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|
subroutine polaut
c ====================================================================
c polynomial stuff
c ====================================================================
c
c Copyright INRIA
include '../stack.h'
integer iadr,sadr
c
integer vol1,vol2,vol3,var(4)
double precision v,eps,errl2,phi,gnrm
logical all
common/no2f/gnrm
common/arl2c/info,ierr
c
c
iadr(l)=l+l-1
sadr(l)=(l/2)+1
c
if (ddt .eq. 4) write(wte,1000) fin
1000 format(1x,'polaut',i4)
c
c functions/fin
c 1 2 3 4 5
c arl2 resi ldiv
c
if(top+lhs-rhs.ge.bot) then
call error(18)
return
endif
if(rhs.le.0) then
call error(39)
return
endif
c
eps=stk(leps)
c
lw=lstk(top+1)
c
il1=iadr(lstk(top+1-rhs))
if(istk(il1).gt.2) then
err=1
call error(44)
return
endif
m1=istk(il1+1)
n1=istk(il1+2)
it1=istk(il1+3)
mn1=m1*n1
if(istk(il1).eq.1) goto 01
id1=il1+8
vol1=istk(id1+mn1)-1
l1r=sadr(id1+mn1+1)
l1i=l1r+vol1
goto 05
01 id1=iadr(lw)
l1r=sadr(il1+4)
l1i=l1r+mn1
lw=sadr(id1+mn1+1)
err=lw-lstk(bot)
if(err.gt.0) then
call error(17)
return
endif
do 02 i=1,mn1
02 istk(id1+i-1)=i
istk(id1+mn1)=mn1+1
vol1=mn1
c
05 goto (80,20,40,99,99) fin
c
c residu
20 continue
if(rhs.ne.3.or.lhs.ne.1) then
call error(39)
return
endif
c
il2=iadr(lstk(top+2-rhs))
if(istk(il2).gt.2) then
err=1
call error(54)
return
endif
m2=istk(il2+1)
n2=istk(il2+2)
it2=istk(il2+3)
mn2=m2*n2
if(istk(il2).eq.1) goto 21
id2=il2+8
vol2=istk(id2+mn2)-1
l2r=sadr(id2+mn2+1)
l2i=l2r+vol2
goto 25
21 id2=iadr(lw)
l2r=sadr(il2+4)
l2i=l2r+mn2
lw=sadr(id2+mn2+1)
err=lw-lstk(bot)
if(err.gt.0) then
call error(17)
return
endif
do 22 i=1,mn2
22 istk(id2+i-1)=i
istk(id2+mn2)=mn2+1
vol2=mn2
c
25 il3=iadr(lstk(top+3-rhs))
if(istk(il3).gt.2) then
err=3
call error(54)
return
endif
m3=istk(il3+1)
n3=istk(il3+2)
it3=istk(il3+3)
mn3=m3*n3
if(istk(il3).eq.1) goto 26
id3=il3+8
vol3=istk(id3+mn3)-1
l3r=sadr(id3+mn3+1)
l3i=l3r+vol3
goto 30
26 id3=iadr(lw)
l3r=sadr(il3+4)
l3i=l3r+mn3
lw=sadr(id3+mn3+1)
err=lw-lstk(bot)
if(err.gt.0) then
call error(17)
return
endif
do 27 i=1,mn3
27 istk(id3+i-1)=i
istk(id3+mn3)=mn3+1
vol3=mn3
c
30 if(m1.ne.m2.or.m1.ne.m3.or.n1.ne.n2.or.n1.ne.n3) then
call error(60)
return
endif
top=top+1-rhs
if(it1+it2+it3.ne.0) goto 35
lr=l1r
do 31 k=1,mn1
nd1=istk(id1+k)-istk(id1+k-1)
nd2=istk(id2+k)-istk(id2+k-1)
nd3=istk(id3+k)-istk(id3+k-1)
nd11=nd1-1
nd21=nd2-1
nd31=nd3-1
call residu(stk(l1r),nd11,stk(l2r),nd21,stk(l3r),nd31,v,
1 eps,ierr)
if(ierr.gt.0) then
call error(27)
return
endif
stk(lr)=v
l1r=l1r+nd1
l2r=l2r+nd2
l3r=l3r+nd3
lr=lr+1
31 continue
l1=sadr(il1+4)
call unsfdcopy(mn1,stk(lr-mn1),1,stk(l1),1)
istk(il1)=1
lstk(top+1)=l1+mn1
goto 99
c
35 if(it1.eq.0) then
l1i=lw
lw=l1i+vol1
err=lw-lstk(bot)
if(err.gt.0) then
call error(17)
return
endif
call dset(vol1,0.0d+0,stk(l1i),1)
endif
if(it2.eq.0) then
l2i=lw
lw=l2i+vol2
err=lw-lstk(bot)
if(err.gt.0) then
call error(17)
return
endif
call dset(vol2,0.0d+0,stk(l2i),1)
endif
if(it3.eq.0) then
l3i=lw
lw=l3i+vol3
err=lw-lstk(bot)
if(err.gt.0) then
call error(17)
return
endif
call dset(vol3,0.0d+0,stk(l3i),1)
endif
lr=lw
lw=lr+mn1*2
err=lw-lstk(bot)
if(err.gt.0) then
call error(17)
return
endif
do 36 k=1,mn1
nd1=istk(id1+k)-istk(id1+k-1)
nd2=istk(id2+k)-istk(id2+k-1)
nd3=istk(id3+k)-istk(id3+k-1)
nd11=nd1-1
nd21=nd2-1
nd31=nd3-1
call wesidu(stk(l1r),stk(l1i),nd11,stk(l2r),stk(l2i),nd21,
& stk(l3r),stk(l3i),nd31,stk(lr+k-1),stk(lr+mn1+k-1),
& eps,ierr)
if(ierr.gt.0) then
call error(27)
return
endif
l1r=l1r+nd1
l1i=l1i+nd1
l2r=l2r+nd2
l2i=l2i+nd2
l3r=l3r+nd3
l3i=l3i+nd3
36 continue
l1=sadr(il1+4)
call unsfdcopy(mn1*2,stk(lr),1,stk(l1),1)
istk(il1)=1
istk(il1+1)=m1
istk(il1+2)=n1
istk(il1+3)=1
lstk(top+1)=l1+mn1*2
goto 99
c
c
c ldiv
40 continue
if(rhs.ne.3.or.lhs.ne.1) then
call error(39)
return
endif
c
il2=iadr(lstk(top+2-rhs))
if(istk(il2).gt.2) then
err=2
call error(54)
return
endif
m2=istk(il2+1)
n2=istk(il2+2)
it2=istk(il2+3)
if(it2.ne.0) then
err=2
call error(52)
return
endif
mn2=m2*n2
if(istk(il2).eq.1) goto 41
id2=il2+8
vol2=istk(id2+mn2)-1
l2r=sadr(id2+mn2+1)
l2i=l2r+vol2
goto 45
41 id2=iadr(lw)
l2r=sadr(il2+4)
l2i=l2r+mn2
lw=sadr(id2+mn2+1)
err=lw-lstk(bot)
if(err.gt.0) then
call error(17)
return
endif
do 42 i=1,mn2
42 istk(id2+i-1)=i
istk(id2+mn2)=mn2+1
vol2=mn2
c
if(m2.ne.m1.or.n2.ne.n1) then
call error(60)
return
endif
if(it1.ne.0) then
err=1
call error(52)
return
endif
c
45 il3=iadr(lstk(top+3-rhs))
if(istk(il3).ne.1) then
err=3
call error(53)
return
endif
l3=sadr(il3+4)
nmax=stk(l3)
c
lr=lw
err=lw+nmax*mn1-lstk(bot)
if(err.gt.0) then
call error(17)
return
endif
c
do 46 k=1,mn1
nd1=istk(id1+k)-istk(id1+k-1)
nd2=istk(id2+k)-istk(id2+k-1)
call dtild(nd1,stk(l1r),1)
call dtild(nd2,stk(l2r),1)
call expan(stk(l2r),nd2,stk(l1r),nd1,stk(lr),nmax)
l2r=l2r+nd2
l1r=l1r+nd1
lr=lr+nmax
46 continue
l1=sadr(il1+4)
call unsfdcopy(nmax*mn1,stk(lw),1,stk(l1),1)
istk(il1)=1
istk(il1+1)=m1*nmax
istk(il1+2)=n1
top=top-rhs+lhs
lstk(top+1)=l1+nmax*mn1
goto 99
c
c arl2
80 continue
all=.false.
il=iadr(lstk(top))
if(istk(il).eq.10) then
all=.true.
top=top-1
rhs=rhs-1
endif
if(rhs.lt.3.or.rhs.gt.4) then
call error(39)
return
endif
c
info=0
if(rhs.eq.4) then
c info parameter
il=iadr(lstk(top))
if(istk(il).ne.1) then
err=4
call error(53)
return
endif
l=sadr(il+4)
if(stk(l).lt.0.0d+0) then
err=4
call error(36)
return
endif
info=int(stk(l))
top=top-1
endif
c
c Final degre parameter
il=iadr(lstk(top))
if(istk(il).ne.1) then
err=3
call error(53)
return
endif
l=sadr(il+4)
if(stk(l).lt.1.0d+0) then
err=3
call error(36)
return
endif
itmax=int(stk(l))
c
c Initial point parameter
c (for arl2a it only gives le formal variable name)
top=top-1
lw=lstk(top+1)
ild=iadr(lstk(top))
if(istk(ild).ne.2) then
err=2
call error(54)
return
endif
if(istk(ild+3).ne.0) then
err=2
call error(52)
return
endif
if(istk(ild+1)*istk(ild+2).ne.1) then
err=2
call error(36)
return
endif
call icopy(4,istk(ild+4),1,var,1)
nd=istk(ild+9)-2
ld=sadr(ild+10)
call idegre(stk(ld),istk(ild+9)-2,nd)
call dscal(nd+1,1.0d+0/stk(ld+nd),stk(ld),1)
c
c fourier coefficients parameters
if(it1.ne.0) then
err=1
call error(52)
return
endif
nf=mn1
if(istk(il1).eq.2) then
if(mn1.ne.1) then
err=1
call error(43)
return
endif
nf=istk(id1+mn1)-1
endif
lf=l1r
ilf=il1
c
if(all) goto 82
c
c look for a solution
ln=ld+itmax+1
lw=ln+itmax+1
ng=nf-1
lww=lw+32+32*itmax+7*ng+itmax*ng+itmax**2*(ng+2)
ilw=iadr(lww)
lww=sadr(ilw+ 29+itmax*itmax+4*itmax)
err=lww-lstk(bot)
if(err.gt.0) then
call error(17)
return
endif
c
call arl2(stk(lf),nf,stk(ln),stk(ld),nd,itmax,errl2,stk(lw),
1 istk(ilw),info,ierr,wte)
if(ierr.ne.0) then
if(ierr.eq.3) then
call msgs(50,0)
else if(ierr.eq.4) then
c Impossible to reach required order
call msgs(51,0)
else if(ierr.eq.5) then
c failure when looking for the intersection with domains boundaries
call msgs(52,0)
else if(ierr.eq.7) then
c too many solutions found
buf='arl2 : too many solutions found'
call error(999)
return
endif
endif
call icopy(4,var,1,istk(ilf+4),1)
istk(ilf+8)=1
istk(ilf+9)=1+itmax+1
l=sadr(ilf+10)
call unsfdcopy(itmax+1,stk(ld),1,stk(l),1)
istk(ilf)=2
istk(ilf+1)=1
istk(ilf+2)=1
l=l+itmax+1
lstk(top)=l+1
if(lhs.eq.1) goto 99
il=iadr(lstk(top))
istk(il)=2
istk(il+1)=1
istk(il+2)=1
istk(il+3)=0
call icopy(4,var,1,istk(il+4),1)
istk(il+8)=1
istk(il+9)=1+itmax
l=sadr(il+10)
call unsfdcopy(itmax,stk(ln),1,stk(l),1)
lstk(top+1)=l+itmax
if(lhs.eq.2) goto 99
c
top=top+1
il=iadr(lstk(top))
istk(il)=1
istk(il+1)=1
istk(il+2)=1
istk(il+3)=0
l=sadr(il+4)
stk(l)=errl2
lstk(top+1)=l+1
goto 99
c
82 continue
c look for "all" solutions
top=top-1
mxsol=20
ld=lf+nf
ng=nf-1
lw=ld+mxsol*(itmax+1)
lww=lw+34+34*itmax+7*ng+itmax*ng+itmax**2*(ng+2)+
$ 4*(itmax+1)*mxsol
ilw=iadr(lww)
lww=sadr(ilw+29+itmax**2+4*itmax+2*mxsol)
err=lww-lstk(bot)
if(err.gt.0) then
call error(17)
return
endif
c
call arl2a(stk(lf),nf,stk(ld),mxsol,nsol,itmax,info,ierr,wte,
$ stk(lw),istk(ilw))
if(ierr.ne.0) then
if(ierr.eq.3) then
buf='arl2a : Loop on two orders detected'
else if(ierr.eq.4) then
buf='arl2a : Impossible to reach required order'
else if(ierr.eq.5) then
call basout(io,wte,'arl2: Failure when looking for'//
& 'the intersection with domains bounds')
else if(ierr.eq.7) then
buf='arl2a : Too many solutions found'
endif
call error(999)
endif
c
l0=lstk(top)
lw0=lww
mv=lw0-l0
c
c denominators
ild=iadr(lww)
istk(ild)=2
istk(ild+1)=nsol
istk(ild+2)=1
istk(ild+3)=0
call icopy(4,var,1,istk(ild+4),1)
istk(ild+8)=1
do 83 is=1,nsol
istk(ild+8+is)=istk(ild+7+is)+itmax+1
83 continue
l=sadr(ild+9+nsol)
ld0=l
do 84 is=1,nsol
call unsfdcopy(itmax,stk(ld-1+is),mxsol,stk(l),1)
stk(l+itmax)=1.0d0
l=l+itmax+1
84 continue
lww=l+1
lstk(top+1)=lww-mv
if(lhs.eq.1) goto 88
c
c numerators
top=top+1
il=iadr(lww)
istk(il)=2
istk(il+1)=nsol
istk(il+2)=1
istk(il+3)=0
call icopy(4,var,1,istk(il+4),1)
istk(il+8)=1
do 85 is=1,nsol
istk(il+8+is)=istk(il+7+is)+itmax
85 continue
l=sadr(il+9+nsol)
gnrm=sqrt(gnrm)
l1=ld0
do 86 is=1,nsol
call lq(itmax,stk(l1),stk(l),stk(lf),ng)
call dscal(itmax,gnrm,stk(l),1)
l1=l1+itmax+1
l=l+itmax
86 continue
lww=l
lstk(top+1)=lww-mv
c
if(lhs.eq.2) goto 88
c errors
top=top+1
il=iadr(lww)
istk(il)=1
istk(il+1)=nsol
istk(il+2)=1
istk(il+3)=0
l=sadr(il+4)
l1=ld0
do 87 i=1,nsol
stk(l)=sqrt(phi(stk(l1),itmax,stk(lf),ng,stk(l+nsol)))*gnrm
l1=l1+itmax+1
l=l+1
87 continue
lww=l
lstk(top+1)=lww-mv
goto 88
88 continue
c Putting in order the stack
call unsfdcopy(lww-lw0,stk(lw0),1,stk(l0),1)
c
99 return
end
|
