module minimm !----------------------------------------------------------------------------- use io_units use names use math ! use MPI_data use geometry_data use energy_data use control_data use minim_data use geometry ! use csa_data ! use energy implicit none !----------------------------------------------------------------------------- ! ! !----------------------------------------------------------------------------- contains !----------------------------------------------------------------------------- ! cored.f !----------------------------------------------------------------------------- subroutine assst(iv, liv, lv, v) ! ! *** assess candidate step (***sol version 2.3) *** ! integer :: liv, l,lv integer :: iv(liv) real(kind=8) :: v(lv) ! ! *** purpose *** ! ! this subroutine is called by an unconstrained minimization ! routine to assess the next candidate step. it may recommend one ! of several courses of action, such as accepting the step, recom- ! puting it using the same or a new quadratic model, or halting due ! to convergence or false convergence. see the return code listing ! below. ! !-------------------------- parameter usage -------------------------- ! ! iv (i/o) integer parameter and scratch vector -- see description ! below of iv values referenced. ! liv (in) length of iv array. ! lv (in) length of v array. ! v (i/o) real parameter and scratch vector -- see description ! below of v values referenced. ! ! *** iv values referenced *** ! ! iv(irc) (i/o) on input for the first step tried in a new iteration, ! iv(irc) should be set to 3 or 4 (the value to which it is ! set when step is definitely to be accepted). on input ! after step has been recomputed, iv(irc) should be ! unchanged since the previous return of assst. ! on output, iv(irc) is a return code having one of the ! following values... ! 1 = switch models or try smaller step. ! 2 = switch models or accept step. ! 3 = accept step and determine v(radfac) by gradient ! tests. ! 4 = accept step, v(radfac) has been determined. ! 5 = recompute step (using the same model). ! 6 = recompute step with radius = v(lmaxs) but do not ! evaulate the objective function. ! 7 = x-convergence (see v(xctol)). ! 8 = relative function convergence (see v(rfctol)). ! 9 = both x- and relative function convergence. ! 10 = absolute function convergence (see v(afctol)). ! 11 = singular convergence (see v(lmaxs)). ! 12 = false convergence (see v(xftol)). ! 13 = iv(irc) was out of range on input. ! return code i has precdence over i+1 for i = 9, 10, 11. ! iv(mlstgd) (i/o) saved value of iv(model). ! iv(model) (i/o) on input, iv(model) should be an integer identifying ! the current quadratic model of the objective function. ! if a previous step yielded a better function reduction, ! then iv(model) will be set to iv(mlstgd) on output. ! iv(nfcall) (in) invocation count for the objective function. ! iv(nfgcal) (i/o) value of iv(nfcall) at step that gave the biggest ! function reduction this iteration. iv(nfgcal) remains ! unchanged until a function reduction is obtained. ! iv(radinc) (i/o) the number of radius increases (or minus the number ! of decreases) so far this iteration. ! iv(restor) (out) set to 1 if v(f) has been restored and x should be ! restored to its initial value, to 2 if x should be saved, ! to 3 if x should be restored from the saved value, and to ! 0 otherwise. ! iv(stage) (i/o) count of the number of models tried so far in the ! current iteration. ! iv(stglim) (in) maximum number of models to consider. ! iv(switch) (out) set to 0 unless a new model is being tried and it ! gives a smaller function value than the previous model, ! in which case assst sets iv(switch) = 1. ! iv(toobig) (in) is nonzero if step was too big (e.g. if it caused ! overflow). ! iv(xirc) (i/o) value that iv(irc) would have in the absence of ! convergence, false convergence, and oversized steps. ! ! *** v values referenced *** ! ! v(afctol) (in) absolute function convergence tolerance. if the ! absolute value of the current function value v(f) is less ! than v(afctol), then assst returns with iv(irc) = 10. ! v(decfac) (in) factor by which to decrease radius when iv(toobig) is ! nonzero. ! v(dstnrm) (in) the 2-norm of d*step. ! v(dstsav) (i/o) value of v(dstnrm) on saved step. ! v(dst0) (in) the 2-norm of d times the newton step (when defined, ! i.e., for v(nreduc) .ge. 0). ! v(f) (i/o) on both input and output, v(f) is the objective func- ! tion value at x. if x is restored to a previous value, ! then v(f) is restored to the corresponding value. ! v(fdif) (out) the function reduction v(f0) - v(f) (for the output ! value of v(f) if an earlier step gave a bigger function ! decrease, and for the input value of v(f) otherwise). ! v(flstgd) (i/o) saved value of v(f). ! v(f0) (in) objective function value at start of iteration. ! v(gtslst) (i/o) value of v(gtstep) on saved step. ! v(gtstep) (in) inner product between step and gradient. ! v(incfac) (in) minimum factor by which to increase radius. ! v(lmaxs) (in) maximum reasonable step size (and initial step bound). ! if the actual function decrease is no more than twice ! what was predicted, if a return with iv(irc) = 7, 8, 9, ! or 10 does not occur, if v(dstnrm) .gt. v(lmaxs), and if ! v(preduc) .le. v(sctol) * abs(v(f0)), then assst re- ! turns with iv(irc) = 11. if so doing appears worthwhile, ! then assst repeats this test with v(preduc) computed for ! a step of length v(lmaxs) (by a return with iv(irc) = 6). ! v(nreduc) (i/o) function reduction predicted by quadratic model for ! newton step. if assst is called with iv(irc) = 6, i.e., ! if v(preduc) has been computed with radius = v(lmaxs) for ! use in the singular convervence test, then v(nreduc) is ! set to -v(preduc) before the latter is restored. ! v(plstgd) (i/o) value of v(preduc) on saved step. ! v(preduc) (i/o) function reduction predicted by quadratic model for ! current step. ! v(radfac) (out) factor to be used in determining the new radius, ! which should be v(radfac)*dst, where dst is either the ! output value of v(dstnrm) or the 2-norm of ! diag(newd)*step for the output value of step and the ! updated version, newd, of the scale vector d. for ! iv(irc) = 3, v(radfac) = 1.0 is returned. ! v(rdfcmn) (in) minimum value for v(radfac) in terms of the input ! value of v(dstnrm) -- suggested value = 0.1. ! v(rdfcmx) (in) maximum value for v(radfac) -- suggested value = 4.0. ! v(reldx) (in) scaled relative change in x caused by step, computed ! (e.g.) by function reldst as ! max (d(i)*abs(x(i)-x0(i)), 1 .le. i .le. p) / ! max (d(i)*(abs(x(i))+abs(x0(i))), 1 .le. i .le. p). ! v(rfctol) (in) relative function convergence tolerance. if the ! actual function reduction is at most twice what was pre- ! dicted and v(nreduc) .le. v(rfctol)*abs(v(f0)), then ! assst returns with iv(irc) = 8 or 9. ! v(stppar) (in) marquardt parameter -- 0 means full newton step. ! v(tuner1) (in) tuning constant used to decide if the function ! reduction was much less than expected. suggested ! value = 0.1. ! v(tuner2) (in) tuning constant used to decide if the function ! reduction was large enough to accept step. suggested ! value = 10**-4. ! v(tuner3) (in) tuning constant used to decide if the radius ! should be increased. suggested value = 0.75. ! v(xctol) (in) x-convergence criterion. if step is a newton step ! (v(stppar) = 0) having v(reldx) .le. v(xctol) and giving ! at most twice the predicted function decrease, then ! assst returns iv(irc) = 7 or 9. ! v(xftol) (in) false convergence tolerance. if step gave no or only ! a small function decrease and v(reldx) .le. v(xftol), ! then assst returns with iv(irc) = 12. ! !------------------------------- notes ------------------------------- ! ! *** application and usage restrictions *** ! ! this routine is called as part of the nl2sol (nonlinear ! least-squares) package. it may be used in any unconstrained ! minimization solver that uses dogleg, goldfeld-quandt-trotter, ! or levenberg-marquardt steps. ! ! *** algorithm notes *** ! ! see (1) for further discussion of the assessing and model ! switching strategies. while nl2sol considers only two models, ! assst is designed to handle any number of models. ! ! *** usage notes *** ! ! on the first call of an iteration, only the i/o variables ! step, x, iv(irc), iv(model), v(f), v(dstnrm), v(gtstep), and ! v(preduc) need have been initialized. between calls, no i/o ! values execpt step, x, iv(model), v(f) and the stopping toler- ! ances should be changed. ! after a return for convergence or false convergence, one can ! change the stopping tolerances and call assst again, in which ! case the stopping tests will be repeated. ! ! *** references *** ! ! (1) dennis, j.e., jr., gay, d.m., and welsch, r.e. (1981), ! an adaptive nonlinear least-squares algorithm, ! acm trans. math. software, vol. 7, no. 3. ! ! (2) powell, m.j.d. (1970) a fortran subroutine for solving ! systems of nonlinear algebraic equations, in numerical ! methods for nonlinear algebraic equations, edited by ! p. rabinowitz, gordon and breach, london. ! ! *** history *** ! ! john dennis designed much of this routine, starting with ! ideas in (2). roy welsch suggested the model switching strategy. ! david gay and stephen peters cast this subroutine into a more ! portable form (winter 1977), and david gay cast it into its ! present form (fall 1978). ! ! *** general *** ! ! this subroutine was written in connection with research ! supported by the national science foundation under grants ! mcs-7600324, dcr75-10143, 76-14311dss, mcs76-11989, and ! mcs-7906671. ! !------------------------ external quantities ------------------------ ! ! *** no external functions and subroutines *** ! ! *** intrinsic functions *** !/+ !el real(kind=8) :: dabs, dmax1 !/ ! *** no common blocks *** ! !-------------------------- local variables -------------------------- ! logical :: goodx integer :: i, nfc real(kind=8) :: emax, emaxs, gts, rfac1, xmax !el real(kind=8) :: half, one, onep2, two, zero ! ! *** subscripts for iv and v *** ! !el integer :: afctol, decfac, dstnrm, dstsav, dst0, f, fdif, flstgd, f0,& !el gtslst, gtstep, incfac, irc, lmaxs, mlstgd, model, nfcall,& !el nfgcal, nreduc, plstgd, preduc, radfac, radinc, rdfcmn,& !el rdfcmx, reldx, restor, rfctol, sctol, stage, stglim,& !el stppar, switch, toobig, tuner1, tuner2, tuner3, xctol,& !el xftol, xirc ! ! ! *** data initializations *** ! !/6 ! data half/0.5d+0/, one/1.d+0/, onep2/1.2d+0/, two/2.d+0/, ! 1 zero/0.d+0/ !/7 real(kind=8),parameter :: half=0.5d+0, one=1.d+0, onep2=1.2d+0, two=2.d+0,& zero=0.d+0 !/ ! !/6 ! data irc/29/, mlstgd/32/, model/5/, nfcall/6/, nfgcal/7/, ! 1 radinc/8/, restor/9/, stage/10/, stglim/11/, switch/12/, ! 2 toobig/2/, xirc/13/ !/7 integer,parameter :: irc=29, mlstgd=32, model=5, nfcall=6, nfgcal=7,& radinc=8, restor=9, stage=10, stglim=11, switch=12,& toobig=2, xirc=13 !/ !/6 ! data afctol/31/, decfac/22/, dstnrm/2/, dst0/3/, dstsav/18/, ! 1 f/10/, fdif/11/, flstgd/12/, f0/13/, gtslst/14/, gtstep/4/, ! 2 incfac/23/, lmaxs/36/, nreduc/6/, plstgd/15/, preduc/7/, ! 3 radfac/16/, rdfcmn/24/, rdfcmx/25/, reldx/17/, rfctol/32/, ! 4 sctol/37/, stppar/5/, tuner1/26/, tuner2/27/, tuner3/28/, ! 5 xctol/33/, xftol/34/ !/7 integer,parameter :: afctol=31, decfac=22, dstnrm=2, dst0=3, dstsav=18,& f=10, fdif=11, flstgd=12, f0=13, gtslst=14, gtstep=4,& incfac=23, lmaxs=36, nreduc=6, plstgd=15, preduc=7,& radfac=16, rdfcmn=24, rdfcmx=25, reldx=17, rfctol=32,& sctol=37, stppar=5, tuner1=26, tuner2=27, tuner3=28,& xctol=33, xftol=34 !/ ! !+++++++++++++++++++++++++++++++ body ++++++++++++++++++++++++++++++++ ! nfc = iv(nfcall) iv(switch) = 0 iv(restor) = 0 rfac1 = one goodx = .true. i = iv(irc) if (i .ge. 1 .and. i .le. 12) & go to (20,30,10,10,40,280,220,220,220,220,220,170), i iv(irc) = 13 go to 999 ! ! *** initialize for new iteration *** ! 10 iv(stage) = 1 iv(radinc) = 0 v(flstgd) = v(f0) if (iv(toobig) .eq. 0) go to 110 iv(stage) = -1 iv(xirc) = i go to 60 ! ! *** step was recomputed with new model or smaller radius *** ! *** first decide which *** ! 20 if (iv(model) .ne. iv(mlstgd)) go to 30 ! *** old model retained, smaller radius tried *** ! *** do not consider any more new models this iteration *** iv(stage) = iv(stglim) iv(radinc) = -1 go to 110 ! ! *** a new model is being tried. decide whether to keep it. *** ! 30 iv(stage) = iv(stage) + 1 ! ! *** now we add the possibiltiy that step was recomputed with *** ! *** the same model, perhaps because of an oversized step. *** ! 40 if (iv(stage) .gt. 0) go to 50 ! ! *** step was recomputed because it was too big. *** ! if (iv(toobig) .ne. 0) go to 60 ! ! *** restore iv(stage) and pick up where we left off. *** ! iv(stage) = -iv(stage) i = iv(xirc) go to (20, 30, 110, 110, 70), i ! 50 if (iv(toobig) .eq. 0) go to 70 ! ! *** handle oversize step *** ! if (iv(radinc) .gt. 0) go to 80 iv(stage) = -iv(stage) iv(xirc) = iv(irc) ! 60 v(radfac) = v(decfac) iv(radinc) = iv(radinc) - 1 iv(irc) = 5 iv(restor) = 1 go to 999 ! 70 if (v(f) .lt. v(flstgd)) go to 110 ! ! *** the new step is a loser. restore old model. *** ! if (iv(model) .eq. iv(mlstgd)) go to 80 iv(model) = iv(mlstgd) iv(switch) = 1 ! ! *** restore step, etc. only if a previous step decreased v(f). ! 80 if (v(flstgd) .ge. v(f0)) go to 110 iv(restor) = 1 v(f) = v(flstgd) v(preduc) = v(plstgd) v(gtstep) = v(gtslst) if (iv(switch) .eq. 0) rfac1 = v(dstnrm) / v(dstsav) v(dstnrm) = v(dstsav) nfc = iv(nfgcal) goodx = .false. ! 110 v(fdif) = v(f0) - v(f) if (v(fdif) .gt. v(tuner2) * v(preduc)) go to 140 if(iv(radinc).gt.0) go to 140 ! ! *** no (or only a trivial) function decrease ! *** -- so try new model or smaller radius ! if (v(f) .lt. v(f0)) go to 120 iv(mlstgd) = iv(model) v(flstgd) = v(f) v(f) = v(f0) iv(restor) = 1 go to 130 120 iv(nfgcal) = nfc 130 iv(irc) = 1 if (iv(stage) .lt. iv(stglim)) go to 160 iv(irc) = 5 iv(radinc) = iv(radinc) - 1 go to 160 ! ! *** nontrivial function decrease achieved *** ! 140 iv(nfgcal) = nfc rfac1 = one v(dstsav) = v(dstnrm) if (v(fdif) .gt. v(preduc)*v(tuner1)) go to 190 ! ! *** decrease was much less than predicted -- either change models ! *** or accept step with decreased radius. ! if (iv(stage) .ge. iv(stglim)) go to 150 ! *** consider switching models *** iv(irc) = 2 go to 160 ! ! *** accept step with decreased radius *** ! 150 iv(irc) = 4 ! ! *** set v(radfac) to fletcher*s decrease factor *** ! 160 iv(xirc) = iv(irc) emax = v(gtstep) + v(fdif) v(radfac) = half * rfac1 if (emax .lt. v(gtstep)) v(radfac) = rfac1 * dmax1(v(rdfcmn),& half * v(gtstep)/emax) ! ! *** do false convergence test *** ! 170 if (v(reldx) .le. v(xftol)) go to 180 iv(irc) = iv(xirc) if (v(f) .lt. v(f0)) go to 200 go to 230 ! 180 iv(irc) = 12 go to 240 ! ! *** handle good function decrease *** ! 190 if (v(fdif) .lt. (-v(tuner3) * v(gtstep))) go to 210 ! ! *** increasing radius looks worthwhile. see if we just ! *** recomputed step with a decreased radius or restored step ! *** after recomputing it with a larger radius. ! if (iv(radinc) .lt. 0) go to 210 if (iv(restor) .eq. 1) go to 210 ! ! *** we did not. try a longer step unless this was a newton ! *** step. v(radfac) = v(rdfcmx) gts = v(gtstep) if (v(fdif) .lt. (half/v(radfac) - one) * gts) & v(radfac) = dmax1(v(incfac), half*gts/(gts + v(fdif))) iv(irc) = 4 if (v(stppar) .eq. zero) go to 230 if (v(dst0) .ge. zero .and. (v(dst0) .lt. two*v(dstnrm) & .or. v(nreduc) .lt. onep2*v(fdif))) go to 230 ! *** step was not a newton step. recompute it with ! *** a larger radius. iv(irc) = 5 iv(radinc) = iv(radinc) + 1 ! ! *** save values corresponding to good step *** ! 200 v(flstgd) = v(f) iv(mlstgd) = iv(model) if (iv(restor) .ne. 1) iv(restor) = 2 v(dstsav) = v(dstnrm) iv(nfgcal) = nfc v(plstgd) = v(preduc) v(gtslst) = v(gtstep) go to 230 ! ! *** accept step with radius unchanged *** ! 210 v(radfac) = one iv(irc) = 3 go to 230 ! ! *** come here for a restart after convergence *** ! 220 iv(irc) = iv(xirc) if (v(dstsav) .ge. zero) go to 240 iv(irc) = 12 go to 240 ! ! *** perform convergence tests *** ! 230 iv(xirc) = iv(irc) 240 if (iv(restor) .eq. 1 .and. v(flstgd) .lt. v(f0)) iv(restor) = 3 if (half * v(fdif) .gt. v(preduc)) go to 999 emax = v(rfctol) * dabs(v(f0)) emaxs = v(sctol) * dabs(v(f0)) if (v(dstnrm) .gt. v(lmaxs) .and. v(preduc) .le. emaxs) & iv(irc) = 11 if (v(dst0) .lt. zero) go to 250 i = 0 if ((v(nreduc) .gt. zero .and. v(nreduc) .le. emax) .or. & (v(nreduc) .eq. zero .and. v(preduc) .eq. zero)) i = 2 if (v(stppar) .eq. zero .and. v(reldx) .le. v(xctol) & .and. goodx) i = i + 1 if (i .gt. 0) iv(irc) = i + 6 ! ! *** consider recomputing step of length v(lmaxs) for singular ! *** convergence test. ! 250 if (iv(irc) .gt. 5 .and. iv(irc) .ne. 12) go to 999 if (v(dstnrm) .gt. v(lmaxs)) go to 260 if (v(preduc) .ge. emaxs) go to 999 if (v(dst0) .le. zero) go to 270 if (half * v(dst0) .le. v(lmaxs)) go to 999 go to 270 260 if (half * v(dstnrm) .le. v(lmaxs)) go to 999 xmax = v(lmaxs) / v(dstnrm) if (xmax * (two - xmax) * v(preduc) .ge. emaxs) go to 999 270 if (v(nreduc) .lt. zero) go to 290 ! ! *** recompute v(preduc) for use in singular convergence test *** ! v(gtslst) = v(gtstep) v(dstsav) = v(dstnrm) if (iv(irc) .eq. 12) v(dstsav) = -v(dstsav) v(plstgd) = v(preduc) i = iv(restor) iv(restor) = 2 if (i .eq. 3) iv(restor) = 0 iv(irc) = 6 go to 999 ! ! *** perform singular convergence test with recomputed v(preduc) *** ! 280 v(gtstep) = v(gtslst) v(dstnrm) = dabs(v(dstsav)) iv(irc) = iv(xirc) if (v(dstsav) .le. zero) iv(irc) = 12 v(nreduc) = -v(preduc) v(preduc) = v(plstgd) iv(restor) = 3 290 if (-v(nreduc) .le. v(sctol) * dabs(v(f0))) iv(irc) = 11 ! 999 return ! ! *** last card of assst follows *** end subroutine assst !----------------------------------------------------------------------------- subroutine deflt(alg, iv, liv, lv, v) ! ! *** supply ***sol (version 2.3) default values to iv and v *** ! ! *** alg = 1 means regression constants. ! *** alg = 2 means general unconstrained optimization constants. ! integer :: liv, l,lv integer :: alg, iv(liv) real(kind=8) :: v(lv) ! !el external imdcon, vdflt !el integer imdcon ! imdcon... returns machine-dependent integer constants. ! vdflt.... provides default values to v. ! integer :: miv, m integer :: miniv(2), minv(2) ! ! *** subscripts for iv *** ! !el integer algsav, covprt, covreq, dtype, hc, ierr, inith, inits, !el 1 ipivot, ivneed, lastiv, lastv, lmat, mxfcal, mxiter, !el 2 nfcov, ngcov, nvdflt, outlev, parprt, parsav, perm, !el 3 prunit, qrtyp, rdreq, rmat, solprt, statpr, vneed, !el 4 vsave, x0prt ! ! *** iv subscript values *** ! !/6 ! data algsav/51/, covprt/14/, covreq/15/, dtype/16/, hc/71/, ! 1 ierr/75/, inith/25/, inits/25/, ipivot/76/, ivneed/3/, ! 2 lastiv/44/, lastv/45/, lmat/42/, mxfcal/17/, mxiter/18/, ! 3 nfcov/52/, ngcov/53/, nvdflt/50/, outlev/19/, parprt/20/, ! 4 parsav/49/, perm/58/, prunit/21/, qrtyp/80/, rdreq/57/, ! 5 rmat/78/, solprt/22/, statpr/23/, vneed/4/, vsave/60/, ! 6 x0prt/24/ !/7 integer,parameter :: algsav=51, covprt=14, covreq=15, dtype=16, hc=71,& ierr=75, inith=25, inits=25, ipivot=76, ivneed=3,& lastiv=44, lastv=45, lmat=42, mxfcal=17, mxiter=18,& nfcov=52, ngcov=53, nvdflt=50, outlev=19, parprt=20,& parsav=49, perm=58, prunit=21, qrtyp=80, rdreq=57,& rmat=78, solprt=22, statpr=23, vneed=4, vsave=60,& x0prt=24 !/ data miniv(1)/80/, miniv(2)/59/, minv(1)/98/, minv(2)/71/ !el local variables integer :: mv ! !------------------------------- body -------------------------------- ! if (alg .lt. 1 .or. alg .gt. 2) go to 40 miv = miniv(alg) if (liv .lt. miv) go to 20 mv = minv(alg) if (lv .lt. mv) go to 30 call vdflt(alg, lv, v) iv(1) = 12 iv(algsav) = alg iv(ivneed) = 0 iv(lastiv) = miv iv(lastv) = mv iv(lmat) = mv + 1 iv(mxfcal) = 200 iv(mxiter) = 150 iv(outlev) = 1 iv(parprt) = 1 iv(perm) = miv + 1 iv(prunit) = imdcon(1) iv(solprt) = 1 iv(statpr) = 1 iv(vneed) = 0 iv(x0prt) = 1 ! if (alg .ge. 2) go to 10 ! ! *** regression values ! iv(covprt) = 3 iv(covreq) = 1 iv(dtype) = 1 iv(hc) = 0 iv(ierr) = 0 iv(inits) = 0 iv(ipivot) = 0 iv(nvdflt) = 32 iv(parsav) = 67 iv(qrtyp) = 1 iv(rdreq) = 3 iv(rmat) = 0 iv(vsave) = 58 go to 999 ! ! *** general optimization values ! 10 iv(dtype) = 0 iv(inith) = 1 iv(nfcov) = 0 iv(ngcov) = 0 iv(nvdflt) = 25 iv(parsav) = 47 go to 999 ! 20 iv(1) = 15 go to 999 ! 30 iv(1) = 16 go to 999 ! 40 iv(1) = 67 ! 999 return ! *** last card of deflt follows *** end subroutine deflt !----------------------------------------------------------------------------- real(kind=8) function dotprd(p,x,y) ! ! *** return the inner product of the p-vectors x and y. *** ! integer :: p real(kind=8) :: x(p), y(p) ! integer :: i !el real(kind=8) :: one, zero real(kind=8) :: sqteta, t !/+ !el real(kind=8) :: dmax1, dabs !/ !el external rmdcon !el real(kind=8) :: rmdcon ! ! *** rmdcon(2) returns a machine-dependent constant, sqteta, which ! *** is slightly larger than the smallest positive number that ! *** can be squared without underflowing. ! !/6 ! data one/1.d+0/, sqteta/0.d+0/, zero/0.d+0/ !/7 real(kind=8),parameter :: one=1.d+0, zero=0.d+0 data sqteta/0.d+0/ !/ ! dotprd = zero if (p .le. 0) go to 999 !rc if (sqteta .eq. zero) sqteta = rmdcon(2) do 20 i = 1, p !rc t = dmax1(dabs(x(i)), dabs(y(i))) !rc if (t .gt. one) go to 10 !rc if (t .lt. sqteta) go to 20 !rc t = (x(i)/sqteta)*y(i) !rc if (dabs(t) .lt. sqteta) go to 20 10 dotprd = dotprd + x(i)*y(i) 20 continue ! 999 return ! *** last card of dotprd follows *** end function dotprd !----------------------------------------------------------------------------- subroutine itsum(d, g, iv, liv, lv, p, v, x) ! ! *** print iteration summary for ***sol (version 2.3) *** ! ! *** parameter declarations *** ! integer :: liv, lv, p integer :: iv(liv) real(kind=8) :: d(p), g(p), v(lv), x(p) ! !+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ ! ! *** local variables *** ! integer :: alg, i, iv1, m, nf, ng, ol, pu !/6 ! real model1(6), model2(6) !/7 character(len=4) :: model1(6), model2(6) !/ real(kind=8) :: nreldf, oldf, preldf, reldf !el, zero ! ! *** intrinsic functions *** !/+ !el integer :: iabs !el real(kind=8) :: dabs, dmax1 !/ ! *** no external functions or subroutines *** ! ! *** subscripts for iv and v *** ! !el integer algsav, dstnrm, f, fdif, f0, needhd, nfcall, nfcov, ngcov, !el 1 ngcall, niter, nreduc, outlev, preduc, prntit, prunit, !el 2 reldx, solprt, statpr, stppar, sused, x0prt ! ! *** iv subscript values *** ! !/6 ! data algsav/51/, needhd/36/, nfcall/6/, nfcov/52/, ngcall/30/, ! 1 ngcov/53/, niter/31/, outlev/19/, prntit/39/, prunit/21/, ! 2 solprt/22/, statpr/23/, sused/64/, x0prt/24/ !/7 integer,parameter :: algsav=51, needhd=36, nfcall=6, nfcov=52, ngcall=30,& ngcov=53, niter=31, outlev=19, prntit=39, prunit=21,& solprt=22, statpr=23, sused=64, x0prt=24 !/ ! ! *** v subscript values *** ! !/6 ! data dstnrm/2/, f/10/, f0/13/, fdif/11/, nreduc/6/, preduc/7/, ! 1 reldx/17/, stppar/5/ !/7 integer,parameter :: dstnrm=2, f=10, f0=13, fdif=11, nreduc=6, preduc=7,& reldx=17, stppar=5 !/ ! !/6 ! data zero/0.d+0/ !/7 real(kind=8),parameter :: zero=0.d+0 !/ !/6 ! data model1(1)/4h /, model1(2)/4h /, model1(3)/4h /, ! 1 model1(4)/4h /, model1(5)/4h g /, model1(6)/4h s /, ! 2 model2(1)/4h g /, model2(2)/4h s /, model2(3)/4hg-s /, ! 3 model2(4)/4hs-g /, model2(5)/4h-s-g/, model2(6)/4h-g-s/ !/7 data model1/' ',' ',' ',' ',' g ',' s '/,& model2/' g ',' s ','g-s ','s-g ','-s-g','-g-s'/ !/ ! !------------------------------- body -------------------------------- ! pu = iv(prunit) if (pu .eq. 0) go to 999 iv1 = iv(1) if (iv1 .gt. 62) iv1 = iv1 - 51 ol = iv(outlev) alg = iv(algsav) if (iv1 .lt. 2 .or. iv1 .gt. 15) go to 370 if (iv1 .ge. 12) go to 120 if (iv1 .eq. 2 .and. iv(niter) .eq. 0) go to 390 if (ol .eq. 0) go to 120 if (iv1 .ge. 10 .and. iv(prntit) .eq. 0) go to 120 if (iv1 .gt. 2) go to 10 iv(prntit) = iv(prntit) + 1 if (iv(prntit) .lt. iabs(ol)) go to 999 10 nf = iv(nfcall) - iabs(iv(nfcov)) iv(prntit) = 0 reldf = zero preldf = zero oldf = dmax1(dabs(v(f0)), dabs(v(f))) if (oldf .le. zero) go to 20 reldf = v(fdif) / oldf preldf = v(preduc) / oldf 20 if (ol .gt. 0) go to 60 ! ! *** print short summary line *** ! if (iv(needhd) .eq. 1 .and. alg .eq. 1) write(pu,30) 30 format(/10h it nf,6x,1hf,7x,5hreldf,3x,6hpreldf,3x,5hreldx,& 2x,13hmodel stppar) if (iv(needhd) .eq. 1 .and. alg .eq. 2) write(pu,40) 40 format(/11h it nf,7x,1hf,8x,5hreldf,4x,6hpreldf,4x,5hreldx,& 3x,6hstppar) iv(needhd) = 0 if (alg .eq. 2) go to 50 m = iv(sused) write(pu,100) iv(niter), nf, v(f), reldf, preldf, v(reldx),& model1(m), model2(m), v(stppar) go to 120 ! 50 write(pu,110) iv(niter), nf, v(f), reldf, preldf, v(reldx),& v(stppar) go to 120 ! ! *** print long summary line *** ! 60 if (iv(needhd) .eq. 1 .and. alg .eq. 1) write(pu,70) 70 format(/11h it nf,6x,1hf,7x,5hreldf,3x,6hpreldf,3x,5hreldx,& 2x,13hmodel stppar,2x,6hd*step,2x,7hnpreldf) if (iv(needhd) .eq. 1 .and. alg .eq. 2) write(pu,80) 80 format(/11h it nf,7x,1hf,8x,5hreldf,4x,6hpreldf,4x,5hreldx,& 3x,6hstppar,3x,6hd*step,3x,7hnpreldf) iv(needhd) = 0 nreldf = zero if (oldf .gt. zero) nreldf = v(nreduc) / oldf if (alg .eq. 2) go to 90 m = iv(sused) write(pu,100) iv(niter), nf, v(f), reldf, preldf, v(reldx),& model1(m), model2(m), v(stppar), v(dstnrm), nreldf go to 120 ! 90 write(pu,110) iv(niter), nf, v(f), reldf, preldf,& v(reldx), v(stppar), v(dstnrm), nreldf 100 format(i6,i5,d10.3,2d9.2,d8.1,a3,a4,2d8.1,d9.2) 110 format(i6,i5,d11.3,2d10.2,3d9.1,d10.2) ! 120 if (iv(statpr) .lt. 0) go to 430 go to (999, 999, 130, 150, 170, 190, 210, 230, 250, 270, 290, 310,& 330, 350, 520), iv1 ! 130 write(pu,140) 140 format(/26h ***** x-convergence *****) go to 430 ! 150 write(pu,160) 160 format(/42h ***** relative function convergence *****) go to 430 ! 170 write(pu,180) 180 format(/49h ***** x- and relative function convergence *****) go to 430 ! 190 write(pu,200) 200 format(/42h ***** absolute function convergence *****) go to 430 ! 210 write(pu,220) 220 format(/33h ***** singular convergence *****) go to 430 ! 230 write(pu,240) 240 format(/30h ***** false convergence *****) go to 430 ! 250 write(pu,260) 260 format(/38h ***** function evaluation limit *****) go to 430 ! 270 write(pu,280) 280 format(/28h ***** iteration limit *****) go to 430 ! 290 write(pu,300) 300 format(/18h ***** stopx *****) go to 430 ! 310 write(pu,320) 320 format(/44h ***** initial f(x) cannot be computed *****) ! go to 390 ! 330 write(pu,340) 340 format(/37h ***** bad parameters to assess *****) go to 999 ! 350 write(pu,360) 360 format(/43h ***** gradient could not be computed *****) if (iv(niter) .gt. 0) go to 480 go to 390 ! 370 write(pu,380) iv(1) 380 format(/14h ***** iv(1) =,i5,6h *****) go to 999 ! ! *** initial call on itsum *** ! 390 if (iv(x0prt) .ne. 0) write(pu,400) (i, x(i), d(i), i = 1, p) 400 format(/23h i initial x(i),8x,4hd(i)//(1x,i5,d17.6,d14.3)) ! *** the following are to avoid undefined variables when the ! *** function evaluation limit is 1... v(dstnrm) = zero v(fdif) = zero v(nreduc) = zero v(preduc) = zero v(reldx) = zero if (iv1 .ge. 12) go to 999 iv(needhd) = 0 iv(prntit) = 0 if (ol .eq. 0) go to 999 if (ol .lt. 0 .and. alg .eq. 1) write(pu,30) if (ol .lt. 0 .and. alg .eq. 2) write(pu,40) if (ol .gt. 0 .and. alg .eq. 1) write(pu,70) if (ol .gt. 0 .and. alg .eq. 2) write(pu,80) if (alg .eq. 1) write(pu,410) v(f) if (alg .eq. 2) write(pu,420) v(f) 410 format(/11h 0 1,d10.3) !365 format(/11h 0 1,e11.3) 420 format(/11h 0 1,d11.3) go to 999 ! ! *** print various information requested on solution *** ! 430 iv(needhd) = 1 if (iv(statpr) .eq. 0) go to 480 oldf = dmax1(dabs(v(f0)), dabs(v(f))) preldf = zero nreldf = zero if (oldf .le. zero) go to 440 preldf = v(preduc) / oldf nreldf = v(nreduc) / oldf 440 nf = iv(nfcall) - iv(nfcov) ng = iv(ngcall) - iv(ngcov) write(pu,450) v(f), v(reldx), nf, ng, preldf, nreldf 450 format(/9h function,d17.6,8h reldx,d17.3/12h func. evals,& i8,9x,11hgrad. evals,i8/7h preldf,d16.3,6x,7hnpreldf,d15.3) ! if (iv(nfcov) .gt. 0) write(pu,460) iv(nfcov) 460 format(/1x,i4,50h extra func. evals for covariance and diagnostics.) if (iv(ngcov) .gt. 0) write(pu,470) iv(ngcov) 470 format(1x,i4,50h extra grad. evals for covariance and diagnostics.) ! 480 if (iv(solprt) .eq. 0) go to 999 iv(needhd) = 1 write(pu,490) 490 format(/22h i final x(i),8x,4hd(i),10x,4hg(i)/) do 500 i = 1, p write(pu,510) i, x(i), d(i), g(i) 500 continue 510 format(1x,i5,d16.6,2d14.3) go to 999 ! 520 write(pu,530) 530 format(/24h inconsistent dimensions) 999 return ! *** last card of itsum follows *** end subroutine itsum !----------------------------------------------------------------------------- subroutine litvmu(n, x, l, y) ! ! *** solve (l**t)*x = y, where l is an n x n lower triangular ! *** matrix stored compactly by rows. x and y may occupy the same ! *** storage. *** ! integer :: n !al real(kind=8) :: x(n), l(1), y(n) real(kind=8) :: x(n), l(n*(n+1)/2), y(n) integer :: i, ii, ij, im1, i0, j, np1 real(kind=8) :: xi !el, zero !/6 ! data zero/0.d+0/ !/7 real(kind=8),parameter :: zero=0.d+0 !/ ! do 10 i = 1, n 10 x(i) = y(i) np1 = n + 1 i0 = n*(n+1)/2 do 30 ii = 1, n i = np1 - ii xi = x(i)/l(i0) x(i) = xi if (i .le. 1) go to 999 i0 = i0 - i if (xi .eq. zero) go to 30 im1 = i - 1 do 20 j = 1, im1 ij = i0 + j x(j) = x(j) - xi*l(ij) 20 continue 30 continue 999 return ! *** last card of litvmu follows *** end subroutine litvmu !----------------------------------------------------------------------------- subroutine livmul(n, x, l, y) ! ! *** solve l*x = y, where l is an n x n lower triangular ! *** matrix stored compactly by rows. x and y may occupy the same ! *** storage. *** ! integer :: n !al real(kind=8) :: x(n), l(1), y(n) real(kind=8) :: x(n), l(n*(n+1)/2), y(n) !el external dotprd !el real(kind=8) :: dotprd integer :: i, j, k real(kind=8) :: t !el, zero !/6 ! data zero/0.d+0/ !/7 real(kind=8),parameter :: zero=0.d+0 !/ ! do 10 k = 1, n if (y(k) .ne. zero) go to 20 x(k) = zero 10 continue go to 999 20 j = k*(k+1)/2 x(k) = y(k) / l(j) if (k .ge. n) go to 999 k = k + 1 do 30 i = k, n t = dotprd(i-1, l(j+1), x) j = j + i x(i) = (y(i) - t)/l(j) 30 continue 999 return ! *** last card of livmul follows *** end subroutine livmul !----------------------------------------------------------------------------- subroutine parck(alg, d, iv, liv, lv, n, v) ! ! *** check ***sol (version 2.3) parameters, print changed values *** ! ! *** alg = 1 for regression, alg = 2 for general unconstrained opt. ! integer :: alg, liv, lv, n integer :: iv(liv) real(kind=8) :: d(n), v(lv) ! !el external rmdcon, vcopy, vdflt !el real(kind=8) :: rmdcon ! rmdcon -- returns machine-dependent constants. ! vcopy -- copies one vector to another. ! vdflt -- supplies default parameter values to v alone. !/+ !el integer :: max0 !/ ! ! *** local variables *** ! integer :: i, ii, iv1, j, k, l, m, miv1, miv2, ndfalt, parsv1, pu integer :: ijmp, jlim(2), miniv(2), ndflt(2) !/6 ! integer varnm(2), sh(2) ! real cngd(3), dflt(3), vn(2,34), which(3) !/7 character(len=1) :: varnm(2), sh(2) character(len=4) :: cngd(3), dflt(3), vn(2,34), which(3) !/ real(kind=8) :: big, machep, tiny, vk, vm(34), vx(34), zero ! ! *** iv and v subscripts *** ! !el integer algsav, dinit, dtype, dtype0, epslon, inits, ivneed, !el 1 lastiv, lastv, lmat, nextiv, nextv, nvdflt, oldn, !el 2 parprt, parsav, perm, prunit, vneed ! ! !/6 ! data algsav/51/, dinit/38/, dtype/16/, dtype0/54/, epslon/19/, ! 1 inits/25/, ivneed/3/, lastiv/44/, lastv/45/, lmat/42/, ! 2 nextiv/46/, nextv/47/, nvdflt/50/, oldn/38/, parprt/20/, ! 3 parsav/49/, perm/58/, prunit/21/, vneed/4/ !/7 integer,parameter :: algsav=51, dinit=38, dtype=16, dtype0=54, epslon=19,& inits=25, ivneed=3, lastiv=44, lastv=45, lmat=42,& nextiv=46, nextv=47, nvdflt=50, oldn=38, parprt=20,& parsav=49, perm=58, prunit=21, vneed=4 save big, machep, tiny !/ ! data big/0.d+0/, machep/-1.d+0/, tiny/1.d+0/, zero/0.d+0/ !/6 ! data vn(1,1),vn(2,1)/4hepsl,4hon../ ! data vn(1,2),vn(2,2)/4hphmn,4hfc../ ! data vn(1,3),vn(2,3)/4hphmx,4hfc../ ! data vn(1,4),vn(2,4)/4hdecf,4hac../ ! data vn(1,5),vn(2,5)/4hincf,4hac../ ! data vn(1,6),vn(2,6)/4hrdfc,4hmn../ ! data vn(1,7),vn(2,7)/4hrdfc,4hmx../ ! data vn(1,8),vn(2,8)/4htune,4hr1../ ! data vn(1,9),vn(2,9)/4htune,4hr2../ ! data vn(1,10),vn(2,10)/4htune,4hr3../ ! data vn(1,11),vn(2,11)/4htune,4hr4../ ! data vn(1,12),vn(2,12)/4htune,4hr5../ ! data vn(1,13),vn(2,13)/4hafct,4hol../ ! data vn(1,14),vn(2,14)/4hrfct,4hol../ ! data vn(1,15),vn(2,15)/4hxcto,4hl.../ ! data vn(1,16),vn(2,16)/4hxfto,4hl.../ ! data vn(1,17),vn(2,17)/4hlmax,4h0.../ ! data vn(1,18),vn(2,18)/4hlmax,4hs.../ ! data vn(1,19),vn(2,19)/4hscto,4hl.../ ! data vn(1,20),vn(2,20)/4hdini,4ht.../ ! data vn(1,21),vn(2,21)/4hdtin,4hit../ ! data vn(1,22),vn(2,22)/4hd0in,4hit../ ! data vn(1,23),vn(2,23)/4hdfac,4h..../ ! data vn(1,24),vn(2,24)/4hdltf,4hdc../ ! data vn(1,25),vn(2,25)/4hdltf,4hdj../ ! data vn(1,26),vn(2,26)/4hdelt,4ha0../ ! data vn(1,27),vn(2,27)/4hfuzz,4h..../ ! data vn(1,28),vn(2,28)/4hrlim,4hit../ ! data vn(1,29),vn(2,29)/4hcosm,4hin../ ! data vn(1,30),vn(2,30)/4hhube,4hrc../ ! data vn(1,31),vn(2,31)/4hrspt,4hol../ ! data vn(1,32),vn(2,32)/4hsigm,4hin../ ! data vn(1,33),vn(2,33)/4heta0,4h..../ ! data vn(1,34),vn(2,34)/4hbias,4h..../ !/7 data vn(1,1),vn(2,1)/'epsl','on..'/ data vn(1,2),vn(2,2)/'phmn','fc..'/ data vn(1,3),vn(2,3)/'phmx','fc..'/ data vn(1,4),vn(2,4)/'decf','ac..'/ data vn(1,5),vn(2,5)/'incf','ac..'/ data vn(1,6),vn(2,6)/'rdfc','mn..'/ data vn(1,7),vn(2,7)/'rdfc','mx..'/ data vn(1,8),vn(2,8)/'tune','r1..'/ data vn(1,9),vn(2,9)/'tune','r2..'/ data vn(1,10),vn(2,10)/'tune','r3..'/ data vn(1,11),vn(2,11)/'tune','r4..'/ data vn(1,12),vn(2,12)/'tune','r5..'/ data vn(1,13),vn(2,13)/'afct','ol..'/ data vn(1,14),vn(2,14)/'rfct','ol..'/ data vn(1,15),vn(2,15)/'xcto','l...'/ data vn(1,16),vn(2,16)/'xfto','l...'/ data vn(1,17),vn(2,17)/'lmax','0...'/ data vn(1,18),vn(2,18)/'lmax','s...'/ data vn(1,19),vn(2,19)/'scto','l...'/ data vn(1,20),vn(2,20)/'dini','t...'/ data vn(1,21),vn(2,21)/'dtin','it..'/ data vn(1,22),vn(2,22)/'d0in','it..'/ data vn(1,23),vn(2,23)/'dfac','....'/ data vn(1,24),vn(2,24)/'dltf','dc..'/ data vn(1,25),vn(2,25)/'dltf','dj..'/ data vn(1,26),vn(2,26)/'delt','a0..'/ data vn(1,27),vn(2,27)/'fuzz','....'/ data vn(1,28),vn(2,28)/'rlim','it..'/ data vn(1,29),vn(2,29)/'cosm','in..'/ data vn(1,30),vn(2,30)/'hube','rc..'/ data vn(1,31),vn(2,31)/'rspt','ol..'/ data vn(1,32),vn(2,32)/'sigm','in..'/ data vn(1,33),vn(2,33)/'eta0','....'/ data vn(1,34),vn(2,34)/'bias','....'/ !/ ! data vm(1)/1.0d-3/, vm(2)/-0.99d+0/, vm(3)/1.0d-3/, vm(4)/1.0d-2/,& vm(5)/1.2d+0/, vm(6)/1.d-2/, vm(7)/1.2d+0/, vm(8)/0.d+0/,& vm(9)/0.d+0/, vm(10)/1.d-3/, vm(11)/-1.d+0/, vm(13)/0.d+0/,& vm(15)/0.d+0/, vm(16)/0.d+0/, vm(19)/0.d+0/, vm(20)/-10.d+0/,& vm(21)/0.d+0/, vm(22)/0.d+0/, vm(23)/0.d+0/, vm(27)/1.01d+0/,& vm(28)/1.d+10/, vm(30)/0.d+0/, vm(31)/0.d+0/, vm(32)/0.d+0/,& vm(34)/0.d+0/ data vx(1)/0.9d+0/, vx(2)/-1.d-3/, vx(3)/1.d+1/, vx(4)/0.8d+0/,& vx(5)/1.d+2/, vx(6)/0.8d+0/, vx(7)/1.d+2/, vx(8)/0.5d+0/,& vx(9)/0.5d+0/, vx(10)/1.d+0/, vx(11)/1.d+0/, vx(14)/0.1d+0/,& vx(15)/1.d+0/, vx(16)/1.d+0/, vx(19)/1.d+0/, vx(23)/1.d+0/,& vx(24)/1.d+0/, vx(25)/1.d+0/, vx(26)/1.d+0/, vx(27)/1.d+10/,& vx(29)/1.d+0/, vx(31)/1.d+0/, vx(32)/1.d+0/, vx(33)/1.d+0/,& vx(34)/1.d+0/ ! !/6 ! data varnm(1)/1hp/, varnm(2)/1hn/, sh(1)/1hs/, sh(2)/1hh/ ! data cngd(1),cngd(2),cngd(3)/4h---c,4hhang,4hed v/, ! 1 dflt(1),dflt(2),dflt(3)/4hnond,4hefau,4hlt v/ !/7 data varnm(1)/'p'/, varnm(2)/'n'/, sh(1)/'s'/, sh(2)/'h'/ data cngd(1),cngd(2),cngd(3)/'---c','hang','ed v'/,& dflt(1),dflt(2),dflt(3)/'nond','efau','lt v'/ !/ data ijmp/33/, jlim(1)/0/, jlim(2)/24/, ndflt(1)/32/, ndflt(2)/25/ data miniv(1)/80/, miniv(2)/59/ ! !............................... body ................................ ! pu = 0 if (prunit .le. liv) pu = iv(prunit) if (alg .lt. 1 .or. alg .gt. 2) go to 340 if (iv(1) .eq. 0) call deflt(alg, iv, liv, lv, v) iv1 = iv(1) if (iv1 .ne. 13 .and. iv1 .ne. 12) go to 10 miv1 = miniv(alg) if (perm .le. liv) miv1 = max0(miv1, iv(perm) - 1) if (ivneed .le. liv) miv2 = miv1 + max0(iv(ivneed), 0) if (lastiv .le. liv) iv(lastiv) = miv2 if (liv .lt. miv1) go to 300 iv(ivneed) = 0 iv(lastv) = max0(iv(vneed), 0) + iv(lmat) - 1 iv(vneed) = 0 if (liv .lt. miv2) go to 300 if (lv .lt. iv(lastv)) go to 320 10 if (alg .eq. iv(algsav)) go to 30 if (pu .ne. 0) write(pu,20) alg, iv(algsav) 20 format(/39h the first parameter to deflt should be,i3,& 12h rather than,i3) iv(1) = 82 go to 999 30 if (iv1 .lt. 12 .or. iv1 .gt. 14) go to 60 if (n .ge. 1) go to 50 iv(1) = 81 if (pu .eq. 0) go to 999 write(pu,40) varnm(alg), n 40 format(/8h /// bad,a1,2h =,i5) go to 999 50 if (iv1 .ne. 14) iv(nextiv) = iv(perm) if (iv1 .ne. 14) iv(nextv) = iv(lmat) if (iv1 .eq. 13) go to 999 k = iv(parsav) - epslon call vdflt(alg, lv-k, v(k+1)) iv(dtype0) = 2 - alg iv(oldn) = n which(1) = dflt(1) which(2) = dflt(2) which(3) = dflt(3) go to 110 60 if (n .eq. iv(oldn)) go to 80 iv(1) = 17 if (pu .eq. 0) go to 999 write(pu,70) varnm(alg), iv(oldn), n 70 format(/5h /// ,1a1,14h changed from ,i5,4h to ,i5) go to 999 ! 80 if (iv1 .le. 11 .and. iv1 .ge. 1) go to 100 iv(1) = 80 if (pu .ne. 0) write(pu,90) iv1 90 format(/13h /// iv(1) =,i5,28h should be between 0 and 14.) go to 999 ! 100 which(1) = cngd(1) which(2) = cngd(2) which(3) = cngd(3) ! 110 if (iv1 .eq. 14) iv1 = 12 if (big .gt. tiny) go to 120 tiny = rmdcon(1) machep = rmdcon(3) big = rmdcon(6) vm(12) = machep vx(12) = big vx(13) = big vm(14) = machep vm(17) = tiny vx(17) = big vm(18) = tiny vx(18) = big vx(20) = big vx(21) = big vx(22) = big vm(24) = machep vm(25) = machep vm(26) = machep vx(28) = rmdcon(5) vm(29) = machep vx(30) = big vm(33) = machep 120 m = 0 i = 1 j = jlim(alg) k = epslon ndfalt = ndflt(alg) do 150 l = 1, ndfalt vk = v(k) if (vk .ge. vm(i) .and. vk .le. vx(i)) go to 140 m = k if (pu .ne. 0) write(pu,130) vn(1,i), vn(2,i), k, vk,& vm(i), vx(i) 130 format(/6h /// ,2a4,5h.. v(,i2,3h) =,d11.3,7h should,& 11h be between,d11.3,4h and,d11.3) 140 k = k + 1 i = i + 1 if (i .eq. j) i = ijmp 150 continue ! if (iv(nvdflt) .eq. ndfalt) go to 170 iv(1) = 51 if (pu .eq. 0) go to 999 write(pu,160) iv(nvdflt), ndfalt 160 format(/13h iv(nvdflt) =,i5,13h rather than ,i5) go to 999 170 if ((iv(dtype) .gt. 0 .or. v(dinit) .gt. zero) .and. iv1 .eq. 12) & go to 200 do 190 i = 1, n if (d(i) .gt. zero) go to 190 m = 18 if (pu .ne. 0) write(pu,180) i, d(i) 180 format(/8h /// d(,i3,3h) =,d11.3,19h should be positive) 190 continue 200 if (m .eq. 0) go to 210 iv(1) = m go to 999 ! 210 if (pu .eq. 0 .or. iv(parprt) .eq. 0) go to 999 if (iv1 .ne. 12 .or. iv(inits) .eq. alg-1) go to 230 m = 1 write(pu,220) sh(alg), iv(inits) 220 format(/22h nondefault values..../5h init,a1,14h..... iv(25) =,& i3) 230 if (iv(dtype) .eq. iv(dtype0)) go to 250 if (m .eq. 0) write(pu,260) which m = 1 write(pu,240) iv(dtype) 240 format(20h dtype..... iv(16) =,i3) 250 i = 1 j = jlim(alg) k = epslon l = iv(parsav) ndfalt = ndflt(alg) do 290 ii = 1, ndfalt if (v(k) .eq. v(l)) go to 280 if (m .eq. 0) write(pu,260) which 260 format(/1h ,3a4,9halues..../) m = 1 write(pu,270) vn(1,i), vn(2,i), k, v(k) 270 format(1x,2a4,5h.. v(,i2,3h) =,d15.7) 280 k = k + 1 l = l + 1 i = i + 1 if (i .eq. j) i = ijmp 290 continue ! iv(dtype0) = iv(dtype) parsv1 = iv(parsav) call vcopy(iv(nvdflt), v(parsv1), v(epslon)) go to 999 ! 300 iv(1) = 15 if (pu .eq. 0) go to 999 write(pu,310) liv, miv2 310 format(/10h /// liv =,i5,17h must be at least,i5) if (liv .lt. miv1) go to 999 if (lv .lt. iv(lastv)) go to 320 go to 999 ! 320 iv(1) = 16 if (pu .eq. 0) go to 999 write(pu,330) lv, iv(lastv) 330 format(/9h /// lv =,i5,17h must be at least,i5) go to 999 ! 340 iv(1) = 67 if (pu .eq. 0) go to 999 write(pu,350) alg 350 format(/10h /// alg =,i5,15h must be 1 or 2) ! 999 return ! *** last card of parck follows *** end subroutine parck !----------------------------------------------------------------------------- real(kind=8) function reldst(p, d, x, x0) ! ! *** compute and return relative difference between x and x0 *** ! *** nl2sol version 2.2 *** ! integer :: p real(kind=8) :: d(p), x(p), x0(p) !/+ !el real(kind=8) :: dabs !/ integer :: i real(kind=8) :: emax, t, xmax !el, zero !/6 ! data zero/0.d+0/ !/7 real(kind=8),parameter :: zero=0.d+0 !/ ! emax = zero xmax = zero do 10 i = 1, p t = dabs(d(i) * (x(i) - x0(i))) if (emax .lt. t) emax = t t = d(i) * (dabs(x(i)) + dabs(x0(i))) if (xmax .lt. t) xmax = t 10 continue reldst = zero if (xmax .gt. zero) reldst = emax / xmax 999 return ! *** last card of reldst follows *** end function reldst !----------------------------------------------------------------------------- subroutine vaxpy(p, w, a, x, y) ! ! *** set w = a*x + y -- w, x, y = p-vectors, a = scalar *** ! integer :: p real(kind=8) :: a, w(p), x(p), y(p) ! integer :: i ! do 10 i = 1, p 10 w(i) = a*x(i) + y(i) return end subroutine vaxpy !----------------------------------------------------------------------------- subroutine vcopy(p, y, x) ! ! *** set y = x, where x and y are p-vectors *** ! integer :: p real(kind=8) :: x(p), y(p) ! integer :: i ! do 10 i = 1, p 10 y(i) = x(i) return end subroutine vcopy !----------------------------------------------------------------------------- subroutine vdflt(alg, lv, v) ! ! *** supply ***sol (version 2.3) default values to v *** ! ! *** alg = 1 means regression constants. ! *** alg = 2 means general unconstrained optimization constants. ! integer :: alg, l,lv real(kind=8) :: v(lv) !/+ !el real(kind=8) :: dmax1 !/ !el external rmdcon !el real(kind=8) :: rmdcon ! rmdcon... returns machine-dependent constants ! real(kind=8) :: machep, mepcrt, sqteps !el one, three ! ! *** subscripts for v *** ! !el integer afctol, bias, cosmin, decfac, delta0, dfac, dinit, dltfdc, !el 1 dltfdj, dtinit, d0init, epslon, eta0, fuzz, huberc, !el 2 incfac, lmax0, lmaxs, phmnfc, phmxfc, rdfcmn, rdfcmx, !el 3 rfctol, rlimit, rsptol, sctol, sigmin, tuner1, tuner2, !el 4 tuner3, tuner4, tuner5, xctol, xftol ! !/6 ! data one/1.d+0/, three/3.d+0/ !/7 real(kind=8),parameter :: one=1.d+0, three=3.d+0 !/ ! ! *** v subscript values *** ! !/6 ! data afctol/31/, bias/43/, cosmin/47/, decfac/22/, delta0/44/, ! 1 dfac/41/, dinit/38/, dltfdc/42/, dltfdj/43/, dtinit/39/, ! 2 d0init/40/, epslon/19/, eta0/42/, fuzz/45/, huberc/48/, ! 3 incfac/23/, lmax0/35/, lmaxs/36/, phmnfc/20/, phmxfc/21/, ! 4 rdfcmn/24/, rdfcmx/25/, rfctol/32/, rlimit/46/, rsptol/49/, ! 5 sctol/37/, sigmin/50/, tuner1/26/, tuner2/27/, tuner3/28/, ! 6 tuner4/29/, tuner5/30/, xctol/33/, xftol/34/ !/7 integer,parameter :: afctol=31, bias=43, cosmin=47, decfac=22, delta0=44,& dfac=41, dinit=38, dltfdc=42, dltfdj=43, dtinit=39,& d0init=40, epslon=19, eta0=42, fuzz=45, huberc=48,& incfac=23, lmax0=35, lmaxs=36, phmnfc=20, phmxfc=21,& rdfcmn=24, rdfcmx=25, rfctol=32, rlimit=46, rsptol=49,& sctol=37, sigmin=50, tuner1=26, tuner2=27, tuner3=28,& tuner4=29, tuner5=30, xctol=33, xftol=34 !/ ! !------------------------------- body -------------------------------- ! machep = rmdcon(3) v(afctol) = 1.d-20 if (machep .gt. 1.d-10) v(afctol) = machep**2 v(decfac) = 0.5d+0 sqteps = rmdcon(4) v(dfac) = 0.6d+0 v(delta0) = sqteps v(dtinit) = 1.d-6 mepcrt = machep ** (one/three) v(d0init) = 1.d+0 v(epslon) = 0.1d+0 v(incfac) = 2.d+0 v(lmax0) = 1.d+0 v(lmaxs) = 1.d+0 v(phmnfc) = -0.1d+0 v(phmxfc) = 0.1d+0 v(rdfcmn) = 0.1d+0 v(rdfcmx) = 4.d+0 v(rfctol) = dmax1(1.d-10, mepcrt**2) v(sctol) = v(rfctol) v(tuner1) = 0.1d+0 v(tuner2) = 1.d-4 v(tuner3) = 0.75d+0 v(tuner4) = 0.5d+0 v(tuner5) = 0.75d+0 v(xctol) = sqteps v(xftol) = 1.d+2 * machep ! if (alg .ge. 2) go to 10 ! ! *** regression values ! v(cosmin) = dmax1(1.d-6, 1.d+2 * machep) v(dinit) = 0.d+0 v(dltfdc) = mepcrt v(dltfdj) = sqteps v(fuzz) = 1.5d+0 v(huberc) = 0.7d+0 v(rlimit) = rmdcon(5) v(rsptol) = 1.d-3 v(sigmin) = 1.d-4 go to 999 ! ! *** general optimization values ! 10 v(bias) = 0.8d+0 v(dinit) = -1.0d+0 v(eta0) = 1.0d+3 * machep ! 999 return ! *** last card of vdflt follows *** end subroutine vdflt !----------------------------------------------------------------------------- subroutine vscopy(p, y, s) ! ! *** set p-vector y to scalar s *** ! integer :: p real(kind=8) :: s, y(p) ! integer :: i ! do 10 i = 1, p 10 y(i) = s return end subroutine vscopy !----------------------------------------------------------------------------- real(kind=8) function v2norm(p, x) ! ! *** return the 2-norm of the p-vector x, taking *** ! *** care to avoid the most likely underflows. *** ! integer :: p real(kind=8) :: x(p) ! integer :: i, j real(kind=8) :: r, scale, sqteta, t, xi !el, one, zero !/+ !el real(kind=8) :: dabs, dsqrt !/ !el external rmdcon !el real(kind=8) :: rmdcon ! !/6 ! data one/1.d+0/, zero/0.d+0/ !/7 real(kind=8),parameter :: one=1.d+0, zero=0.d+0 save sqteta !/ data sqteta/0.d+0/ ! if (p .gt. 0) go to 10 v2norm = zero go to 999 10 do 20 i = 1, p if (x(i) .ne. zero) go to 30 20 continue v2norm = zero go to 999 ! 30 scale = dabs(x(i)) if (i .lt. p) go to 40 v2norm = scale go to 999 40 t = one if (sqteta .eq. zero) sqteta = rmdcon(2) ! ! *** sqteta is (slightly larger than) the square root of the ! *** smallest positive floating point number on the machine. ! *** the tests involving sqteta are done to prevent underflows. ! j = i + 1 do 60 i = j, p xi = dabs(x(i)) if (xi .gt. scale) go to 50 r = xi / scale if (r .gt. sqteta) t = t + r*r go to 60 50 r = scale / xi if (r .le. sqteta) r = zero t = one + t * r*r scale = xi 60 continue ! v2norm = scale * dsqrt(t) 999 return ! *** last card of v2norm follows *** end function v2norm !----------------------------------------------------------------------------- subroutine humsl(n,d,x,calcf,calcgh,iv,liv,lv,v,uiparm,urparm,ufparm) ! ! *** minimize general unconstrained objective function using *** ! *** (analytic) gradient and hessian provided by the caller. *** ! integer :: liv, lv, n integer :: iv(liv), uiparm(1) real(kind=8) :: d(n), x(n), v(lv), urparm(1) real(kind=8),external :: ufparm ! dimension v(78 + n*(n+12)), uiparm(*), urparm(*) external :: calcf, calcgh ! !------------------------------ discussion --------------------------- ! ! this routine is like sumsl, except that the subroutine para- ! meter calcg of sumsl (which computes the gradient of the objec- ! tive function) is replaced by the subroutine parameter calcgh, ! which computes both the gradient and (lower triangle of the) ! hessian of the objective function. the calling sequence is... ! call calcgh(n, x, nf, g, h, uiparm, urparm, ufparm) ! parameters n, x, nf, g, uiparm, urparm, and ufparm are the same ! as for sumsl, while h is an array of length n*(n+1)/2 in which ! calcgh must store the lower triangle of the hessian at x. start- ! ing at h(1), calcgh must store the hessian entries in the order ! (1,1), (2,1), (2,2), (3,1), (3,2), (3,3), ... ! the value printed (by itsum) in the column labelled stppar ! is the levenberg-marquardt used in computing the current step. ! zero means a full newton step. if the special case described in ! ref. 1 is detected, then stppar is negated. the value printed ! in the column labelled npreldf is zero if the current hessian ! is not positive definite. ! it sometimes proves worthwhile to let d be determined from the ! diagonal of the hessian matrix by setting iv(dtype) = 1 and ! v(dinit) = 0. the following iv and v components are relevant... ! ! iv(dtol)..... iv(59) gives the starting subscript in v of the dtol ! array used when d is updated. (iv(dtol) can be ! initialized by calling humsl with iv(1) = 13.) ! iv(dtype).... iv(16) tells how the scale vector d should be chosen. ! iv(dtype) .le. 0 means that d should not be updated, and ! iv(dtype) .ge. 1 means that d should be updated as ! described below with v(dfac). default = 0. ! v(dfac)..... v(41) and the dtol and d0 arrays (see v(dtinit) and ! v(d0init)) are used in updating the scale vector d when ! iv(dtype) .gt. 0. (d is initialized according to ! v(dinit), described in sumsl.) let ! d1(i) = max(sqrt(abs(h(i,i))), v(dfac)*d(i)), ! where h(i,i) is the i-th diagonal element of the current ! hessian. if iv(dtype) = 1, then d(i) is set to d1(i) ! unless d1(i) .lt. dtol(i), in which case d(i) is set to ! max(d0(i), dtol(i)). ! if iv(dtype) .ge. 2, then d is updated during the first ! iteration as for iv(dtype) = 1 (after any initialization ! due to v(dinit)) and is left unchanged thereafter. ! default = 0.6. ! v(dtinit)... v(39), if positive, is the value to which all components ! of the dtol array (see v(dfac)) are initialized. if ! v(dtinit) = 0, then it is assumed that the caller has ! stored dtol in v starting at v(iv(dtol)). ! default = 10**-6. ! v(d0init)... v(40), if positive, is the value to which all components ! of the d0 vector (see v(dfac)) are initialized. if ! v(dfac) = 0, then it is assumed that the caller has ! stored d0 in v starting at v(iv(dtol)+n). default = 1.0. ! ! *** reference *** ! ! 1. gay, d.m. (1981), computing optimal locally constrained steps, ! siam j. sci. statist. comput. 2, pp. 186-197. !. ! *** general *** ! ! coded by david m. gay (winter 1980). revised sept. 1982. ! this subroutine was written in connection with research supported ! in part by the national science foundation under grants ! mcs-7600324 and mcs-7906671. ! !---------------------------- declarations --------------------------- ! !el external deflt, humit ! ! deflt... provides default input values for iv and v. ! humit... reverse-communication routine that does humsl algorithm. ! integer :: g1, h1, iv1, lh, nf real(kind=8) :: f ! ! *** subscripts for iv *** ! !el integer g, h, nextv, nfcall, nfgcal, toobig, vneed ! !/6 ! data nextv/47/, nfcall/6/, nfgcal/7/, g/28/, h/56/, toobig/2/, ! 1 vneed/4/ !/7 integer,parameter :: nextv=47, nfcall=6, nfgcal=7, g=28, h=56,& toobig=2,vneed=4 !/ ! !+++++++++++++++++++++++++++++++ body ++++++++++++++++++++++++++++++++ ! lh = n * (n + 1) / 2 if (iv(1) .eq. 0) call deflt(2, iv, liv, lv, v) if (iv(1) .eq. 12 .or. iv(1) .eq. 13) & iv(vneed) = iv(vneed) + n*(n+3)/2 iv1 = iv(1) if (iv1 .eq. 14) go to 10 if (iv1 .gt. 2 .and. iv1 .lt. 12) go to 10 g1 = 1 h1 = 1 if (iv1 .eq. 12) iv(1) = 13 go to 20 ! 10 g1 = iv(g) h1 = iv(h) ! 20 call humit(d, f, v(g1), v(h1), iv, lh, liv, lv, n, v, x) if (iv(1) - 2) 30, 40, 50 ! 30 nf = iv(nfcall) call calcf(n, x, nf, f, uiparm, urparm, ufparm) if (nf .le. 0) iv(toobig) = 1 go to 20 ! 40 call calcgh(n, x, iv(nfgcal), v(g1), v(h1), uiparm, urparm,& ufparm) go to 20 ! 50 if (iv(1) .ne. 14) go to 999 ! ! *** storage allocation ! iv(g) = iv(nextv) iv(h) = iv(g) + n iv(nextv) = iv(h) + n*(n+1)/2 if (iv1 .ne. 13) go to 10 ! 999 return ! *** last card of humsl follows *** end subroutine humsl !----------------------------------------------------------------------------- subroutine humit(d, fx, g, h, iv, lh, liv, lv, n, v, x) ! ! *** carry out humsl (unconstrained minimization) iterations, using ! *** hessian matrix provided by the caller. ! !el use control use control, only:stopx ! *** parameter declarations *** ! integer :: lh, liv, lv, n integer :: iv(liv) real(kind=8) :: d(n), fx, g(n), h(lh), v(lv), x(n) ! !-------------------------- parameter usage -------------------------- ! ! d.... scale vector. ! fx... function value. ! g.... gradient vector. ! h.... lower triangle of the hessian, stored rowwise. ! iv... integer value array. ! lh... length of h = p*(p+1)/2. ! liv.. length of iv (at least 60). ! lv... length of v (at least 78 + n*(n+21)/2). ! n.... number of variables (components in x and g). ! v.... floating-point value array. ! x.... parameter vector. ! ! *** discussion *** ! ! parameters iv, n, v, and x are the same as the corresponding ! ones to humsl (which see), except that v can be shorter (since ! the part of v that humsl uses for storing g and h is not needed). ! moreover, compared with humsl, iv(1) may have the two additional ! output values 1 and 2, which are explained below, as is the use ! of iv(toobig) and iv(nfgcal). the value iv(g), which is an ! output value from humsl, is not referenced by humit or the ! subroutines it calls. ! ! iv(1) = 1 means the caller should set fx to f(x), the function value ! at x, and call humit again, having changed none of the ! other parameters. an exception occurs if f(x) cannot be ! computed (e.g. if overflow would occur), which may happen ! because of an oversized step. in this case the caller ! should set iv(toobig) = iv(2) to 1, which will cause ! humit to ignore fx and try a smaller step. the para- ! meter nf that humsl passes to calcf (for possible use by ! calcgh) is a copy of iv(nfcall) = iv(6). ! iv(1) = 2 means the caller should set g to g(x), the gradient of f at ! x, and h to the lower triangle of h(x), the hessian of f ! at x, and call humit again, having changed none of the ! other parameters except perhaps the scale vector d. ! the parameter nf that humsl passes to calcg is ! iv(nfgcal) = iv(7). if g(x) and h(x) cannot be evaluated, ! then the caller may set iv(nfgcal) to 0, in which case ! humit will return with iv(1) = 65. ! note -- humit overwrites h with the lower triangle ! of diag(d)**-1 * h(x) * diag(d)**-1. !. ! *** general *** ! ! coded by david m. gay (winter 1980). revised sept. 1982. ! this subroutine was written in connection with research supported ! in part by the national science foundation under grants ! mcs-7600324 and mcs-7906671. ! ! (see sumsl and humsl for references.) ! !+++++++++++++++++++++++++++ declarations ++++++++++++++++++++++++++++ ! ! *** local variables *** ! integer :: dg1, dummy, i, j, k, l, lstgst, nn1o2, step1,& temp1, w1, x01 real(kind=8) :: t ! ! *** constants *** ! !el real(kind=8) :: one, onep2, zero ! ! *** no intrinsic functions *** ! ! *** external functions and subroutines *** ! !el external assst, deflt, dotprd, dupdu, gqtst, itsum, parck, !el 1 reldst, slvmul, stopx, vaxpy, vcopy, vscopy, v2norm !el logical stopx !el real(kind=8) :: dotprd, reldst, v2norm ! ! assst.... assesses candidate step. ! deflt.... provides default iv and v input values. ! dotprd... returns inner product of two vectors. ! dupdu.... updates scale vector d. ! gqtst.... computes optimally locally constrained step. ! itsum.... prints iteration summary and info on initial and final x. ! parck.... checks validity of input iv and v values. ! reldst... computes v(reldx) = relative step size. ! slvmul... multiplies symmetric matrix times vector, given the lower ! triangle of the matrix. ! stopx.... returns .true. if the break key has been pressed. ! vaxpy.... computes scalar times one vector plus another. ! vcopy.... copies one vector to another. ! vscopy... sets all elements of a vector to a scalar. ! v2norm... returns the 2-norm of a vector. ! ! *** subscripts for iv and v *** ! !el integer cnvcod, dg, dgnorm, dinit, dstnrm, dtinit, dtol, !el 1 dtype, d0init, f, f0, fdif, gtstep, incfac, irc, kagqt, !el 2 lmat, lmax0, lmaxs, mode, model, mxfcal, mxiter, nextv, !el 3 nfcall, nfgcal, ngcall, niter, preduc, radfac, radinc, !el 4 radius, rad0, reldx, restor, step, stglim, stlstg, stppar, !el 5 toobig, tuner4, tuner5, vneed, w, xirc, x0 ! ! *** iv subscript values *** ! !/6 ! data cnvcod/55/, dg/37/, dtol/59/, dtype/16/, irc/29/, kagqt/33/, ! 1 lmat/42/, mode/35/, model/5/, mxfcal/17/, mxiter/18/, ! 2 nextv/47/, nfcall/6/, nfgcal/7/, ngcall/30/, niter/31/, ! 3 radinc/8/, restor/9/, step/40/, stglim/11/, stlstg/41/, ! 4 toobig/2/, vneed/4/, w/34/, xirc/13/, x0/43/ !/7 integer,parameter :: cnvcod=55, dg=37, dtol=59, dtype=16, irc=29, kagqt=33,& lmat=42, mode=35, model=5, mxfcal=17, mxiter=18,& nextv=47, nfcall=6, nfgcal=7, ngcall=30, niter=31,& radinc=8, restor=9, step=40, stglim=11, stlstg=41,& toobig=2, vneed=4, w=34, xirc=13, x0=43 !/ ! ! *** v subscript values *** ! !/6 ! data dgnorm/1/, dinit/38/, dstnrm/2/, dtinit/39/, d0init/40/, ! 1 f/10/, f0/13/, fdif/11/, gtstep/4/, incfac/23/, lmax0/35/, ! 2 lmaxs/36/, preduc/7/, radfac/16/, radius/8/, rad0/9/, ! 3 reldx/17/, stppar/5/, tuner4/29/, tuner5/30/ !/7 integer,parameter :: dgnorm=1, dinit=38, dstnrm=2, dtinit=39, d0init=40,& f=10, f0=13, fdif=11, gtstep=4, incfac=23, lmax0=35,& lmaxs=36, preduc=7, radfac=16, radius=8, rad0=9,& reldx=17, stppar=5, tuner4=29, tuner5=30 !/ ! !/6 ! data one/1.d+0/, onep2/1.2d+0/, zero/0.d+0/ !/7 real(kind=8),parameter :: one=1.d+0, onep2=1.2d+0, zero=0.d+0 !/ ! !+++++++++++++++++++++++++++++++ body ++++++++++++++++++++++++++++++++ ! i = iv(1) if (i .eq. 1) go to 30 if (i .eq. 2) go to 40 ! ! *** check validity of iv and v input values *** ! if (iv(1) .eq. 0) call deflt(2, iv, liv, lv, v) if (iv(1) .eq. 12 .or. iv(1) .eq. 13) & iv(vneed) = iv(vneed) + n*(n+21)/2 + 7 call parck(2, d, iv, liv, lv, n, v) i = iv(1) - 2 if (i .gt. 12) go to 999 nn1o2 = n * (n + 1) / 2 if (lh .ge. nn1o2) go to (210,210,210,210,210,210,160,120,160,& 10,10,20), i iv(1) = 66 go to 350 ! ! *** storage allocation *** ! 10 iv(dtol) = iv(lmat) + nn1o2 iv(x0) = iv(dtol) + 2*n iv(step) = iv(x0) + n iv(stlstg) = iv(step) + n iv(dg) = iv(stlstg) + n iv(w) = iv(dg) + n iv(nextv) = iv(w) + 4*n + 7 if (iv(1) .ne. 13) go to 20 iv(1) = 14 go to 999 ! ! *** initialization *** ! 20 iv(niter) = 0 iv(nfcall) = 1 iv(ngcall) = 1 iv(nfgcal) = 1 iv(mode) = -1 iv(model) = 1 iv(stglim) = 1 iv(toobig) = 0 iv(cnvcod) = 0 iv(radinc) = 0 v(rad0) = zero v(stppar) = zero if (v(dinit) .ge. zero) call vscopy(n, d, v(dinit)) k = iv(dtol) if (v(dtinit) .gt. zero) call vscopy(n, v(k), v(dtinit)) k = k + n if (v(d0init) .gt. zero) call vscopy(n, v(k), v(d0init)) iv(1) = 1 go to 999 ! 30 v(f) = fx if (iv(mode) .ge. 0) go to 210 iv(1) = 2 if (iv(toobig) .eq. 0) go to 999 iv(1) = 63 go to 350 ! ! *** make sure gradient could be computed *** ! 40 if (iv(nfgcal) .ne. 0) go to 50 iv(1) = 65 go to 350 ! ! *** update the scale vector d *** ! 50 dg1 = iv(dg) if (iv(dtype) .le. 0) go to 70 k = dg1 j = 0 do 60 i = 1, n j = j + i v(k) = h(j) k = k + 1 60 continue call dupdu(d, v(dg1), iv, liv, lv, n, v) ! ! *** compute scaled gradient and its norm *** ! 70 dg1 = iv(dg) k = dg1 do 80 i = 1, n v(k) = g(i) / d(i) k = k + 1 80 continue v(dgnorm) = v2norm(n, v(dg1)) ! ! *** compute scaled hessian *** ! k = 1 do 100 i = 1, n t = one / d(i) do 90 j = 1, i h(k) = t * h(k) / d(j) k = k + 1 90 continue 100 continue ! if (iv(cnvcod) .ne. 0) go to 340 if (iv(mode) .eq. 0) go to 300 ! ! *** allow first step to have scaled 2-norm at most v(lmax0) *** ! v(radius) = v(lmax0) ! iv(mode) = 0 ! ! !----------------------------- main loop ----------------------------- ! ! ! *** print iteration summary, check iteration limit *** ! 110 call itsum(d, g, iv, liv, lv, n, v, x) 120 k = iv(niter) if (k .lt. iv(mxiter)) go to 130 iv(1) = 10 go to 350 ! 130 iv(niter) = k + 1 ! ! *** initialize for start of next iteration *** ! dg1 = iv(dg) x01 = iv(x0) v(f0) = v(f) iv(irc) = 4 iv(kagqt) = -1 ! ! *** copy x to x0 *** ! call vcopy(n, v(x01), x) ! ! *** update radius *** ! if (k .eq. 0) go to 150 step1 = iv(step) k = step1 do 140 i = 1, n v(k) = d(i) * v(k) k = k + 1 140 continue v(radius) = v(radfac) * v2norm(n, v(step1)) ! ! *** check stopx and function evaluation limit *** ! ! AL 4/30/95 dummy=iv(nfcall) 150 if (.not. stopx(dummy)) go to 170 iv(1) = 11 go to 180 ! ! *** come here when restarting after func. eval. limit or stopx. ! 160 if (v(f) .ge. v(f0)) go to 170 v(radfac) = one k = iv(niter) go to 130 ! 170 if (iv(nfcall) .lt. iv(mxfcal)) go to 190 iv(1) = 9 180 if (v(f) .ge. v(f0)) go to 350 ! ! *** in case of stopx or function evaluation limit with ! *** improved v(f), evaluate the gradient at x. ! iv(cnvcod) = iv(1) go to 290 ! !. . . . . . . . . . . . . compute candidate step . . . . . . . . . . ! 190 step1 = iv(step) dg1 = iv(dg) l = iv(lmat) w1 = iv(w) call gqtst(d, v(dg1), h, iv(kagqt), v(l), n, v(step1), v, v(w1)) if (iv(irc) .eq. 6) go to 210 ! ! *** check whether evaluating f(x0 + step) looks worthwhile *** ! if (v(dstnrm) .le. zero) go to 210 if (iv(irc) .ne. 5) go to 200 if (v(radfac) .le. one) go to 200 if (v(preduc) .le. onep2 * v(fdif)) go to 210 ! ! *** compute f(x0 + step) *** ! 200 x01 = iv(x0) step1 = iv(step) call vaxpy(n, x, one, v(step1), v(x01)) iv(nfcall) = iv(nfcall) + 1 iv(1) = 1 iv(toobig) = 0 go to 999 ! !. . . . . . . . . . . . . assess candidate step . . . . . . . . . . . ! 210 x01 = iv(x0) v(reldx) = reldst(n, d, x, v(x01)) call assst(iv, liv, lv, v) step1 = iv(step) lstgst = iv(stlstg) if (iv(restor) .eq. 1) call vcopy(n, x, v(x01)) if (iv(restor) .eq. 2) call vcopy(n, v(lstgst), v(step1)) if (iv(restor) .ne. 3) go to 220 call vcopy(n, v(step1), v(lstgst)) call vaxpy(n, x, one, v(step1), v(x01)) v(reldx) = reldst(n, d, x, v(x01)) ! 220 k = iv(irc) go to (230,260,260,260,230,240,250,250,250,250,250,250,330,300), k ! ! *** recompute step with new radius *** ! 230 v(radius) = v(radfac) * v(dstnrm) go to 150 ! ! *** compute step of length v(lmaxs) for singular convergence test. ! 240 v(radius) = v(lmaxs) go to 190 ! ! *** convergence or false convergence *** ! 250 iv(cnvcod) = k - 4 if (v(f) .ge. v(f0)) go to 340 if (iv(xirc) .eq. 14) go to 340 iv(xirc) = 14 ! !. . . . . . . . . . . . process acceptable step . . . . . . . . . . . ! 260 if (iv(irc) .ne. 3) go to 290 temp1 = lstgst ! ! *** prepare for gradient tests *** ! *** set temp1 = hessian * step + g(x0) ! *** = diag(d) * (h * step + g(x0)) ! ! use x0 vector as temporary. k = x01 do 270 i = 1, n v(k) = d(i) * v(step1) k = k + 1 step1 = step1 + 1 270 continue call slvmul(n, v(temp1), h, v(x01)) do 280 i = 1, n v(temp1) = d(i) * v(temp1) + g(i) temp1 = temp1 + 1 280 continue ! ! *** compute gradient and hessian *** ! 290 iv(ngcall) = iv(ngcall) + 1 iv(1) = 2 go to 999 ! 300 iv(1) = 2 if (iv(irc) .ne. 3) go to 110 ! ! *** set v(radfac) by gradient tests *** ! temp1 = iv(stlstg) step1 = iv(step) ! ! *** set temp1 = diag(d)**-1 * (hessian*step + (g(x0)-g(x))) *** ! k = temp1 do 310 i = 1, n v(k) = (v(k) - g(i)) / d(i) k = k + 1 310 continue ! ! *** do gradient tests *** ! if (v2norm(n, v(temp1)) .le. v(dgnorm) * v(tuner4)) go to 320 if (dotprd(n, g, v(step1)) & .ge. v(gtstep) * v(tuner5)) go to 110 320 v(radfac) = v(incfac) go to 110 ! !. . . . . . . . . . . . . . misc. details . . . . . . . . . . . . . . ! ! *** bad parameters to assess *** ! 330 iv(1) = 64 go to 350 ! ! *** print summary of final iteration and other requested items *** ! 340 iv(1) = iv(cnvcod) iv(cnvcod) = 0 350 call itsum(d, g, iv, liv, lv, n, v, x) ! 999 return ! ! *** last card of humit follows *** end subroutine humit !----------------------------------------------------------------------------- subroutine dupdu(d, hdiag, iv, liv, lv, n, v) ! ! *** update scale vector d for humsl *** ! ! *** parameter declarations *** ! integer :: liv, lv, n integer :: iv(liv) real(kind=8) :: d(n), hdiag(n), v(lv) ! ! *** local variables *** ! integer :: dtoli, d0i, i real(kind=8) :: t, vdfac ! ! *** intrinsic functions *** !/+ !el real(kind=8) :: dabs, dmax1, dsqrt !/ ! *** subscripts for iv and v *** ! !el integer :: dfac, dtol, dtype, niter !/6 ! data dfac/41/, dtol/59/, dtype/16/, niter/31/ !/7 integer,parameter :: dfac=41, dtol=59, dtype=16, niter=31 !/ ! !------------------------------- body -------------------------------- ! i = iv(dtype) if (i .eq. 1) go to 10 if (iv(niter) .gt. 0) go to 999 ! 10 dtoli = iv(dtol) d0i = dtoli + n vdfac = v(dfac) do 20 i = 1, n t = dmax1(dsqrt(dabs(hdiag(i))), vdfac*d(i)) if (t .lt. v(dtoli)) t = dmax1(v(dtoli), v(d0i)) d(i) = t dtoli = dtoli + 1 d0i = d0i + 1 20 continue ! 999 return ! *** last card of dupdu follows *** end subroutine dupdu !----------------------------------------------------------------------------- subroutine gqtst(d, dig, dihdi, ka, l, p, step, v, w) ! ! *** compute goldfeld-quandt-trotter step by more-hebden technique *** ! *** (nl2sol version 2.2), modified a la more and sorensen *** ! ! *** parameter declarations *** ! integer :: ka, p !al real(kind=8) :: d(p), dig(p), dihdi(1), l(1), v(21), step(p), !al 1 w(1) real(kind=8) :: d(p), dig(p), dihdi(p*(p+1)/2), l(p*(p+1)/2),& v(21), step(p),w(4*p+7) ! dimension dihdi(p*(p+1)/2), l(p*(p+1)/2), w(4*p+7) ! !+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ ! ! *** purpose *** ! ! given the (compactly stored) lower triangle of a scaled ! hessian (approximation) and a nonzero scaled gradient vector, ! this subroutine computes a goldfeld-quandt-trotter step of ! approximate length v(radius) by the more-hebden technique. in ! other words, step is computed to (approximately) minimize ! psi(step) = (g**t)*step + 0.5*(step**t)*h*step such that the ! 2-norm of d*step is at most (approximately) v(radius), where ! g is the gradient, h is the hessian, and d is a diagonal ! scale matrix whose diagonal is stored in the parameter d. ! (gqtst assumes dig = d**-1 * g and dihdi = d**-1 * h * d**-1.) ! ! *** parameter description *** ! ! d (in) = the scale vector, i.e. the diagonal of the scale ! matrix d mentioned above under purpose. ! dig (in) = the scaled gradient vector, d**-1 * g. if g = 0, then ! step = 0 and v(stppar) = 0 are returned. ! dihdi (in) = lower triangle of the scaled hessian (approximation), ! i.e., d**-1 * h * d**-1, stored compactly by rows., i.e., ! in the order (1,1), (2,1), (2,2), (3,1), (3,2), etc. ! ka (i/o) = the number of hebden iterations (so far) taken to deter- ! mine step. ka .lt. 0 on input means this is the first ! attempt to determine step (for the present dig and dihdi) ! -- ka is initialized to 0 in this case. output with ! ka = 0 (or v(stppar) = 0) means step = -(h**-1)*g. ! l (i/o) = workspace of length p*(p+1)/2 for cholesky factors. ! p (in) = number of parameters -- the hessian is a p x p matrix. ! step (i/o) = the step computed. ! v (i/o) contains various constants and variables described below. ! w (i/o) = workspace of length 4*p + 6. ! ! *** entries in v *** ! ! v(dgnorm) (i/o) = 2-norm of (d**-1)*g. ! v(dstnrm) (output) = 2-norm of d*step. ! v(dst0) (i/o) = 2-norm of d*(h**-1)*g (for pos. def. h only), or ! overestimate of smallest eigenvalue of (d**-1)*h*(d**-1). ! v(epslon) (in) = max. rel. error allowed for psi(step). for the ! step returned, psi(step) will exceed its optimal value ! by less than -v(epslon)*psi(step). suggested value = 0.1. ! v(gtstep) (out) = inner product between g and step. ! v(nreduc) (out) = psi(-(h**-1)*g) = psi(newton step) (for pos. def. ! h only -- v(nreduc) is set to zero otherwise). ! v(phmnfc) (in) = tol. (together with v(phmxfc)) for accepting step ! (more*s sigma). the error v(dstnrm) - v(radius) must lie ! between v(phmnfc)*v(radius) and v(phmxfc)*v(radius). ! v(phmxfc) (in) (see v(phmnfc).) ! suggested values -- v(phmnfc) = -0.25, v(phmxfc) = 0.5. ! v(preduc) (out) = psi(step) = predicted obj. func. reduction for step. ! v(radius) (in) = radius of current (scaled) trust region. ! v(rad0) (i/o) = value of v(radius) from previous call. ! v(stppar) (i/o) is normally the marquardt parameter, i.e. the alpha ! described below under algorithm notes. if h + alpha*d**2 ! (see algorithm notes) is (nearly) singular, however, ! then v(stppar) = -alpha. ! ! *** usage notes *** ! ! if it is desired to recompute step using a different value of ! v(radius), then this routine may be restarted by calling it ! with all parameters unchanged except v(radius). (this explains ! why step and w are listed as i/o). on an initial call (one with ! ka .lt. 0), step and w need not be initialized and only compo- ! nents v(epslon), v(stppar), v(phmnfc), v(phmxfc), v(radius), and ! v(rad0) of v must be initialized. ! ! *** algorithm notes *** ! ! the desired g-q-t step (ref. 2, 3, 4, 6) satisfies ! (h + alpha*d**2)*step = -g for some nonnegative alpha such that ! h + alpha*d**2 is positive semidefinite. alpha and step are ! computed by a scheme analogous to the one described in ref. 5. ! estimates of the smallest and largest eigenvalues of the hessian ! are obtained from the gerschgorin circle theorem enhanced by a ! simple form of the scaling described in ref. 7. cases in which ! h + alpha*d**2 is nearly (or exactly) singular are handled by ! the technique discussed in ref. 2. in these cases, a step of ! (exact) length v(radius) is returned for which psi(step) exceeds ! its optimal value by less than -v(epslon)*psi(step). the test ! suggested in ref. 6 for detecting the special case is performed ! once two matrix factorizations have been done -- doing so sooner ! seems to degrade the performance of optimization routines that ! call this routine. ! ! *** functions and subroutines called *** ! ! dotprd - returns inner product of two vectors. ! litvmu - applies inverse-transpose of compact lower triang. matrix. ! livmul - applies inverse of compact lower triang. matrix. ! lsqrt - finds cholesky factor (of compactly stored lower triang.). ! lsvmin - returns approx. to min. sing. value of lower triang. matrix. ! rmdcon - returns machine-dependent constants. ! v2norm - returns 2-norm of a vector. ! ! *** references *** ! ! 1. dennis, j.e., gay, d.m., and welsch, r.e. (1981), an adaptive ! nonlinear least-squares algorithm, acm trans. math. ! software, vol. 7, no. 3. ! 2. gay, d.m. (1981), computing optimal locally constrained steps, ! siam j. sci. statist. computing, vol. 2, no. 2, pp. ! 186-197. ! 3. goldfeld, s.m., quandt, r.e., and trotter, h.f. (1966), ! maximization by quadratic hill-climbing, econometrica 34, ! pp. 541-551. ! 4. hebden, m.d. (1973), an algorithm for minimization using exact ! second derivatives, report t.p. 515, theoretical physics ! div., a.e.r.e. harwell, oxon., england. ! 5. more, j.j. (1978), the levenberg-marquardt algorithm, implemen- ! tation and theory, pp.105-116 of springer lecture notes ! in mathematics no. 630, edited by g.a. watson, springer- ! verlag, berlin and new york. ! 6. more, j.j., and sorensen, d.c. (1981), computing a trust region ! step, technical report anl-81-83, argonne national lab. ! 7. varga, r.s. (1965), minimal gerschgorin sets, pacific j. math. 15, ! pp. 719-729. ! ! *** general *** ! ! coded by david m. gay. ! this subroutine was written in connection with research ! supported by the national science foundation under grants ! mcs-7600324, dcr75-10143, 76-14311dss, mcs76-11989, and ! mcs-7906671. ! !+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ ! ! *** local variables *** ! logical :: restrt integer :: dggdmx, diag, diag0, dstsav, emax, emin, i, im1, inc, irc,& j, k, kalim, kamin, k1, lk0, phipin, q, q0, uk0, x real(kind=8) :: alphak, aki, akk, delta, dst, eps, gtsta, lk,& oldphi, phi, phimax, phimin, psifac, rad, radsq,& root, si, sk, sw, t, twopsi, t1, t2, uk, wi ! ! *** constants *** real(kind=8) :: big, dgxfac !el, epsfac, four, half, kappa, negone, !el 1 one, p001, six, three, two, zero ! ! *** intrinsic functions *** !/+ !el real(kind=8) :: dabs, dmax1, dmin1, dsqrt !/ ! *** external functions and subroutines *** ! !el external dotprd, litvmu, livmul, lsqrt, lsvmin, rmdcon, v2norm !el real(kind=8) :: dotprd, lsvmin, rmdcon, v2norm ! ! *** subscripts for v *** ! !el integer dgnorm, dstnrm, dst0, epslon, gtstep, stppar, nreduc, !el 1 phmnfc, phmxfc, preduc, radius, rad0 !/6 ! data dgnorm/1/, dstnrm/2/, dst0/3/, epslon/19/, gtstep/4/, ! 1 nreduc/6/, phmnfc/20/, phmxfc/21/, preduc/7/, radius/8/, ! 2 rad0/9/, stppar/5/ !/7 integer,parameter :: dgnorm=1, dstnrm=2, dst0=3, epslon=19, gtstep=4,& nreduc=6, phmnfc=20, phmxfc=21, preduc=7, radius=8,& rad0=9, stppar=5 !/ ! !/6 ! data epsfac/50.0d+0/, four/4.0d+0/, half/0.5d+0/, ! 1 kappa/2.0d+0/, negone/-1.0d+0/, one/1.0d+0/, p001/1.0d-3/, ! 2 six/6.0d+0/, three/3.0d+0/, two/2.0d+0/, zero/0.0d+0/ !/7 real(kind=8), parameter :: epsfac=50.0d+0, four=4.0d+0, half=0.5d+0,& kappa=2.0d+0, negone=-1.0d+0, one=1.0d+0, p001=1.0d-3,& six=6.0d+0, three=3.0d+0, two=2.0d+0, zero=0.0d+0 save dgxfac !/ data big/0.d+0/, dgxfac/0.d+0/ ! ! *** body *** ! ! *** store largest abs. entry in (d**-1)*h*(d**-1) at w(dggdmx). dggdmx = p + 1 ! *** store gerschgorin over- and underestimates of the largest ! *** and smallest eigenvalues of (d**-1)*h*(d**-1) at w(emax) ! *** and w(emin) respectively. emax = dggdmx + 1 emin = emax + 1 ! *** for use in recomputing step, the final values of lk, uk, dst, ! *** and the inverse derivative of more*s phi at 0 (for pos. def. ! *** h) are stored in w(lk0), w(uk0), w(dstsav), and w(phipin) ! *** respectively. lk0 = emin + 1 phipin = lk0 + 1 uk0 = phipin + 1 dstsav = uk0 + 1 ! *** store diag of (d**-1)*h*(d**-1) in w(diag),...,w(diag0+p). diag0 = dstsav diag = diag0 + 1 ! *** store -d*step in w(q),...,w(q0+p). q0 = diag0 + p q = q0 + 1 ! *** allocate storage for scratch vector x *** x = q + p rad = v(radius) radsq = rad**2 ! *** phitol = max. error allowed in dst = v(dstnrm) = 2-norm of ! *** d*step. phimax = v(phmxfc) * rad phimin = v(phmnfc) * rad psifac = two * v(epslon) / (three * (four * (v(phmnfc) + one) * & (kappa + one) + kappa + two) * rad**2) ! *** oldphi is used to detect limits of numerical accuracy. if ! *** we recompute step and it does not change, then we accept it. oldphi = zero eps = v(epslon) irc = 0 restrt = .false. kalim = ka + 50 ! ! *** start or restart, depending on ka *** ! if (ka .ge. 0) go to 290 ! ! *** fresh start *** ! k = 0 uk = negone ka = 0 kalim = 50 v(dgnorm) = v2norm(p, dig) v(nreduc) = zero v(dst0) = zero kamin = 3 if (v(dgnorm) .eq. zero) kamin = 0 ! ! *** store diag(dihdi) in w(diag0+1),...,w(diag0+p) *** ! j = 0 do 10 i = 1, p j = j + i k1 = diag0 + i w(k1) = dihdi(j) 10 continue ! ! *** determine w(dggdmx), the largest element of dihdi *** ! t1 = zero j = p * (p + 1) / 2 do 20 i = 1, j t = dabs(dihdi(i)) if (t1 .lt. t) t1 = t 20 continue w(dggdmx) = t1 ! ! *** try alpha = 0 *** ! 30 call lsqrt(1, p, l, dihdi, irc) if (irc .eq. 0) go to 50 ! *** indef. h -- underestimate smallest eigenvalue, use this ! *** estimate to initialize lower bound lk on alpha. j = irc*(irc+1)/2 t = l(j) l(j) = one do 40 i = 1, irc 40 w(i) = zero w(irc) = one call litvmu(irc, w, l, w) t1 = v2norm(irc, w) lk = -t / t1 / t1 v(dst0) = -lk if (restrt) go to 210 go to 70 ! ! *** positive definite h -- compute unmodified newton step. *** 50 lk = zero t = lsvmin(p, l, w(q), w(q)) if (t .ge. one) go to 60 if (big .le. zero) big = rmdcon(6) if (v(dgnorm) .ge. t*t*big) go to 70 60 call livmul(p, w(q), l, dig) gtsta = dotprd(p, w(q), w(q)) v(nreduc) = half * gtsta call litvmu(p, w(q), l, w(q)) dst = v2norm(p, w(q)) v(dst0) = dst phi = dst - rad if (phi .le. phimax) go to 260 if (restrt) go to 210 ! ! *** prepare to compute gerschgorin estimates of largest (and ! *** smallest) eigenvalues. *** ! 70 k = 0 do 100 i = 1, p wi = zero if (i .eq. 1) go to 90 im1 = i - 1 do 80 j = 1, im1 k = k + 1 t = dabs(dihdi(k)) wi = wi + t w(j) = w(j) + t 80 continue 90 w(i) = wi k = k + 1 100 continue ! ! *** (under-)estimate smallest eigenvalue of (d**-1)*h*(d**-1) *** ! k = 1 t1 = w(diag) - w(1) if (p .le. 1) go to 120 do 110 i = 2, p j = diag0 + i t = w(j) - w(i) if (t .ge. t1) go to 110 t1 = t k = i 110 continue ! 120 sk = w(k) j = diag0 + k akk = w(j) k1 = k*(k-1)/2 + 1 inc = 1 t = zero do 150 i = 1, p if (i .eq. k) go to 130 aki = dabs(dihdi(k1)) si = w(i) j = diag0 + i t1 = half * (akk - w(j) + si - aki) t1 = t1 + dsqrt(t1*t1 + sk*aki) if (t .lt. t1) t = t1 if (i .lt. k) go to 140 130 inc = i 140 k1 = k1 + inc 150 continue ! w(emin) = akk - t uk = v(dgnorm)/rad - w(emin) if (v(dgnorm) .eq. zero) uk = uk + p001 + p001*uk if (uk .le. zero) uk = p001 ! ! *** compute gerschgorin (over-)estimate of largest eigenvalue *** ! k = 1 t1 = w(diag) + w(1) if (p .le. 1) go to 170 do 160 i = 2, p j = diag0 + i t = w(j) + w(i) if (t .le. t1) go to 160 t1 = t k = i 160 continue ! 170 sk = w(k) j = diag0 + k akk = w(j) k1 = k*(k-1)/2 + 1 inc = 1 t = zero do 200 i = 1, p if (i .eq. k) go to 180 aki = dabs(dihdi(k1)) si = w(i) j = diag0 + i t1 = half * (w(j) + si - aki - akk) t1 = t1 + dsqrt(t1*t1 + sk*aki) if (t .lt. t1) t = t1 if (i .lt. k) go to 190 180 inc = i 190 k1 = k1 + inc 200 continue ! w(emax) = akk + t lk = dmax1(lk, v(dgnorm)/rad - w(emax)) ! ! *** alphak = current value of alpha (see alg. notes above). we ! *** use more*s scheme for initializing it. alphak = dabs(v(stppar)) * v(rad0)/rad ! if (irc .ne. 0) go to 210 ! ! *** compute l0 for positive definite h *** ! call livmul(p, w, l, w(q)) t = v2norm(p, w) w(phipin) = dst / t / t lk = dmax1(lk, phi*w(phipin)) ! ! *** safeguard alphak and add alphak*i to (d**-1)*h*(d**-1) *** ! 210 ka = ka + 1 if (-v(dst0) .ge. alphak .or. alphak .lt. lk .or. alphak .ge. uk) & alphak = uk * dmax1(p001, dsqrt(lk/uk)) if (alphak .le. zero) alphak = half * uk if (alphak .le. zero) alphak = uk k = 0 do 220 i = 1, p k = k + i j = diag0 + i dihdi(k) = w(j) + alphak 220 continue ! ! *** try computing cholesky decomposition *** ! call lsqrt(1, p, l, dihdi, irc) if (irc .eq. 0) go to 240 ! ! *** (d**-1)*h*(d**-1) + alphak*i is indefinite -- overestimate ! *** smallest eigenvalue for use in updating lk *** ! j = (irc*(irc+1))/2 t = l(j) l(j) = one do 230 i = 1, irc 230 w(i) = zero w(irc) = one call litvmu(irc, w, l, w) t1 = v2norm(irc, w) lk = alphak - t/t1/t1 v(dst0) = -lk go to 210 ! ! *** alphak makes (d**-1)*h*(d**-1) positive definite. ! *** compute q = -d*step, check for convergence. *** ! 240 call livmul(p, w(q), l, dig) gtsta = dotprd(p, w(q), w(q)) call litvmu(p, w(q), l, w(q)) dst = v2norm(p, w(q)) phi = dst - rad if (phi .le. phimax .and. phi .ge. phimin) go to 270 if (phi .eq. oldphi) go to 270 oldphi = phi if (phi .lt. zero) go to 330 ! ! *** unacceptable alphak -- update lk, uk, alphak *** ! 250 if (ka .ge. kalim) go to 270 ! *** the following dmin1 is necessary because of restarts *** if (phi .lt. zero) uk = dmin1(uk, alphak) ! *** kamin = 0 only iff the gradient vanishes *** if (kamin .eq. 0) go to 210 call livmul(p, w, l, w(q)) t1 = v2norm(p, w) alphak = alphak + (phi/t1) * (dst/t1) * (dst/rad) lk = dmax1(lk, alphak) go to 210 ! ! *** acceptable step on first try *** ! 260 alphak = zero ! ! *** successful step in general. compute step = -(d**-1)*q *** ! 270 do 280 i = 1, p j = q0 + i step(i) = -w(j)/d(i) 280 continue v(gtstep) = -gtsta v(preduc) = half * (dabs(alphak)*dst*dst + gtsta) go to 410 ! ! ! *** restart with new radius *** ! 290 if (v(dst0) .le. zero .or. v(dst0) - rad .gt. phimax) go to 310 ! ! *** prepare to return newton step *** ! restrt = .true. ka = ka + 1 k = 0 do 300 i = 1, p k = k + i j = diag0 + i dihdi(k) = w(j) 300 continue uk = negone go to 30 ! 310 kamin = ka + 3 if (v(dgnorm) .eq. zero) kamin = 0 if (ka .eq. 0) go to 50 ! dst = w(dstsav) alphak = dabs(v(stppar)) phi = dst - rad t = v(dgnorm)/rad uk = t - w(emin) if (v(dgnorm) .eq. zero) uk = uk + p001 + p001*uk if (uk .le. zero) uk = p001 if (rad .gt. v(rad0)) go to 320 ! ! *** smaller radius *** lk = zero if (alphak .gt. zero) lk = w(lk0) lk = dmax1(lk, t - w(emax)) if (v(dst0) .gt. zero) lk = dmax1(lk, (v(dst0)-rad)*w(phipin)) go to 250 ! ! *** bigger radius *** 320 if (alphak .gt. zero) uk = dmin1(uk, w(uk0)) lk = dmax1(zero, -v(dst0), t - w(emax)) if (v(dst0) .gt. zero) lk = dmax1(lk, (v(dst0)-rad)*w(phipin)) go to 250 ! ! *** decide whether to check for special case... in practice (from ! *** the standpoint of the calling optimization code) it seems best ! *** not to check until a few iterations have failed -- hence the ! *** test on kamin below. ! 330 delta = alphak + dmin1(zero, v(dst0)) twopsi = alphak*dst*dst + gtsta if (ka .ge. kamin) go to 340 ! *** if the test in ref. 2 is satisfied, fall through to handle ! *** the special case (as soon as the more-sorensen test detects ! *** it). if (delta .ge. psifac*twopsi) go to 370 ! ! *** check for the special case of h + alpha*d**2 (nearly) ! *** singular. use one step of inverse power method with start ! *** from lsvmin to obtain approximate eigenvector corresponding ! *** to smallest eigenvalue of (d**-1)*h*(d**-1). lsvmin returns ! *** x and w with l*w = x. ! 340 t = lsvmin(p, l, w(x), w) ! ! *** normalize w *** do 350 i = 1, p 350 w(i) = t*w(i) ! *** complete current inv. power iter. -- replace w by (l**-t)*w. call litvmu(p, w, l, w) t2 = one/v2norm(p, w) do 360 i = 1, p 360 w(i) = t2*w(i) t = t2 * t ! ! *** now w is the desired approximate (unit) eigenvector and ! *** t*x = ((d**-1)*h*(d**-1) + alphak*i)*w. ! sw = dotprd(p, w(q), w) t1 = (rad + dst) * (rad - dst) root = dsqrt(sw*sw + t1) if (sw .lt. zero) root = -root si = t1 / (sw + root) ! ! *** the actual test for the special case... ! if ((t2*si)**2 .le. eps*(dst**2 + alphak*radsq)) go to 380 ! ! *** update upper bound on smallest eigenvalue (when not positive) ! *** (as recommended by more and sorensen) and continue... ! if (v(dst0) .le. zero) v(dst0) = dmin1(v(dst0), t2**2 - alphak) lk = dmax1(lk, -v(dst0)) ! ! *** check whether we can hope to detect the special case in ! *** the available arithmetic. accept step as it is if not. ! ! *** if not yet available, obtain machine dependent value dgxfac. 370 if (dgxfac .eq. zero) dgxfac = epsfac * rmdcon(3) ! if (delta .gt. dgxfac*w(dggdmx)) go to 250 go to 270 ! ! *** special case detected... negate alphak to indicate special case ! 380 alphak = -alphak v(preduc) = half * twopsi ! ! *** accept current step if adding si*w would lead to a ! *** further relative reduction in psi of less than v(epslon)/3. ! t1 = zero t = si*(alphak*sw - half*si*(alphak + t*dotprd(p,w(x),w))) if (t .lt. eps*twopsi/six) go to 390 v(preduc) = v(preduc) + t dst = rad t1 = -si 390 do 400 i = 1, p j = q0 + i w(j) = t1*w(i) - w(j) step(i) = w(j) / d(i) 400 continue v(gtstep) = dotprd(p, dig, w(q)) ! ! *** save values for use in a possible restart *** ! 410 v(dstnrm) = dst v(stppar) = alphak w(lk0) = lk w(uk0) = uk v(rad0) = rad w(dstsav) = dst ! ! *** restore diagonal of dihdi *** ! j = 0 do 420 i = 1, p j = j + i k = diag0 + i dihdi(j) = w(k) 420 continue ! 999 return ! ! *** last card of gqtst follows *** end subroutine gqtst !----------------------------------------------------------------------------- subroutine lsqrt(n1, n, l, a, irc) ! ! *** compute rows n1 through n of the cholesky factor l of ! *** a = l*(l**t), where l and the lower triangle of a are both ! *** stored compactly by rows (and may occupy the same storage). ! *** irc = 0 means all went well. irc = j means the leading ! *** principal j x j submatrix of a is not positive definite -- ! *** and l(j*(j+1)/2) contains the (nonpos.) reduced j-th diagonal. ! ! *** parameters *** ! integer :: n1, n, irc !al real(kind=8) :: l(1), a(1) real(kind=8) :: l(n*(n+1)/2), a(n*(n+1)/2) ! dimension l(n*(n+1)/2), a(n*(n+1)/2) ! ! *** local variables *** ! integer :: i, ij, ik, im1, i0, j, jk, jm1, j0, k real(kind=8) :: t, td !el, zero ! ! *** intrinsic functions *** !/+ !el real(kind=8) :: dsqrt !/ !/6 ! data zero/0.d+0/ !/7 real(kind=8),parameter :: zero=0.d+0 !/ ! ! *** body *** ! i0 = n1 * (n1 - 1) / 2 do 50 i = n1, n td = zero if (i .eq. 1) go to 40 j0 = 0 im1 = i - 1 do 30 j = 1, im1 t = zero if (j .eq. 1) go to 20 jm1 = j - 1 do 10 k = 1, jm1 ik = i0 + k jk = j0 + k t = t + l(ik)*l(jk) 10 continue 20 ij = i0 + j j0 = j0 + j t = (a(ij) - t) / l(j0) l(ij) = t td = td + t*t 30 continue 40 i0 = i0 + i t = a(i0) - td if (t .le. zero) go to 60 l(i0) = dsqrt(t) 50 continue ! irc = 0 go to 999 ! 60 l(i0) = t irc = i ! 999 return ! ! *** last card of lsqrt *** end subroutine lsqrt !----------------------------------------------------------------------------- real(kind=8) function lsvmin(p, l, x, y) ! ! *** estimate smallest sing. value of packed lower triang. matrix l ! ! *** parameter declarations *** ! integer :: p !al real(kind=8) :: l(1), x(p), y(p) real(kind=8) :: l(p*(p+1)/2), x(p), y(p) ! dimension l(p*(p+1)/2) ! !+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ ! ! *** purpose *** ! ! this function returns a good over-estimate of the smallest ! singular value of the packed lower triangular matrix l. ! ! *** parameter description *** ! ! p (in) = the order of l. l is a p x p lower triangular matrix. ! l (in) = array holding the elements of l in row order, i.e. ! l(1,1), l(2,1), l(2,2), l(3,1), l(3,2), l(3,3), etc. ! x (out) if lsvmin returns a positive value, then x is a normalized ! approximate left singular vector corresponding to the ! smallest singular value. this approximation may be very ! crude. if lsvmin returns zero, then some components of x ! are zero and the rest retain their input values. ! y (out) if lsvmin returns a positive value, then y = (l**-1)*x is an ! unnormalized approximate right singular vector correspond- ! ing to the smallest singular value. this approximation ! may be crude. if lsvmin returns zero, then y retains its ! input value. the caller may pass the same vector for x ! and y (nonstandard fortran usage), in which case y over- ! writes x (for nonzero lsvmin returns). ! ! *** algorithm notes *** ! ! the algorithm is based on (1), with the additional provision that ! lsvmin = 0 is returned if the smallest diagonal element of l ! (in magnitude) is not more than the unit roundoff times the ! largest. the algorithm uses a random number generator proposed ! in (4), which passes the spectral test with flying colors -- see ! (2) and (3). ! ! *** subroutines and functions called *** ! ! v2norm - function, returns the 2-norm of a vector. ! ! *** references *** ! ! (1) cline, a., moler, c., stewart, g., and wilkinson, j.h.(1977), ! an estimate for the condition number of a matrix, report ! tm-310, applied math. div., argonne national laboratory. ! ! (2) hoaglin, d.c. (1976), theoretical properties of congruential ! random-number generators -- an empirical view, ! memorandum ns-340, dept. of statistics, harvard univ. ! ! (3) knuth, d.e. (1969), the art of computer programming, vol. 2 ! (seminumerical algorithms), addison-wesley, reading, mass. ! ! (4) smith, c.s. (1971), multiplicative pseudo-random number ! generators with prime modulus, j. assoc. comput. mach. 18, ! pp. 586-593. ! ! *** history *** ! ! designed and coded by david m. gay (winter 1977/summer 1978). ! ! *** general *** ! ! this subroutine was written in connection with research ! supported by the national science foundation under grants ! mcs-7600324, dcr75-10143, 76-14311dss, and mcs76-11989. ! !+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ ! ! *** local variables *** ! integer :: i, ii, ix, j, ji, jj, jjj, jm1, j0, pm1 real(kind=8) :: b, sminus, splus, t, xminus, xplus ! ! *** constants *** ! !el real(kind=8) :: half, one, r9973, zero ! ! *** intrinsic functions *** !/+ !el integer mod !el real float !el real(kind=8) :: dabs !/ ! *** external functions and subroutines *** ! !el external dotprd, v2norm, vaxpy !el real(kind=8) :: dotprd, v2norm ! !/6 ! data half/0.5d+0/, one/1.d+0/, r9973/9973.d+0/, zero/0.d+0/ !/7 real(kind=8),parameter :: half=0.5d+0, one=1.d+0, r9973=9973.d+0, zero=0.d+0 !/ ! ! *** body *** ! ix = 2 pm1 = p - 1 ! ! *** first check whether to return lsvmin = 0 and initialize x *** ! ii = 0 j0 = p*pm1/2 jj = j0 + p if (l(jj) .eq. zero) go to 110 ix = mod(3432*ix, 9973) b = half*(one + float(ix)/r9973) xplus = b / l(jj) x(p) = xplus if (p .le. 1) go to 60 do 10 i = 1, pm1 ii = ii + i if (l(ii) .eq. zero) go to 110 ji = j0 + i x(i) = xplus * l(ji) 10 continue ! ! *** solve (l**t)*x = b, where the components of b have randomly ! *** chosen magnitudes in (.5,1) with signs chosen to make x large. ! ! do j = p-1 to 1 by -1... do 50 jjj = 1, pm1 j = p - jjj ! *** determine x(j) in this iteration. note for i = 1,2,...,j ! *** that x(i) holds the current partial sum for row i. ix = mod(3432*ix, 9973) b = half*(one + float(ix)/r9973) xplus = (b - x(j)) xminus = (-b - x(j)) splus = dabs(xplus) sminus = dabs(xminus) jm1 = j - 1 j0 = j*jm1/2 jj = j0 + j xplus = xplus/l(jj) xminus = xminus/l(jj) if (jm1 .eq. 0) go to 30 do 20 i = 1, jm1 ji = j0 + i splus = splus + dabs(x(i) + l(ji)*xplus) sminus = sminus + dabs(x(i) + l(ji)*xminus) 20 continue 30 if (sminus .gt. splus) xplus = xminus x(j) = xplus ! *** update partial sums *** if (jm1 .gt. 0) call vaxpy(jm1, x, xplus, l(j0+1), x) 50 continue ! ! *** normalize x *** ! 60 t = one/v2norm(p, x) do 70 i = 1, p 70 x(i) = t*x(i) ! ! *** solve l*y = x and return lsvmin = 1/twonorm(y) *** ! do 100 j = 1, p jm1 = j - 1 j0 = j*jm1/2 jj = j0 + j t = zero if (jm1 .gt. 0) t = dotprd(jm1, l(j0+1), y) y(j) = (x(j) - t) / l(jj) 100 continue ! lsvmin = one/v2norm(p, y) go to 999 ! 110 lsvmin = zero 999 return ! *** last card of lsvmin follows *** end function lsvmin !----------------------------------------------------------------------------- subroutine slvmul(p, y, s, x) ! ! *** set y = s * x, s = p x p symmetric matrix. *** ! *** lower triangle of s stored rowwise. *** ! ! *** parameter declarations *** ! integer :: p !al real(kind=8) :: s(1), x(p), y(p) real(kind=8) :: s(p*(p+1)/2), x(p), y(p) ! dimension s(p*(p+1)/2) ! ! *** local variables *** ! integer :: i, im1, j, k real(kind=8) :: xi ! ! *** no intrinsic functions *** ! ! *** external function *** ! !el external dotprd !el real(kind=8) :: dotprd ! !----------------------------------------------------------------------- ! j = 1 do 10 i = 1, p y(i) = dotprd(i, s(j), x) j = j + i 10 continue ! if (p .le. 1) go to 999 j = 1 do 40 i = 2, p xi = x(i) im1 = i - 1 j = j + 1 do 30 k = 1, im1 y(k) = y(k) + s(j)*xi j = j + 1 30 continue 40 continue ! 999 return ! *** last card of slvmul follows *** end subroutine slvmul !----------------------------------------------------------------------------- ! minimize_p.F !----------------------------------------------------------------------------- subroutine minimize(etot,x,iretcode,nfun) use energy, only: func,gradient,fdum!,etotal,enerprint use comm_srutu ! implicit real*8 (a-h,o-z) ! include 'DIMENSIONS' integer,parameter :: liv=60 ! integer :: lv=(77+(6*nres)*(6*nres+17)/2) !(77+maxvar*(maxvar+17)/2)) (maxvar=6*maxres) !******************************************************************** ! OPTIMIZE sets up SUMSL or DFP and provides a simple interface for * ! the calling subprogram. * ! when d(i)=1.0, then v(35) is the length of the initial step, * ! calculated in the usual pythagorean way. * ! absolute convergence occurs when the function is within v(31) of * ! zero. unless you know the minimum value in advance, abs convg * ! is probably not useful. * ! relative convergence is when the model predicts that the function * ! will decrease by less than v(32)*abs(fun). * !******************************************************************** ! include 'COMMON.IOUNITS' ! include 'COMMON.VAR' ! include 'COMMON.GEO' ! include 'COMMON.MINIM' integer :: i !el common /srutu/ icall integer,dimension(liv) :: iv real(kind=8) :: minval !,v(1:77+(6*nres)*(6*nres+17)/2) !(1:lv) !el real(kind=8),dimension(6*nres) :: x,d,xx !(maxvar) (maxvar=6*maxres) real(kind=8),dimension(6*nres) :: x,d,xx !(maxvar) (maxvar=6*maxres) real(kind=8) :: energia(0:n_ene) ! external func,gradient,fdum ! external func_restr,grad_restr logical :: not_done,change,reduce !el common /przechowalnia/ v !el local variables integer :: iretcode,nfun,lv,nvar_restr,idum(1),j real(kind=8) :: etot,rdum(1) !,fdum lv=(77+(6*nres)*(6*nres+17)/2) !(77+maxvar*(maxvar+17)/2)) (maxvar=6*maxres) if (.not.allocated(v)) allocate(v(1:lv)) icall = 1 NOT_DONE=.TRUE. ! DO WHILE (NOT_DONE) call deflt(2,iv,liv,lv,v) ! 12 means fresh start, dont call deflt iv(1)=12 ! max num of fun calls if (maxfun.eq.0) maxfun=500 iv(17)=maxfun ! max num of iterations if (maxmin.eq.0) maxmin=1000 iv(18)=maxmin ! controls output iv(19)=2 ! selects output unit iv(21)=0 if (print_min_ini+print_min_stat+print_min_res.gt.0) iv(21)=iout ! 1 means to print out result iv(22)=print_min_res ! 1 means to print out summary stats iv(23)=print_min_stat ! 1 means to print initial x and d iv(24)=print_min_ini ! min val for v(radfac) default is 0.1 v(24)=0.1D0 ! max val for v(radfac) default is 4.0 v(25)=2.0D0 ! v(25)=4.0D0 ! check false conv if (act fnctn decrease) .lt. v(26)*(exp decrease) ! the sumsl default is 0.1 v(26)=0.1D0 ! false conv if (act fnctn decrease) .lt. v(34) ! the sumsl default is 100*machep v(34)=v(34)/100.0D0 ! absolute convergence if (tolf.eq.0.0D0) tolf=1.0D-4 v(31)=tolf ! relative convergence if (rtolf.eq.0.0D0) rtolf=1.0D-4 v(32)=rtolf ! controls initial step size v(35)=1.0D-1 ! large vals of d correspond to small components of step do i=1,nphi d(i)=1.0D-1 enddo do i=nphi+1,nvar d(i)=1.0D-1 enddo !d print *,'Calling SUMSL' ! call var_to_geom(nvar,x) ! call chainbuild ! call etotal(energia(0)) ! etot = energia(0) !elmask_r=.true. IF (mask_r) THEN call x2xx(x,xx,nvar_restr) call sumsl(nvar_restr,d,xx,func_restr,grad_restr,& iv,liv,lv,v,idum,rdum,fdum) call xx2x(x,xx) ELSE call sumsl(nvar,d,x,func,gradient,iv,liv,lv,v,idum,rdum,fdum) ENDIF etot=v(10) iretcode=iv(1) !d print *,'Exit SUMSL; return code:',iretcode,' energy:',etot !d write (iout,'(/a,i4/)') 'SUMSL return code:',iv(1) ! call intout ! change=reduce(x) call var_to_geom(nvar,x) ! if (change) then ! write (iout,'(a)') 'Reduction worked, minimizing again...' ! else ! not_done=.false. ! endif call chainbuild !el--------------------- ! write (iout,'(/a)') & ! "Cartesian coordinates of the reference structure after SUMSL" ! write (iout,'(a,3(3x,a5),5x,3(3x,a5))') & ! "Residue","X(CA)","Y(CA)","Z(CA)","X(SC)","Y(SC)","Z(SC)" ! do i=1,nres ! write (iout,'(a3,1x,i3,3f8.3,5x,3f8.3)') & ! restyp(itype(i)),i,(c(j,i),j=1,3),& ! (c(j,i+nres),j=1,3) ! enddo !el---------------------------- ! call etotal(energia) !sp ! etot=energia(0) ! call enerprint(energia) !sp nfun=iv(6) ! write (*,*) 'Processor',MyID,' leaves MINIMIZE.' ! ENDDO ! NOT_DONE return end subroutine minimize !----------------------------------------------------------------------------- ! gradient_p.F !----------------------------------------------------------------------------- subroutine grad_restr(n,x,nf,g,uiparm,urparm,ufparm) use energy, only: cartder,zerograd,etotal,sum_gradient ! implicit real*8 (a-h,o-z) ! include 'DIMENSIONS' ! include 'COMMON.CHAIN' ! include 'COMMON.DERIV' ! include 'COMMON.VAR' ! include 'COMMON.INTERACT' ! include 'COMMON.FFIELD' ! include 'COMMON.IOUNITS' !EL external ufparm integer :: uiparm(1) real(kind=8) :: urparm(1) real(kind=8),dimension(6*nres) :: x,g !(maxvar) (maxvar=6*maxres) integer :: n,nf,ig,ind,i,j,ij,k,igall real(kind=8) :: f,gphii,gthetai,galphai,gomegai real(kind=8),external :: ufparm icg=mod(nf,2)+1 if (nf-nfl+1) 20,30,40 20 call func_restr(n,x,nf,f,uiparm,urparm,ufparm) ! write (iout,*) 'grad 20' if (nf.eq.0) return goto 40 30 continue #ifdef OSF ! Intercept NaNs in the coordinates ! write(iout,*) (var(i),i=1,nvar) x_sum=0.D0 do i=1,n x_sum=x_sum+x(i) enddo if (x_sum.ne.x_sum) then write(iout,*)" *** grad_restr : Found NaN in coordinates" call flush(iout) print *," *** grad_restr : Found NaN in coordinates" return endif #endif call var_to_geom_restr(n,x) call chainbuild ! ! Evaluate the derivatives of virtual bond lengths and SC vectors in variables. ! 40 call cartder ! ! Convert the Cartesian gradient into internal-coordinate gradient. ! ig=0 ind=nres-2 do i=2,nres-2 IF (mask_phi(i+2).eq.1) THEN gphii=0.0D0 do j=i+1,nres-1 ind=ind+1 do k=1,3 gphii=gphii+dcdv(k+3,ind)*gradc(k,j,icg) gphii=gphii+dxdv(k+3,ind)*gradx(k,j,icg) enddo enddo ig=ig+1 g(ig)=gphii ELSE ind=ind+nres-1-i ENDIF enddo ind=0 do i=1,nres-2 IF (mask_theta(i+2).eq.1) THEN ig=ig+1 gthetai=0.0D0 do j=i+1,nres-1 ind=ind+1 do k=1,3 gthetai=gthetai+dcdv(k,ind)*gradc(k,j,icg) gthetai=gthetai+dxdv(k,ind)*gradx(k,j,icg) enddo enddo g(ig)=gthetai ELSE ind=ind+nres-1-i ENDIF enddo do i=2,nres-1 if (itype(i).ne.10) then IF (mask_side(i).eq.1) THEN ig=ig+1 galphai=0.0D0 do k=1,3 galphai=galphai+dxds(k,i)*gradx(k,i,icg) enddo g(ig)=galphai ENDIF endif enddo do i=2,nres-1 if (itype(i).ne.10) then IF (mask_side(i).eq.1) THEN ig=ig+1 gomegai=0.0D0 do k=1,3 gomegai=gomegai+dxds(k+3,i)*gradx(k,i,icg) enddo g(ig)=gomegai ENDIF endif enddo ! ! Add the components corresponding to local energy terms. ! ig=0 igall=0 do i=4,nres igall=igall+1 if (mask_phi(i).eq.1) then ig=ig+1 g(ig)=g(ig)+gloc(igall,icg) endif enddo do i=3,nres igall=igall+1 if (mask_theta(i).eq.1) then ig=ig+1 g(ig)=g(ig)+gloc(igall,icg) endif enddo do ij=1,2 do i=2,nres-1 if (itype(i).ne.10) then igall=igall+1 if (mask_side(i).eq.1) then ig=ig+1 g(ig)=g(ig)+gloc(igall,icg) endif endif enddo enddo !d do i=1,ig !d write (iout,'(a2,i5,a3,f25.8)') 'i=',i,' g=',g(i) !d enddo return end subroutine grad_restr !----------------------------------------------------------------------------- subroutine func_restr(n,x,nf,f,uiparm,urparm,ufparm) !from minimize_p.F use comm_chu use energy, only: zerograd,etotal,sum_gradient ! implicit real*8 (a-h,o-z) ! include 'DIMENSIONS' ! include 'COMMON.DERIV' ! include 'COMMON.IOUNITS' ! include 'COMMON.GEO' integer :: n,nf !el integer :: jjj !el common /chuju/ jjj real(kind=8) :: energia(0:n_ene) real(kind=8) :: f real(kind=8),external :: ufparm integer :: uiparm(1) real(kind=8) :: urparm(1) real(kind=8),dimension(6*nres) :: x !(maxvar) (maxvar=6*maxres) ! if (jjj.gt.0) then ! write (iout,'(10f8.3)') (rad2deg*x(i),i=1,n) ! endif nfl=nf icg=mod(nf,2)+1 call var_to_geom_restr(n,x) call zerograd call chainbuild !d write (iout,*) 'ETOTAL called from FUNC' call etotal(energia) call sum_gradient f=energia(0) ! if (jjj.gt.0) then ! write (iout,'(10f8.3)') (rad2deg*x(i),i=1,n) ! write (iout,*) 'f=',etot ! jjj=0 ! endif return end subroutine func_restr !----------------------------------------------------------------------------- ! subroutine func(n,x,nf,f,uiparm,urparm,ufparm) in module energy !----------------------------------------------------------------------------- subroutine x2xx(x,xx,n) ! implicit real*8 (a-h,o-z) ! include 'DIMENSIONS' ! include 'COMMON.VAR' ! include 'COMMON.CHAIN' ! include 'COMMON.INTERACT' integer :: n,i,ij,ig,igall real(kind=8),dimension(6*nres) :: xx,x !(maxvar) (maxvar=6*maxres) !el allocate(varall(nvar)) allocated in alioc_ener_arrays do i=1,nvar varall(i)=x(i) enddo ig=0 igall=0 do i=4,nres igall=igall+1 if (mask_phi(i).eq.1) then ig=ig+1 xx(ig)=x(igall) endif enddo do i=3,nres igall=igall+1 if (mask_theta(i).eq.1) then ig=ig+1 xx(ig)=x(igall) endif enddo do ij=1,2 do i=2,nres-1 if (itype(i).ne.10) then igall=igall+1 if (mask_side(i).eq.1) then ig=ig+1 xx(ig)=x(igall) endif endif enddo enddo n=ig return end subroutine x2xx !----------------------------------------------------------------------------- !el subroutine xx2x(x,xx) in module math !----------------------------------------------------------------------------- subroutine minim_dc(etot,iretcode,nfun) use MPI_data use energy, only: fdum,check_ecartint ! implicit real*8 (a-h,o-z) ! include 'DIMENSIONS' #ifdef MPI include 'mpif.h' #endif integer,parameter :: liv=60 ! integer :: lv=(77+(6*nres)*(6*nres+17)/2) !(77+maxvar*(maxvar+17)/2)) (maxvar=6*maxres) ! include 'COMMON.SETUP' ! include 'COMMON.IOUNITS' ! include 'COMMON.VAR' ! include 'COMMON.GEO' ! include 'COMMON.MINIM' ! include 'COMMON.CHAIN' integer :: iretcode,nfun,k,i,j,lv,idum(1) integer,dimension(liv) :: iv real(kind=8) :: minval !,v(1:77+(6*nres)*(6*nres+17)/2) !(1:lv) real(kind=8),dimension(6*nres) :: x,d,xx !(maxvar) (maxvar=6*maxres) !el common /przechowalnia/ v real(kind=8) :: energia(0:n_ene) ! external func_dc,grad_dc ,fdum logical :: not_done,change,reduce real(kind=8) :: g(6*nres),f1,etot,rdum(1) !,fdum lv=(77+(6*nres)*(6*nres+17)/2) !(77+maxvar*(maxvar+17)/2)) (maxvar=6*maxres) if (.not. allocated(v)) allocate(v(1:lv)) call deflt(2,iv,liv,lv,v) ! 12 means fresh start, dont call deflt iv(1)=12 ! max num of fun calls if (maxfun.eq.0) maxfun=500 iv(17)=maxfun ! max num of iterations if (maxmin.eq.0) maxmin=1000 iv(18)=maxmin ! controls output iv(19)=2 ! selects output unit iv(21)=0 if (print_min_ini+print_min_stat+print_min_res.gt.0) iv(21)=iout ! 1 means to print out result iv(22)=print_min_res ! 1 means to print out summary stats iv(23)=print_min_stat ! 1 means to print initial x and d iv(24)=print_min_ini ! min val for v(radfac) default is 0.1 v(24)=0.1D0 ! max val for v(radfac) default is 4.0 v(25)=2.0D0 ! v(25)=4.0D0 ! check false conv if (act fnctn decrease) .lt. v(26)*(exp decrease) ! the sumsl default is 0.1 v(26)=0.1D0 ! false conv if (act fnctn decrease) .lt. v(34) ! the sumsl default is 100*machep v(34)=v(34)/100.0D0 ! absolute convergence if (tolf.eq.0.0D0) tolf=1.0D-4 v(31)=tolf ! relative convergence if (rtolf.eq.0.0D0) rtolf=1.0D-4 v(32)=rtolf ! controls initial step size v(35)=1.0D-1 ! large vals of d correspond to small components of step do i=1,6*nres d(i)=1.0D-1 enddo k=0 do i=1,nres-1 do j=1,3 k=k+1 x(k)=dc(j,i) enddo enddo do i=2,nres-1 if (ialph(i,1).gt.0) then do j=1,3 k=k+1 x(k)=dc(j,i+nres) enddo endif enddo call check_ecartint call sumsl(k,d,x,func_dc,grad_dc,iv,liv,lv,v,idum,rdum,fdum) call check_ecartint k=0 do i=1,nres-1 do j=1,3 k=k+1 dc(j,i)=x(k) enddo enddo do i=2,nres-1 if (ialph(i,1).gt.0) then do j=1,3 k=k+1 dc(j,i+nres)=x(k) enddo endif enddo call chainbuild_cart !d call zerograd !d nf=0 !d call func_dc(k,x,nf,f,idum,rdum,fdum) !d call grad_dc(k,x,nf,g,idum,rdum,fdum) !d !d do i=1,k !d x(i)=x(i)+1.0D-5 !d call func_dc(k,x,nf,f1,idum,rdum,fdum) !d x(i)=x(i)-1.0D-5 !d print '(i5,2f15.5)',i,g(i),(f1-f)/1.0D-5 !d enddo !el--------------------- ! write (iout,'(/a)') & ! "Cartesian coordinates of the reference structure after SUMSL" ! write (iout,'(a,3(3x,a5),5x,3(3x,a5))') & ! "Residue","X(CA)","Y(CA)","Z(CA)","X(SC)","Y(SC)","Z(SC)" ! do i=1,nres ! write (iout,'(a3,1x,i3,3f8.3,5x,3f8.3)') & ! restyp(itype(i)),i,(c(j,i),j=1,3),& ! (c(j,i+nres),j=1,3) ! enddo !el---------------------------- etot=v(10) iretcode=iv(1) nfun=iv(6) return end subroutine minim_dc !----------------------------------------------------------------------------- subroutine func_dc(n,x,nf,f,uiparm,urparm,ufparm) use MPI_data use energy, only: zerograd,etotal ! implicit real*8 (a-h,o-z) ! include 'DIMENSIONS' #ifdef MPI include 'mpif.h' #endif ! include 'COMMON.SETUP' ! include 'COMMON.DERIV' ! include 'COMMON.IOUNITS' ! include 'COMMON.GEO' ! include 'COMMON.CHAIN' ! include 'COMMON.VAR' integer :: n,nf,k,i,j real(kind=8) :: energia(0:n_ene) real(kind=8),external :: ufparm integer :: uiparm(1) real(kind=8) :: urparm(1) real(kind=8),dimension(6*nres) :: x !(maxvar) (maxvar=6*maxres) real(kind=8) :: f nfl=nf !bad icg=mod(nf,2)+1 icg=1 k=0 do i=1,nres-1 do j=1,3 k=k+1 dc(j,i)=x(k) enddo enddo do i=2,nres-1 if (ialph(i,1).gt.0) then do j=1,3 k=k+1 dc(j,i+nres)=x(k) enddo endif enddo call chainbuild_cart call zerograd call etotal(energia) f=energia(0) !d print *,'func_dc ',nf,nfl,f return end subroutine func_dc !----------------------------------------------------------------------------- subroutine grad_dc(n,x,nf,g,uiparm,urparm,ufparm) use MPI_data use energy, only: cartgrad,zerograd,etotal ! use MD_data ! implicit real*8 (a-h,o-z) ! include 'DIMENSIONS' #ifdef MPI include 'mpif.h' #endif ! include 'COMMON.SETUP' ! include 'COMMON.CHAIN' ! include 'COMMON.DERIV' ! include 'COMMON.VAR' ! include 'COMMON.INTERACT' ! include 'COMMON.FFIELD' ! include 'COMMON.MD' ! include 'COMMON.IOUNITS' real(kind=8),external :: ufparm integer :: n,nf,i,j,k integer :: uiparm(1) real(kind=8) :: urparm(1) real(kind=8),dimension(6*nres) :: x,g !(maxvar) (maxvar=6*maxres) real(kind=8) :: f ! !elwrite(iout,*) "jestesmy w grad dc" ! !bad icg=mod(nf,2)+1 icg=1 !d print *,'grad_dc ',nf,nfl,nf-nfl+1,icg !elwrite(iout,*) "jestesmy w grad dc nf-nfl+1", nf-nfl+1 if (nf-nfl+1) 20,30,40 20 call func_dc(n,x,nf,f,uiparm,urparm,ufparm) !d print *,20 if (nf.eq.0) return goto 40 30 continue !d print *,30 k=0 do i=1,nres-1 do j=1,3 k=k+1 dc(j,i)=x(k) enddo enddo do i=2,nres-1 if (ialph(i,1).gt.0) then do j=1,3 k=k+1 dc(j,i+nres)=x(k) enddo endif enddo !elwrite(iout,*) "jestesmy w grad dc" call chainbuild_cart ! ! Evaluate the derivatives of virtual bond lengths and SC vectors in variables. ! 40 call cartgrad !d print *,40 !elwrite(iout,*) "jestesmy w grad dc" k=0 do i=1,nres-1 do j=1,3 k=k+1 g(k)=gcart(j,i) enddo enddo do i=2,nres-1 if (ialph(i,1).gt.0) then do j=1,3 k=k+1 g(k)=gxcart(j,i) enddo endif enddo !elwrite(iout,*) "jestesmy w grad dc" return end subroutine grad_dc !----------------------------------------------------------------------------- ! minim_mcmf.F !----------------------------------------------------------------------------- #ifdef MPI subroutine minim_mcmf use MPI_data use csa_data use energy, only: func,gradient,fdum ! implicit real*8 (a-h,o-z) ! include 'DIMENSIONS' include 'mpif.h' integer,parameter :: liv=60 ! integer :: lv=(77+(6*nres)*(6*nres+17)/2) !(77+maxvar*(maxvar+17)/2)) (maxvar=6*maxres) ! include 'COMMON.VAR' ! include 'COMMON.IOUNITS' ! include 'COMMON.MINIM' ! real(kind=8) :: fdum ! external func,gradient,fdum !el real(kind=4) :: ran1,ran2,ran3 ! include 'COMMON.SETUP' ! include 'COMMON.GEO' ! include 'COMMON.CHAIN' ! include 'COMMON.FFIELD' real(kind=8),dimension(6*nres) :: var !(maxvar) (maxvar=6*maxres) real(kind=8),dimension(mxch*(mxch+1)/2+1) :: erg real(kind=8),dimension(6*nres) :: d,garbage !(maxvar) (maxvar=6*maxres) !el real(kind=8) :: v(1:77+(6*nres)*(6*nres+17)/2+1) integer,dimension(6) :: indx integer,dimension(liv) :: iv integer :: lv,idum(1),nf ! real(kind=8) :: rdum(1) real(kind=8) :: przes(3),obrot(3,3),eee logical :: non_conv integer,dimension(MPI_STATUS_SIZE) :: muster integer :: ichuj,i,ierr real(kind=8) :: rad,ene0 data rad /1.745329252d-2/ !el common /przechowalnia/ v lv=(77+(6*nres)*(6*nres+17)/2) !(77+maxvar*(maxvar+17)/2)) (maxvar=6*maxres) if (.not. allocated(v)) allocate(v(1:lv)) ichuj=0 10 continue ichuj = ichuj + 1 call mpi_recv(indx,6,mpi_integer,king,idint,CG_COMM,& muster,ierr) if (indx(1).eq.0) return ! print *, 'worker ',me,' received order ',n,ichuj call mpi_recv(var,nvar,mpi_double_precision,& king,idreal,CG_COMM,muster,ierr) call mpi_recv(ene0,1,mpi_double_precision,& king,idreal,CG_COMM,muster,ierr) ! print *, 'worker ',me,' var read ' call deflt(2,iv,liv,lv,v) ! 12 means fresh start, dont call deflt iv(1)=12 ! max num of fun calls if (maxfun.eq.0) maxfun=500 iv(17)=maxfun ! max num of iterations if (maxmin.eq.0) maxmin=1000 iv(18)=maxmin ! controls output iv(19)=2 ! selects output unit ! iv(21)=iout iv(21)=0 ! 1 means to print out result iv(22)=0 ! 1 means to print out summary stats iv(23)=0 ! 1 means to print initial x and d iv(24)=0 ! min val for v(radfac) default is 0.1 v(24)=0.1D0 ! max val for v(radfac) default is 4.0 v(25)=2.0D0 ! check false conv if (act fnctn decrease) .lt. v(26)*(exp decrease) ! the sumsl default is 0.1 v(26)=0.1D0 ! false conv if (act fnctn decrease) .lt. v(34) ! the sumsl default is 100*machep v(34)=v(34)/100.0D0 ! absolute convergence if (tolf.eq.0.0D0) tolf=1.0D-4 v(31)=tolf ! relative convergence if (rtolf.eq.0.0D0) rtolf=1.0D-4 v(32)=rtolf ! controls initial step size v(35)=1.0D-1 ! large vals of d correspond to small components of step do i=1,nphi d(i)=1.0D-1 enddo do i=nphi+1,nvar d(i)=1.0D-1 enddo ! minimize energy call func(nvar,var,nf,eee,idum,rdum,fdum) if(eee.gt.1.0d18) then ! print *,'MINIM_JLEE: ',me,' CHUJ NASTAPIL' ! print *,' energy before SUMSL =',eee ! print *,' aborting local minimization' iv(1)=-1 v(10)=eee nf=1 go to 201 endif call sumsl(nvar,d,var,func,gradient,iv,liv,lv,v,idum,rdum,fdum) ! find which conformation was returned from sumsl nf=iv(7)+1 201 continue ! total # of ftn evaluations (for iwf=0, it includes all minimizations). indx(4)=nf indx(5)=iv(1) eee=v(10) call mpi_send(indx,6,mpi_integer,king,idint,CG_COMM,& ierr) ! print '(a5,i3,15f10.5)', 'ENEX0',indx(1),v(10) call mpi_send(var,nvar,mpi_double_precision,& king,idreal,CG_COMM,ierr) call mpi_send(eee,1,mpi_double_precision,king,idreal,& CG_COMM,ierr) call mpi_send(ene0,1,mpi_double_precision,king,idreal,& CG_COMM,ierr) go to 10 return end subroutine minim_mcmf #endif !----------------------------------------------------------------------------- ! rmdd.f !----------------------------------------------------------------------------- ! algorithm 611, collected algorithms from acm. ! algorithm appeared in acm-trans. math. software, vol.9, no. 4, ! dec., 1983, p. 503-524. integer function imdcon(k) ! integer :: k ! ! *** return integer machine-dependent constants *** ! ! *** k = 1 means return standard output unit number. *** ! *** k = 2 means return alternate output unit number. *** ! *** k = 3 means return input unit number. *** ! (note -- k = 2, 3 are used only by test programs.) ! ! +++ port version follows... ! external i1mach ! integer i1mach ! integer mdperm(3) ! data mdperm(1)/2/, mdperm(2)/4/, mdperm(3)/1/ ! imdcon = i1mach(mdperm(k)) ! +++ end of port version +++ ! ! +++ non-port version follows... integer :: mdcon(3) data mdcon(1)/6/, mdcon(2)/8/, mdcon(3)/5/ imdcon = mdcon(k) ! +++ end of non-port version +++ ! 999 return ! *** last card of imdcon follows *** end function imdcon !----------------------------------------------------------------------------- real(kind=8) function rmdcon(k) ! ! *** return machine dependent constants used by nl2sol *** ! ! +++ comments below contain data statements for various machines. +++ ! +++ to convert to another machine, place a c in column 1 of the +++ ! +++ data statement line(s) that correspond to the current machine +++ ! +++ and remove the c from column 1 of the data statement line(s) +++ ! +++ that correspond to the new machine. +++ ! integer :: k ! ! *** the constant returned depends on k... ! ! *** k = 1... smallest pos. eta such that -eta exists. ! *** k = 2... square root of eta. ! *** k = 3... unit roundoff = smallest pos. no. machep such ! *** that 1 + machep .gt. 1 .and. 1 - machep .lt. 1. ! *** k = 4... square root of machep. ! *** k = 5... square root of big (see k = 6). ! *** k = 6... largest machine no. big such that -big exists. ! real(kind=8) :: big, eta, machep integer :: bigi(4), etai(4), machei(4) !/+ !el real(kind=8) :: dsqrt !/ equivalence (big,bigi(1)), (eta,etai(1)), (machep,machei(1)) ! ! +++ ibm 360, ibm 370, or xerox +++ ! ! data big/z7fffffffffffffff/, eta/z0010000000000000/, ! 1 machep/z3410000000000000/ ! ! +++ data general +++ ! ! data big/0.7237005577d+76/, eta/0.5397605347d-78/, ! 1 machep/2.22044605d-16/ ! ! +++ dec 11 +++ ! ! data big/1.7d+38/, eta/2.938735878d-39/, machep/2.775557562d-17/ ! ! +++ hp3000 +++ ! ! data big/1.157920892d+77/, eta/8.636168556d-78/, ! 1 machep/5.551115124d-17/ ! ! +++ honeywell +++ ! ! data big/1.69d+38/, eta/5.9d-39/, machep/2.1680435d-19/ ! ! +++ dec10 +++ ! ! data big/"377777100000000000000000/, ! 1 eta/"002400400000000000000000/, ! 2 machep/"104400000000000000000000/ ! ! +++ burroughs +++ ! ! data big/o0777777777777777,o7777777777777777/, ! 1 eta/o1771000000000000,o7770000000000000/, ! 2 machep/o1451000000000000,o0000000000000000/ ! ! +++ control data +++ ! ! data big/37767777777777777777b,37167777777777777777b/, ! 1 eta/00014000000000000000b,00000000000000000000b/, ! 2 machep/15614000000000000000b,15010000000000000000b/ ! ! +++ prime +++ ! ! data big/1.0d+9786/, eta/1.0d-9860/, machep/1.4210855d-14/ ! ! +++ univac +++ ! ! data big/8.988d+307/, eta/1.2d-308/, machep/1.734723476d-18/ ! ! +++ vax +++ ! data big/1.7d+38/, eta/2.939d-39/, machep/1.3877788d-17/ ! ! +++ cray 1 +++ ! ! data bigi(1)/577767777777777777777b/, ! 1 bigi(2)/000007777777777777776b/, ! 2 etai(1)/200004000000000000000b/, ! 3 etai(2)/000000000000000000000b/, ! 4 machei(1)/377224000000000000000b/, ! 5 machei(2)/000000000000000000000b/ ! ! +++ port library -- requires more than just a data statement... +++ ! ! external d1mach ! double precision d1mach, zero ! data big/0.d+0/, eta/0.d+0/, machep/0.d+0/, zero/0.d+0/ ! if (big .gt. zero) go to 1 ! big = d1mach(2) ! eta = d1mach(1) ! machep = d1mach(4) !1 continue ! ! +++ end of port +++ ! !------------------------------- body -------------------------------- ! go to (10, 20, 30, 40, 50, 60), k ! 10 rmdcon = eta go to 999 ! 20 rmdcon = dsqrt(256.d+0*eta)/16.d+0 go to 999 ! 30 rmdcon = machep go to 999 ! 40 rmdcon = dsqrt(machep) go to 999 ! 50 rmdcon = dsqrt(big/256.d+0)*16.d+0 go to 999 ! 60 rmdcon = big ! 999 return ! *** last card of rmdcon follows *** end function rmdcon !----------------------------------------------------------------------------- ! sc_move.F !----------------------------------------------------------------------------- subroutine sc_move(n_start,n_end,n_maxtry,e_drop,n_fun,etot) use control use random, only: iran_num use energy, only: esc ! Perform a quick search over side-chain arrangments (over ! residues n_start to n_end) for a given (frozen) CA trace ! Only side-chains are minimized (at most n_maxtry times each), ! not CA positions ! Stops if energy drops by e_drop, otherwise tries all residues ! in the given range ! If there is an energy drop, full minimization may be useful ! n_start, n_end CAN be modified by this routine, but only if ! out of bounds (n_start <= 1, n_end >= nres, n_start < n_end) ! NOTE: this move should never increase the energy !rc implicit none ! Includes ! implicit real*8 (a-h,o-z) ! include 'DIMENSIONS' include 'mpif.h' ! include 'COMMON.GEO' ! include 'COMMON.VAR' ! include 'COMMON.HEADER' ! include 'COMMON.IOUNITS' ! include 'COMMON.CHAIN' ! include 'COMMON.FFIELD' ! External functions !el integer iran_num !el external iran_num ! Input arguments integer :: n_start,n_end,n_maxtry real(kind=8) :: e_drop ! Output arguments integer :: n_fun real(kind=8) :: etot ! Local variables ! real(kind=8) :: energy(0:n_ene) real(kind=8) :: cur_alph(2:nres-1),cur_omeg(2:nres-1) real(kind=8) :: orig_e,cur_e integer :: n,n_steps,n_first,n_cur,n_tot !,i real(kind=8) :: orig_w(0:n_ene) real(kind=8) :: wtime !elwrite(iout,*) "in sc_move etot= ", etot ! Set non side-chain weights to zero (minimization is faster) ! NOTE: e(2) does not actually depend on the side-chain, only CA orig_w(2)=wscp orig_w(3)=welec orig_w(4)=wcorr orig_w(5)=wcorr5 orig_w(6)=wcorr6 orig_w(7)=wel_loc orig_w(8)=wturn3 orig_w(9)=wturn4 orig_w(10)=wturn6 orig_w(11)=wang orig_w(13)=wtor orig_w(14)=wtor_d orig_w(15)=wvdwpp wscp=0.D0 welec=0.D0 wcorr=0.D0 wcorr5=0.D0 wcorr6=0.D0 wel_loc=0.D0 wturn3=0.D0 wturn4=0.D0 wturn6=0.D0 wang=0.D0 wtor=0.D0 wtor_d=0.D0 wvdwpp=0.D0 ! Make sure n_start, n_end are within proper range if (n_start.lt.2) n_start=2 if (n_end.gt.nres-1) n_end=nres-1 !rc if (n_start.lt.n_end) then if (n_start.gt.n_end) then n_start=2 n_end=nres-1 endif ! Save the initial values of energy and coordinates !d call chainbuild !d call etotal(energy) !d write (iout,*) 'start sc ene',energy(0) !d call enerprint(energy(0)) !rc etot=energy(0) n_fun=0 !rc orig_e=etot !rc cur_e=orig_e !rc do i=2,nres-1 !rc cur_alph(i)=alph(i) !rc cur_omeg(i)=omeg(i) !rc enddo !t wtime=MPI_WTIME() ! Try (one by one) all specified residues, starting from a ! random position in sequence ! Stop early if the energy has decreased by at least e_drop n_tot=n_end-n_start+1 n_first=iran_num(0,n_tot-1) n_steps=0 n=0 !rc do while (n.lt.n_tot .and. orig_e-etot.lt.e_drop) do while (n.lt.n_tot) n_cur=n_start+mod(n_first+n,n_tot) call single_sc_move(n_cur,n_maxtry,e_drop,& n_steps,n_fun,etot) !elwrite(iout,*) "after msingle sc_move etot= ", etot ! If a lower energy was found, update the current structure... !rc if (etot.lt.cur_e) then !rc cur_e=etot !rc do i=2,nres-1 !rc cur_alph(i)=alph(i) !rc cur_omeg(i)=omeg(i) !rc enddo !rc else ! ...else revert to the previous one !rc etot=cur_e !rc do i=2,nres-1 !rc alph(i)=cur_alph(i) !rc omeg(i)=cur_omeg(i) !rc enddo !rc endif n=n+1 !d !d call chainbuild !d call etotal(energy) !d print *,'running',n,energy(0) enddo !d call chainbuild !d call etotal(energy) !d write (iout,*) 'end sc ene',energy(0) ! Put the original weights back to calculate the full energy wscp=orig_w(2) welec=orig_w(3) wcorr=orig_w(4) wcorr5=orig_w(5) wcorr6=orig_w(6) wel_loc=orig_w(7) wturn3=orig_w(8) wturn4=orig_w(9) wturn6=orig_w(10) wang=orig_w(11) wtor=orig_w(13) wtor_d=orig_w(14) wvdwpp=orig_w(15) !rc n_fun=n_fun+1 !t write (iout,*) 'sc_local time= ',MPI_WTIME()-wtime return end subroutine sc_move !----------------------------------------------------------------------------- subroutine single_sc_move(res_pick,n_maxtry,e_drop,n_steps,n_fun,e_sc) ! Perturb one side-chain (res_pick) and minimize the ! neighbouring region, keeping all CA's and non-neighbouring ! side-chains fixed ! Try until e_drop energy improvement is achieved, or n_maxtry ! attempts have been made ! At the start, e_sc should contain the side-chain-only energy(0) ! nsteps and nfun for this move are ADDED to n_steps and n_fun !rc implicit none use energy, only: esc use geometry, only:dist ! Includes ! implicit real*8 (a-h,o-z) ! include 'DIMENSIONS' ! include 'COMMON.VAR' ! include 'COMMON.INTERACT' ! include 'COMMON.CHAIN' ! include 'COMMON.MINIM' ! include 'COMMON.FFIELD' ! include 'COMMON.IOUNITS' ! External functions !el double precision dist !el external dist ! Input arguments integer :: res_pick,n_maxtry real(kind=8) :: e_drop ! Input/Output arguments integer :: n_steps,n_fun real(kind=8) :: e_sc ! Local variables logical :: fail integer :: i,j integer :: nres_moved integer :: iretcode,loc_nfun,orig_maxfun,n_try real(kind=8) :: sc_dist,sc_dist_cutoff ! real(kind=8) :: energy_(0:n_ene) real(kind=8) :: evdw,escloc,orig_e,cur_e real(kind=8) :: cur_alph(2:nres-1),cur_omeg(2:nres-1) real(kind=8) :: var(6*nres) !(maxvar) (maxvar=6*maxres) real(kind=8) :: orig_theta(1:nres),orig_phi(1:nres),& orig_alph(1:nres),orig_omeg(1:nres) !elwrite(iout,*) "in sinle etot/ e_sc",e_sc ! Define what is meant by "neighbouring side-chain" sc_dist_cutoff=5.0D0 ! Don't do glycine or ends i=itype(res_pick) if (i.eq.10 .or. i.eq.ntyp1) return ! Freeze everything (later will relax only selected side-chains) mask_r=.true. do i=1,nres mask_phi(i)=0 mask_theta(i)=0 mask_side(i)=0 enddo ! Find the neighbours of the side-chain to move ! and save initial variables !rc orig_e=e_sc !rc cur_e=orig_e nres_moved=0 do i=2,nres-1 ! Don't do glycine (itype(j)==10) if (itype(i).ne.10) then sc_dist=dist(nres+i,nres+res_pick) else sc_dist=sc_dist_cutoff endif if (sc_dist.lt.sc_dist_cutoff) then nres_moved=nres_moved+1 mask_side(i)=1 cur_alph(i)=alph(i) cur_omeg(i)=omeg(i) endif enddo call chainbuild call egb1(evdw) call esc(escloc) !elwrite(iout,*) "in sinle etot/ e_sc",e_sc !elwrite(iout,*) "in sinle wsc=",wsc,"evdw",evdw,"wscloc",wscloc,"escloc",escloc e_sc=wsc*evdw+wscloc*escloc !elwrite(iout,*) "in sinle etot/ e_sc",e_sc !d call etotal(energy) !d print *,'new ',(energy(k),k=0,n_ene) orig_e=e_sc cur_e=orig_e n_try=0 do while (n_try.lt.n_maxtry .and. orig_e-cur_e.lt.e_drop) ! Move the selected residue (don't worry if it fails) call gen_side(iabs(itype(res_pick)),theta(res_pick+1),& alph(res_pick),omeg(res_pick),fail) ! Minimize the side-chains starting from the new arrangement call geom_to_var(nvar,var) orig_maxfun=maxfun maxfun=7 !rc do i=1,nres !rc orig_theta(i)=theta(i) !rc orig_phi(i)=phi(i) !rc orig_alph(i)=alph(i) !rc orig_omeg(i)=omeg(i) !rc enddo !elwrite(iout,*) "in sinle etot/ e_sc",e_sc call minimize_sc1(e_sc,var,iretcode,loc_nfun) !elwrite(iout,*) "in sinle etot/ e_sc",e_sc !v write(*,'(2i3,2f12.5,2i3)') !v & res_pick,nres_moved,orig_e,e_sc-cur_e, !v & iretcode,loc_nfun !$$$ if (iretcode.eq.8) then !$$$ write(iout,*)'Coordinates just after code 8' !$$$ call chainbuild !$$$ call all_varout !$$$ call flush(iout) !$$$ do i=1,nres !$$$ theta(i)=orig_theta(i) !$$$ phi(i)=orig_phi(i) !$$$ alph(i)=orig_alph(i) !$$$ omeg(i)=orig_omeg(i) !$$$ enddo !$$$ write(iout,*)'Coordinates just before code 8' !$$$ call chainbuild !$$$ call all_varout !$$$ call flush(iout) !$$$ endif n_fun=n_fun+loc_nfun maxfun=orig_maxfun call var_to_geom(nvar,var) ! If a lower energy was found, update the current structure... if (e_sc.lt.cur_e) then !v call chainbuild !v call etotal(energy) !d call egb1(evdw) !d call esc(escloc) !d e_sc1=wsc*evdw+wscloc*escloc !d print *,' new',e_sc1,energy(0) !v print *,'new ',energy(0) !d call enerprint(energy(0)) cur_e=e_sc do i=2,nres-1 if (mask_side(i).eq.1) then cur_alph(i)=alph(i) cur_omeg(i)=omeg(i) endif enddo else ! ...else revert to the previous one e_sc=cur_e do i=2,nres-1 if (mask_side(i).eq.1) then alph(i)=cur_alph(i) omeg(i)=cur_omeg(i) endif enddo endif n_try=n_try+1 enddo n_steps=n_steps+n_try ! Reset the minimization mask_r to false mask_r=.false. return end subroutine single_sc_move !----------------------------------------------------------------------------- subroutine sc_minimize(etot,iretcode,nfun) ! Minimizes side-chains only, leaving backbone frozen !rc implicit none use energy, only: etotal ! Includes ! implicit real*8 (a-h,o-z) ! include 'DIMENSIONS' ! include 'COMMON.VAR' ! include 'COMMON.CHAIN' ! include 'COMMON.FFIELD' ! Output arguments real(kind=8) :: etot integer :: iretcode,nfun ! Local variables integer :: i real(kind=8) :: orig_w(0:n_ene),energy_(0:n_ene) real(kind=8) :: var(6*nres) !(maxvar)(maxvar=6*maxres) ! Set non side-chain weights to zero (minimization is faster) ! NOTE: e(2) does not actually depend on the side-chain, only CA orig_w(2)=wscp orig_w(3)=welec orig_w(4)=wcorr orig_w(5)=wcorr5 orig_w(6)=wcorr6 orig_w(7)=wel_loc orig_w(8)=wturn3 orig_w(9)=wturn4 orig_w(10)=wturn6 orig_w(11)=wang orig_w(13)=wtor orig_w(14)=wtor_d wscp=0.D0 welec=0.D0 wcorr=0.D0 wcorr5=0.D0 wcorr6=0.D0 wel_loc=0.D0 wturn3=0.D0 wturn4=0.D0 wturn6=0.D0 wang=0.D0 wtor=0.D0 wtor_d=0.D0 ! Prepare to freeze backbone do i=1,nres mask_phi(i)=0 mask_theta(i)=0 mask_side(i)=1 enddo ! Minimize the side-chains mask_r=.true. call geom_to_var(nvar,var) call minimize(etot,var,iretcode,nfun) call var_to_geom(nvar,var) mask_r=.false. ! Put the original weights back and calculate the full energy wscp=orig_w(2) welec=orig_w(3) wcorr=orig_w(4) wcorr5=orig_w(5) wcorr6=orig_w(6) wel_loc=orig_w(7) wturn3=orig_w(8) wturn4=orig_w(9) wturn6=orig_w(10) wang=orig_w(11) wtor=orig_w(13) wtor_d=orig_w(14) call chainbuild call etotal(energy_) etot=energy_(0) return end subroutine sc_minimize !----------------------------------------------------------------------------- subroutine minimize_sc1(etot,x,iretcode,nfun) use energy, only: func,gradient,fdum,etotal,enerprint use comm_srutu ! implicit real*8 (a-h,o-z) ! include 'DIMENSIONS' integer,parameter :: liv=60 integer :: iretcode,nfun ! integer :: lv=(77+(6*nres)*(6*nres+17)/2) !(77+maxvar*(maxvar+17)/2)) (maxvar=6*maxres) ! include 'COMMON.IOUNITS' ! include 'COMMON.VAR' ! include 'COMMON.GEO' ! include 'COMMON.MINIM' !el integer :: icall !el common /srutu/ icall integer,dimension(liv) :: iv real(kind=8) :: minval !,v(1:77+(6*nres)*(6*nres+17)/2) !(1:lv) real(kind=8),dimension(6*nres) :: x,d,xx !(maxvar) (maxvar=6*maxres) real(kind=8) :: energia(0:n_ene) !el real(kind=8) :: fdum ! external gradient,fdum !func, ! external func_restr1,grad_restr1 logical :: not_done,change,reduce !el common /przechowalnia/ v integer :: nvar_restr,lv,i,j integer :: idum(1) real(kind=8) :: rdum(1),etot !,fdum lv=(77+(6*nres)*(6*nres+17)/2) !(77+maxvar*(maxvar+17)/2)) (maxvar=6*maxres) if (.not. allocated(v)) allocate(v(1:lv)) call deflt(2,iv,liv,lv,v) ! 12 means fresh start, dont call deflt iv(1)=12 ! max num of fun calls if (maxfun.eq.0) maxfun=500 iv(17)=maxfun ! max num of iterations if (maxmin.eq.0) maxmin=1000 iv(18)=maxmin ! controls output iv(19)=2 ! selects output unit ! iv(21)=iout iv(21)=0 ! 1 means to print out result iv(22)=0 ! 1 means to print out summary stats iv(23)=0 ! 1 means to print initial x and d iv(24)=0 ! min val for v(radfac) default is 0.1 v(24)=0.1D0 ! max val for v(radfac) default is 4.0 v(25)=2.0D0 ! v(25)=4.0D0 ! check false conv if (act fnctn decrease) .lt. v(26)*(exp decrease) ! the sumsl default is 0.1 v(26)=0.1D0 ! false conv if (act fnctn decrease) .lt. v(34) ! the sumsl default is 100*machep v(34)=v(34)/100.0D0 ! absolute convergence if (tolf.eq.0.0D0) tolf=1.0D-4 v(31)=tolf ! relative convergence if (rtolf.eq.0.0D0) rtolf=1.0D-4 v(32)=rtolf ! controls initial step size v(35)=1.0D-1 ! large vals of d correspond to small components of step do i=1,nphi d(i)=1.0D-1 enddo do i=nphi+1,nvar d(i)=1.0D-1 enddo !elmask_r=.false. IF (mask_r) THEN call x2xx(x,xx,nvar_restr) call sumsl(nvar_restr,d,xx,func_restr1,grad_restr1,& iv,liv,lv,v,idum,rdum,fdum) call xx2x(x,xx) ELSE call sumsl(nvar,d,x,func,gradient,iv,liv,lv,v,idum,rdum,fdum) ENDIF !el--------------------- ! write (iout,'(/a)') & ! "Cartesian coordinates of the reference structure after SUMSL" ! write (iout,'(a,3(3x,a5),5x,3(3x,a5))') & ! "Residue","X(CA)","Y(CA)","Z(CA)","X(SC)","Y(SC)","Z(SC)" ! do i=1,nres ! write (iout,'(a3,1x,i3,3f8.3,5x,3f8.3)') & ! restyp(itype(i)),i,(c(j,i),j=1,3),& ! (c(j,i+nres),j=1,3) ! enddo ! call etotal(energia) ! call enerprint(energia) !el---------------------------- etot=v(10) iretcode=iv(1) nfun=iv(6) return end subroutine minimize_sc1 !----------------------------------------------------------------------------- subroutine func_restr1(n,x,nf,f,uiparm,urparm,ufparm) use comm_chu use energy, only: zerograd,esc,sc_grad ! implicit real*8 (a-h,o-z) ! include 'DIMENSIONS' ! include 'COMMON.DERIV' ! include 'COMMON.IOUNITS' ! include 'COMMON.GEO' ! include 'COMMON.FFIELD' ! include 'COMMON.INTERACT' ! include 'COMMON.TIME1' integer :: n,nf,i,j !el common /chuju/ jjj real(kind=8) :: energia(0:n_ene),evdw,escloc real(kind=8) :: e1,e2,f real(kind=8),external :: ufparm integer :: uiparm(1) real(kind=8) :: urparm(1) real(kind=8),dimension(6*nres) :: x !(maxvar) (maxvar=6*maxres) nfl=nf icg=mod(nf,2)+1 #ifdef OSF ! Intercept NaNs in the coordinates, before calling etotal x_sum=0.D0 do i=1,n x_sum=x_sum+x(i) enddo FOUND_NAN=.false. if (x_sum.ne.x_sum) then write(iout,*)" *** func_restr1 : Found NaN in coordinates" f=1.0D+73 FOUND_NAN=.true. return endif #endif call var_to_geom_restr(n,x) call zerograd call chainbuild !d write (iout,*) 'ETOTAL called from FUNC' call egb1(evdw) call esc(escloc) f=wsc*evdw+wscloc*escloc !d call etotal(energia(0)) !d f=wsc*energia(1)+wscloc*energia(12) !d print *,f,evdw,escloc,energia(0) ! ! Sum up the components of the Cartesian gradient. ! do i=1,nct do j=1,3 gradx(j,i,icg)=wsc*gvdwx(j,i) enddo enddo return end subroutine func_restr1 !----------------------------------------------------------------------------- subroutine grad_restr1(n,x,nf,g,uiparm,urparm,ufparm) use energy, only: cartder,zerograd,esc,sc_grad ! implicit real*8 (a-h,o-z) ! include 'DIMENSIONS' ! include 'COMMON.CHAIN' ! include 'COMMON.DERIV' ! include 'COMMON.VAR' ! include 'COMMON.INTERACT' ! include 'COMMON.FFIELD' ! include 'COMMON.IOUNITS' !el external ufparm integer :: i,j,k,ind,n,nf,uiparm(1) real(kind=8) :: f,urparm(1) real(kind=8),dimension(6*nres) :: x,g !(maxvar) (maxvar=6*maxres) integer :: ig,igall,ij real(kind=8) :: gphii,gthetai,galphai,gomegai real(kind=8),external :: ufparm icg=mod(nf,2)+1 if (nf-nfl+1) 20,30,40 20 call func_restr1(n,x,nf,f,uiparm,urparm,ufparm) ! write (iout,*) 'grad 20' if (nf.eq.0) return goto 40 30 call var_to_geom_restr(n,x) call chainbuild ! ! Evaluate the derivatives of virtual bond lengths and SC vectors in variables. ! 40 call cartder ! ! Convert the Cartesian gradient into internal-coordinate gradient. ! ig=0 ind=nres-2 do i=2,nres-2 IF (mask_phi(i+2).eq.1) THEN gphii=0.0D0 do j=i+1,nres-1 ind=ind+1 do k=1,3 gphii=gphii+dcdv(k+3,ind)*gradc(k,j,icg) gphii=gphii+dxdv(k+3,ind)*gradx(k,j,icg) enddo enddo ig=ig+1 g(ig)=gphii ELSE ind=ind+nres-1-i ENDIF enddo ind=0 do i=1,nres-2 IF (mask_theta(i+2).eq.1) THEN ig=ig+1 gthetai=0.0D0 do j=i+1,nres-1 ind=ind+1 do k=1,3 gthetai=gthetai+dcdv(k,ind)*gradc(k,j,icg) gthetai=gthetai+dxdv(k,ind)*gradx(k,j,icg) enddo enddo g(ig)=gthetai ELSE ind=ind+nres-1-i ENDIF enddo do i=2,nres-1 if (itype(i).ne.10) then IF (mask_side(i).eq.1) THEN ig=ig+1 galphai=0.0D0 do k=1,3 galphai=galphai+dxds(k,i)*gradx(k,i,icg) enddo g(ig)=galphai ENDIF endif enddo do i=2,nres-1 if (itype(i).ne.10) then IF (mask_side(i).eq.1) THEN ig=ig+1 gomegai=0.0D0 do k=1,3 gomegai=gomegai+dxds(k+3,i)*gradx(k,i,icg) enddo g(ig)=gomegai ENDIF endif enddo ! ! Add the components corresponding to local energy terms. ! ig=0 igall=0 do i=4,nres igall=igall+1 if (mask_phi(i).eq.1) then ig=ig+1 g(ig)=g(ig)+gloc(igall,icg) endif enddo do i=3,nres igall=igall+1 if (mask_theta(i).eq.1) then ig=ig+1 g(ig)=g(ig)+gloc(igall,icg) endif enddo do ij=1,2 do i=2,nres-1 if (itype(i).ne.10) then igall=igall+1 if (mask_side(i).eq.1) then ig=ig+1 g(ig)=g(ig)+gloc(igall,icg) endif endif enddo enddo !d do i=1,ig !d write (iout,'(a2,i5,a3,f25.8)') 'i=',i,' g=',g(i) !d enddo return end subroutine grad_restr1 !----------------------------------------------------------------------------- subroutine egb1(evdw) ! ! This subroutine calculates the interaction energy of nonbonded side chains ! assuming the Gay-Berne potential of interaction. ! use calc_data use energy, only: sc_grad ! use control, only:stopx ! implicit real*8 (a-h,o-z) ! include 'DIMENSIONS' ! include 'COMMON.GEO' ! include 'COMMON.VAR' ! include 'COMMON.LOCAL' ! include 'COMMON.CHAIN' ! include 'COMMON.DERIV' ! include 'COMMON.NAMES' ! include 'COMMON.INTERACT' ! include 'COMMON.IOUNITS' ! include 'COMMON.CALC' ! include 'COMMON.CONTROL' logical :: lprn real(kind=8) :: evdw !el local variables integer :: iint,ind,itypi,itypi1,itypj real(kind=8) :: xi,yi,zi,rrij,sig,sig0ij,rij_shift,fac,e1,e2,& sigm,epsi !elwrite(iout,*) "check evdw" ! print *,'Entering EGB nnt=',nnt,' nct=',nct,' expon=',expon evdw=0.0D0 lprn=.false. ! if (icall.eq.0) lprn=.true. ind=0 do i=iatsc_s,iatsc_e itypi=iabs(itype(i)) itypi1=iabs(itype(i+1)) xi=c(1,nres+i) yi=c(2,nres+i) zi=c(3,nres+i) dxi=dc_norm(1,nres+i) dyi=dc_norm(2,nres+i) dzi=dc_norm(3,nres+i) dsci_inv=dsc_inv(itypi) !elwrite(iout,*) itypi,itypi1,xi,yi,zi,dxi,dyi,dzi,dsci_inv ! ! Calculate SC interaction energy. ! do iint=1,nint_gr(i) do j=istart(i,iint),iend(i,iint) IF (mask_side(j).eq.1.or.mask_side(i).eq.1) THEN ind=ind+1 itypj=iabs(itype(j)) dscj_inv=dsc_inv(itypj) sig0ij=sigma(itypi,itypj) chi1=chi(itypi,itypj) chi2=chi(itypj,itypi) chi12=chi1*chi2 chip1=chip(itypi) chip2=chip(itypj) chip12=chip1*chip2 alf1=alp(itypi) alf2=alp(itypj) alf12=0.5D0*(alf1+alf2) ! For diagnostics only!!! ! chi1=0.0D0 ! chi2=0.0D0 ! chi12=0.0D0 ! chip1=0.0D0 ! chip2=0.0D0 ! chip12=0.0D0 ! alf1=0.0D0 ! alf2=0.0D0 ! alf12=0.0D0 xj=c(1,nres+j)-xi yj=c(2,nres+j)-yi zj=c(3,nres+j)-zi dxj=dc_norm(1,nres+j) dyj=dc_norm(2,nres+j) dzj=dc_norm(3,nres+j) rrij=1.0D0/(xj*xj+yj*yj+zj*zj) rij=dsqrt(rrij) ! Calculate angle-dependent terms of energy and contributions to their ! derivatives. call sc_angular sigsq=1.0D0/sigsq sig=sig0ij*dsqrt(sigsq) rij_shift=1.0D0/rij-sig+sig0ij ! I hate to put IF's in the loops, but here don't have another choice!!!! if (rij_shift.le.0.0D0) then evdw=1.0D20 !d write (iout,'(2(a3,i3,2x),17(0pf7.3))') & !d restyp(itypi),i,restyp(itypj),j, & !d rij_shift,1.0D0/rij,sig,sig0ij,sigsq,1-dsqrt(sigsq) return endif sigder=-sig*sigsq !--------------------------------------------------------------- rij_shift=1.0D0/rij_shift fac=rij_shift**expon e1=fac*fac*aa(itypi,itypj) e2=fac*bb(itypi,itypj) evdwij=eps1*eps2rt*eps3rt*(e1+e2) eps2der=evdwij*eps3rt eps3der=evdwij*eps2rt evdwij=evdwij*eps2rt*eps3rt evdw=evdw+evdwij if (lprn) then sigm=dabs(aa(itypi,itypj)/bb(itypi,itypj))**(1.0D0/6.0D0) epsi=bb(itypi,itypj)**2/aa(itypi,itypj) !d write (iout,'(2(a3,i3,2x),17(0pf7.3))') & !d restyp(itypi),i,restyp(itypj),j, & !d epsi,sigm,chi1,chi2,chip1,chip2, & !d eps1,eps2rt**2,eps3rt**2,sig,sig0ij, & !d om1,om2,om12,1.0D0/rij,1.0D0/rij_shift, & !d evdwij endif if (energy_dec) write (iout,'(a6,2i5,0pf7.3)') & 'evdw',i,j,evdwij ! Calculate gradient components. e1=e1*eps1*eps2rt**2*eps3rt**2 fac=-expon*(e1+evdwij)*rij_shift sigder=fac*sigder fac=rij*fac ! Calculate the radial part of the gradient gg(1)=xj*fac gg(2)=yj*fac gg(3)=zj*fac ! Calculate angular part of the gradient. !elwrite(iout,*) evdw call sc_grad !elwrite(iout,*) "evdw=",evdw,j,iint,i ENDIF !elwrite(iout,*) evdw enddo ! j !elwrite(iout,*) evdw enddo ! iint !elwrite(iout,*) evdw enddo ! i !elwrite(iout,*) evdw,i end subroutine egb1 !----------------------------------------------------------------------------- ! sumsld.f !----------------------------------------------------------------------------- subroutine sumsl(n,d,x,calcf,calcg,iv,liv,lv,v,uiparm,urparm,ufparm) ! ! *** minimize general unconstrained objective function using *** ! *** analytic gradient and hessian approx. from secant update *** ! ! use control integer :: n, liv, lv integer :: iv(liv), uiparm(1) real(kind=8) :: d(n), x(n), v(lv), urparm(1) real(kind=8),external :: ufparm !funtion name as an argument ! dimension v(71 + n*(n+15)/2), uiparm(*), urparm(*) external :: calcf, calcg !subroutine name as an argument ! ! *** purpose *** ! ! this routine interacts with subroutine sumit in an attempt ! to find an n-vector x* that minimizes the (unconstrained) ! objective function computed by calcf. (often the x* found is ! a local minimizer rather than a global one.) ! !-------------------------- parameter usage -------------------------- ! ! n........ (input) the number of variables on which f depends, i.e., ! the number of components in x. ! d........ (input/output) a scale vector such that d(i)*x(i), ! i = 1,2,...,n, are all in comparable units. ! d can strongly affect the behavior of sumsl. ! finding the best choice of d is generally a trial- ! and-error process. choosing d so that d(i)*x(i) ! has about the same value for all i often works well. ! the defaults provided by subroutine deflt (see i ! below) require the caller to supply d. ! x........ (input/output) before (initially) calling sumsl, the call- ! er should set x to an initial guess at x*. when ! sumsl returns, x contains the best point so far ! found, i.e., the one that gives the least value so ! far seen for f(x). ! calcf.... (input) a subroutine that, given x, computes f(x). calcf ! must be declared external in the calling program. ! it is invoked by ! call calcf(n, x, nf, f, uiparm, urparm, ufparm) ! when calcf is called, nf is the invocation ! count for calcf. nf is included for possible use ! with calcg. if x is out of bounds (e.g., if it ! would cause overflow in computing f(x)), then calcf ! should set nf to 0. this will cause a shorter step ! to be attempted. (if x is in bounds, then calcf ! should not change nf.) the other parameters are as ! described above and below. calcf should not change ! n, p, or x. ! calcg.... (input) a subroutine that, given x, computes g(x), the gra- ! dient of f at x. calcg must be declared external in ! the calling program. it is invoked by ! call calcg(n, x, nf, g, uiparm, urparm, ufaprm) ! when calcg is called, nf is the invocation ! count for calcf at the time f(x) was evaluated. the ! x passed to calcg is usually the one passed to calcf ! on either its most recent invocation or the one ! prior to it. if calcf saves intermediate results ! for use by calcg, then it is possible to tell from ! nf whether they are valid for the current x (or ! which copy is valid if two copies are kept). if g ! cannot be computed at x, then calcg should set nf to ! 0. in this case, sumsl will return with iv(1) = 65. ! (if g can be computed at x, then calcg should not ! changed nf.) the other parameters to calcg are as ! described above and below. calcg should not change ! n or x. ! iv....... (input/output) an integer value array of length liv (see ! below) that helps control the sumsl algorithm and ! that is used to store various intermediate quanti- ! ties. of particular interest are the initialization/ ! return code iv(1) and the entries in iv that control ! printing and limit the number of iterations and func- ! tion evaluations. see the section on iv input ! values below. ! liv...... (input) length of iv array. must be at least 60. if li ! is too small, then sumsl returns with iv(1) = 15. ! when sumsl returns, the smallest allowed value of ! liv is stored in iv(lastiv) -- see the section on ! iv output values below. (this is intended for use ! with extensions of sumsl that handle constraints.) ! lv....... (input) length of v array. must be at least 71+n*(n+15)/2. ! (at least 77+n*(n+17)/2 for smsno, at least ! 78+n*(n+12) for humsl). if lv is too small, then ! sumsl returns with iv(1) = 16. when sumsl returns, ! the smallest allowed value of lv is stored in ! iv(lastv) -- see the section on iv output values ! below. ! v........ (input/output) a floating-point value array of length l ! (see below) that helps control the sumsl algorithm ! and that is used to store various intermediate ! quantities. of particular interest are the entries ! in v that limit the length of the first step ! attempted (lmax0) and specify convergence tolerances ! (afctol, lmaxs, rfctol, sctol, xctol, xftol). ! uiparm... (input) user integer parameter array passed without change ! to calcf and calcg. ! urparm... (input) user floating-point parameter array passed without ! change to calcf and calcg. ! ufparm... (input) user external subroutine or function passed without ! change to calcf and calcg. ! ! *** iv input values (from subroutine deflt) *** ! ! iv(1)... on input, iv(1) should have a value between 0 and 14...... ! 0 and 12 mean this is a fresh start. 0 means that ! deflt(2, iv, liv, lv, v) ! is to be called to provide all default values to iv and ! v. 12 (the value that deflt assigns to iv(1)) means the ! caller has already called deflt and has possibly changed ! some iv and/or v entries to non-default values. ! 13 means deflt has been called and that sumsl (and ! sumit) should only do their storage allocation. that is, ! they should set the output components of iv that tell ! where various subarrays arrays of v begin, such as iv(g) ! (and, for humsl and humit only, iv(dtol)), and return. ! 14 means that a storage has been allocated (by a call ! with iv(1) = 13) and that the algorithm should be ! started. when called with iv(1) = 13, sumsl returns ! iv(1) = 14 unless liv or lv is too small (or n is not ! positive). default = 12. ! iv(inith).... iv(25) tells whether the hessian approximation h should ! be initialized. 1 (the default) means sumit should ! initialize h to the diagonal matrix whose i-th diagonal ! element is d(i)**2. 0 means the caller has supplied a ! cholesky factor l of the initial hessian approximation ! h = l*(l**t) in v, starting at v(iv(lmat)) = v(iv(42)) ! (and stored compactly by rows). note that iv(lmat) may ! be initialized by calling sumsl with iv(1) = 13 (see ! the iv(1) discussion above). default = 1. ! iv(mxfcal)... iv(17) gives the maximum number of function evaluations ! (calls on calcf) allowed. if this number does not suf- ! fice, then sumsl returns with iv(1) = 9. default = 200. ! iv(mxiter)... iv(18) gives the maximum number of iterations allowed. ! it also indirectly limits the number of gradient evalua- ! tions (calls on calcg) to iv(mxiter) + 1. if iv(mxiter) ! iterations do not suffice, then sumsl returns with ! iv(1) = 10. default = 150. ! iv(outlev)... iv(19) controls the number and length of iteration sum- ! mary lines printed (by itsum). iv(outlev) = 0 means do ! not print any summary lines. otherwise, print a summary ! line after each abs(iv(outlev)) iterations. if iv(outlev) ! is positive, then summary lines of length 78 (plus carri- ! age control) are printed, including the following... the ! iteration and function evaluation counts, f = the current ! function value, relative difference in function values ! achieved by the latest step (i.e., reldf = (f0-v(f))/f01, ! where f01 is the maximum of abs(v(f)) and abs(v(f0)) and ! v(f0) is the function value from the previous itera- ! tion), the relative function reduction predicted for the ! step just taken (i.e., preldf = v(preduc) / f01, where ! v(preduc) is described below), the scaled relative change ! in x (see v(reldx) below), the step parameter for the ! step just taken (stppar = 0 means a full newton step, ! between 0 and 1 means a relaxed newton step, between 1 ! and 2 means a double dogleg step, greater than 2 means ! a scaled down cauchy step -- see subroutine dbldog), the ! 2-norm of the scale vector d times the step just taken ! (see v(dstnrm) below), and npreldf, i.e., ! v(nreduc)/f01, where v(nreduc) is described below -- if ! npreldf is positive, then it is the relative function ! reduction predicted for a newton step (one with ! stppar = 0). if npreldf is negative, then it is the ! negative of the relative function reduction predicted ! for a step computed with step bound v(lmaxs) for use in ! testing for singular convergence. ! if iv(outlev) is negative, then lines of length 50 ! are printed, including only the first 6 items listed ! above (through reldx). ! default = 1. ! iv(parprt)... iv(20) = 1 means print any nondefault v values on a ! fresh start or any changed v values on a restart. ! iv(parprt) = 0 means skip this printing. default = 1. ! iv(prunit)... iv(21) is the output unit number on which all printing ! is done. iv(prunit) = 0 means suppress all printing. ! default = standard output unit (unit 6 on most systems). ! iv(solprt)... iv(22) = 1 means print out the value of x returned (as ! well as the gradient and the scale vector d). ! iv(solprt) = 0 means skip this printing. default = 1. ! iv(statpr)... iv(23) = 1 means print summary statistics upon return- ! ing. these consist of the function value, the scaled ! relative change in x caused by the most recent step (see ! v(reldx) below), the number of function and gradient ! evaluations (calls on calcf and calcg), and the relative ! function reductions predicted for the last step taken and ! for a newton step (or perhaps a step bounded by v(lmaxs) ! -- see the descriptions of preldf and npreldf under ! iv(outlev) above). ! iv(statpr) = 0 means skip this printing. ! iv(statpr) = -1 means skip this printing as well as that ! of the one-line termination reason message. default = 1. ! iv(x0prt).... iv(24) = 1 means print the initial x and scale vector d ! (on a fresh start only). iv(x0prt) = 0 means skip this ! printing. default = 1. ! ! *** (selected) iv output values *** ! ! iv(1)........ on output, iv(1) is a return code.... ! 3 = x-convergence. the scaled relative difference (see ! v(reldx)) between the current parameter vector x and ! a locally optimal parameter vector is very likely at ! most v(xctol). ! 4 = relative function convergence. the relative differ- ! ence between the current function value and its lo- ! cally optimal value is very likely at most v(rfctol). ! 5 = both x- and relative function convergence (i.e., the ! conditions for iv(1) = 3 and iv(1) = 4 both hold). ! 6 = absolute function convergence. the current function ! value is at most v(afctol) in absolute value. ! 7 = singular convergence. the hessian near the current ! iterate appears to be singular or nearly so, and a ! step of length at most v(lmaxs) is unlikely to yield ! a relative function decrease of more than v(sctol). ! 8 = false convergence. the iterates appear to be converg- ! ing to a noncritical point. this may mean that the ! convergence tolerances (v(afctol), v(rfctol), ! v(xctol)) are too small for the accuracy to which ! the function and gradient are being computed, that ! there is an error in computing the gradient, or that ! the function or gradient is discontinuous near x. ! 9 = function evaluation limit reached without other con- ! vergence (see iv(mxfcal)). ! 10 = iteration limit reached without other convergence ! (see iv(mxiter)). ! 11 = stopx returned .true. (external interrupt). see the ! usage notes below. ! 14 = storage has been allocated (after a call with ! iv(1) = 13). ! 17 = restart attempted with n changed. ! 18 = d has a negative component and iv(dtype) .le. 0. ! 19...43 = v(iv(1)) is out of range. ! 63 = f(x) cannot be computed at the initial x. ! 64 = bad parameters passed to assess (which should not ! occur). ! 65 = the gradient could not be computed at x (see calcg ! above). ! 67 = bad first parameter to deflt. ! 80 = iv(1) was out of range. ! 81 = n is not positive. ! iv(g)........ iv(28) is the starting subscript in v of the current ! gradient vector (the one corresponding to x). ! iv(lastiv)... iv(44) is the least acceptable value of liv. (it is ! only set if liv is at least 44.) ! iv(lastv).... iv(45) is the least acceptable value of lv. (it is ! only set if liv is large enough, at least iv(lastiv).) ! iv(nfcall)... iv(6) is the number of calls so far made on calcf (i.e., ! function evaluations). ! iv(ngcall)... iv(30) is the number of gradient evaluations (calls on ! calcg). ! iv(niter).... iv(31) is the number of iterations performed. ! ! *** (selected) v input values (from subroutine deflt) *** ! ! v(bias)..... v(43) is the bias parameter used in subroutine dbldog -- ! see that subroutine for details. default = 0.8. ! v(afctol)... v(31) is the absolute function convergence tolerance. ! if sumsl finds a point where the function value is less ! than v(afctol) in absolute value, and if sumsl does not ! return with iv(1) = 3, 4, or 5, then it returns with ! iv(1) = 6. this test can be turned off by setting ! v(afctol) to zero. default = max(10**-20, machep**2), ! where machep is the unit roundoff. ! v(dinit).... v(38), if nonnegative, is the value to which the scale ! vector d is initialized. default = -1. ! v(lmax0).... v(35) gives the maximum 2-norm allowed for d times the ! very first step that sumsl attempts. this parameter can ! markedly affect the performance of sumsl. ! v(lmaxs).... v(36) is used in testing for singular convergence -- if ! the function reduction predicted for a step of length ! bounded by v(lmaxs) is at most v(sctol) * abs(f0), where ! f0 is the function value at the start of the current ! iteration, and if sumsl does not return with iv(1) = 3, ! 4, 5, or 6, then it returns with iv(1) = 7. default = 1. ! v(rfctol)... v(32) is the relative function convergence tolerance. ! if the current model predicts a maximum possible function ! reduction (see v(nreduc)) of at most v(rfctol)*abs(f0) ! at the start of the current iteration, where f0 is the ! then current function value, and if the last step attempt- ! ed achieved no more than twice the predicted function ! decrease, then sumsl returns with iv(1) = 4 (or 5). ! default = max(10**-10, machep**(2/3)), where machep is ! the unit roundoff. ! v(sctol).... v(37) is the singular convergence tolerance -- see the ! description of v(lmaxs) above. ! v(tuner1)... v(26) helps decide when to check for false convergence. ! this is done if the actual function decrease from the ! current step is no more than v(tuner1) times its predict- ! ed value. default = 0.1. ! v(xctol).... v(33) is the x-convergence tolerance. if a newton step ! (see v(nreduc)) is tried that has v(reldx) .le. v(xctol) ! and if this step yields at most twice the predicted func- ! tion decrease, then sumsl returns with iv(1) = 3 (or 5). ! (see the description of v(reldx) below.) ! default = machep**0.5, where machep is the unit roundoff. ! v(xftol).... v(34) is the false convergence tolerance. if a step is ! tried that gives no more than v(tuner1) times the predict- ! ed function decrease and that has v(reldx) .le. v(xftol), ! and if sumsl does not return with iv(1) = 3, 4, 5, 6, or ! 7, then it returns with iv(1) = 8. (see the description ! of v(reldx) below.) default = 100*machep, where ! machep is the unit roundoff. ! v(*)........ deflt supplies to v a number of tuning constants, with ! which it should ordinarily be unnecessary to tinker. see ! section 17 of version 2.2 of the nl2sol usage summary ! (i.e., the appendix to ref. 1) for details on v(i), ! i = decfac, incfac, phmnfc, phmxfc, rdfcmn, rdfcmx, ! tuner2, tuner3, tuner4, tuner5. ! ! *** (selected) v output values *** ! ! v(dgnorm)... v(1) is the 2-norm of (diag(d)**-1)*g, where g is the ! most recently computed gradient. ! v(dstnrm)... v(2) is the 2-norm of diag(d)*step, where step is the ! current step. ! v(f)........ v(10) is the current function value. ! v(f0)....... v(13) is the function value at the start of the current ! iteration. ! v(nreduc)... v(6), if positive, is the maximum function reduction ! possible according to the current model, i.e., the func- ! tion reduction predicted for a newton step (i.e., ! step = -h**-1 * g, where g is the current gradient and ! h is the current hessian approximation). ! if v(nreduc) is negative, then it is the negative of ! the function reduction predicted for a step computed with ! a step bound of v(lmaxs) for use in testing for singular ! convergence. ! v(preduc)... v(7) is the function reduction predicted (by the current ! quadratic model) for the current step. this (divided by ! v(f0)) is used in testing for relative function ! convergence. ! v(reldx).... v(17) is the scaled relative change in x caused by the ! current step, computed as ! max(abs(d(i)*(x(i)-x0(i)), 1 .le. i .le. p) / ! max(d(i)*(abs(x(i))+abs(x0(i))), 1 .le. i .le. p), ! where x = x0 + step. ! !------------------------------- notes ------------------------------- ! ! *** algorithm notes *** ! ! this routine uses a hessian approximation computed from the ! bfgs update (see ref 3). only a cholesky factor of the hessian ! approximation is stored, and this is updated using ideas from ! ref. 4. steps are computed by the double dogleg scheme described ! in ref. 2. the steps are assessed as in ref. 1. ! ! *** usage notes *** ! ! after a return with iv(1) .le. 11, it is possible to restart, ! i.e., to change some of the iv and v input values described above ! and continue the algorithm from the point where it was interrupt- ! ed. iv(1) should not be changed, nor should any entries of i ! and v other than the input values (those supplied by deflt). ! those who do not wish to write a calcg which computes the ! gradient analytically should call smsno rather than sumsl. ! smsno uses finite differences to compute an approximate gradient. ! those who would prefer to provide f and g (the function and ! gradient) by reverse communication rather than by writing subrou- ! tines calcf and calcg may call on sumit directly. see the com- ! ments at the beginning of sumit. ! those who use sumsl interactively may wish to supply their ! own stopx function, which should return .true. if the break key ! has been pressed since stopx was last invoked. this makes it ! possible to externally interrupt sumsl (which will return with ! iv(1) = 11 if stopx returns .true.). ! storage for g is allocated at the end of v. thus the caller ! may make v longer than specified above and may allow calcg to use ! elements of g beyond the first n as scratch storage. ! ! *** portability notes *** ! ! the sumsl distribution tape contains both single- and double- ! precision versions of the sumsl source code, so it should be un- ! necessary to change precisions. ! only the functions imdcon and rmdcon contain machine-dependent ! constants. to change from one machine to another, it should ! suffice to change the (few) relevant lines in these functions. ! intrinsic functions are explicitly declared. on certain com- ! puters (e.g. univac), it may be necessary to comment out these ! declarations. so that this may be done automatically by a simple ! program, such declarations are preceded by a comment having c/+ ! in columns 1-3 and blanks in columns 4-72 and are followed by ! a comment having c/ in columns 1 and 2 and blanks in columns 3-72. ! the sumsl source code is expressed in 1966 ansi standard ! fortran. it may be converted to fortran 77 by commenting out all ! lines that fall between a line having c/6 in columns 1-3 and a ! line having c/7 in columns 1-3 and by removing (i.e., replacing ! by a blank) the c in column 1 of the lines that follow the c/7 ! line and precede a line having c/ in columns 1-2 and blanks in ! columns 3-72. these changes convert some data statements into ! parameter statements, convert some variables from real to ! character*4, and make the data statements that initialize these ! variables use character strings delimited by primes instead ! of hollerith constants. (such variables and data statements ! appear only in modules itsum and parck. parameter statements ! appear nearly everywhere.) these changes also add save state- ! ments for variables given machine-dependent constants by rmdcon. ! ! *** references *** ! ! 1. dennis, j.e., gay, d.m., and welsch, r.e. (1981), algorithm 573 -- ! an adaptive nonlinear least-squares algorithm, acm trans. ! math. software 7, pp. 369-383. ! ! 2. dennis, j.e., and mei, h.h.w. (1979), two new unconstrained opti- ! mization algorithms which use function and gradient ! values, j. optim. theory applic. 28, pp. 453-482. ! ! 3. dennis, j.e., and more, j.j. (1977), quasi-newton methods, motiva- ! tion and theory, siam rev. 19, pp. 46-89. ! ! 4. goldfarb, d. (1976), factorized variable metric methods for uncon- ! strained optimization, math. comput. 30, pp. 796-811. ! ! *** general *** ! ! coded by david m. gay (winter 1980). revised summer 1982. ! this subroutine was written in connection with research ! supported in part by the national science foundation under ! grants mcs-7600324, dcr75-10143, 76-14311dss, mcs76-11989, ! and mcs-7906671. !. ! !---------------------------- declarations --------------------------- ! !el external deflt, sumit ! ! deflt... supplies default iv and v input components. ! sumit... reverse-communication routine that carries out sumsl algo- ! rithm. ! integer :: g1, iv1, nf real(kind=8) :: f ! ! *** subscripts for iv *** ! !el integer nextv, nfcall, nfgcal, g, toobig, vneed ! !/6 ! data nextv/47/, nfcall/6/, nfgcal/7/, g/28/, toobig/2/, vneed/4/ !/7 integer,parameter :: nextv=47, nfcall=6, nfgcal=7, g=28,& toobig=2, vneed=4 !/ ! !+++++++++++++++++++++++++++++++ body ++++++++++++++++++++++++++++++++ ! !elwrite(iout,*) "in sumsl" if (iv(1) .eq. 0) call deflt(2, iv, liv, lv, v) iv1 = iv(1) if (iv1 .eq. 12 .or. iv1 .eq. 13) iv(vneed) = iv(vneed) + n if (iv1 .eq. 14) go to 10 if (iv1 .gt. 2 .and. iv1 .lt. 12) go to 10 g1 = 1 if (iv1 .eq. 12) iv(1) = 13 go to 20 ! 10 g1 = iv(g) !elwrite(iout,*) "in sumsl go to 10" ! !elwrite(iout,*) "in sumsl" 20 call sumit(d, f, v(g1), iv, liv, lv, n, v, x) !elwrite(iout,*) "in sumsl, go to 20" !elwrite(iout,*) "in sumsl, go to 20, po sumit" !elwrite(iout,*) "in sumsl iv()", iv(1)-2 if (iv(1) - 2) 30, 40, 50 ! 30 nf = iv(nfcall) !elwrite(iout,*) "in sumsl iv",iv(nfcall) call calcf(n, x, nf, f, uiparm, urparm, ufparm) !elwrite(iout,*) "in sumsl" if (nf .le. 0) iv(toobig) = 1 go to 20 ! !elwrite(iout,*) "in sumsl" 40 call calcg(n, x, iv(nfgcal), v(g1), uiparm, urparm, ufparm) !elwrite(iout,*) "in sumsl" go to 20 ! 50 if (iv(1) .ne. 14) go to 999 ! ! *** storage allocation ! iv(g) = iv(nextv) iv(nextv) = iv(g) + n if (iv1 .ne. 13) go to 10 !elwrite(iout,*) "in sumsl" ! 999 return ! *** last card of sumsl follows *** end subroutine sumsl !----------------------------------------------------------------------------- subroutine sumit(d,fx,g,iv,liv,lv,n,v,x) use control, only:stopx ! ! *** carry out sumsl (unconstrained minimization) iterations, using ! *** double-dogleg/bfgs steps. ! ! *** parameter declarations *** ! integer :: liv, lv, n integer :: iv(liv) real(kind=8) :: d(n), fx, g(n), v(lv), x(n) ! !-------------------------- parameter usage -------------------------- ! ! d.... scale vector. ! fx... function value. ! g.... gradient vector. ! iv... integer value array. ! liv.. length of iv (at least 60). ! lv... length of v (at least 71 + n*(n+13)/2). ! n.... number of variables (components in x and g). ! v.... floating-point value array. ! x.... vector of parameters to be optimized. ! ! *** discussion *** ! ! parameters iv, n, v, and x are the same as the corresponding ! ones to sumsl (which see), except that v can be shorter (since ! the part of v that sumsl uses for storing g is not needed). ! moreover, compared with sumsl, iv(1) may have the two additional ! output values 1 and 2, which are explained below, as is the use ! of iv(toobig) and iv(nfgcal). the value iv(g), which is an ! output value from sumsl (and smsno), is not referenced by ! sumit or the subroutines it calls. ! fx and g need not have been initialized when sumit is called ! with iv(1) = 12, 13, or 14. ! ! iv(1) = 1 means the caller should set fx to f(x), the function value ! at x, and call sumit again, having changed none of the ! other parameters. an exception occurs if f(x) cannot be ! (e.g. if overflow would occur), which may happen because ! of an oversized step. in this case the caller should set ! iv(toobig) = iv(2) to 1, which will cause sumit to ig- ! nore fx and try a smaller step. the parameter nf that ! sumsl passes to calcf (for possible use by calcg) is a ! copy of iv(nfcall) = iv(6). ! iv(1) = 2 means the caller should set g to g(x), the gradient vector ! of f at x, and call sumit again, having changed none of ! the other parameters except possibly the scale vector d ! when iv(dtype) = 0. the parameter nf that sumsl passes ! to calcg is iv(nfgcal) = iv(7). if g(x) cannot be ! evaluated, then the caller may set iv(nfgcal) to 0, in ! which case sumit will return with iv(1) = 65. !. ! *** general *** ! ! coded by david m. gay (december 1979). revised sept. 1982. ! this subroutine was written in connection with research supported ! in part by the national science foundation under grants ! mcs-7600324 and mcs-7906671. ! ! (see sumsl for references.) ! !+++++++++++++++++++++++++++ declarations ++++++++++++++++++++++++++++ ! ! *** local variables *** ! integer :: dg1, dummy, g01, i, k, l, lstgst, nwtst1, step1,& temp1, w, x01, z real(kind=8) :: t !el logical :: lstopx ! ! *** constants *** ! !el real(kind=8) :: half, negone, one, onep2, zero ! ! *** no intrinsic functions *** ! ! *** external functions and subroutines *** ! !el external assst, dbdog, deflt, dotprd, itsum, litvmu, livmul, !el 1 ltvmul, lupdat, lvmul, parck, reldst, stopx, vaxpy, !el 2 vcopy, vscopy, vvmulp, v2norm, wzbfgs !el logical stopx !el real(kind=8) :: dotprd, reldst, v2norm ! ! assst.... assesses candidate step. ! dbdog.... computes double-dogleg (candidate) step. ! deflt.... supplies default iv and v input components. ! dotprd... returns inner product of two vectors. ! itsum.... prints iteration summary and info on initial and final x. ! litvmu... multiplies inverse transpose of lower triangle times vector. ! livmul... multiplies inverse of lower triangle times vector. ! ltvmul... multiplies transpose of lower triangle times vector. ! lupdt.... updates cholesky factor of hessian approximation. ! lvmul.... multiplies lower triangle times vector. ! parck.... checks validity of input iv and v values. ! reldst... computes v(reldx) = relative step size. ! stopx.... returns .true. if the break key has been pressed. ! vaxpy.... computes scalar times one vector plus another. ! vcopy.... copies one vector to another. ! vscopy... sets all elements of a vector to a scalar. ! vvmulp... multiplies vector by vector raised to power (componentwise). ! v2norm... returns the 2-norm of a vector. ! wzbfgs... computes w and z for lupdat corresponding to bfgs update. ! ! *** subscripts for iv and v *** ! !el integer afctol !el integer cnvcod, dg, dgnorm, dinit, dstnrm, dst0, f, f0, fdif, !el 1 gthg, gtstep, g0, incfac, inith, irc, kagqt, lmat, lmax0, !el 2 lmaxs, mode, model, mxfcal, mxiter, nextv, nfcall, nfgcal, !el 3 ngcall, niter, nreduc, nwtstp, preduc, radfac, radinc, !el 4 radius, rad0, reldx, restor, step, stglim, stlstg, toobig, !el 5 tuner4, tuner5, vneed, xirc, x0 ! ! *** iv subscript values *** ! !/6 ! data cnvcod/55/, dg/37/, g0/48/, inith/25/, irc/29/, kagqt/33/, ! 1 mode/35/, model/5/, mxfcal/17/, mxiter/18/, nfcall/6/, ! 2 nfgcal/7/, ngcall/30/, niter/31/, nwtstp/34/, radinc/8/, ! 3 restor/9/, step/40/, stglim/11/, stlstg/41/, toobig/2/, ! 4 vneed/4/, xirc/13/, x0/43/ !/7 integer,parameter :: cnvcod=55, dg=37, g0=48, inith=25, irc=29, kagqt=33,& mode=35, model=5, mxfcal=17, mxiter=18, nfcall=6,& nfgcal=7, ngcall=30, niter=31, nwtstp=34, radinc=8,& restor=9, step=40, stglim=11, stlstg=41, toobig=2,& vneed=4, xirc=13, x0=43 !/ ! ! *** v subscript values *** ! !/6 ! data afctol/31/ ! data dgnorm/1/, dinit/38/, dstnrm/2/, dst0/3/, f/10/, f0/13/, ! 1 fdif/11/, gthg/44/, gtstep/4/, incfac/23/, lmat/42/, ! 2 lmax0/35/, lmaxs/36/, nextv/47/, nreduc/6/, preduc/7/, ! 3 radfac/16/, radius/8/, rad0/9/, reldx/17/, tuner4/29/, ! 4 tuner5/30/ !/7 integer,parameter :: afctol=31 integer,parameter :: dgnorm=1, dinit=38, dstnrm=2, dst0=3, f=10, f0=13,& fdif=11, gthg=44, gtstep=4, incfac=23, lmat=42,& lmax0=35, lmaxs=36, nextv=47, nreduc=6, preduc=7,& radfac=16, radius=8, rad0=9, reldx=17, tuner4=29,& tuner5=30 !/ ! !/6 ! data half/0.5d+0/, negone/-1.d+0/, one/1.d+0/, onep2/1.2d+0/, ! 1 zero/0.d+0/ !/7 real(kind=8),parameter :: half=0.5d+0, negone=-1.d+0, one=1.d+0,& onep2=1.2d+0,zero=0.d+0 !/ ! !+++++++++++++++++++++++++++++++ body ++++++++++++++++++++++++++++++++ ! ! Following SAVE statement inserted. save l i = iv(1) if (i .eq. 1) go to 50 if (i .eq. 2) go to 60 ! ! *** check validity of iv and v input values *** ! if (iv(1) .eq. 0) call deflt(2, iv, liv, lv, v) if (iv(1) .eq. 12 .or. iv(1) .eq. 13) & iv(vneed) = iv(vneed) + n*(n+13)/2 call parck(2, d, iv, liv, lv, n, v) i = iv(1) - 2 if (i .gt. 12) go to 999 go to (180, 180, 180, 180, 180, 180, 120, 90, 120, 10, 10, 20), i ! ! *** storage allocation *** ! 10 l = iv(lmat) iv(x0) = l + n*(n+1)/2 iv(step) = iv(x0) + n iv(stlstg) = iv(step) + n iv(g0) = iv(stlstg) + n iv(nwtstp) = iv(g0) + n iv(dg) = iv(nwtstp) + n iv(nextv) = iv(dg) + n if (iv(1) .ne. 13) go to 20 iv(1) = 14 go to 999 ! ! *** initialization *** ! 20 iv(niter) = 0 iv(nfcall) = 1 iv(ngcall) = 1 iv(nfgcal) = 1 iv(mode) = -1 iv(model) = 1 iv(stglim) = 1 iv(toobig) = 0 iv(cnvcod) = 0 iv(radinc) = 0 v(rad0) = zero if (v(dinit) .ge. zero) call vscopy(n, d, v(dinit)) if (iv(inith) .ne. 1) go to 40 ! ! *** set the initial hessian approximation to diag(d)**-2 *** ! l = iv(lmat) call vscopy(n*(n+1)/2, v(l), zero) k = l - 1 do 30 i = 1, n k = k + i t = d(i) if (t .le. zero) t = one v(k) = t 30 continue ! ! *** compute initial function value *** ! 40 iv(1) = 1 go to 999 ! 50 v(f) = fx if (iv(mode) .ge. 0) go to 180 iv(1) = 2 if (iv(toobig) .eq. 0) go to 999 iv(1) = 63 go to 300 ! ! *** make sure gradient could be computed *** ! 60 if (iv(nfgcal) .ne. 0) go to 70 iv(1) = 65 go to 300 ! 70 dg1 = iv(dg) call vvmulp(n, v(dg1), g, d, -1) v(dgnorm) = v2norm(n, v(dg1)) ! ! *** test norm of gradient *** ! if (v(dgnorm) .gt. v(afctol)) go to 75 iv(irc) = 10 iv(cnvcod) = iv(irc) - 4 ! 75 if (iv(cnvcod) .ne. 0) go to 290 if (iv(mode) .eq. 0) go to 250 ! ! *** allow first step to have scaled 2-norm at most v(lmax0) *** ! v(radius) = v(lmax0) ! iv(mode) = 0 ! ! !----------------------------- main loop ----------------------------- ! ! ! *** print iteration summary, check iteration limit *** ! 80 call itsum(d, g, iv, liv, lv, n, v, x) 90 k = iv(niter) if (k .lt. iv(mxiter)) go to 100 iv(1) = 10 go to 300 ! ! *** update radius *** ! 100 iv(niter) = k + 1 if(k.gt.0)v(radius) = v(radfac) * v(dstnrm) ! ! *** initialize for start of next iteration *** ! g01 = iv(g0) x01 = iv(x0) v(f0) = v(f) iv(irc) = 4 iv(kagqt) = -1 ! ! *** copy x to x0, g to g0 *** ! call vcopy(n, v(x01), x) call vcopy(n, v(g01), g) ! ! *** check stopx and function evaluation limit *** ! ! AL 4/30/95 dummy=iv(nfcall) !el lstopx = stopx(dummy) !elwrite(iout,*) "lstopx",lstopx,dummy 110 if (.not. stopx(dummy)) go to 130 iv(1) = 11 ! write (iout,*) "iv(1)=11 !!!!" go to 140 ! ! *** come here when restarting after func. eval. limit or stopx. ! 120 if (v(f) .ge. v(f0)) go to 130 v(radfac) = one k = iv(niter) go to 100 ! 130 if (iv(nfcall) .lt. iv(mxfcal)) go to 150 iv(1) = 9 140 if (v(f) .ge. v(f0)) go to 300 ! ! *** in case of stopx or function evaluation limit with ! *** improved v(f), evaluate the gradient at x. ! iv(cnvcod) = iv(1) go to 240 ! !. . . . . . . . . . . . . compute candidate step . . . . . . . . . . ! 150 step1 = iv(step) dg1 = iv(dg) nwtst1 = iv(nwtstp) if (iv(kagqt) .ge. 0) go to 160 l = iv(lmat) call livmul(n, v(nwtst1), v(l), g) v(nreduc) = half * dotprd(n, v(nwtst1), v(nwtst1)) call litvmu(n, v(nwtst1), v(l), v(nwtst1)) call vvmulp(n, v(step1), v(nwtst1), d, 1) v(dst0) = v2norm(n, v(step1)) call vvmulp(n, v(dg1), v(dg1), d, -1) call ltvmul(n, v(step1), v(l), v(dg1)) v(gthg) = v2norm(n, v(step1)) iv(kagqt) = 0 160 call dbdog(v(dg1), lv, n, v(nwtst1), v(step1), v) if (iv(irc) .eq. 6) go to 180 ! ! *** check whether evaluating f(x0 + step) looks worthwhile *** ! if (v(dstnrm) .le. zero) go to 180 if (iv(irc) .ne. 5) go to 170 if (v(radfac) .le. one) go to 170 if (v(preduc) .le. onep2 * v(fdif)) go to 180 ! ! *** compute f(x0 + step) *** ! 170 x01 = iv(x0) step1 = iv(step) call vaxpy(n, x, one, v(step1), v(x01)) iv(nfcall) = iv(nfcall) + 1 iv(1) = 1 iv(toobig) = 0 go to 999 ! !. . . . . . . . . . . . . assess candidate step . . . . . . . . . . . ! 180 x01 = iv(x0) v(reldx) = reldst(n, d, x, v(x01)) call assst(iv, liv, lv, v) step1 = iv(step) lstgst = iv(stlstg) if (iv(restor) .eq. 1) call vcopy(n, x, v(x01)) if (iv(restor) .eq. 2) call vcopy(n, v(lstgst), v(step1)) if (iv(restor) .ne. 3) go to 190 call vcopy(n, v(step1), v(lstgst)) call vaxpy(n, x, one, v(step1), v(x01)) v(reldx) = reldst(n, d, x, v(x01)) ! 190 k = iv(irc) go to (200,230,230,230,200,210,220,220,220,220,220,220,280,250), k ! ! *** recompute step with changed radius *** ! 200 v(radius) = v(radfac) * v(dstnrm) go to 110 ! ! *** compute step of length v(lmaxs) for singular convergence test. ! 210 v(radius) = v(lmaxs) go to 150 ! ! *** convergence or false convergence *** ! 220 iv(cnvcod) = k - 4 if (v(f) .ge. v(f0)) go to 290 if (iv(xirc) .eq. 14) go to 290 iv(xirc) = 14 ! !. . . . . . . . . . . . process acceptable step . . . . . . . . . . . ! 230 if (iv(irc) .ne. 3) go to 240 step1 = iv(step) temp1 = iv(stlstg) ! ! *** set temp1 = hessian * step for use in gradient tests *** ! l = iv(lmat) call ltvmul(n, v(temp1), v(l), v(step1)) call lvmul(n, v(temp1), v(l), v(temp1)) ! ! *** compute gradient *** ! 240 iv(ngcall) = iv(ngcall) + 1 iv(1) = 2 go to 999 ! ! *** initializations -- g0 = g - g0, etc. *** ! 250 g01 = iv(g0) call vaxpy(n, v(g01), negone, v(g01), g) step1 = iv(step) temp1 = iv(stlstg) if (iv(irc) .ne. 3) go to 270 ! ! *** set v(radfac) by gradient tests *** ! ! *** set temp1 = diag(d)**-1 * (hessian*step + (g(x0)-g(x))) *** ! call vaxpy(n, v(temp1), negone, v(g01), v(temp1)) call vvmulp(n, v(temp1), v(temp1), d, -1) ! ! *** do gradient tests *** ! if (v2norm(n, v(temp1)) .le. v(dgnorm) * v(tuner4)) & go to 260 if (dotprd(n, g, v(step1)) & .ge. v(gtstep) * v(tuner5)) go to 270 260 v(radfac) = v(incfac) ! ! *** update h, loop *** ! 270 w = iv(nwtstp) z = iv(x0) l = iv(lmat) call wzbfgs(v(l), n, v(step1), v(w), v(g01), v(z)) ! ! ** use the n-vectors starting at v(step1) and v(g01) for scratch.. call lupdat(v(temp1), v(step1), v(l), v(g01), v(l), n, v(w), v(z)) iv(1) = 2 go to 80 ! !. . . . . . . . . . . . . . misc. details . . . . . . . . . . . . . . ! ! *** bad parameters to assess *** ! 280 iv(1) = 64 go to 300 ! ! *** print summary of final iteration and other requested items *** ! 290 iv(1) = iv(cnvcod) iv(cnvcod) = 0 300 call itsum(d, g, iv, liv, lv, n, v, x) ! 999 return ! ! *** last line of sumit follows *** end subroutine sumit !----------------------------------------------------------------------------- subroutine dbdog(dig,lv,n,nwtstp,step,v) ! ! *** compute double dogleg step *** ! ! *** parameter declarations *** ! integer :: lv, n real(kind=8) :: dig(n), nwtstp(n), step(n), v(lv) ! ! *** purpose *** ! ! this subroutine computes a candidate step (for use in an uncon- ! strained minimization code) by the double dogleg algorithm of ! dennis and mei (ref. 1), which is a variation on powell*s dogleg ! scheme (ref. 2, p. 95). ! !-------------------------- parameter usage -------------------------- ! ! dig (input) diag(d)**-2 * g -- see algorithm notes. ! g (input) the current gradient vector. ! lv (input) length of v. ! n (input) number of components in dig, g, nwtstp, and step. ! nwtstp (input) negative newton step -- see algorithm notes. ! step (output) the computed step. ! v (i/o) values array, the following components of which are ! used here... ! v(bias) (input) bias for relaxed newton step, which is v(bias) of ! the way from the full newton to the fully relaxed newton ! step. recommended value = 0.8 . ! v(dgnorm) (input) 2-norm of diag(d)**-1 * g -- see algorithm notes. ! v(dstnrm) (output) 2-norm of diag(d) * step, which is v(radius) ! unless v(stppar) = 0 -- see algorithm notes. ! v(dst0) (input) 2-norm of diag(d) * nwtstp -- see algorithm notes. ! v(grdfac) (output) the coefficient of dig in the step returned -- ! step(i) = v(grdfac)*dig(i) + v(nwtfac)*nwtstp(i). ! v(gthg) (input) square-root of (dig**t) * (hessian) * dig -- see ! algorithm notes. ! v(gtstep) (output) inner product between g and step. ! v(nreduc) (output) function reduction predicted for the full newton ! step. ! v(nwtfac) (output) the coefficient of nwtstp in the step returned -- ! see v(grdfac) above. ! v(preduc) (output) function reduction predicted for the step returned. ! v(radius) (input) the trust region radius. d times the step returned ! has 2-norm v(radius) unless v(stppar) = 0. ! v(stppar) (output) code telling how step was computed... 0 means a ! full newton step. between 0 and 1 means v(stppar) of the ! way from the newton to the relaxed newton step. between ! 1 and 2 means a true double dogleg step, v(stppar) - 1 of ! the way from the relaxed newton to the cauchy step. ! greater than 2 means 1 / (v(stppar) - 1) times the cauchy ! step. ! !------------------------------- notes ------------------------------- ! ! *** algorithm notes *** ! ! let g and h be the current gradient and hessian approxima- ! tion respectively and let d be the current scale vector. this ! routine assumes dig = diag(d)**-2 * g and nwtstp = h**-1 * g. ! the step computed is the same one would get by replacing g and h ! by diag(d)**-1 * g and diag(d)**-1 * h * diag(d)**-1, ! computing step, and translating step back to the original ! variables, i.e., premultiplying it by diag(d)**-1. ! ! *** references *** ! ! 1. dennis, j.e., and mei, h.h.w. (1979), two new unconstrained opti- ! mization algorithms which use function and gradient ! values, j. optim. theory applic. 28, pp. 453-482. ! 2. powell, m.j.d. (1970), a hybrid method for non-linear equations, ! in numerical methods for non-linear equations, edited by ! p. rabinowitz, gordon and breach, london. ! ! *** general *** ! ! coded by david m. gay. ! this subroutine was written in connection with research supported ! by the national science foundation under grants mcs-7600324 and ! mcs-7906671. ! !------------------------ external quantities ------------------------ ! ! *** functions and subroutines called *** ! !el external dotprd, v2norm !el real(kind=8) :: dotprd, v2norm ! ! dotprd... returns inner product of two vectors. ! v2norm... returns 2-norm of a vector. ! ! *** intrinsic functions *** !/+ !el real(kind=8) :: dsqrt !/ !-------------------------- local variables -------------------------- ! integer :: i real(kind=8) :: cfact, cnorm, ctrnwt, ghinvg, femnsq, gnorm,& nwtnrm, relax, rlambd, t, t1, t2 !el real(kind=8) :: half, one, two, zero ! ! *** v subscripts *** ! !el integer bias, dgnorm, dstnrm, dst0, grdfac, gthg, gtstep, !el 1 nreduc, nwtfac, preduc, radius, stppar ! ! *** data initializations *** ! !/6 ! data half/0.5d+0/, one/1.d+0/, two/2.d+0/, zero/0.d+0/ !/7 real(kind=8),parameter :: half=0.5d+0, one=1.d+0, two=2.d+0, zero=0.d+0 !/ ! !/6 ! data bias/43/, dgnorm/1/, dstnrm/2/, dst0/3/, grdfac/45/, ! 1 gthg/44/, gtstep/4/, nreduc/6/, nwtfac/46/, preduc/7/, ! 2 radius/8/, stppar/5/ !/7 integer,parameter :: bias=43, dgnorm=1, dstnrm=2, dst0=3, grdfac=45,& gthg=44, gtstep=4, nreduc=6, nwtfac=46, preduc=7,& radius=8, stppar=5 !/ ! !+++++++++++++++++++++++++++++++ body ++++++++++++++++++++++++++++++++ ! nwtnrm = v(dst0) rlambd = one if (nwtnrm .gt. zero) rlambd = v(radius) / nwtnrm gnorm = v(dgnorm) ghinvg = two * v(nreduc) v(grdfac) = zero v(nwtfac) = zero if (rlambd .lt. one) go to 30 ! ! *** the newton step is inside the trust region *** ! v(stppar) = zero v(dstnrm) = nwtnrm v(gtstep) = -ghinvg v(preduc) = v(nreduc) v(nwtfac) = -one do 20 i = 1, n 20 step(i) = -nwtstp(i) go to 999 ! 30 v(dstnrm) = v(radius) cfact = (gnorm / v(gthg))**2 ! *** cauchy step = -cfact * g. cnorm = gnorm * cfact relax = one - v(bias) * (one - gnorm*cnorm/ghinvg) if (rlambd .lt. relax) go to 50 ! ! *** step is between relaxed newton and full newton steps *** ! v(stppar) = one - (rlambd - relax) / (one - relax) t = -rlambd v(gtstep) = t * ghinvg v(preduc) = rlambd * (one - half*rlambd) * ghinvg v(nwtfac) = t do 40 i = 1, n 40 step(i) = t * nwtstp(i) go to 999 ! 50 if (cnorm .lt. v(radius)) go to 70 ! ! *** the cauchy step lies outside the trust region -- ! *** step = scaled cauchy step *** ! t = -v(radius) / gnorm v(grdfac) = t v(stppar) = one + cnorm / v(radius) v(gtstep) = -v(radius) * gnorm v(preduc) = v(radius)*(gnorm - half*v(radius)*(v(gthg)/gnorm)**2) do 60 i = 1, n 60 step(i) = t * dig(i) go to 999 ! ! *** compute dogleg step between cauchy and relaxed newton *** ! *** femur = relaxed newton step minus cauchy step *** ! 70 ctrnwt = cfact * relax * ghinvg / gnorm ! *** ctrnwt = inner prod. of cauchy and relaxed newton steps, ! *** scaled by gnorm**-1. t1 = ctrnwt - gnorm*cfact**2 ! *** t1 = inner prod. of femur and cauchy step, scaled by ! *** gnorm**-1. t2 = v(radius)*(v(radius)/gnorm) - gnorm*cfact**2 t = relax * nwtnrm femnsq = (t/gnorm)*t - ctrnwt - t1 ! *** femnsq = square of 2-norm of femur, scaled by gnorm**-1. t = t2 / (t1 + dsqrt(t1**2 + femnsq*t2)) ! *** dogleg step = cauchy step + t * femur. t1 = (t - one) * cfact v(grdfac) = t1 t2 = -t * relax v(nwtfac) = t2 v(stppar) = two - t v(gtstep) = t1*gnorm**2 + t2*ghinvg v(preduc) = -t1*gnorm * ((t2 + one)*gnorm) & - t2 * (one + half*t2)*ghinvg & - half * (v(gthg)*t1)**2 do 80 i = 1, n 80 step(i) = t1*dig(i) + t2*nwtstp(i) ! 999 return ! *** last line of dbdog follows *** end subroutine dbdog !----------------------------------------------------------------------------- subroutine ltvmul(n,x,l,y) ! ! *** compute x = (l**t)*y, where l is an n x n lower ! *** triangular matrix stored compactly by rows. x and y may ! *** occupy the same storage. *** ! integer :: n !al real(kind=8) :: x(n), l(1), y(n) real(kind=8) :: x(n), l(n*(n+1)/2), y(n) ! dimension l(n*(n+1)/2) integer :: i, ij, i0, j real(kind=8) :: yi !el, zero !/6 ! data zero/0.d+0/ !/7 real(kind=8),parameter :: zero=0.d+0 !/ ! i0 = 0 do 20 i = 1, n yi = y(i) x(i) = zero do 10 j = 1, i ij = i0 + j x(j) = x(j) + yi*l(ij) 10 continue i0 = i0 + i 20 continue 999 return ! *** last card of ltvmul follows *** end subroutine ltvmul !----------------------------------------------------------------------------- subroutine lupdat(beta,gamma,l,lambda,lplus,n,w,z) ! ! *** compute lplus = secant update of l *** ! ! *** parameter declarations *** ! integer :: n !al double precision beta(n), gamma(n), l(1), lambda(n), lplus(1), real(kind=8) :: beta(n), gamma(n), l(n*(n+1)/2), lambda(n), & lplus(n*(n+1)/2),w(n), z(n) ! dimension l(n*(n+1)/2), lplus(n*(n+1)/2) ! !-------------------------- parameter usage -------------------------- ! ! beta = scratch vector. ! gamma = scratch vector. ! l (input) lower triangular matrix, stored rowwise. ! lambda = scratch vector. ! lplus (output) lower triangular matrix, stored rowwise, which may ! occupy the same storage as l. ! n (input) length of vector parameters and order of matrices. ! w (input, destroyed on output) right singular vector of rank 1 ! correction to l. ! z (input, destroyed on output) left singular vector of rank 1 ! correction to l. ! !------------------------------- notes ------------------------------- ! ! *** application and usage restrictions *** ! ! this routine updates the cholesky factor l of a symmetric ! positive definite matrix to which a secant update is being ! applied -- it computes a cholesky factor lplus of ! l * (i + z*w**t) * (i + w*z**t) * l**t. it is assumed that w ! and z have been chosen so that the updated matrix is strictly ! positive definite. ! ! *** algorithm notes *** ! ! this code uses recurrence 3 of ref. 1 (with d(j) = 1 for all j) ! to compute lplus of the form l * (i + z*w**t) * q, where q ! is an orthogonal matrix that makes the result lower triangular. ! lplus may have some negative diagonal elements. ! ! *** references *** ! ! 1. goldfarb, d. (1976), factorized variable metric methods for uncon- ! strained optimization, math. comput. 30, pp. 796-811. ! ! *** general *** ! ! coded by david m. gay (fall 1979). ! this subroutine was written in connection with research supported ! by the national science foundation under grants mcs-7600324 and ! mcs-7906671. ! !------------------------ external quantities ------------------------ ! ! *** intrinsic functions *** !/+ !el real(kind=8) :: dsqrt !/ !-------------------------- local variables -------------------------- ! integer :: i, ij, j, jj, jp1, k, nm1, np1 real(kind=8) :: a, b, bj, eta, gj, lj, lij, ljj, nu, s, theta,& wj, zj !el real(kind=8) :: one, zero ! ! *** data initializations *** ! !/6 ! data one/1.d+0/, zero/0.d+0/ !/7 real(kind=8),parameter :: one=1.d+0, zero=0.d+0 !/ ! !+++++++++++++++++++++++++++++++ body ++++++++++++++++++++++++++++++++ ! nu = one eta = zero if (n .le. 1) go to 30 nm1 = n - 1 ! ! *** temporarily store s(j) = sum over k = j+1 to n of w(k)**2 in ! *** lambda(j). ! s = zero do 10 i = 1, nm1 j = n - i s = s + w(j+1)**2 lambda(j) = s 10 continue ! ! *** compute lambda, gamma, and beta by goldfarb*s recurrence 3. ! do 20 j = 1, nm1 wj = w(j) a = nu*z(j) - eta*wj theta = one + a*wj s = a*lambda(j) lj = dsqrt(theta**2 + a*s) if (theta .gt. zero) lj = -lj lambda(j) = lj b = theta*wj + s gamma(j) = b * nu / lj beta(j) = (a - b*eta) / lj nu = -nu / lj eta = -(eta + (a**2)/(theta - lj)) / lj 20 continue 30 lambda(n) = one + (nu*z(n) - eta*w(n))*w(n) ! ! *** update l, gradually overwriting w and z with l*w and l*z. ! np1 = n + 1 jj = n * (n + 1) / 2 do 60 k = 1, n j = np1 - k lj = lambda(j) ljj = l(jj) lplus(jj) = lj * ljj wj = w(j) w(j) = ljj * wj zj = z(j) z(j) = ljj * zj if (k .eq. 1) go to 50 bj = beta(j) gj = gamma(j) ij = jj + j jp1 = j + 1 do 40 i = jp1, n lij = l(ij) lplus(ij) = lj*lij + bj*w(i) + gj*z(i) w(i) = w(i) + lij*wj z(i) = z(i) + lij*zj ij = ij + i 40 continue 50 jj = jj - j 60 continue ! 999 return ! *** last card of lupdat follows *** end subroutine lupdat !----------------------------------------------------------------------------- subroutine lvmul(n,x,l,y) ! ! *** compute x = l*y, where l is an n x n lower triangular ! *** matrix stored compactly by rows. x and y may occupy the same ! *** storage. *** ! integer :: n !al double precision x(n), l(1), y(n) real(kind=8) :: x(n), l(n*(n+1)/2), y(n) ! dimension l(n*(n+1)/2) integer :: i, ii, ij, i0, j, np1 real(kind=8) :: t !el, zero !/6 ! data zero/0.d+0/ !/7 real(kind=8),parameter :: zero=0.d+0 !/ ! np1 = n + 1 i0 = n*(n+1)/2 do 20 ii = 1, n i = np1 - ii i0 = i0 - i t = zero do 10 j = 1, i ij = i0 + j t = t + l(ij)*y(j) 10 continue x(i) = t 20 continue 999 return ! *** last card of lvmul follows *** end subroutine lvmul !----------------------------------------------------------------------------- subroutine vvmulp(n,x,y,z,k) ! ! *** set x(i) = y(i) * z(i)**k, 1 .le. i .le. n (for k = 1 or -1) *** ! integer :: n, k real(kind=8) :: x(n), y(n), z(n) integer :: i ! if (k .ge. 0) go to 20 do 10 i = 1, n 10 x(i) = y(i) / z(i) go to 999 ! 20 do 30 i = 1, n 30 x(i) = y(i) * z(i) 999 return ! *** last card of vvmulp follows *** end subroutine vvmulp !----------------------------------------------------------------------------- subroutine wzbfgs(l,n,s,w,y,z) ! ! *** compute y and z for lupdat corresponding to bfgs update. ! integer :: n !al double precision l(1), s(n), w(n), y(n), z(n) real(kind=8) :: l(n*(n+1)/2), s(n), w(n), y(n), z(n) ! dimension l(n*(n+1)/2) ! !-------------------------- parameter usage -------------------------- ! ! l (i/o) cholesky factor of hessian, a lower triang. matrix stored ! compactly by rows. ! n (input) order of l and length of s, w, y, z. ! s (input) the step just taken. ! w (output) right singular vector of rank 1 correction to l. ! y (input) change in gradients corresponding to s. ! z (output) left singular vector of rank 1 correction to l. ! !------------------------------- notes ------------------------------- ! ! *** algorithm notes *** ! ! when s is computed in certain ways, e.g. by gqtstp or ! dbldog, it is possible to save n**2/2 operations since (l**t)*s ! or l*(l**t)*s is then known. ! if the bfgs update to l*(l**t) would reduce its determinant to ! less than eps times its old value, then this routine in effect ! replaces y by theta*y + (1 - theta)*l*(l**t)*s, where theta ! (between 0 and 1) is chosen to make the reduction factor = eps. ! ! *** general *** ! ! coded by david m. gay (fall 1979). ! this subroutine was written in connection with research supported ! by the national science foundation under grants mcs-7600324 and ! mcs-7906671. ! !------------------------ external quantities ------------------------ ! ! *** functions and subroutines called *** ! !el external dotprd, livmul, ltvmul !el real(kind=8) :: dotprd ! dotprd returns inner product of two vectors. ! livmul multiplies l**-1 times a vector. ! ltvmul multiplies l**t times a vector. ! ! *** intrinsic functions *** !/+ !el real(kind=8) :: dsqrt !/ !-------------------------- local variables -------------------------- ! integer :: i real(kind=8) :: cs, cy, epsrt, shs, ys, theta !el, eps, one ! ! *** data initializations *** ! !/6 ! data eps/0.1d+0/, one/1.d+0/ !/7 real(kind=8),parameter :: eps=0.1d+0, one=1.d+0 !/ ! !+++++++++++++++++++++++++++++++ body ++++++++++++++++++++++++++++++++ ! call ltvmul(n, w, l, s) shs = dotprd(n, w, w) ys = dotprd(n, y, s) if (ys .ge. eps*shs) go to 10 theta = (one - eps) * shs / (shs - ys) epsrt = dsqrt(eps) cy = theta / (shs * epsrt) cs = (one + (theta-one)/epsrt) / shs go to 20 10 cy = one / (dsqrt(ys) * dsqrt(shs)) cs = one / shs 20 call livmul(n, z, l, y) do 30 i = 1, n 30 z(i) = cy * z(i) - cs * w(i) ! 999 return ! *** last card of wzbfgs follows *** end subroutine wzbfgs !----------------------------------------------------------------------------- !----------------------------------------------------------------------------- end module minimm