Files
piscal/dataassim/math/nonlinsystems/nonsyssolver.f
T
2022-09-12 16:40:28 +00:00

139 lines
4.9 KiB
FortranFixed

subroutine nonsyssolver(funcnleq1,fmin_funcnleq1,
&f1dim_funcnleq1,DNQFJ_funcnleq1,x0min,x0ori,xp,x0max,fp,
&nunknowns,iwhichsolver)
implicit none
integer nunknowns,iwhichsolver
double precision x0min(nunknowns),x0ori(nunknowns),
& xp(nunknowns),x0max(nunknowns),fp(nunknowns)
!-------- Specified values ---------------------------------------
!funcnleq1: the subroutine that calculates the functional values of the
! the nonlinear system in the following form:
! funcnleq1(nunknowns,xp,fp,fsqsum)
!fmin_funcnleq1: the subroutine that calls funcnleq1 and returns fsqsum
! fmin_funcnleq1(nunknowns,xp,fsqsum)
!f1dim_funcnleq1: a function subroutine that returns fsqsum
! f1dim_funcnleq1(xp)
! nunknowns: The number of unknowns to be solved
! x0ori(1:nunknowns): initial guess for the unknowns
! x0min(1:nunknowns): lower bound of the solution
! x0max(1:nunknowns): upper bound of the solution
! --------- Calculated values -------------------------------------
! fp(1:nunknowns): function values at the last step of iteration
! xp(1:nunknowns): final solutions
! iwhichsolver:
! =1 solved by plain fixed point method 1
! =2 solved by fixed point method 2
! =3 solved by fixed point method 3
! =4 solved by fixed point method 4
! =6 solved by broydn
! =7 Solved by multiobjective minimization.
! =8 Solved by DNQSOL
! =-9999 Best approximation returned. Solution may not be accurate.
! --------- Local variables ---------------------------------------
double precision x0(nunknowns),TOLF,stpmax,scldstpmax,ran2,
&sum,tb,tp,xb(nunknowns),fb(nunknowns),fsqsum,f1dim_funcnleq1,
&D1MACH,Warray(3+(15*nunknowns+3*nunknowns*nunknowns)/2+1)
integer i,irepeat,maxrepeats,IERR,notfound,IOPT(5),IDIMW
intrinsic dble
parameter(maxrepeats=100,notfound=-9999)
external funcnleq1,fmin_funcnleq1,f1dim_funcnleq1,
&DNQFJ_funcnleq1
!-------------------------------------------------------------------
do i=1, nunknowns
xp(i)=x0ori(i)
enddo
iwhichsolver=notfound
TOLF=dsqrt(D1MACH(4))
do irepeat=1,maxrepeats
IDIMW=3+(15*nunknowns+3*nunknowns*nunknowns)/2+1
do i=1,5
IOPT(i)=0
enddo
IOPT(4)=1
call DNQSOL(DNQFJ_funcnleq1,nunknowns,xp,fp,TOLF,
&IOPT,Warray,IDIMW)
if(IOPT(1).eq.0)then
iwhichsolver=8
return
endif
do i=1,nunknowns
x0(i)=x0min(i)+ran2()*(x0max(i)-x0min(i))
enddo
stpmax=0.0d0
sum=0.0d0
do i=1, nunknowns
sum=sum+x0(i)*x0(i)
stpmax=stpmax+(x0min(i)-x0max(i))*(x0min(i)-x0max(i))
enddo
stpmax=dsqrt(stpmax)/4.0d0
scldstpmax=stpmax/dmax1(dsqrt(sum),dble(nunknowns))
! In Numerical Recipes, scldstpmax (STPMX) is 100
scldstpmax=dmax1(100.0d0,scldstpmax)
call fixedpoint(funcnleq1,x0min,x0,xp,
& x0max,fp,nunknowns,TOLF,stpmax,iwhichsolver)
if(iwhichsolver.ne.notfound)return
tp=dabs(fp(1))
xb(1)=xp(1)
do i=2,nunknowns
if(dabs(fp(i)).gt.tp)tp=dabs(fp(i))
xb(i)=xp(i)
enddo
call broydn(x0min,xb,x0max,scldstpmax,nunknowns,
& fb,funcnleq1,TOLF,IERR)
call funcnleq1(nunknowns,xb,fb,fsqsum)
tb=dabs(fb(1))
do i=2,nunknowns
if(dabs(fb(i)).gt.tb)tb=dabs(fb(i))
enddo
do i=1,nunknowns
if(xb(i).lt.x0min(i).or.xb(i).gt.x0max(i))then
tb=1.0d+100
endif
enddo
if(tb.lt.tp)then
do i=1,nunknowns
xp(i)=xb(i)
fp(i)=fb(i)
enddo
if(tb.lt.TOLF)then
iwhichsolver=6
return
endif
endif
do i=1,nunknowns
xp(i)=x0min(i)+ran2()*(x0max(i)-x0min(i))
enddo
call funcnleq1(nunknowns,xp,fp,fsqsum)
fsqsum=0.0d0
do i=1,nunknowns
fsqsum=fsqsum+fp(i)*fp(i)
enddo
tp=fsqsum
call nongradopt(nunknowns,fmin_funcnleq1,
& f1dim_funcnleq1,xp,x0min,x0max,TOLF,fsqsum)
if(dabs(tp-fsqsum).gt.TOLF)then
call RepeatCompassSearch(nunknowns,xp,fsqsum,
& x0min,x0max,fmin_funcnleq1,f1dim_funcnleq1,
& TOLF)
endif
call funcnleq1(nunknowns,xp,fp,fsqsum)
tp=dabs(fp(1))
do i=2,nunknowns
if(dabs(fp(i)).gt.tp)tp=dabs(fp(i))
enddo
if(tp.lt.TOLF)then
iwhichsolver=7
return
endif
IERR=0
do i=1,nunknowns
if(dabs(xp(i)-x0(i)).gt.TOLF)IERR=1
enddo
if(IERR.eq.0)return
do i=1,nunknowns
xp(i)=x0min(i)+ran2()*(x0max(i)-x0min(i))
enddo
enddo
end subroutine nonsyssolver