https://github.com/cran/nleqslv
Tip revision: 841972b2cdbfaddf568c3813f28ee733b4382d77 authored by Berend Hasselman on 26 November 2023, 23:30:14 UTC
version 3.3.5
version 3.3.5
Tip revision: 841972b
nwnwtn.f
subroutine nwsolv(ldr,xc,n,scalex,maxit,
* jacflg,xtol,ftol,btol,cndtol,global,xscalm,
* stepmx,delta,sigma,
* rjac,wrk1,wrk2,wrk3,wrk4,fc,fq,dn,d,qtf,
* rcdwrk,icdwrk,qrwork,qrwsiz,epsm,
* fjac,fvec,outopt,xp,fp,gp,njcnt,nfcnt,iter,
* termcd)
integer ldr,n,termcd,njcnt,nfcnt,iter
integer maxit,jacflg(*),global,xscalm,qrwsiz
integer outopt(*)
double precision xtol,ftol,btol,cndtol
double precision stepmx,delta,sigma,fpnorm,epsm
double precision rjac(ldr,*)
double precision xc(*),fc(*),xp(*),fp(*),dn(*),d(*)
double precision wrk1(*),wrk2(*),wrk3(*),wrk4(*)
double precision qtf(*),gp(*),fq(*)
double precision scalex(*)
double precision rcdwrk(*),qrwork(*)
integer icdwrk(*)
external fjac,fvec
c-----------------------------------------------------------------------
c
c Solve system of nonlinear equations with Newton and global strategy
c
c
c Arguments
c
c In ldr Integer leading dimension of rjac
c In xc Real(*) initial estimate of solution
c In n Integer dimensions of problem
c Inout scalex Real(*) scaling factors x(*)
c In maxit Integer maximum number of allowable iterations
c In jacflg Integer(*) jacobian flag array
c jacflg[1]: 0 numeric; 1 user supplied; 2 numerical banded
c 3: user supplied banded
c jacflg[2]: number of sub diagonals or -1 if not banded
c jacflg[3]: number of super diagonals or -1 if not banded
c jacflg[4]: 1 if adjusting step allowed when
c singular or illconditioned
c In xtol Real tolerance at which successive iterates x()
c are considered close enough to
c terminate algorithm
c In ftol Real tolerance at which function values f()
c are considered close enough to zero
c Inout btol Real x tolerance for backtracking
c Inout cndtol Real tolerance of test for ill conditioning
c In global Integer global strategy to use
c 1 cubic linesearch
c 2 quadratic linesearch
c 3 geometric linesearch
c 4 double dogleg
c 5 powell dogleg
c 6 hookstep (More-Hebden Levenberg-Marquardt)
c In xscalm Integer x scaling method
c 1 from column norms of first jacobian
c increased if needed after first iteration
c 0 scaling user supplied
c In stepmx Real maximum allowable step size
c In delta Real trust region radius
c In sigma Real reduction factor geometric linesearch
c Inout rjac Real(ldr,*) jacobian (n columns)
c Wk wrk1 Real(*) workspace
c Wk wrk2 Real(*) workspace
c Wk wrk3 Real(*) workspace
c Wk wrk4 Real(*) workspace
c Inout fc Real(*) function values f(xc)
c Wk fq Real(*) workspace
c Wk dn Real(*) workspace
c Wk d Real(*) workspace
c Wk qtf Real(*) workspace
c Wk rcdwrk Real(*) workspace
c Wk icdwrk Integer(*) workspace
c In qrwork Real(*) workspace for Lapack QR routines (call liqsiz)
c In qrwsiz Integer size of qrwork
c In epsm Real machine precision
c In fjac Name name of routine to calculate jacobian
c (optional)
c In fvec Name name of routine to calculate f()
c In outopt Integer(*) output options
c Out xp Real(*) final x()
c Out fp Real(*) final f(xp)
c Out gp Real(*) gradient at xp()
c Out njcnt Integer number of jacobian evaluations
c Out nfcnt Integer number of function evaluations
c Out iter Integer number of (outer) iterations
c Out termcd Integer termination code
c
c-----------------------------------------------------------------------
integer gcnt,retcd,ierr
double precision dum(2),fcnorm,rcond
logical fstjac
integer priter
integer idamax
c initialization
retcd = 0
iter = 0
njcnt = 0
nfcnt = 0
ierr = 0
dum(1) = 0
if( outopt(1) .eq. 1 ) then
priter = 1
else
priter = -1
endif
c evaluate function
call vscal(n,xc,scalex)
call nwfvec(xc,n,scalex,fvec,fc,fcnorm,wrk1)
c evaluate user supplied or finite difference jacobian and check user supplied
c jacobian, if requested
fstjac = .false.
if(mod(jacflg(1),2) .eq. 1) then
if( outopt(2) .eq. 1 ) then
fstjac = .true.
njcnt = njcnt + 1
call nwfjac(xc,scalex,fc,fq,n,epsm,jacflg,fvec,fjac,rjac,
* ldr,wrk1,wrk2,wrk3)
call chkjac(rjac,ldr,xc,fc,n,epsm,jacflg,scalex,
* fq,wrk1,wrk2,fvec,termcd)
if(termcd .lt. 0) then
c copy initial values
call dcopy(n,xc,1,xp,1)
call dcopy(n,fc,1,fp,1)
call vunsc(n,xp,scalex)
fpnorm = fcnorm
return
endif
endif
endif
c check stopping criteria for input xc
call nwtcvg(xc,fc,xc,xtol,retcd,ftol,iter,maxit,n,ierr,termcd)
if(termcd .gt. 0) then
call dcopy(n,xc,1,xp,1)
call dcopy(n,fc,1,fp,1)
fpnorm = fcnorm
if( outopt(3) .eq. 1 .and. .not. fstjac ) then
njcnt = njcnt + 1
call nwfjac(xp,scalex,fp,fq,n,epsm,jacflg,fvec,fjac,rjac,
* ldr,wrk1,wrk2,wrk3)
endif
return
endif
if( priter .gt. 0 ) then
dum(1) = fcnorm
dum(2) = abs(fc(idamax(n,fc,1)))
if( global .eq. 0 ) then
call nwprot(iter, -1, dum)
elseif( global .le. 3 ) then
call nwlsot(iter,-1,dum)
elseif( global .eq. 4 ) then
call nwdgot(iter,-1,0,dum)
elseif( global .eq. 5 ) then
call nwpwot(iter,-1,0,dum)
elseif( global .eq. 6 ) then
call nwmhot(iter,-1,0,dum)
endif
endif
do while( termcd .eq. 0 )
iter = iter + 1
call nwnjac(rjac,ldr,n,xc,fc,fq,fvec,fjac,epsm,jacflg,wrk1,
* wrk2,wrk3,
* xscalm,scalex,gp,cndtol,rcdwrk,icdwrk,dn,
* qtf,rcond,qrwork,qrwsiz,njcnt,iter,fstjac,ierr)
c - choose the next iterate xp by a global strategy
if( ierr .gt. 0 ) then
c jacobian singular or too ill-conditioned
call nweset(n,xc,fc,fcnorm,xp,fp,fpnorm,gcnt,priter,iter)
elseif(global .eq. 0) then
call nwpure(n,xc,dn,stepmx,scalex,
* fvec,xp,fp,fpnorm,wrk1,retcd,gcnt,
* priter,iter)
elseif(global .eq. 1) then
call nwclsh(n,xc,fcnorm,dn,gp,stepmx,btol,scalex,
* fvec,xp,fp,fpnorm,wrk1,retcd,gcnt,
* priter,iter)
elseif(global .eq. 2) then
call nwqlsh(n,xc,fcnorm,dn,gp,stepmx,btol,scalex,
* fvec,xp,fp,fpnorm,wrk1,retcd,gcnt,
* priter,iter)
elseif(global .eq. 3) then
call nwglsh(n,xc,fcnorm,dn,gp,sigma,stepmx,btol,scalex,
* fvec,xp,fp,fpnorm,wrk1,retcd,gcnt,
* priter,iter)
elseif(global .eq. 4) then
call nwddlg(n,rjac,ldr,dn,gp,xc,fcnorm,stepmx,
* btol,delta,qtf,scalex,
* fvec,d,fq,wrk1,wrk2,wrk3,wrk4,
* xp,fp,fpnorm,retcd,gcnt,priter,iter)
elseif(global .eq. 5) then
call nwpdlg(n,rjac,ldr,dn,gp,xc,fcnorm,stepmx,
* btol,delta,qtf,scalex,
* fvec,d,fq,wrk1,wrk2,wrk3,wrk4,
* xp,fp,fpnorm,retcd,gcnt,priter,iter)
elseif(global .eq. 6) then
call nwmhlm(n,rjac,ldr,dn,gp,xc,fcnorm,stepmx,
* btol,delta,qtf,scalex,
* fvec,d,fq,wrk1,wrk2,wrk3,wrk4,
* xp,fp,fpnorm,retcd,gcnt,priter,iter)
endif
nfcnt = nfcnt + gcnt
c - check stopping criteria for the new iterate xp
call nwtcvg(xp,fp,xc,xtol,retcd,ftol,iter,maxit,n,ierr,termcd)
if(termcd .eq. 0) then
c update xc, fc, and fcnorm
call dcopy(n,xp,1,xc,1)
call dcopy(n,fp,1,fc,1)
fcnorm = fpnorm
endif
enddo
if( outopt(3) .eq. 1 ) then
call nwfjac(xp,scalex,fp,fq,n,epsm,jacflg,fvec,fjac,rjac,
* ldr,wrk1,wrk2,wrk3)
endif
call vunsc(n,xp,scalex)
return
end