,id,igg,idiag,iaux,ialpha,iybar,isbar,m,mmemo, |
| 118 |
& reentry |
| 119 |
double precision gnorm,ps |
| 120 |
save inmemo,sscale,ntravu,id,igg,idiag,iaux,ialpha,iybar,isbar,m, |
| 121 |
& mmemo,reentry,gnorm,ps |
| 122 |
c |
| 123 |
c data |
| 124 |
c |
| 125 |
data reentry /0/ |
| 126 |
c |
| 127 |
c --- function |
| 128 |
c |
| 129 |
double precision ddot,dnrmi |
| 130 |
c |
| 131 |
c --- stop if reverse < 0 (m1qn3 should not be called with reverse < 0) |
| 132 |
c |
| 133 |
if (reverse.lt.0) then |
| 134 |
write (io,'(/a,a,i0,a/)') |
| 135 |
& " >>> m1qn3 should not be called with a negative reverse", |
| 136 |
& " (=", reverse, ")" |
| 137 |
stop |
| 138 |
endif |
| 139 |
c |
| 140 |
c --- possible jumps |
| 141 |
c 9999: go directly in m1qn3a |
| 142 |
c |
| 143 |
if (reentry.gt.0) goto 9999 |
| 144 |
c |
| 145 |
c---- license notice |
| 146 |
c |
| 147 |
if (impres.ge.5) then |
| 148 |
write (io,934) |
| 149 |
endif |
| 150 |
934 format (1x,79("-") |
| 151 |
& /1x,"M1QN3 Copyright (C) 2008, J. Ch. Gilbert, Cl. ", |
| 152 |
& "Lemarechal." |
| 153 |
& /1x,79("-") |
| 154 |
& /1x,"This program comes with ABSOLUTELY NO WARRANTY. This is", |
| 155 |
& " free software, and you" |
| 156 |
& /1x,"are welcome to redistribute it under certain ", |
| 157 |
& "conditions. See the file COPYING " |
| 158 |
& /1x,"in the root directory of the M1QN3 distribution for ", |
| 159 |
& "details." |
| 160 |
& /1x,79("-")) |
| 161 |
c |
| 162 |
c---- impressions initiales et controle des arguments |
| 163 |
c |
| 164 |
if (impres.ge.1) then |
| 165 |
write (io,900) n,dxmin,df1,epsg,normtype,niter,nsim,impres |
| 166 |
if (reverse.gt.0) then |
| 167 |
write (io,'(5x,a)') "reverse communication" |
| 168 |
else |
| 169 |
write (io,'(5x,a)') "direct communication" |
| 170 |
endif |
| 171 |
endif |
| 172 |
900 format (/" M1QN3 (Version 3.3, October 2009): entry point"/ |
| 173 |
& 5x,"dimension of the problem (n):",i14/ |
| 174 |
& 5x,"absolute precision on x (dxmin):",9x,1pd9.2/ |
| 175 |
& 5x,"expected decrease for f (df1):",11x,1pd9.2/ |
| 176 |
& 5x,"relative precision on g (epsg):",10x,1pd9.2, |
| 177 |
& " (",a3,"-norm)"/ |
| 178 |
& 5x,"maximal number of iterations (niter):",i6/ |
| 179 |
& 5x,"maximal number of simulations (nsim):",i6/ |
| 180 |
& 5x,"printing level (impres):",15x,i4) |
| 181 |
c |
| 182 |
c---- check the arguments |
| 183 |
c |
| 184 |
if (n.le.0) then |
| 185 |
omode=2 |
| 186 |
if (reverse.gt.0) reverse = -1 |
| 187 |
if (impres.ge.1) write (io,'(/a)') |
| 188 |
& " >>> m1qn3: n should be > 0" |
| 189 |
return |
| 190 |
endif |
| 191 |
if (niter.le.0) then |
| 192 |
omode=2 |
| 193 |
if (reverse.gt.0) reverse = -1 |
| 194 |
if (impres.ge.1) write (io,'(/a)') |
| 195 |
& " >>> m1qn3: niter should be > 0" |
| 196 |
return |
| 197 |
endif |
| 198 |
if (nsim.le.0) then |
| 199 |
omode=2 |
| 200 |
if (reverse.gt.0) reverse = -1 |
| 201 |
if (impres.ge.1) write (io,'(/a)') |
| 202 |
& " >>> m1qn3: nsim should be > 0" |
| 203 |
return |
| 204 |
endif |
| 205 |
if (dxmin.le.0.d0) then |
| 206 |
omode=2 |
| 207 |
if (reverse.gt.0) reverse = -1 |
| 208 |
if (impres.ge.1) write (io,'(/a)') |
| 209 |
& " >>> m1qn3: dxmin should be > 0.d0" |
| 210 |
return |
| 211 |
endif |
| 212 |
c if (epsg.le.0.d0 .or. epsg.gt.1.d0) then |
| 213 |
if (epsg.le.0.d0) then |
| 214 |
omode=2 |
| 215 |
if (reverse.gt.0) reverse = -1 |
| 216 |
if (impres.ge.1) write (io,'(/a)') |
| 217 |
& " >>> m1qn3: epsg should be > 0.d0" |
| 218 |
return |
| 219 |
endif |
| 220 |
if (epsg.ge.1.d0) then |
| 221 |
omode=1 |
| 222 |
niter=0 |
| 223 |
nsim=0 |
| 224 |
epsg=1.d0 |
| 225 |
if (reverse.gt.0) reverse = -1 |
| 226 |
if (impres.ge.1) write (io,'(/a)') |
| 227 |
& " >>> m1qn3: epsg is >= 1.d0, no need to make progress" |
| 228 |
goto 1000 |
| 229 |
endif |
| 230 |
if ((normtype.ne.'two') .and. |
| 231 |
& (normtype.ne.'sup') .and. |
| 232 |
& (normtype.ne.'dfn')) then |
| 233 |
omode=2 |
| 234 |
if (reverse.gt.0) reverse = -1 |
| 235 |
write (io,'(/a,a,a/)') " >>> m1qn3: unknown norm type '", |
| 236 |
& normtype, "'" |
| 237 |
return |
| 238 |
endif |
| 239 |
if (impres.lt.0) then |
| 240 |
omode=2 |
| 241 |
if (reverse.gt.0) reverse = -1 |
| 242 |
write (io,'(/a,i0/)') |
| 243 |
& " >>> m1qn3: impres should be >= 0 and has the value ", |
| 244 |
& impres |
| 245 |
return |
| 246 |
endif |
| 247 |
c |
| 248 |
c---- what method |
| 249 |
c |
| 250 |
if (imode(1).eq.0) then |
| 251 |
if (impres.ge.1) write (io,920) |
| 252 |
920 format (/" m1qn3: Diagonal Initial Scaling mode") |
| 253 |
sscale=.false. |
| 254 |
else |
| 255 |
if (impres.ge.1) write (io,921) |
| 256 |
921 format (/" m1qn3: Scalar Initial Scaling mode") |
| 257 |
sscale=.true. |
| 258 |
endif |
| 259 |
c |
| 260 |
if ((ndz.lt.5*n+1).or.((.not.sscale).and.(ndz.lt.6*n+1))) then |
| 261 |
omode=2 |
| 262 |
if (reverse.gt.0) reverse = -1 |
| 263 |
if (impres.ge.1) write (io,922) |
| 264 |
922 format (/" >>> m1qn3: not enough memory allocated") |
| 265 |
return |
| 266 |
endif |
| 267 |
c |
| 268 |
c---- Compute m |
| 269 |
c |
| 270 |
call mupdts (sscale,inmemo,n,m,ndz) |
| 271 |
c |
| 272 |
c --- Check the value of m (if (y,s) pairs in core, m will be >= 1) |
| 273 |
c |
| 274 |
if (m.lt.1) then |
| 275 |
omode=2 |
| 276 |
if (reverse.gt.0) reverse = -1 |
| 277 |
if (impres.ge.1) write (io,930) |
| 278 |
930 format (/" >>> m1qn3: m is set too small in mupdts") |
| 279 |
return |
| 280 |
endif |
| 281 |
c |
| 282 |
c --- mmemo = number of (y,s) pairs in core memory |
| 283 |
c |
| 284 |
mmemo=1 |
| 285 |
if (inmemo) mmemo=m |
| 286 |
c |
| 287 |
ntravu=2*(2+mmemo)*n+m |
| 288 |
if (sscale) ntravu=ntravu-n |
| 289 |
if (impres.ge.1) write (io,931) ndz,ntravu,m |
| 290 |
931 format (/5x,"allocated memory (ndz) :",i9/ |
| 291 |
& 5x,"used memory : ",i9/ |
| 292 |
& 5x,"number of updates : ",i9) |
| 293 |
if (ndz.lt.ntravu) then |
| 294 |
omode=2 |
| 295 |
if (reverse.gt.0) reverse = -1 |
| 296 |
if (impres.ge.1) write (io,922) |
| 297 |
return |
| 298 |
endif |
| 299 |
c |
| 300 |
if (impres.ge.1) then |
| 301 |
if (inmemo) then |
| 302 |
write (io,932) |
| 303 |
else |
| 304 |
write (io,933) |
| 305 |
endif |
| 306 |
endif |
| 307 |
932 format (5x,"(y,s) pairs are stored in core memory") |
| 308 |
933 format (5x,"(y,s) pairs are stored by the user") |
| 309 |
c |
| 310 |
c---- cold start or warm restart ? |
| 311 |
c check iz: iz(1)=n, iz(2)=(0 if DIS, 1 if SIS), |
| 312 |
c iz(3)=m, iz(4)=jmin, iz(5)=jmax |
| 313 |
c |
| 314 |
if (imode(2).eq.0) then |
| 315 |
if (impres.ge.1) write (io,940) |
| 316 |
else |
| 317 |
if (iz(1).ne.n .or. iz(2).ne.imode(1) .or. iz(3).ne.m .or. |
| 318 |
& iz(4).lt.1 .or. iz(5).lt.0 .or. iz(4).gt.iz(3) .or. |
| 319 |
& iz(5).gt.iz(3)) |
| 320 |
& then |
| 321 |
omode=2 |
| 322 |
if (reverse.gt.0) reverse = -1 |
| 323 |
if (impres.ge.1) then |
| 324 |
write (io,941) |
| 325 |
if (iz(1).ne.n) write (io,942) |
| 326 |
if (iz(2).ne.imode(1)) write (io,943) |
| 327 |
if (iz(3).ne.m) write (io,944) |
| 328 |
if (iz(4).lt.1 .or. iz(5).lt.0 .or. iz(4).gt.iz(3) |
| 329 |
& .or. iz(5).gt.iz(3)) write (io,945) |
| 330 |
endif |
| 331 |
return |
| 332 |
endif |
| 333 |
if (impres.ge.1) write (io,946) |
| 334 |
endif |
| 335 |
940 format (/" m1qn3: cold start"/1x) |
| 336 |
941 format (/" >>> m1qn3: inconsistent warm restart ") |
| 337 |
942 format (" >>> m1qn3: (the number of variables has changed)") |
| 338 |
943 format (" >>> m1qn3: (the scaling mode has changed)") |
| 339 |
944 format (" >>> m1qn3: (the number of updates has changed)") |
| 340 |
945 format (" >>> m1qn3: (wrong pointers)") |
| 341 |
946 format (/" m1qn3: warm restart"/1x) |
| 342 |
iz(1)=n |
| 343 |
iz(2)=0 |
| 344 |
if (sscale) iz(2)=1 |
| 345 |
iz(3)=m |
| 346 |
c |
| 347 |
c---- split the working zone dz |
| 348 |
c |
| 349 |
idiag=1 |
| 350 |
iybar=idiag+n |
| 351 |
if (sscale) iybar=1 |
| 352 |
isbar=iybar+n*mmemo |
| 353 |
id=isbar+n*mmemo |
| 354 |
igg=id+n |
| 355 |
iaux=igg+n |
| 356 |
ialpha=iaux+n |
| 357 |
c |
| 358 |
c---- call the optimization code |
| 359 |
c |
| 360 |
9999 continue |
| 361 |
call m1qn3a (simul,prosca,ctonb,ctcab,n,x,f,g,dxmin,df1,epsg, |
| 362 |
& normtype,impres,io,imode,omode,niter,nsim,inmemo, |
| 363 |
& iz(3),iz(4),iz(5),dz(id),dz(igg),dz(idiag),dz(iaux), |
| 364 |
& dz(ialpha),dz(iybar),dz(isbar),reverse,reentry,indic, |
| 365 |
& izs,rzs,dzs) |
| 366 |
if (reentry.gt.0) return |
| 367 |
c |
| 368 |
c---- impressions finales |
| 369 |
c |
| 370 |
1000 continue |
| 371 |
if (impres.ge.1) write (io,960) omode,niter,nsim,epsg |
| 372 |
960 format (/1x,79("-")/ |
| 373 |
& /" m1qn3: output mode is ",i2 |
| 374 |
& /5x,"number of iterations: ",i14 |
| 375 |
& /5x,"number of simulations: ",i13 |
| 376 |
& /5x,"realized relative precision on g: ",1pd9.2) |
| 377 |
if (normtype.eq.'two') then |
| 378 |
gnorm = sqrt(ddot(n,g,1,g,1)) |
| 379 |
elseif (normtype.eq.'sup') then |
| 380 |
gnorm = dnrmi(n,g) |
| 381 |
elseif (normtype.eq.'dfn') then |
| 382 |
call prosca (n,g,g,ps,izs,rzs,dzs) |
| 383 |
gnorm=dsqrt(ps) |
| 384 |
endif |
| 385 |
|
| 386 |
if (impres.ge.1) write (io,961) f,normtype,gnorm |
| 387 |
961 format (5x,"f = ",1pd15.8 |
| 388 |
& /5x,a3,"-norm of g = ",1pd15.8) |
| 389 |
|
| 390 |
return |
| 391 |
end |
| 392 |
c |
| 393 |
c--------0---------0---------0---------0---------0---------0---------0-- |
| 394 |
c |
| 395 |
subroutine m1qn3a (simul,prosca,ctonb,ctcab,n,x,f,g,dxmin,df1, |
| 396 |
& epsg,normtype,impres,io,imode,omode,niter,nsim, |
| 397 |
& inmemo,m,jmin,jmax,d,gg,diag,aux,alpha,ybar, |
| 398 |
& sbar,reverse,reentry,indic,izs,rzs,dzs) |
| 399 |
c---- |
| 400 |
c |
| 401 |
c Code d optimisation proprement dit. |
| 402 |
c |
| 403 |
c---- |
| 404 |
c |
| 405 |
implicit none |
| 406 |
c |
| 407 |
c arguments |
| 408 |
c |
| 409 |
logical inmemo |
| 410 |
character*3 normtype |
| 411 |
integer n,impres,io,imode(3),omode,niter,nsim,m,jmin,jmax,indic, |
| 412 |
& reverse,reentry,izs(*) |
| 413 |
real rzs(*) |
| 414 |
double precision x(n),f,g(n),dxmin,df1,epsg,d(n),gg(n),diag(n), |
| 415 |
& aux(n),alpha(m),ybar(n,1),sbar(n,1),dzs(*) |
| 416 |
external simul,prosca,ctonb,ctcab |
| 417 |
c |
| 418 |
c variables locales |
| 419 |
c |
| 420 |
logical sscale,cold,warm,skip_update |
| 421 |
integer i,itmax,moderl,isim,jcour |
| 422 |
double precision d1,t,tmin,tmax,gnorm,gnorms,eps1,ff,preco,precos, |
| 423 |
& ys,den,dk,dk1,ps,ps2,hp0 |
| 424 |
save sscale,cold,warm,i,itmax,moderl,isim,jcour,d1,t,tmin,tmax, |
| 425 |
& gnorm,gnorms,eps1,ff,preco,precos,ys,den,dk,dk1,ps,ps2,hp0 |
| 426 |
c |
| 427 |
c parametres |
| 428 |
c |
| 429 |
double precision rm1,rm2 |
| 430 |
parameter (rm1=0.0001d+0,rm2=0.99d+0) |
| 431 |
double precision pi |
| 432 |
parameter (pi=3.1415927d+0) |
| 433 |
double precision rmin |
| 434 |
c |
| 435 |
c function |
| 436 |
c |
| 437 |
double precision ddot,dnrmi |
| 438 |
c |
| 439 |
c --- possible jumps |
| 440 |
c 9998: call of the simulator in m1qn3a with indic = 1 |
| 441 |
c 9999: call of the simulator in mlis3 with indic = 4 |
| 442 |
c |
| 443 |
if (reentry.eq.1) goto 9998 |
| 444 |
if (reentry.eq.2) goto 9999 |
| 445 |
c |
| 446 |
c---- initialisation |
| 447 |
c |
| 448 |
rmin=1.d-20 |
| 449 |
c |
| 450 |
sscale=.true. |
| 451 |
if (imode(1).eq.0) sscale=.false. |
| 452 |
c |
| 453 |
warm=.false. |
| 454 |
if (imode(2).eq.1) warm=.true. |
| 455 |
cold=.not.warm |
| 456 |
c |
| 457 |
skip_update = .false. |
| 458 |
c |
| 459 |
itmax=niter |
| 460 |
niter=0 |
| 461 |
isim=1 |
| 462 |
eps1=1.d+0 |
| 463 |
c |
| 464 |
call prosca (n,g,g,ps,izs,rzs,dzs) |
| 465 |
gnorm = dsqrt(ps) |
| 466 |
if (normtype.eq.'two') then |
| 467 |
gnorms = sqrt(ddot(n,g,1,g,1)) |
| 468 |
elseif (normtype.eq.'sup') then |
| 469 |
gnorms = dnrmi(n,g) |
| 470 |
elseif (normtype.eq.'dfn') then |
| 471 |
gnorms = gnorm |
| 472 |
endif |
| 473 |
if (impres.ge.1) write (io,900) f,normtype,gnorms |
| 474 |
900 format (5x,"f = ",1pd15.8 |
| 475 |
& /5x,a3,"-norm of g = ",1pd15.8) |
| 476 |
if (gnorms.lt.rmin) then |
| 477 |
omode=2 |
| 478 |
if (impres.ge.1) write (io,901) |
| 479 |
goto 1000 |
| 480 |
endif |
| 481 |
901 format (/" >>> m1qn3a: initial gradient is too small") |
| 482 |
c |
| 483 |
c --- initialisation pour dd |
| 484 |
c |
| 485 |
if (cold) then |
| 486 |
jmin=1 |
| 487 |
jmax=0 |
| 488 |
endif |
| 489 |
jcour=1 |
| 490 |
if (inmemo) jcour=jmax |
| 491 |
c |
| 492 |
c --- mise a l'echelle de la premiere direction de descente |
| 493 |
c |
| 494 |
if (cold) then |
| 495 |
c |
| 496 |
c --- use Fletcher's scaling and initialize diag to 1. |
| 497 |
c |
| 498 |
precos=2.d+0*df1/gnorm**2 |
| 499 |
do 10 i=1,n |
| 500 |
d(i)=-g(i)*precos |
| 501 |
diag(i)=1.d+0 |
| 502 |
10 continue |
| 503 |
if (impres.ge.5) write(io,902) precos |
| 504 |
902 format (/" m1qn3a: descent direction -g: precon = ",d10.3) |
| 505 |
else |
| 506 |
c |
| 507 |
c --- use the matrix stored in [diag and] the (y,s) pairs |
| 508 |
c |
| 509 |
if (sscale) then |
| 510 |
call prosca (n,ybar(1,jcour),ybar(1,jcour),ps,izs,rzs,dzs) |
| 511 |
precos=1.d+0/ps |
| 512 |
endif |
| 513 |
do 11 i=1,n |
| 514 |
d(i)=-g(i) |
| 515 |
11 continue |
| 516 |
if (inmemo) then |
| 517 |
call dd (prosca,ctonb,ctcab,n,sscale,m,d,aux,jmin,jmax, |
| 518 |
& precos,diag,alpha,ybar,sbar,izs,rzs,dzs) |
| 519 |
else |
| 520 |
call dds (prosca,ctonb,ctcab,n,sscale,m,d,aux,jmin,jmax, |
| 521 |
& precos,diag,alpha,ybar,sbar,izs,rzs,dzs) |
| 522 |
endif |
| 523 |
endif |
| 524 |
c |
| 525 |
if (impres.eq.3) write(io,903) |
| 526 |
if (impres.eq.4) write(io,903) |
| 527 |
903 format (/1x,79("-")) |
| 528 |
904 format (1x) |
| 529 |
c |
| 530 |
c --- initialisation pour mlis3 |
| 531 |
c |
| 532 |
tmax=1.d+20 |
| 533 |
call prosca (n,d,g,hp0,izs,rzs,dzs) |
| 534 |
if (hp0.ge.0.d+0) then |
| 535 |
omode=7 |
| 536 |
if (impres.ge.1) write (io,905) niter,hp0 |
| 537 |
goto 1000 |
| 538 |
endif |
| 539 |
905 format (/" >>> m1qn3 (iteration ",i2,"): " |
| 540 |
& /5x," the search direction d is not a ", |
| 541 |
& "descent direction: (g,d) = ",d12.5) |
| 542 |
c |
| 543 |
c --- compute the angle (-g,d) |
| 544 |
c |
| 545 |
if (warm.and.impres.ge.5) then |
| 546 |
call prosca (n,g,g,ps,izs,rzs,dzs) |
| 547 |
ps=dsqrt(ps) |
| 548 |
call prosca (n,d,d,ps2,izs,rzs,dzs) |
| 549 |
ps2=dsqrt(ps2) |
| 550 |
ps=hp0/ps/ps2 |
| 551 |
ps=dmin1(-ps,1.d+0) |
| 552 |
ps=dacos(ps) |
| 553 |
d1=ps*180.d+0/pi |
| 554 |
write (io,906) sngl(d1) |
| 555 |
endif |
| 556 |
906 format (/" m1qn3: descent direction d: ", |
| 557 |
& "angle(-g,d) = ",f5.1," degrees") |
| 558 |
c |
| 559 |
c---- Debut de l iteration. on cherche x(k+1) de la forme x(k) + t*d, |
| 560 |
c avec t > 0. On connait d. |
| 561 |
c |
| 562 |
c Debut de la boucle: etiquette 100, |
| 563 |
c Sortie de la boucle: goto 1000. |
| 564 |
c |
| 565 |
100 niter=niter+1 |
| 566 |
if (impres.ge.5) write(io,903) |
| 567 |
if (impres.ge.4) write(io,904) |
| 568 |
if (impres.ge.4) write (io,910) niter,isim,f,hp0 |
| 569 |
910 format (" m1qn3: iter ",i0,", simul ",i0, |
| 570 |
& ", f=",1pd15.8,", h'(0)=",d12.5) |
| 571 |
c |
| 572 |
c --- free simulation if desired |
| 573 |
c |
| 574 |
if (imode(3).gt.0) then |
| 575 |
if (mod(niter-1,imode(3)).eq.0) then |
| 576 |
indic=1 |
| 577 |
if (reverse.gt.0) then |
| 578 |
reentry = 1 |
| 579 |
return |
| 580 |
else |
| 581 |
call simul(indic,n,x,f,g,izs,rzs,dzs) |
| 582 |
endif |
| 583 |
endif |
| 584 |
endif |
| 585 |
9998 continue |
| 586 |
c |
| 587 |
c --- recherche lineaire et nouveau point x(k+1) |
| 588 |
c |
| 589 |
do 101 i=1,n |
| 590 |
gg(i)=g(i) |
| 591 |
101 continue |
| 592 |
ff=f |
| 593 |
if (impres.ge.5) write (io,911) |
| 594 |
911 format (/" m1qn3: line search") |
| 595 |
c |
| 596 |
c --- calcul de tmin |
| 597 |
c |
| 598 |
tmin=0.d+0 |
| 599 |
do 200 i=1,n |
| 600 |
tmin=dmax1(tmin,dabs(d(i))) |
| 601 |
200 continue |
| 602 |
tmin=dxmin/tmin |
| 603 |
t=1.d+0 |
| 604 |
d1=hp0 |
| 605 |
c |
| 606 |
9999 continue |
| 607 |
call mlis3 (n,simul,prosca,x,f,d1,t,tmin,tmax,d,g,rm2,rm1,impres, |
| 608 |
& io,moderl,isim,nsim,aux,reverse,reentry,indic,izs,rzs, |
| 609 |
& dzs) |
| 610 |
if (reentry.gt.0) return |
| 611 |
c |
| 612 |
c --- mlis3 renvoie les nouvelles valeurs de x, f et g |
| 613 |
c |
| 614 |
if (moderl.ne.0) then |
| 615 |
if (moderl.lt.0) then |
| 616 |
c |
| 617 |
c --- calcul impossible |
| 618 |
c t, g: ou les calculs sont impossibles |
| 619 |
c x, f: ceux du t_gauche (donc f <= ff) |
| 620 |
c |
| 621 |
omode=moderl |
| 622 |
goto 1000 |
| 623 |
elseif (moderl.eq.1) then |
| 624 |
c |
| 625 |
c --- descente bloquee sur tmax |
| 626 |
c |
| 627 |
skip_update = .true. |
| 628 |
c omode=3 |
| 629 |
c if (impres.ge.1) write(io,912) niter |
| 630 |
c 912 format (/" >>> m1qn3 (iteration ",i0, |
| 631 |
c & "): line search blocked on tmax: "/ |
| 632 |
c & " >>> possible reasons: bad scaling,", |
| 633 |
c & " unbounded problem") |
| 634 |
elseif (moderl.eq.4) then |
| 635 |
c |
| 636 |
c --- nsim atteint |
| 637 |
c x, f: ceux du t_gauche (donc f <= ff) |
| 638 |
c |
| 639 |
omode=5 |
| 640 |
goto 1000 |
| 641 |
elseif (moderl.eq.5) then |
| 642 |
c |
| 643 |
c --- arret demande par l utilisateur (indic = 0) |
| 644 |
c x, f: ceux en sortie du simulateur |
| 645 |
c |
| 646 |
omode=0 |
| 647 |
goto 1000 |
| 648 |
elseif (moderl.eq.6) then |
| 649 |
c |
| 650 |
c --- arret sur dxmin ou appel incoherent |
| 651 |
c x, f: ceux du t_gauche (donc f <= ff) |
| 652 |
c |
| 653 |
omode=6 |
| 654 |
goto 1000 |
| 655 |
endif |
| 656 |
else |
| 657 |
skip_update = .false. |
| 658 |
endif |
| 659 |
c |
| 660 |
c NOTE: stopping tests are now done after having updated the matrix, so |
| 661 |
c that update information can be stored in case of a later warm restart |
| 662 |
c |
| 663 |
c --- mise a jour de la matrice |
| 664 |
c |
| 665 |
if (skip_update) then |
| 666 |
if (impres.ge.5) write(io,'(/a)') |
| 667 |
& " m1qn3: matrix update is skipped" |
| 668 |
elseif (m.gt.0) then |
| 669 |
c |
| 670 |
c --- mise a jour des pointeurs |
| 671 |
c |
| 672 |
jmax=jmax+1 |
| 673 |
if (jmax.gt.m) jmax=jmax-m |
| 674 |
if ((cold.and.niter.gt.m).or.(warm.and.jmin.eq.jmax)) then |
| 675 |
jmin=jmin+1 |
| 676 |
if (jmin.gt.m) jmin=jmin-m |
| 677 |
endif |
| 678 |
if (inmemo) jcour=jmax |
| 679 |
c |
| 680 |
c --- y, s et (y,s) |
| 681 |
c |
| 682 |
do 400 i=1,n |
| 683 |
sbar(i,jcour)=t*d(i) |
| 684 |
ybar(i,jcour)=g(i)-gg(i) |
| 685 |
400 continue |
| 686 |
if (impres.ge.5) then |
| 687 |
call prosca (n,sbar(1,jcour),sbar(1,jcour),ps,izs,rzs,dzs) |
| 688 |
dk1=dsqrt(ps) |
| 689 |
if (niter.gt.1) write (io,930) dk1/dk |
| 690 |
930 format (/" m1qn3: convergence rate, s(k)/s(k-1) = ", |
| 691 |
& 1pd12.5) |
| 692 |
dk=dk1 |
| 693 |
endif |
| 694 |
call prosca (n,ybar(1,jcour),sbar(1,jcour),ys,izs,rzs,dzs) |
| 695 |
if (ys.le.0.d+0) then |
| 696 |
omode=7 |
| 697 |
if (impres.ge.1) write (io,931) niter,ys |
| 698 |
931 format (/" >>> m1qn3 (iteration ",i2, |
| 699 |
& "): the scalar product (y,s) = ",d12.5 |
| 700 |
& /27x,"is not positive") |
| 701 |
goto 1000 |
| 702 |
endif |
| 703 |
c |
| 704 |
c --- ybar et sbar |
| 705 |
c |
| 706 |
d1=dsqrt(1.d+0/ys) |
| 707 |
do 410 i=1,n |
| 708 |
sbar(i,jcour)=d1*sbar(i,jcour) |
| 709 |
ybar(i,jcour)=d1*ybar(i,jcour) |
| 710 |
410 continue |
| 711 |
if (.not.inmemo) call ystbl (.true.,ybar,sbar,n,jmax) |
| 712 |
c |
| 713 |
c --- compute the scalar or diagonal preconditioner |
| 714 |
c |
| 715 |
if (impres.ge.5) write(io,932) |
| 716 |
932 format (/" m1qn3: matrix update:") |
| 717 |
c |
| 718 |
c --- Here is the Oren-Spedicato factor, for scalar scaling |
| 719 |
c |
| 720 |
if (sscale) then |
| 721 |
call prosca (n,ybar(1,jcour),ybar(1,jcour),ps,izs,rzs,dzs) |
| 722 |
precos=1.d+0/ps |
| 723 |
c |
| 724 |
if (impres.ge.5) write (io,933) precos |
| 725 |
933 format (5x,"Oren-Spedicato factor = ",d10.3) |
| 726 |
c |
| 727 |
c --- Scale the diagonal to Rayleigh s ellipsoid. |
| 728 |
c Initially (niter.eq.1) and for a cold start, this is |
| 729 |
c equivalent to an Oren-Spedicato scaling of the |
| 730 |
c identity matrix. |
| 731 |
c |
| 732 |
else |
| 733 |
call ctonb (n,ybar(1,jcour),aux,izs,rzs,dzs) |
| 734 |
ps=0.d0 |
| 735 |
do 420 i=1,n |
| 736 |
ps=ps+diag(i)*aux(i)*aux(i) |
| 737 |
420 continue |
| 738 |
d1=1.d0/ps |
| 739 |
if (impres.ge.5) then |
| 740 |
write (io,934) d1 |
| 741 |
934 format(5x,"fitting the ellipsoid: factor = ",1pd10.3) |
| 742 |
endif |
| 743 |
do 421 i=1,n |
| 744 |
diag(i)=diag(i)*d1 |
| 745 |
421 continue |
| 746 |
c |
| 747 |
c --- update the diagonal |
| 748 |
c (gg is used as an auxiliary vector) |
| 749 |
c |
| 750 |
call ctonb (n,sbar(1,jcour),gg,izs,rzs,dzs) |
| 751 |
ps=0.d0 |
| 752 |
do 430 i=1,n |
| 753 |
ps=ps+gg(i)*gg(i)/diag(i) |
| 754 |
430 continue |
| 755 |
den=ps |
| 756 |
do 431 i=1,n |
| 757 |
diag(i)=1.d0/ |
| 758 |
& (1.d0/diag(i)+aux(i)**2-(gg(i)/diag(i))**2/den) |
| 759 |
if (diag(i).le.0.d0) then |
| 760 |
if (impres.ge.5) write (io,935) i,diag(i),rmin |
| 761 |
diag(i)=rmin |
| 762 |
endif |
| 763 |
431 continue |
| 764 |
935 format (/" >>> m1qn3-WARNING: diagonal element ",i8, |
| 765 |
& " is negative (",d10.3,"), reset to ",d10.3) |
| 766 |
c |
| 767 |
if (impres.ge.5) then |
| 768 |
ps=0.d0 |
| 769 |
do 440 i=1,n |
| 770 |
ps=ps+diag(i) |
| 771 |
440 continue |
| 772 |
ps=ps/n |
| 773 |
preco=ps |
| 774 |
c |
| 775 |
ps2=0.d0 |
| 776 |
do 441 i=1,n |
| 777 |
ps2=ps2+(diag(i)-ps)**2 |
| 778 |
441 continue |
| 779 |
ps2=dsqrt(ps2/n) |
| 780 |
write (io,936) preco,ps2 |
| 781 |
936 format (5x,"updated diagonal: average value = ", |
| 782 |
& 1pd10.3,", sqrt(variance) = ",d10.3) |
| 783 |
endif |
| 784 |
endif |
| 785 |
endif |
| 786 |
c |
| 787 |
c --- printings |
| 788 |
c |
| 789 |
c |
| 790 |
c --- tests d arret |
| 791 |
c |
| 792 |
call prosca(n,g,g,ps,izs,rzs,dzs) |
| 793 |
if (normtype.eq.'two') then |
| 794 |
gnorm = sqrt(ddot(n,g,1,g,1)) |
| 795 |
elseif (normtype.eq.'sup') then |
| 796 |
gnorm = dnrmi(n,g) |
| 797 |
elseif (normtype.eq.'dfn') then |
| 798 |
gnorm = dsqrt(ps) |
| 799 |
endif |
| 800 |
eps1 = gnorm/gnorms |
| 801 |
c |
| 802 |
if (impres.eq.3) then |
| 803 |
if (mod(niter-1,50).eq.0) write(io,'(/a,a)') |
| 804 |
& " iter simul stepsize f |g|", |
| 805 |
& " |g|/|g0|" |
| 806 |
write(io, |
| 807 |
& '(1x,i5,2x,i5,2x,1pd8.2,2x,d21.14,2x,d11.5,2x,d10.4)') |
| 808 |
& niter, isim, t, f, gnorm, eps1 |
| 809 |
endif |
| 810 |
if (impres.ge.5) write (io,940) eps1 |
| 811 |
940 format (/" m1qn3: stopping criterion on g: ",1pd12.5) |
| 812 |
if (eps1.lt.epsg) then |
| 813 |
omode=1 |
| 814 |
goto 1000 |
| 815 |
endif |
| 816 |
if (niter.eq.itmax) then |
| 817 |
omode=4 |
| 818 |
if (impres.ge.1) write (io,941) niter |
| 819 |
941 format (/" >>> m1qn3 (iteration ",i0, |
| 820 |
& "): maximal number of iterations") |
| 821 |
goto 1000 |
| 822 |
endif |
| 823 |
if (isim.gt.nsim) then |
| 824 |
omode=5 |
| 825 |
if (impres.ge.1) write (io,942) niter,isim |
| 826 |
942 format (/" >>> m1qn3 (iteration ",i3,"): ",i6, |
| 827 |
& " simulations (maximal number reached)") |
| 828 |
goto 1000 |
| 829 |
endif |
| 830 |
c |
| 831 |
c --- calcul de la nouvelle direction de descente d = - H.g |
| 832 |
c |
| 833 |
if (m.eq.0) then |
| 834 |
preco=2.d0*(ff-f)/ps |
| 835 |
do 500 i=1,n |
| 836 |
d(i)=-g(i)*preco |
| 837 |
500 continue |
| 838 |
else |
| 839 |
do 510 i=1,n |
| 840 |
d(i)=-g(i) |
| 841 |
510 continue |
| 842 |
if (inmemo) then |
| 843 |
call dd (prosca,ctonb,ctcab,n,sscale,m,d,aux,jmin,jmax, |
| 844 |
& precos,diag,alpha,ybar,sbar,izs,rzs,dzs) |
| 845 |
else |
| 846 |
call dds (prosca,ctonb,ctcab,n,sscale,m,d,aux,jmin,jmax, |
| 847 |
& precos,diag,alpha,ybar,sbar,izs,rzs,dzs) |
| 848 |
endif |
| 849 |
endif |
| 850 |
c |
| 851 |
c --- test: la direction d est-elle de descente ? |
| 852 |
c hp0 sera utilise par mlis3 |
| 853 |
c |
| 854 |
call prosca (n,d,g,hp0,izs,rzs,dzs) |
| 855 |
if (hp0.ge.0.d+0) then |
| 856 |
omode=7 |
| 857 |
if (impres.ge.1) write (io,905) niter,hp0 |
| 858 |
goto 1000 |
| 859 |
endif |
| 860 |
if (impres.ge.5) then |
| 861 |
call prosca (n,g,g,ps,izs,rzs,dzs) |
| 862 |
ps=dsqrt(ps) |
| 863 |
call prosca (n,d,d,ps2,izs,rzs,dzs) |
| 864 |
ps2=dsqrt(ps2) |
| 865 |
ps=hp0/ps/ps2 |
| 866 |
ps=dmin1(-ps,1.d+0) |
| 867 |
ps=dacos(ps) |
| 868 |
d1=ps |
| 869 |
d1=d1*180.d0/pi |
| 870 |
write (io,906) sngl(d1) |
| 871 |
endif |
| 872 |
c |
| 873 |
c---- on poursuit les iterations |
| 874 |
c |
| 875 |
goto 100 |
| 876 |
c |
| 877 |
c --- n1qn3 has finished for ever |
| 878 |
c |
| 879 |
1000 continue |
| 880 |
if (reverse.ne.0) reverse = -1 |
| 881 |
reentry = 0 |
| 882 |
nsim=isim |
| 883 |
epsg=eps1 |
| 884 |
return |
| 885 |
end |
| 886 |
c |
| 887 |
c--------0---------0---------0---------0---------0---------0---------0-- |
| 888 |
c |
| 889 |
subroutine dd (prosca,ctonb,ctcab,n,sscale,nm,depl,aux,jmin,jmax, |
| 890 |
& precos,diag,alpha,ybar,sbar,izs,rzs,dzs) |
| 891 |
c---- |
| 892 |
c |
| 893 |
c calcule le produit H.g ou |
| 894 |
c . H est une matrice construite par la formule de bfgs inverse |
| 895 |
c a nm memoires a partir de la matrice diagonale diag |
| 896 |
c dans un espace hilbertien dont le produit scalaire |
| 897 |
c est donne par prosca |
| 898 |
c (cf. J. Nocedal, Math. of Comp. 35/151 (1980) 773-782) |
| 899 |
c . g est un vecteur de dimension n (en general le gradient) |
| 900 |
c |
| 901 |
c la matrice diag apparait donc comme un preconditionneur diagonal |
| 902 |
c |
| 903 |
c depl = g (en entree), = H g (en sortie) |
| 904 |
c |
| 905 |
c la matrice H est memorisee par les vecteurs des tableaux |
| 906 |
c ybar, sbar et les pointeurs jmin, jmax |
| 907 |
c |
| 908 |
c alpha(nm) est une zone de travail |
| 909 |
c |
| 910 |
c izs(*),rzs(*),dzs(*) sont des zones de travail pour prosca |
| 911 |
c |
| 912 |
c---- |
| 913 |
c |
| 914 |
implicit none |
| 915 |
c |
| 916 |
c arguments |
| 917 |
c |
| 918 |
logical sscale |
| 919 |
integer n,nm,jmin,jmax,izs(*) |
| 920 |
real rzs(*) |
| 921 |
double precision depl(n),precos,diag(n),alpha(nm),ybar(n,1), |
| 922 |
& sbar(n,1),aux(n),dzs(*) |
| 923 |
external prosca,ctonb,ctcab |
| 924 |
c |
| 925 |
c variables locales |
| 926 |
c |
| 927 |
integer jfin,i,j,jp |
| 928 |
double precision r,ps |
| 929 |
c |
| 930 |
jfin=jmax |
| 931 |
if (jfin.lt.jmin) jfin=jmax+nm |
| 932 |
c |
| 933 |
c phase de descente |
| 934 |
c |
| 935 |
do 100 j=jfin,jmin,-1 |
| 936 |
jp=j |
| 937 |
if (jp.gt.nm) jp=jp-nm |
| 938 |
call prosca (n,depl,sbar(1,jp),ps,izs,rzs,dzs) |
| 939 |
r=ps |
| 940 |
alpha(jp)=r |
| 941 |
do 20 i=1,n |
| 942 |
depl(i)=depl(i)-r*ybar(i,jp) |
| 943 |
20 continue |
| 944 |
100 continue |
| 945 |
c |
| 946 |
c preconditionnement |
| 947 |
c |
| 948 |
if (sscale) then |
| 949 |
do 150 i=1,n |
| 950 |
depl(i)=depl(i)*precos |
| 951 |
150 continue |
| 952 |
else |
| 953 |
call ctonb (n,depl,aux,izs,rzs,dzs) |
| 954 |
do 151 i=1,n |
| 955 |
aux(i)=aux(i)*diag(i) |
| 956 |
151 continue |
| 957 |
call ctcab (n,aux,depl,izs,rzs,dzs) |
| 958 |
endif |
| 959 |
c |
| 960 |
c remontee |
| 961 |
c |
| 962 |
do 200 j=jmin,jfin |
| 963 |
jp=j |
| 964 |
if (jp.gt.nm) jp=jp-nm |
| 965 |
call prosca (n,depl,ybar(1,jp),ps,izs,rzs,dzs) |
| 966 |
r=alpha(jp)-ps |
| 967 |
do 120 i=1,n |
| 968 |
depl(i)=depl(i)+r*sbar(i,jp) |
| 969 |
120 continue |
| 970 |
200 continue |
| 971 |
return |
| 972 |
end |
| 973 |
c |
| 974 |
c--------0---------0---------0---------0---------0---------0---------0-- |
| 975 |
c |
| 976 |
subroutine dds (prosca,ctonb,ctcab,n,sscale,nm,depl,aux,jmin, |
| 977 |
& jmax,precos,diag,alpha,ybar,sbar,izs,rzs,dzs) |
| 978 |
c---- |
| 979 |
c |
| 980 |
c This subroutine has the same role as dd (computation of the |
| 981 |
c product H.g). It supposes however that the (y,s) pairs are not |
| 982 |
c stored in core memory, but on a devise chosen by the user. |
| 983 |
c The access to this devise is performed via the subroutine ystbl. |
| 984 |
c |
| 985 |
c---- |
| 986 |
c |
| 987 |
implicit none |
| 988 |
c |
| 989 |
c arguments |
| 990 |
c |
| 991 |
logical sscale |
| 992 |
integer n,nm,jmin,jmax,izs(*) |
| 993 |
real rzs(*) |
| 994 |
double precision depl(n),precos,diag(n),alpha(nm),ybar(n),sbar(n), |
| 995 |
& aux(n),dzs(*) |
| 996 |
external prosca,ctonb,ctcab |
| 997 |
c |
| 998 |
c variables locales |
| 999 |
c |
| 1000 |
integer jfin,i,j,jp |
| 1001 |
double precision r,ps |
| 1002 |
c |
| 1003 |
jfin=jmax |
| 1004 |
if (jfin.lt.jmin) jfin=jmax+nm |
| 1005 |
c |
| 1006 |
c phase de descente |
| 1007 |
c |
| 1008 |
do 100 j=jfin,jmin,-1 |
| 1009 |
jp=j |
| 1010 |
if (jp.gt.nm) jp=jp-nm |
| 1011 |
call ystbl (.false.,ybar,sbar,n,jp) |
| 1012 |
call prosca (n,depl,sbar,ps,izs,rzs,dzs) |
| 1013 |
r=ps |
| 1014 |
alpha(jp)=r |
| 1015 |
do 20 i=1,n |
| 1016 |
depl(i)=depl(i)-r*ybar(i) |
| 1017 |
20 continue |
| 1018 |
100 continue |
| 1019 |
c |
| 1020 |
c preconditionnement |
| 1021 |
c |
| 1022 |
if (sscale) then |
| 1023 |
do 150 i=1,n |
| 1024 |
depl(i)=depl(i)*precos |
| 1025 |
150 continue |
| 1026 |
else |
| 1027 |
call ctonb (n,depl,aux,izs,rzs,dzs) |
| 1028 |
do 151 i=1,n |
| 1029 |
aux(i)=aux(i)*diag(i) |
| 1030 |
151 continue |
| 1031 |
call ctcab (n,aux,depl,izs,rzs,dzs) |
| 1032 |
endif |
| 1033 |
c |
| 1034 |
c remontee |
| 1035 |
c |
| 1036 |
do 200 j=jmin,jfin |
| 1037 |
jp=j |
| 1038 |
if (jp.gt.nm) jp=jp-nm |
| 1039 |
call ystbl (.false.,ybar,sbar,n,jp) |
| 1040 |
call prosca (n,depl,ybar(1),ps,izs,rzs,dzs) |
| 1041 |
r=alpha(jp)-ps |
| 1042 |
do 120 i=1,n |
| 1043 |
depl(i)=depl(i)+r*sbar(i) |
| 1044 |
120 continue |
| 1045 |
200 continue |
| 1046 |
return |
| 1047 |
end |
| 1048 |
c |
| 1049 |
c--------0---------0---------0---------0---------0---------0---------0-- |
| 1050 |
c |
| 1051 |
subroutine mlis3 (n,simul,prosca,x,f,fpn,t,tmin,tmax,d,g, |
| 1052 |
1 amd,amf,imp,io,logic,nap,napmax,xn, |
| 1053 |
1 reverse,reentry,indic,izs,rzs,dzs) |
| 1054 |
c |
| 1055 |
c ---- |
| 1056 |
c |
| 1057 |
c mlis3 + minuscules + commentaires |
| 1058 |
c + version amelioree (XII 88): interpolation cubique systematique |
| 1059 |
c et anti-overflows |
| 1060 |
c + declaration variables (II/89, JCG). |
| 1061 |
c + barr is also progressively decreased (12/93, CL & JChG). |
| 1062 |
c barmul is set to 5. |
| 1063 |
c |
| 1064 |
c ---------------------------------------------------------------- |
| 1065 |
c |
| 1066 |
c en sortie logic = |
| 1067 |
c |
| 1068 |
c 0 descente serieuse |
| 1069 |
c 1 descente bloquee sur tmax |
| 1070 |
c 4 nap > napmax |
| 1071 |
c 5 arret demande par le simulateur |
| 1072 |
c 6 fonction et gradient pas d accord |
| 1073 |
c < 0 contrainte implicite active |
| 1074 |
c |
| 1075 |
c indic on entry (in reverse communication) |
| 1076 |
c |
| 1077 |
c < 0: the simulator cannot compute f and g |
| 1078 |
c = 0: the simulator wants to stop |
| 1079 |
c > 0: the simulator has done its work |
| 1080 |
c |
| 1081 |
c indic on return (in reverse communication) |
| 1082 |
c |
| 1083 |
c = 4: the simulator is asked to compute f and g |
| 1084 |
c |
| 1085 |
c reverse |
| 1086 |
c |
| 1087 |
c = 0: direct communication |
| 1088 |
c = 1: reverse communication |
| 1089 |
c |
| 1090 |
c reentry on entry |
| 1091 |
c |
| 1092 |
c = 2: reverse communication, return from a simulation, skip to |
| 1093 |
c the place where the simulator was called (9999) |
| 1094 |
c |
| 1095 |
c reentry return |
| 1096 |
c |
| 1097 |
c = 0: reverse communication, the linesearch has finished its job |
| 1098 |
c = 2: reverse communication, a simulation is required |
| 1099 |
c |
| 1100 |
c ---- |
| 1101 |
c |
| 1102 |
implicit none |
| 1103 |
c |
| 1104 |
c --- arguments |
| 1105 |
c |
| 1106 |
integer n,imp,io,logic,nap,napmax,indic,reverse,reentry,izs(*) |
| 1107 |
real rzs(*) |
| 1108 |
double precision x(n),f,fpn,t,tmin,tmax,d(n),g(n),amd,amf,xn(n), |
| 1109 |
& dzs(*) |
| 1110 |
external simul,prosca |
| 1111 |
c |
| 1112 |
c --- variables locales |
| 1113 |
c |
| 1114 |
logical t_increased |
| 1115 |
integer i,indica,indicd |
| 1116 |
double precision tesf,tesd,tg,fg,fpg,td,ta,fa,fpa,d2,fn,fp,ffn,fd, |
| 1117 |
& fpd,z,test,barmin,barmul,barmax,barr,gauche,droite,taa,ps |
| 1118 |
save t_increased,i,indica,indicd,tesf,tesd,tg,fg,fpg,td,ta,fa, |
| 1119 |
& fpa,d2,fn,fp,ffn,fd,fpd,z,test,barmin,barmul,barmax,barr, |
| 1120 |
& gauche,droite,taa,ps |
| 1121 |
c |
| 1122 |
1000 format (/4x," mlis3 ",4x,"fpn=",1pd10.3," d2=",d9.2, |
| 1123 |
1 " tmin=",d9.2," tmax=",d9.2) |
| 1124 |
1001 format (/4x," mlis3",3x,"stop on tmin",5x, |
| 1125 |
1 "stepsizes",11x,"functions",8x,"derivatives") |
| 1126 |
1002 format (4x," mlis3",37x,1pd10.3,2d11.3) |
| 1127 |
1003 format (4x," mlis3",1pd14.3,2d11.3) |
| 1128 |
1004 format (4x," mlis3",37x,1pd10.3," indic=",i3) |
| 1129 |
1005 format (4x," mlis3",14x,1pd18.8,2x,d21.14,2x,d11.4) |
| 1130 |
1006 format (4x," mlis3",14x,1pd18.8," indic=",i3) |
| 1131 |
1007 format (/4x," mlis3",10x,"tmin forced to tmax") |
| 1132 |
1008 format (/4x," mlis3",10x,"inconsistent call") |
| 1133 |
c |
| 1134 |
c --- possible jump |
| 1135 |
c |
| 1136 |
if (reentry.eq.2) goto 9999 |
| 1137 |
c |
| 1138 |
if (n.gt.0 .and. fpn.lt.0.d0 .and. t.gt.0.d0 |
| 1139 |
1 .and. tmax.gt.0.d0 .and. amf.gt.0.d0 |
| 1140 |
1 .and. amd.gt.amf .and. amd.lt.1.d0) go to 5 |
| 1141 |
logic=6 |
| 1142 |
go to 999 |
| 1143 |
5 tesf=amf*fpn |
| 1144 |
tesd=amd*fpn |
| 1145 |
barmin=0.01d0 |
| 1146 |
barmul=5.d0 |
| 1147 |
barmax=0.3d0 |
| 1148 |
barr=barmin |
| 1149 |
td=0.d0 |
| 1150 |
tg=0.d0 |
| 1151 |
fn=f |
| 1152 |
fg=fn |
| 1153 |
fpg=fpn |
| 1154 |
ta=0.d0 |
| 1155 |
fa=fn |
| 1156 |
fpa=fpn |
| 1157 |
call prosca (n,d,d,ps,izs,rzs,dzs) |
| 1158 |
d2=ps |
| 1159 |
c |
| 1160 |
c elimination d un t initial ridiculement petit |
| 1161 |
c |
| 1162 |
c< |
| 1163 |
c if (t.gt.tmin) go to 20 |
| 1164 |
c t=tmin |
| 1165 |
c if (t.le.tmax) go to 20 |
| 1166 |
c if (imp.gt.0) write (io,1007) |
| 1167 |
c tmin=tmax |
| 1168 |
c 20 if (fn+t*fpn.lt.fn+0.9d0*t*fpn) go to 30 |
| 1169 |
c t=2.d0*t |
| 1170 |
c go to 20 |
| 1171 |
c changed into |
| 1172 |
if (t.lt.tmin) then |
| 1173 |
t=tmin |
| 1174 |
if (imp.ge.4) write (io,'(a)') |
| 1175 |
& ' mlis3: initial step-size increased to tmin' |
| 1176 |
if (t.gt.tmax) then |
| 1177 |
if (imp.gt.0) write (io,1007) |
| 1178 |
tmin=tmax |
| 1179 |
endif |
| 1180 |
endif |
| 1181 |
t_increased = .false. |
| 1182 |
do while (fn+t*fpn.ge.fn+0.9d0*t*fpn) |
| 1183 |
t_increased = .true. |
| 1184 |
t = 2.d0*t |
| 1185 |
enddo |
| 1186 |
if (t_increased .and. (imp.ge.4)) write (io,'(a,1pd10.3)') |
| 1187 |
& ' mlis3: initial step-size increased to ',t |
| 1188 |
c> |
| 1189 |
30 indica=1 |
| 1190 |
logic=0 |
| 1191 |
if (t.gt.tmax) then |
| 1192 |
t=tmax |
| 1193 |
logic=1 |
| 1194 |
endif |
| 1195 |
if (imp.ge.4) write (io,1000) fpn,d2,tmin,tmax |
| 1196 |
c |
| 1197 |
c --- nouveau x |
| 1198 |
c initialize xn to the current iterate |
| 1199 |
c use x as the trial iterate |
| 1200 |
c |
| 1201 |
do i=1,n |
| 1202 |
xn(i)=x(i) |
| 1203 |
x(i)=xn(i)+t*d(i) |
| 1204 |
enddo |
| 1205 |
c |
| 1206 |
c --- boucle |
| 1207 |
c |
| 1208 |
100 nap=nap+1 |
| 1209 |
if(nap.gt.napmax) then |
| 1210 |
logic=4 |
| 1211 |
fn=fg |
| 1212 |
do i=1,n |
| 1213 |
xn(i)=xn(i)+tg*d(i) |
| 1214 |
enddo |
| 1215 |
go to 999 |
| 1216 |
endif |
| 1217 |
c |
| 1218 |
c --- appel simulateur |
| 1219 |
c |
| 1220 |
indic=4 |
| 1221 |
if (reverse.gt.0) then |
| 1222 |
reentry = 2 |
| 1223 |
return |
| 1224 |
else |
| 1225 |
call simul(indic,n,x,f,g,izs,rzs,dzs) |
| 1226 |
endif |
| 1227 |
9999 continue |
| 1228 |
if (indic.eq.0) then |
| 1229 |
c |
| 1230 |
c --- arret demande par l utilisateur |
| 1231 |
c |
| 1232 |
logic=5 |
| 1233 |
fn=f |
| 1234 |
do 170 i=1,n |
| 1235 |
xn(i)=x(i) |
| 1236 |
170 continue |
| 1237 |
go to 999 |
| 1238 |
endif |
| 1239 |
if(indic.lt.0) then |
| 1240 |
c |
| 1241 |
c --- les calculs n ont pas pu etre effectues par le simulateur |
| 1242 |
c |
| 1243 |
td=t |
| 1244 |
indicd=indic |
| 1245 |
logic=0 |
| 1246 |
if (imp.ge.4) write (io,1004) t,indic |
| 1247 |
t=tg+0.1d0*(td-tg) |
| 1248 |
go to 905 |
| 1249 |
endif |
| 1250 |
c |
| 1251 |
c --- les tests elementaires sont faits, on y va |
| 1252 |
c |
| 1253 |
call prosca (n,d,g,ps,izs,rzs,dzs) |
| 1254 |
fp=ps |
| 1255 |
c |
| 1256 |
c --- premier test de Wolfe |
| 1257 |
c |
| 1258 |
ffn=f-fn |
| 1259 |
if(ffn.gt.t*tesf) then |
| 1260 |
td=t |
| 1261 |
fd=f |
| 1262 |
fpd=fp |
| 1263 |
indicd=indic |
| 1264 |
logic=0 |
| 1265 |
if(imp.ge.4) write (io,1002) t,ffn,fp |
| 1266 |
go to 500 |
| 1267 |
endif |
| 1268 |
c |
| 1269 |
c --- test 1 ok, donc deuxieme test de Wolfe |
| 1270 |
c |
| 1271 |
if(imp.ge.4) write (io,1003) t,ffn,fp |
| 1272 |
if(fp.gt.tesd) then |
| 1273 |
logic=0 |
| 1274 |
go to 320 |
| 1275 |
endif |
| 1276 |
if (logic.eq.0) go to 350 |
| 1277 |
c |
| 1278 |
c --- test 2 ok, donc pas serieux, on sort |
| 1279 |
c |
| 1280 |
320 fn=f |
| 1281 |
do 330 i=1,n |
| 1282 |
xn(i)=x(i) |
| 1283 |
330 continue |
| 1284 |
go to 999 |
| 1285 |
c |
| 1286 |
c |
| 1287 |
c |
| 1288 |
350 tg=t |
| 1289 |
fg=f |
| 1290 |
fpg=fp |
| 1291 |
if(td.ne.0.d0) go to 500 |
| 1292 |
c |
| 1293 |
c extrapolation |
| 1294 |
c |
| 1295 |
taa=t |
| 1296 |
gauche=(1.d0+barmin)*t |
| 1297 |
droite=10.d0*t |
| 1298 |
call ecube (t,f,fp,ta,fa,fpa,gauche,droite) |
| 1299 |
ta=taa |
| 1300 |
if(t.lt.tmax) go to 900 |
| 1301 |
logic=1 |
| 1302 |
t=tmax |
| 1303 |
go to 900 |
| 1304 |
c |
| 1305 |
c interpolation |
| 1306 |
c |
| 1307 |
500 if(indica.le.0) then |
| 1308 |
ta=t |
| 1309 |
t=0.9d0*tg+0.1d0*td |
| 1310 |
go to 900 |
| 1311 |
endif |
| 1312 |
test=barr*(td-tg) |
| 1313 |
gauche=tg+test |
| 1314 |
droite=td-test |
| 1315 |
taa=t |
| 1316 |
call ecube (t,f,fp,ta,fa,fpa,gauche,droite) |
| 1317 |
ta=taa |
| 1318 |
if (t.gt.gauche .and. t.lt.droite) then |
| 1319 |
barr=dmax1(barmin,barr/barmul) |
| 1320 |
c barr=barmin |
| 1321 |
else |
| 1322 |
barr=dmin1(barmul*barr,barmax) |
| 1323 |
endif |
| 1324 |
c |
| 1325 |
c --- fin de boucle |
| 1326 |
c - t peut etre bloque sur tmax |
| 1327 |
c (venant de l extrapolation avec logic=1) |
| 1328 |
c |
| 1329 |
900 fa=f |
| 1330 |
fpa=fp |
| 1331 |
905 indica=indic |
| 1332 |
c |
| 1333 |
c --- faut-il continuer ? |
| 1334 |
c |
| 1335 |
if (td.eq.0.d0) go to 950 |
| 1336 |
if (td-tg.lt.tmin) go to 920 |
| 1337 |
c |
| 1338 |
c --- limite de precision machine (arret de secours) ? |
| 1339 |
c |
| 1340 |
do 910 i=1,n |
| 1341 |
z=xn(i)+t*d(i) |
| 1342 |
if (z.ne.xn(i).and.z.ne.x(i)) go to 950 |
| 1343 |
910 continue |
| 1344 |
if (imp.gt.3) write (io,'(5x,a)') "mlis3 no change in x" |
| 1345 |
c |
| 1346 |
c --- arret sur dxmin ou de secours |
| 1347 |
c |
| 1348 |
920 logic=6 |
| 1349 |
c |
| 1350 |
c si indicd<0, derniers calculs non faits par simul |
| 1351 |
c |
| 1352 |
if (indicd.lt.0) logic=indicd |
| 1353 |
c |
| 1354 |
c si tg=0, xn = xn_depart, |
| 1355 |
c sinon on prend xn=x_gauche qui fait decroitre f |
| 1356 |
c |
| 1357 |
if (tg.eq.0.d0) go to 940 |
| 1358 |
fn=fg |
| 1359 |
do 930 i=1,n |
| 1360 |
930 xn(i)=xn(i)+tg*d(i) |
| 1361 |
940 if (imp.le.3) go to 999 |
| 1362 |
write (io,1001) |
| 1363 |
write (io,1005) tg,fg,fpg |
| 1364 |
if (logic.eq.6) write (io,1005) td,fd,fpd |
| 1365 |
if (logic.eq.7) write (io,1006) td,indicd |
| 1366 |
go to 999 |
| 1367 |
c |
| 1368 |
c recopiage de x et boucle |
| 1369 |
c |
| 1370 |
950 do 960 i=1,n |
| 1371 |
960 x(i)=xn(i)+t*d(i) |
| 1372 |
go to 100 |
| 1373 |
c --- linesearch finished, no skip at next entry in mlis3 |
| 1374 |
999 if (reverse.ne.0) reentry = 0 |
| 1375 |
return |
| 1376 |
end |
| 1377 |
c |
| 1378 |
c |
| 1379 |
c--------0---------0---------0---------0---------0---------0---------0-- |
| 1380 |
c |
| 1381 |
subroutine ecube (t,f,fp,ta,fa,fpa,tlower,tupper) |
| 1382 |
c |
| 1383 |
implicit none |
| 1384 |
c |
| 1385 |
c --- arguments |
| 1386 |
c |
| 1387 |
double precision sign,den,anum,t,f,fp,ta,fa,fpa,tlower,tupper |
| 1388 |
c |
| 1389 |
c --- variables locales |
| 1390 |
c |
| 1391 |
double precision z1,b,discri |
| 1392 |
c |
| 1393 |
c Using f and fp at t and ta, computes new t by cubic formula |
| 1394 |
c safeguarded inside [tlower,tupper]. |
| 1395 |
c |
| 1396 |
z1=fp+fpa-3.d0*(fa-f)/(ta-t) |
| 1397 |
b=z1+fp |
| 1398 |
c |
| 1399 |
c first compute the discriminant (without overflow) |
| 1400 |
c |
| 1401 |
if (dabs(z1).le.1.d0) then |
| 1402 |
discri=z1*z1-fp*fpa |
| 1403 |
else |
| 1404 |
discri=fp/z1 |
| 1405 |
discri=discri*fpa |
| 1406 |
discri=z1-discri |
| 1407 |
if (z1.ge.0.d0 .and. discri.ge.0.d0) then |
| 1408 |
discri=dsqrt(z1)*dsqrt(discri) |
| 1409 |
go to 120 |
| 1410 |
endif |
| 1411 |
if (z1.le.0.d0 .and. discri.le.0.d0) then |
| 1412 |
discri=dsqrt(-z1)*dsqrt(-discri) |
| 1413 |
go to 120 |
| 1414 |
endif |
| 1415 |
discri=-1.d0 |
| 1416 |
endif |
| 1417 |
if (discri.lt.0.d0) then |
| 1418 |
if (fp.lt.0.d0) t=tupper |
| 1419 |
if (fp.ge.0.d0) t=tlower |
| 1420 |
go to 900 |
| 1421 |
endif |
| 1422 |
c |
| 1423 |
c discriminant nonnegative, compute solution (without overflow) |
| 1424 |
c |
| 1425 |
discri=dsqrt(discri) |
| 1426 |
120 if (t-ta.lt.0.d0) discri=-discri |
| 1427 |
sign=(t-ta)/dabs(t-ta) |
| 1428 |
if (b*sign.gt.0.d+0) then |
| 1429 |
t=t+fp*(ta-t)/(b+discri) |
| 1430 |
else |
| 1431 |
den=z1+b+fpa |
| 1432 |
anum=b-discri |
| 1433 |
if (dabs((t-ta)*anum).lt.(tupper-tlower)*dabs(den)) then |
| 1434 |
t=t+anum*(ta-t)/den |
| 1435 |
else |
| 1436 |
t=tupper |
| 1437 |
endif |
| 1438 |
endif |
| 1439 |
900 t=dmax1(t,tlower) |
| 1440 |
t=dmin1(t,tupper) |
| 1441 |
return |
| 1442 |
end |
| 1443 |
c |
| 1444 |
c--------0---------0---------0---------0---------0---------0---------0-- |
| 1445 |
c |
| 1446 |
subroutine mupdts (sscale,inmemo,n,m,nrz) |
| 1447 |
c |
| 1448 |
implicit none |
| 1449 |
c |
| 1450 |
c arguments |
| 1451 |
c |
| 1452 |
logical sscale,inmemo |
| 1453 |
integer n,m,nrz |
| 1454 |
c---- |
| 1455 |
c |
| 1456 |
c On entry: |
| 1457 |
c sscale: .true. if scalar initial scaling, |
| 1458 |
c .false. if diagonal initial scaling |
| 1459 |
c n: number of variables |
| 1460 |
c |
| 1461 |
c This routine has to return: |
| 1462 |
c m: the number of updates to form the approximate Hessien H, |
| 1463 |
c inmemo: .true., if the vectors y and s used to form H are stored |
| 1464 |
c in core memory, |
| 1465 |
c .false. otherwise (storage of y and s on disk, for |
| 1466 |
c instance). |
| 1467 |
c When inmemo=.false., the routine "ystbl", which stores and |
| 1468 |
c restores (y,s) pairs, has to be rewritten. |
| 1469 |
c |
| 1470 |
c---- |
| 1471 |
c |
| 1472 |
if (sscale) then |
| 1473 |
m=(nrz-3*n)/(2*n+1) |
| 1474 |
else |
| 1475 |
m=(nrz-4*n)/(2*n+1) |
| 1476 |
endif |
| 1477 |
inmemo=.true. |
| 1478 |
return |
| 1479 |
end |
| 1480 |
c |
| 1481 |
c--------0---------0---------0---------0---------0---------0---------0-- |
| 1482 |
c |
| 1483 |
subroutine ystbl (store,ybar,sbar,n,j) |
| 1484 |
c---- |
| 1485 |
c |
| 1486 |
c This subroutine should store (if store = .true.) or restore |
| 1487 |
c (if store = .false.) a pair (ybar,sbar) at or from position |
| 1488 |
c j in memory. Be sure to have 1 <= j <= m, where m in the number |
| 1489 |
c of updates specified by subroutine mupdts. |
| 1490 |
c |
| 1491 |
c The subroutine is used only when the (y,s) pairs are not |
| 1492 |
c stored in core memory in the arrays ybar(.,.) and sbar(.,.). |
| 1493 |
c In this case, the subroutine has to be written by the user. |
| 1494 |
c |
| 1495 |
c---- |
| 1496 |
c |
| 1497 |
implicit none |
| 1498 |
c |
| 1499 |
c arguments |
| 1500 |
c |
| 1501 |
logical store |
| 1502 |
integer n,j |
| 1503 |
double precision ybar(n),sbar(n) |
| 1504 |
c |
| 1505 |
return |
| 1506 |
end |
| 1507 |
c |
| 1508 |
c--------0---------0---------0---------0---------0---------0---------0-- |
| 1509 |
c |
| 1510 |
subroutine ctonbe (n,u,v,izs,rzs,dzs) |
| 1511 |
c |
| 1512 |
implicit none |
| 1513 |
integer n,izs(*) |
| 1514 |
real rzs(*) |
| 1515 |
double precision u(1),v(1),dzs(*) |
| 1516 |
c |
| 1517 |
integer i |
| 1518 |
c |
| 1519 |
do i=1,n |
| 1520 |
v(i)=u(i) |
| 1521 |
enddo |
| 1522 |
return |
| 1523 |
end |
| 1524 |
c |
| 1525 |
c--------0---------0---------0---------0---------0---------0---------0-- |
| 1526 |
c |
| 1527 |
subroutine ctcabe (n,u,v,izs,rzs,dzs) |
| 1528 |
c |
| 1529 |
implicit none |
| 1530 |
integer n,izs(*) |
| 1531 |
real rzs(*) |
| 1532 |
double precision u(1),v(1),dzs(*) |
| 1533 |
c |
| 1534 |
integer i |
| 1535 |
c |
| 1536 |
do i=1,n |
| 1537 |
v(i)=u(i) |
| 1538 |
enddo |
| 1539 |
return |
| 1540 |
end |
| 1541 |
c |
| 1542 |
c--------0---------0---------0---------0---------0---------0---------0-- |
| 1543 |
c |
| 1544 |
subroutine euclid (n,x,y,ps,izs,rzs,dzs) |
| 1545 |
c |
| 1546 |
implicit none |
| 1547 |
integer n,izs(*) |
| 1548 |
real rzs(*) |
| 1549 |
double precision x(n),y(n),ps,dzs(*) |
| 1550 |
c |
| 1551 |
integer i |
| 1552 |
c |
| 1553 |
ps=0.d0 |
| 1554 |
do i=1,n |
| 1555 |
ps=ps+x(i)*y(i) |
| 1556 |
enddo |
| 1557 |
return |
| 1558 |
end |
| 1559 |
c |
| 1560 |
c--------0---------0---------0---------0---------0---------0---------0-- |
| 1561 |
c |
| 1562 |
subroutine simul_rc (indic,n,x,f,g,izs,rzs,dzs) |
| 1563 |
c |
| 1564 |
implicit none |
| 1565 |
integer indic,n,izs(*) |
| 1566 |
real rzs(*) |
| 1567 |
double precision x(n),f,g(n),dzs(*) |
| 1568 |
c |
| 1569 |
return |
| 1570 |
end |
| 1571 |
c |
| 1572 |
c--------0---------0---------0---------0---------0---------0---------0-- |
| 1573 |
c |
| 1574 |
double precision function dnrmi (n,v) |
| 1575 |
c |
| 1576 |
integer n |
| 1577 |
double precision v(n) |
| 1578 |
c |
| 1579 |
c---- |
| 1580 |
c |
| 1581 |
c Commputes the infinty-norm of the vector v(n) |
| 1582 |
c |
| 1583 |
c---- |
| 1584 |
c |
| 1585 |
c --- local variables |
| 1586 |
c |
| 1587 |
integer i |
| 1588 |
double precision norm |
| 1589 |
c |
| 1590 |
c --- compute |
| 1591 |
c |
| 1592 |
norm = 0.d0 |
| 1593 |
if (n.gt.0) then |
| 1594 |
do i=1,n |
| 1595 |
norm = max(norm,abs(v(i))) |
| 1596 |
enddo |
| 1597 |
endif |
| 1598 |
dnrmi = norm |
| 1599 |
c |
| 1600 |
return |
| 1601 |
end |
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