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|
subroutine polelm
c ====================================================================
c
c evaluation des fonctions polynomiales elementaires
c
c ====================================================================
c
c Copyright INRIA
INCLUDE '../stack.h'
integer iadr, sadr
integer id(nsiz)
c
iadr(l)=l+l-1
sadr(l)=(l/2)+1
c
if (ddt .eq. 4) then
write(buf(1:4),'(i4)') fin
call basout(io,wte,' polelm '//buf(1:4))
endif
c
c functions/fin
c 1 2 3 4 5 6 7 8
c poly roots degre coeff eval pdiv simp sum
c
c 9 10 11 12 13 14 15 16
c prod diag triu tril bezout sfact simp_mode varn
c
c 17
c cleanp
c
goto (10,20,30,40,50,60,73,55,58,25,27,28,70,83,120,100,110) fin
c
c poly
10 call intpoly(id)
goto 900
c
c roots
20 call introots(id)
goto 900
c
c diag
25 call intpdiag(id)
goto 900
c
c triu
27 call intptriu(1,id)
goto 900
c
c tril
28 call intptriu(0,id)
goto 900
c
c degree
30 call intdegree(id)
goto 900
c
c coeff
40 call intcoeff(id)
goto 900
c
c eval
50 continue
goto 900
c
c sum
55 call intpsum(id)
goto 900
c
c prod
58 call intpprod(id)
goto 900
c
c pdiv
60 call intpdiv(id)
goto 900
c
c bezout
70 call intbez(id)
goto 900
c
c simp
73 call intsimp(id)
goto 900
c
c sfact
c
83 call intsfact(id)
goto 900
c
c varn
100 call intvarn(id)
goto 900
c
c cleanp
110 call intpclean(id)
goto 900
c
c simp_mode
120 call intsimpmd(id)
goto 900
c
900 return
end
subroutine intpoly(id)
INCLUDE '../stack.h'
integer id(nsiz)
integer iadr, sadr
integer blank,racine,coeff
logical roots,ref
data blank/40/,racine/27/,coeff/12/
c
iadr(l)=l+l-1
sadr(l)=(l/2)+1
c
lw=lstk(top+1)
if(lhs.ne.1) then
call error(41)
return
endif
if(rhs.lt.1.or.rhs.gt.3) then
call error(42)
return
endif
c
il1=iadr(lstk(top+1-rhs))
ilr=il1
if(istk(il1).lt.0) il1=iadr(istk(il1+1))
if(istk(il1).ne.1) then
fun=-1
call funnam(ids(1,pt+1),'poly',il1)
return
endif
ref=il1.ne.ilr
c
roots=.true.
if(rhs.eq.3) then
il=iadr(lstk(top))
if(istk(il).lt.0) il=iadr(istk(il+1))
rhs=rhs-1
top=top-1
if(istk(il).ne.10) then
err=rhs
call error(55)
return
endif
il=il+5+istk(il+1)*istk(il+2)
if(abs(istk(il)).ne.racine) then
roots=.false.
if(abs(istk(il)).ne.coeff) then
err=rhs
call error(36)
return
endif
endif
else
roots=.true.
endif
c formal variable
il=iadr(lstk(top))
if(istk(il).lt.0) il=iadr(istk(il+1))
if(istk(il).ne.10) then
err=2
call error(55)
return
endif
if(istk(il+1)*istk(il+2).ne.1) then
err=2
call error(89)
return
endif
n=istk(il+5)-1
if(n.gt.4) call msgs(109,0)
do 12 i=1,4
id(i)=blank
if(i.le.n) id(i)=istk(il+5+i)
12 continue
if(abs(id(1)).lt.10.or.abs(id(1)).ge.blank) then
err=2
call error(116)
return
endif
c
c first argument
top=top-1
m1=istk(il1+1)
n1=istk(il1+2)
it1=istk(il1+3)
l1=sadr(il1+4)
mn1=m1*n1
itr=it1
if(.not.roots) goto 17
13 if(mn1.eq.1.or.m1.ne.n1) goto 14
c polynome caracteristique,decomposition spectrale de la matrice
if(ref) then
c necessary while matdsr and matdsc cannot be called by reference
lr=sadr(ilr+4)
err=lr+mn1*(it1+1)-lstk(bot)
if(err.gt.0) then
call error(17)
return
endif
call icopy(4,istk(il1),1,istk(ilr),1)
call unsfdcopy(mn1*(it1+1),stk(l1),1,stk(lr),1)
lstk(top+1)=lr+mn1*(it1+1)
endif
rhs=1
call inteig('spec')
call putlhsvar
if(err.gt.0) return
il1=iadr(lstk(top))
l1=sadr(il1+4)
mn1=m1
m1=1
n1=mn1
itr=min(it1,istk(il1+3))
it1=istk(il1+3)
lw=l1+mn1*(it1+1)
ref=.false.
ilr=il1
goto 14
c
c polynome defini par ses racines
14 ild=ilr+8
lc=sadr(ild+2)
lr=lc+(mn1+1)*(it1+1)
if(ref) then
err=lr-lstk(bot)
if(err.gt.0) then
call error(17)
return
endif
else
err=lr+mn1*(it1+1)-lstk(bot)
if(err.gt.0) then
call error(17)
return
endif
call unsfdcopy(mn1*(it1+1),stk(l1),1,stk(lr),1)
l1=lr
endif
istk(ilr)=2
istk(ilr+1)=1
istk(ilr+2)=1
istk(ilr+3)=itr
call icopy(4,id,1,istk(ilr+4),1)
istk(ild)=1
istk(ild+1)=mn1+2
lstk(top+1)=lc+(mn1+1)*(itr+1)
if(it1.eq.0) then
call dprxc(mn1,stk(l1),stk(lc))
else
call wprxc(mn1,stk(l1),stk(l1+mn1),stk(lc),stk(lc+mn1+1))
do 16 i=1,mn1+1
l=lc-1+i
if( stk(l)+stk(l+mn1+1).ne.stk(l)) goto 999
16 continue
istk(ilr+3)=0
lstk(top+1)=lc+mn1+1
endif
goto 999
c
c polynome defini par ses coefficients
17 if(istk(il1).ne.1) then
err=1
call error(53)
return
endif
if(mn1.eq.0) return
if(n1.ne.1.and.m1.ne.1) then
err=1
call error(89)
return
endif
lr=sadr(ilr+10)
err=lr+mn1*(it1+1)-lstk(bot)
if(err.gt.0) then
call error(17)
return
endif
call unsfdcopy(mn1*(it1+1),stk(l1),-1,stk(lr),-1)
istk(ilr)=2
istk(ilr+1)=1
istk(ilr+2)=1
istk(ilr+3)=it1
call icopy(4,id,1,istk(ilr+4),1)
istk(ilr+8)=1
istk(ilr+9)=1+mn1
lstk(top+1)=lr+mn1*(it1+1)
goto 999
c
999 return
end
subroutine introots(id)
INCLUDE '../stack.h'
integer iadr, sadr
integer id(nsiz)
double precision t,sr,si
integer vol
integer fail
logical ref,eigen
integer eig
data eig/14/
c
iadr(l)=l+l-1
sadr(l)=(l/2)+1
c
lw=lstk(top+1)
if(lhs.ne.1) then
call error(41)
return
endif
if(rhs.ne.1.and.rhs.ne.2) then
call error(42)
return
endif
c
eigen=.false.
if (rhs.eq.2) then
ilopt=iadr(lstk(top))
if(istk(ilopt).lt.0) ilopt=iadr(istk(ilopt+1))
if(istk(ilopt).ne.10) then
err=2
call error(55)
return
endif
if(istk(ilopt+1).ne.1.or.istk(ilopt+2).ne.1) then
err=2
call error(89)
return
endif
if(istk(ilopt+5).ne.2.or.istk(ilopt+6).ne.eig) then
err=2
call error(116)
return
endif
eigen=.true.
rhs=rhs-1
top=top-1
endif
il1=iadr(lstk(top+1-rhs))
ilr=il1
if(istk(il1).lt.0) il1=iadr(istk(il1+1))
ref=il1.ne.ilr
if(istk(il1).gt.2) then
fun=-1
call funnam(ids(1,pt+1),'roots',il1)
return
endif
c
m1=istk(il1+1)
n1=istk(il1+2)
mn1=m1*n1
if(m1*n1.eq.0) return
it1=istk(il1+3)
if(istk(il1).eq.1) then
c for Matlab compatibility root of the vector of coefficients
vol=mn1
l1=sadr(il1+4)
n=mn1
if(.not.ref) then
call dtild(n*(it1+1),stk(l1),1)
lc=l1
else
lc=lw
lw=lc+n*(it1+1)
err=lw-lstk(bot)
if(err.gt.0) then
call error(17)
return
endif
call dcopy(n,stk(l1),1,stk(lc),-1)
if(it1.eq.1) call dcopy(n,stk(l1+n),1,stk(lc+n),-1)
endif
else
if(mn1.ne.1) then
err=1
call error(43)
return
endif
if(istk(il1).lt.2) goto 24
id1=il1+8
lc=sadr(id1+mn1+1)
vol=istk(id1+mn1)-1
call icopy(4,istk(il1+4),1,id,1)
n=vol
endif
l1=sadr(ilr+4)
21 n=n-1
if(n.lt.0) goto 24
t=abs(stk(lc+n))
if(it1.eq.1) t=t+abs(stk(lc+n+vol))
if(t.eq.0.0d+0) goto 21
if (eigen) goto 22
c
c real polynomial: rpoly algorithm
c this alg is much more speedy, but it may happens that it gives
C erroneous results without messages : example
C roots(%s^31-8*%s^30+9*%s^29+0.995) should have two real roots near
C 1.355 and 6.65 and the other ones inside a circle centered in 0
C with radius 1
C
if(it1.eq.0.and.n.le.100) then
lp=max(lw,l1+2*n)
err=lp+n+1-lstk(bot)
if(err.gt.0) then
call error(17)
return
endif
call unsfdcopy(n+1,stk(lc),1,stk(lp),1)
call dtild(n+1,stk(lp),1)
call rpoly(stk(lp),n,stk(l1),stk(l1+n),fail)
if(fail.eq.1) then
call error(24)
return
elseif(fail.eq.2) then
call error(74)
return
elseif(fail.eq.3) then
call error(75)
return
endif
istk(ilr)=1
istk(ilr+1)=n
istk(ilr+2)=1
if(n.eq.0) istk(ilr+2)=0
istk(ilr+3)=1
lstk(top+1)=l1+2*n
goto 999
endif
22 continue
c
c Companion matrix method
lw=lw+n*n*(it1+1)
err=lw+n*(it1+1)-lstk(bot)
if(err.gt.0) then
call error(17)
return
endif
sr=stk(lc+n)
call unsfdcopy(n,stk(lc),-1,stk(lw),1)
if(it1.eq.0) then
call dscal(n,-1.0d+0/sr,stk(lw),1)
else
si=stk(lc+vol+n)
t=sr*sr+si*si
sr=-sr/t
si=si/t
call unsfdcopy(n,stk(lc+vol),-1,stk(lw+n),1)
call wscal(n,sr,si,stk(lw),stk(lw+n),1)
endif
call dset(n*n*(it1+1),0.0d+0,stk(l1),1)
call dset(n-1,1.0d+0,stk(l1+n),n+1)
call unsfdcopy(n,stk(lw),1,stk(l1),1)
if(it1.eq.1) call unsfdcopy(n,stk(lw+n),1,stk(l1+n*n),1)
lstk(top+1)=l1+n*n*(it1+1)
istk(ilr)=1
istk(ilr+1)=n
istk(ilr+2)=n
istk(ilr+3)=it1
fin=3
fun=2
c *call* matds(r c)
goto 999
c polynome de degre 0
24 istk(ilr)=1
istk(ilr+1)=0
istk(ilr+2)=0
istk(ilr+3)=0
lstk(top+1)=sadr(ilr+4)
goto 999
999 return
end
subroutine intpdiag(id)
INCLUDE '../stack.h'
integer iadr, sadr
integer id(nsiz)
integer volr,vol,tops
logical ref
c
iadr(l)=l+l-1
sadr(l)=(l/2)+1
c
lw=lstk(top+1)
tops=top
c
if(lhs.ne.1) then
call error(41)
return
endif
if(rhs.ne.1.and.rhs.ne.2) then
call error(42)
return
endif
c
kdiag=0
if (rhs .eq. 2) then
il=iadr(lstk(top))
if(istk(il).lt.0) il=iadr(istk(il+1))
if(istk(il).ne.1) then
err=1
call error(53)
return
endif
if(istk(il+3).ne.0) then
err=1
call error(52)
return
endif
if(istk(il+1)*istk(il+2).ne.1) then
err=1
call error(89)
return
endif
kdiag = int(stk(sadr(il+4)))
top = top-1
endif
lw=lstk(top+1)
c
il1=iadr(lstk(top))
ilr=il1
if(istk(il1).lt.0) il1=iadr(istk(il1+1))
ref=il1.ne.ilr
if(istk(il1).ne.2) then
fun=-1
top=tops
call funnam(ids(1,pt+1),'diag',il1)
return
endif
c
id1=il1+8
m1=istk(il1+1)
n1=istk(il1+2)
it1=istk(il1+3)
mn1=m1*n1
l1=sadr(id1+mn1+1)
vol=istk(id1+mn1)-1
c
if(ref) then
idr=ilr+8
else
idr=iadr(lw)
endif
if(m1.eq.1.or.n1.eq.1) then
m1=mn1
n1=0
err=sadr(idr+mn1*(mn1+abs(kdiag)))-lstk(bot)
else
err=sadr(idr+min(n1,m1))-lstk(bot)
endif
if(err.gt.0) then
call error(17)
return
endif
c
call mpdiag(istk(id1),m1,n1,kdiag,istk(idr),mr,nr)
if(nr.le.0.or.mr.le.0) then
istk(ilr)=1
istk(ilr+1)=0
istk(ilr+2)=0
istk(ilr+3)=0
lstk(top+1)=sadr(ilr+4)
goto 999
endif
lr=sadr(idr+mr*nr+1)
volr=istk(idr)
err=lr+volr*(it1+1)-lstk(bot)
if(err.gt.0) then
call error(17)
return
endif
if (it1.eq.0) then
call dmpins(stk(l1),istk(id1),mn1,1,stk,1,0,0,
1 stk(lr),istk(idr),mr,nr)
else
call wmpins(stk(l1),stk(l1+vol),istk(id1),mn1,1,
1 stk,stk,1,0,0,stk(lr),stk(lr+volr),istk(idr),mr,nr)
endif
if(ref) then
call icopy(8,istk(il1),1,istk(ilr),1)
l1=sadr(idr+mr*nr+1)
else
call icopy(mr*nr+1,istk(idr),1,istk(id1),1)
l1=sadr(id1+mr*nr+1)
call unsfdcopy(volr*(it1+1),stk(lr),1,stk(l1),1)
endif
istk(ilr+1)=mr
istk(ilr+2)=nr
lstk(top+1)=l1+volr*(it1+1)
goto 999
999 return
end
subroutine intptriu(job,id)
INCLUDE '../stack.h'
integer iadr, sadr
integer id(nsiz)
integer volr,vol,tops
logical ref
c
iadr(l)=l+l-1
sadr(l)=(l/2)+1
c
tops=top
c
if(lhs.ne.1) then
call error(41)
return
endif
if(rhs.ne.1.and.rhs.ne.2) then
call error(42)
return
endif
c
kdiag=0
if (rhs .eq. 2) then
il=iadr(lstk(top))
if(istk(il).lt.0) il=iadr(istk(il+1))
if(istk(il).ne.1) then
err=1
call error(53)
return
endif
if(istk(il+3).ne.0) then
err=1
call error(52)
return
endif
if(istk(il+1)*istk(il+2).ne.1) then
err=1
call error(89)
return
endif
kdiag = int(stk(sadr(il+4)))
top = top-1
endif
lw=lstk(top+1)
c
il1=iadr(lstk(top))
ilr=il1
if(istk(il1).lt.0) il1=iadr(istk(il1+1))
ref=il1.ne.ilr
if(istk(il1).gt.2) then
fun=-1
top=tops
call funnam(ids(1,pt+1),'triu',il1)
return
endif
c
id1=il1+8
m1=istk(il1+1)
n1=istk(il1+2)
it1=istk(il1+3)
mn1=m1*n1
l1=sadr(id1+mn1+1)
vol=istk(id1+mn1)-1
c
if(ref) then
idr=ilr+8
else
idr=iadr(lw)
endif
lr=sadr(idr+mn1+1)
err=lr-lstk(bot)
if(err.gt.0) then
call error(17)
return
endif
call mptri(istk(id1),m1,n1,kdiag,istk(idr),job)
volr=istk(idr)
err=lr+volr*(it1+1)-lstk(bot)
if(err.gt.0) then
call error(17)
return
endif
if (it1.eq.0) then
call dmpins(stk(l1),istk(id1),m1,n1,stk,1,0,0,
1 stk(lr),istk(idr),m1,n1)
else
call wmpins(stk(l1),stk(l1+vol),istk(id1),m1,n1,
1 stk,stk,1,0,0,stk(lr),stk(lr+volr),istk(idr),m1,n1)
endif
if(ref) then
call icopy(8,istk(il1),1,istk(ilr),1)
l1=lr
else
call icopy(mn1+1,istk(idr),1,istk(id1),1)
l1=sadr(id1+mn1+1)
call unsfdcopy(volr*(it1+1),stk(lr),1,stk(l1),1)
endif
istk(ilr+1)=m1
istk(ilr+2)=n1
lstk(top+1)=l1+volr*(it1+1)
999 return
end
subroutine intdegree(id)
INCLUDE '../stack.h'
integer iadr, sadr
integer id(nsiz)
integer volr,vol
logical ref
c
iadr(l)=l+l-1
sadr(l)=(l/2)+1
if(lhs.ne.1) then
call error(41)
return
endif
if(rhs.ne.1) then
call error(42)
return
endif
c
il1=iadr(lstk(top+1-rhs))
ilr=il1
if(istk(il1).lt.0) il1=iadr(istk(il1+1))
ref=il1.ne.ilr
if(istk(il1).gt.2) then
fun=-1
call funnam(ids(1,pt+1),'degree',il1)
return
endif
m1=istk(il1+1)
n1=istk(il1+2)
mn1=m1*n1
if(mn1.eq.0) then
if (ref) then
l=sadr(ilr+4)
err=l-lstk(bot)
if(err.gt.0) then
call error(17)
return
endif
istk(ilr)=1
istk(ilr+1)=0
istk(ilr+2)=0
istk(ilr+3)=0
lstk(top+1)=l
endif
return
endif
c
if(istk(il1).eq.2) then
id1=il1+8
if(ref) then
l1=sadr(ilr+4)
l=l1
else
l1=sadr(id1+mn1+1)
l=sadr(ilr+4)
endif
do 31 k=1,mn1
stk(l1-1+k)=dble(istk(id1+k)-istk(id1+k-1)-1)
31 continue
if(ref) then
istk(ilr)=1
istk(ilr+1)=m1
istk(ilr+2)=n1
istk(ilr+3)=0
else
istk(ilr)=1
istk(ilr+3)=0
call unsfdcopy(mn1,stk(l1),1,stk(l),1)
endif
lstk(top+1)=l+mn1
elseif(istk(il1).eq.1) then
istk(ilr)=1
istk(ilr+1)=m1
istk(ilr+2)=n1
istk(ilr+3)=0
l=sadr(ilr+4)
call dset(mn1,0.0d+0,stk(l),1)
lstk(top+1)=l+mn1
c else
c ????????
c fun=15
c fin=5
endif
return
end
subroutine intcoeff(id)
INCLUDE '../stack.h'
integer iadr, sadr
integer id(nsiz)
integer v2,vol,top0
logical ref
c
iadr(l)=l+l-1
sadr(l)=(l/2)+1
c
if(lhs.ne.1) then
call error(41)
return
endif
if(rhs.ne.1.and.rhs.ne.2) then
call error(42)
return
endif
top0=top
c
il1=iadr(lstk(top+1-rhs))
ilr=il1
if(istk(il1).lt.0) il1=iadr(istk(il1+1))
ref=il1.ne.ilr
if(istk(il1).gt.2) then
fun=-1
call funnam(ids(1,pt+1),'coeff',il1)
return
endif
if(rhs.eq.2) then
ilv=iadr(lstk(top))
if(istk(ilv).lt.0) ilv=iadr(istk(ilv+1))
if(istk(ilv).ne.1) then
err=2
call error(53)
return
endif
if(istk(ilv+3).ne.0) then
err=2
call error(52)
return
endif
nv=istk(ilv+1)*istk(ilv+2)
if(nv.eq.0) then
top=top-1
istk(ilr)=1
istk(ilr+1)=0
istk(ilr+2)=0
istk(ilr+3)=0
lstk(top+1)=sadr(ilr+4)
return
endif
if(istk(ilv+1).ne.1.and.istk(ilv+2).ne.1) then
err=2
call error(89)
return
endif
lv=sadr(ilv+4)
do 10 i=0,nv-1
if(int(stk(lv+i)).lt.0) then
err=2
call error(116)
return
endif
10 continue
top=top-1
endif
c
m1=istk(il1+1)
n1=istk(il1+2)
it1=istk(il1+3)
mn1=m1*n1
c
if(ref) then
lr=sadr(ilr+4)
else
lr=lstk(top+1)
endif
c
if(istk(il1).eq.2) then
c coeff of a matrix of polynomials
id1=il1+8
l1=sadr(id1+mn1+1)
vol=istk(id1+mn1)-1
if(rhs.eq.1) then
mx=0
do 20 ij=1,mn1
nij=istk(id1+ij)-istk(id1+ij-1)
if(nij.gt.mx) mx=nij
20 continue
v2=mn1*mx
err=lr+v2*(it1+1)-lstk(bot)
if(err.gt.0) then
call error(17)
return
endif
call dset(v2*(it1+1),0.0d+0,stk(lr),1)
do 30 ij=1,mn1
nij=istk(id1+ij)-istk(id1+ij-1)
lij=l1-1+istk(id1+ij-1)
call unsfdcopy(nij,stk(lij),1,stk(lr-1+ij),mn1)
if(it1.eq.1) then
call unsfdcopy(nij,stk(lij+vol),1,stk(lr+v2-1+ij),mn1)
endif
30 continue
if(.not.ref) then
l=sadr(ilr+4)
call unsfdcopy(v2*(it1+1),stk(lr),1,stk(l),1)
lr=l
endif
istk(ilr)=1
istk(ilr+1)=m1
istk(ilr+2)=n1*mx
istk(ilr+3)=it1
lstk(top+1)=lr+v2*(it1+1)
else
lw=max(lstk(top0+1),lr+mn1*nv*(it1+1))
err=lw+nv-lstk(bot)
if(err.gt.0) then
call error(17)
return
endif
call unsfdcopy(nv,stk(lv),1,stk(lw),1)
lv=lw
call dset(mn1*nv*(it1+1),0.0d+0,stk(lr),1)
do 41 ij=1,mn1
nij=istk(id1+ij)-istk(id1+ij-1)
lij=l1-1+istk(id1+ij-1)
do 40 k=1,nv
mv=int(stk(lv-1+k))
if(mv.ge.nij) goto 40
stk(lr+ij-1+(k-1)*mn1)=stk(lij+mv)
if(it1.ne.0) stk(lr+ij-1+(k-1+nv)*mn1)=stk(lij+mv+vol)
40 continue
41 continue
l=sadr(ilr+4)
if(.not.ref) call unsfdcopy(mn1*nv*(it1+1),stk(lr),1,
$ stk(l),1)
istk(ilr)=1
istk(ilr+1)=m1
istk(ilr+2)=n1*nv
istk(ilr+3)=it1
lstk(top+1)=l+mn1*nv*(it1+1)
endif
else
c coeff of a matrix of numbers
if(rhs.eq.1) then
c . return the input matrix
if(ref) then
c . copy matrix on the top of the stack
k=istk(ilr+2)
err=lstk(top)+lstk(k+1)-lstk(k)-lstk(bot)
if(err.gt.0) then
call error(17)
return
endif
call unsfdcopy(lstk(k+1)-lstk(k),stk(lstk(k)),1
$ ,stk(lstk(top)),1)
lstk(top+1)=lstk(top)+lstk(k+1)-lstk(k)
endif
return
endif
l1=sadr(il1+4)
vol=mn1
lw=lr+mn1*nv*(it1+1)
err=lw+nv-lstk(bot)
if(err.gt.0) then
call error(17)
return
endif
if(lv.le.lw) then
call unsfdcopy(nv,stk(lv),-1,stk(lw),-1)
lv=lw
endif
call dset(mn1*nv*(it1+1),0.0d+0,stk(lr),1)
do 50 k=1,nv
if(stk(lv-1+k).eq.0.0d0) then
call unsfdcopy(mn1,stk(l1),1,stk(lr+(k-1)*mn1),1)
if(it1.eq.1) call unsfdcopy(mn1,stk(l1+mn1),1,
$ stk(lr+(k-1)*mn1+mn1*nv),1)
endif
50 continue
l=sadr(ilr+4)
if(.not.ref) call unsfdcopy(mn1*nv*(it1+1),stk(lr),1,stk(l),1)
istk(ilr)=1
istk(ilr+1)=m1
istk(ilr+2)=n1*nv
istk(ilr+3)=it1
lstk(top+1)=l+mn1*nv*(it1+1)
endif
return
end
subroutine intpsum(id)
INCLUDE '../stack.h'
integer iadr, sadr
integer id(nsiz)
integer vol
logical ref
c
iadr(l)=l+l-1
sadr(l)=(l/2)+1
c
if(lhs.ne.1) then
call error(41)
return
endif
if(rhs.ne.1) then
if(rhs.eq.2) then
call funnam(ids(1,pt+1),'sum',iadr(lstk(top-rhs+1)))
fun=-1
return
endif
call error(42)
return
endif
c
lw=lstk(top+1)
c
il1=iadr(lstk(top+1-rhs))
ilr=il1
if(istk(il1).lt.0) il1=iadr(istk(il1+1))
ref=il1.ne.ilr
if(istk(il1).ne.2) then
fun=-1
call funnam(ids(1,pt+1),'sum',il1)
return
endif
c
it1=istk(il1+3)
l1=sadr(il1+4)
mn1=istk(il1+1)*istk(il1+2)
id1=il1+8
l1=sadr(id1+mn1+1)
vol=istk(id1+mn1)-1
c
maxd=0
do 56 i=1,mn1
m=istk(id1+i)-istk(id1-1+i)
if(m.gt.maxd) maxd=m
56 continue
if(ref) then
lr=sadr(ilr+10)
else
lr=lw
endif
err=lw+maxd*(it1+1)-lstk(bot)
if(err.gt.0) then
call error(17)
return
endif
call dset(maxd*(it1+1),0.0d+0,stk(lr),1)
do 57 i=1,mn1
li=l1-1+istk(id1-1+i)
n=istk(id1+i)-istk(id1-1+i)
call dadd(n,stk(li),1,stk(lr),1)
if(it1.eq.1) call dadd(n,stk(li+vol),1,stk(lr+maxd),1)
57 continue
if(ref) then
call icopy(9,istk(il1),1,istk(ilr),1)
istk(ilr)=2
istk(ilr+1)=1
istk(ilr+2)=1
istk(ilr+9)=1+maxd
else
istk(ilr+1)=1
istk(ilr+2)=1
istk(ilr+9)=1+maxd
l1=sadr(il1+10)
call unsfdcopy(maxd*(it1+1),stk(lr),1,stk(l1),1)
lr=l1
endif
lstk(top+1)=lr+maxd*(it1+1)
return
end
subroutine intpprod(id)
INCLUDE '../stack.h'
integer iadr, sadr
integer id(nsiz)
integer vol
logical ref
c
iadr(l)=l+l-1
sadr(l)=(l/2)+1
c
if(lhs.ne.1) then
call error(41)
return
endif
if(rhs.ne.1) then
if(rhs.eq.2) then
call funnam(ids(1,pt+1),'prod',iadr(lstk(top-rhs+1)))
fun=-1
return
endif
call error(42)
return
endif
c
lw=lstk(top+1)
c
il1=iadr(lstk(top+1-rhs))
ilr=il1
if(istk(il1).lt.0) il1=iadr(istk(il1+1))
ref=il1.ne.ilr
if(istk(il1).gt.2) then
fun=-1
call funnam(ids(1,pt+1),'prod',il1)
return
endif
c
it1=istk(il1+3)
l1=sadr(il1+4)
mn1=istk(il1+1)*istk(il1+2)
id1=il1+8
l1=sadr(id1+mn1+1)
vol=istk(id1+mn1)-1
if(ref) then
lr=sadr(ilr+10)
else
lr=lw
endif
maxd=istk(id1+mn1)-mn1
err=lr+maxd*(it1+1)-lstk(bot)
if(err.gt.0) then
call error(17)
return
endif
c
stk(lr)=1.0d+0
if(it1.eq.1) stk(lr+maxd)=0.0d+0
m=0
do 59 i=1,mn1
n=istk(id1+i)-istk(id1+i-1)-1
li=l1-1+istk(id1+i-1)
if(it1.eq.0) call dpmul1(stk(li),n,stk(lr),m,stk(lr))
if(it1.eq.1) call wpmul1(stk(li),stk(li+vol),n,stk(lr),
1 stk(lr+maxd),m,stk(lr),stk(lr+maxd))
m=m+n
59 continue
if(ref) then
call icopy(9,istk(il1),1,istk(ilr),1)
istk(ilr)=2
istk(ilr+1)=1
istk(ilr+2)=1
istk(ilr+9)=1+maxd
else
istk(ilr+1)=1
istk(ilr+2)=1
istk(ilr+9)=1+maxd
l1=sadr(il1+10)
call unsfdcopy(maxd*(it1+1),stk(lr),1,stk(l1),1)
lr=l1
endif
lstk(top+1)=lr+maxd*(it1+1)
return
end
subroutine intpdiv(id)
INCLUDE '../stack.h'
integer iadr, sadr
integer id(nsiz)
integer voln,vold,v2
c
iadr(l)=l+l-1
sadr(l)=(l/2)+1
c
if(lhs.ne.1.and.lhs.ne.2) then
call error(41)
return
endif
if(rhs.ne.2) then
call error(42)
return
endif
c
lw=lstk(top+1)
c
iln=iadr(lstk(top+1-rhs))
il=iln
if(istk(il).lt.0) il=iadr(istk(il+1))
if(istk(il).gt.2) then
fun=-1
call funnam(ids(1,pt+1),'pdiv',il)
return
endif
c
ild=iadr(lstk(top))
il=ild
if(istk(il).lt.0) il=iadr(istk(il+1))
if(istk(il).gt.2) then
fun=-1
call funnam(ids(1,pt+1),'pdiv',il)
return
endif
c
if(istk(iln).lt.0) then
c move d and copy value of n in place of its reference
k=istk(iln+2)
voln=lstk(k+1)-lstk(k)
vold=lstk(top+1)-lstk(top)
err=lstk(top)+voln+vold-lstk(bot)
if(err.gt.0) then
call error(17)
return
endif
call unsfdcopy(vold,stk(lstk(top)),-1,stk(lstk(top-1)+voln),-1)
call unsfdcopy(voln,stk(lstk(k)),1,stk(lstk(top-1)),1)
lstk(top)=lstk(top-1)+voln
ild=iadr(lstk(top))
lstk(top+1)=lstk(top)+vold
endif
if(istk(ild).lt.0) then
c copy value of b in place of its reference
k=istk(ild+2)
vold=lstk(k+1)-lstk(k)
err=lstk(top)+vold-lstk(bot)
if(err.gt.0) then
call error(17)
return
endif
call unsfdcopy(vold,stk(lstk(k)),1,stk(lstk(top)),1)
lstk(top+1)=lstk(top)+vold
endif
lw=lstk(top+1)
il1=iln
m1=istk(il1+1)
n1=istk(il1+2)
it1=istk(il1+3)
l1=sadr(il1+4)
mn1=m1*n1
if(mn1.ne.1) then
err=1
call error(89)
return
endif
if(istk(il1).eq.2) then
id1=il1+8
l1=sadr(id1+mn1+1)
vol=istk(id1+mn1)-1
call icopy(4,istk(il1+4),1,id,1)
nn=istk(id1+1)-2
else
nn=0
id(1)=0
endif
c
c denominateur
nd=istk(ild+1)*istk(ild+2)
if(nd.ne.1) then
err=2
call error(89)
return
endif
itd=istk(ild+3)
if(istk(ild).eq.1) then
ld=sadr(ild+4)
nd=0
if (id(1).eq.0) then
err=2
call error(54)
return
endif
v2=1
else
if(id(1).eq.0) call icopy(4,istk(ild+4),1,id,1)
do 61 i=1,4
if(id(i).ne.istk(ild+3+i)) then
call error(43)
return
endif
61 continue
nd=istk(ild+9)-2
ld=sadr(ild+10)
v2=istk(ild+9)-1
endif
c test degre du denominateur
64 continue
if(itd.eq.0) then
if(stk(ld+nd).ne.0.0d+0) goto 65
else
if(abs(stk(ld+nd))+abs(stk(ld+v2+nd)).ne.0.0d+0) goto 65
endif
nd=nd-1
if(nd.lt.0) then
call error(27)
return
endif
goto 64
c
65 if(nn.lt.nd) then
c . No division to perform
if(lhs.eq.2) then
istk(ild)=1
ld=sadr(ild+4)
stk(ld)=0.0d+0
lstk(top+1)=ld+1
else
top=top-1
istk(il1)=1
stk(l1)=0.0d+0
lstk(top+1)=l1+1
endif
goto 999
endif
c
if(it1.eq.0) then
if (itd.eq.0) then
call dpodiv(stk(l1),stk(ld),nn,nd)
else
l1i=lw
lw=l1i+nn+1
err=lw-lstk(bot)
if(err.gt.0) then
call error(17)
return
endif
ldi=ld+v2
call dset(nn+1,0.0d0,stk(l1i),1)
call wpodiv(stk(l1),stk(l1i),stk(ld),stk(ldi),nn,nd,ierr)
endif
else
l1i=l1+nn+1
if (itd.eq.0) then
ldi=lw
lw=ldi+nd+1
err=lw-lstk(bot)
if(err.gt.0) then
call error(17)
return
endif
call dset(nd+1,0.0d0,stk(ldi),1)
call wpodiv(stk(l1),stk(l1i),stk(ld),stk(ldi),nn,nd,ierr)
else
ldi=ld+v2
call wpodiv(stk(l1),stk(l1i),stk(ld),stk(ldi),nn,nd,ierr)
endif
endif
c
itr=max(it1,itd)
nq=nn-nd
if(lhs.eq.1) then
c . only q is returned
top=top-1
c . set type
istk(il1+3)=itr
c . set length
istk(il1+9)=nq+2
c . install real and imaginary part
call unsfdcopy(nq+1,stk(l1+nd),1,stk(l1),1)
if(itr.eq.1) call unsfdcopy(nq+1,stk(l1i+nd),1,stk(l1+nq+1),1)
else
c . computes remainder degree
nr=nd
66 nr=nr-1
if(nr.lt.0) goto 67
if (itr.eq.0) then
if(stk(l1+nr).eq.0.0d+0) goto 66
else
if(stk(l1+nr).eq.0.0d+0.and.stk(l1i+nr).eq.0.0d+0) goto 66
endif
67 continue
c
if(itr.eq.0) then
c . real result
if(nr.gt.0) then
c . remainder is a polynomial
istk(id1+1)=nr+2
lstk(top)=l1+(nr+1)
else
c . remainder is a scalar
istk(il1)=1
istk(il1+1)=1
istk(il1+2)=1
lr=sadr(il1+4)
stk(lr)=stk(l1)
c???? stk(lr+1)=stk(l1i)
lstk(top)=lr+1
endif
ilq=iadr(lstk(top))
lq=sadr(ilq+10)
inc=1
if (l1+nd.lt.lq) inc=-1
call unsfdcopy(nq+1,stk(l1+nd),inc,stk(lq),inc)
if(nr.lt.0) stk(lr)=0.0d+0
istk(ilq)=2
istk(ilq+1)=1
istk(ilq+2)=1
istk(ilq+3)=0
call icopy(4,id,1,istk(ilq+4),1)
idq=ilq+8
istk(idq)=1
istk(idq+1)=nq+2
lstk(top+1)=lq+nq+1
goto 999
else
c . complex result
c . preserve quotient coeff
lqs=lw
lw=lqs+sadr(10)+(nq+1)*2
err=lw-lstk(bot)
if(err.gt.0) then
call error(17)
return
endif
call unsfdcopy(nq+1,stk(l1+nd),1,stk(lqs),1)
call unsfdcopy(nq+1,stk(l1i+nd),1,stk(lqs+nq+1),1)
c . set remainder
if(nr.ge.0) then
istk(il1+3)=1
call unsfdcopy(nr+1,stk(l1i),1,stk(l1+nr+1),1)
istk(id1+1)=nr+2
lstk(top)=l1+(nr+1)*2
else
istk(il1+3)=0
stk(l1)=0.0d0
istk(id1+1)=2
lstk(top)=l1+1
endif
c . set quotient
ilq=iadr(lstk(top))
istk(ilq)=2
istk(ilq+1)=1
istk(ilq+2)=1
istk(ilq+3)=1
call icopy(4,id,1,istk(ilq+4),1)
idq=ilq+8
istk(idq)=1
istk(idq+1)=nq+2
lq=sadr(ilq+10)
call unsfdcopy(2*(nq+1),stk(lqs),1,stk(lq),1)
lstk(top+1)=lq+(nq+1)*2
endif
endif
goto 999
999 return
end
subroutine intbez(id)
INCLUDE '../stack.h'
integer iadr, sadr
integer id(nsiz)
integer vol,v2,blank,ipb(6)
double precision er
logical refa,refb
data blank/40/
c
iadr(l)=l+l-1
sadr(l)=(l/2)+1
c
if(rhs.ne.2) then
call error(42)
return
endif
if(lhs.ne.2.and.lhs.ne.3) then
call error(41)
return
endif
lw =lstk(top+1)
c
ilb=iadr(lstk(top))
ilbr=ilb
if(istk(ilb).lt.0) ilb=iadr(istk(ilb+1))
if(istk(ilb).gt.2) then
fun=-1
call funnam(ids(1,pt+1),'bezout',ilb)
return
endif
refb=ilbr.ne.ilb
itb=istk(ilb+3)
if(itb.ne.0) then
fun=-1
call funnam(ids(1,pt+1),'bezout',ilb)
return
endif
if(istk(ilb+1)*istk(ilb+2).ne.1)then
err=2
call error(89)
return
endif
if(istk(ilb).eq.1) then
nb=0
lb=sadr(ilb+4)
id(1)=0
else
nb=istk(ilb+9)-2
lb=sadr(ilb+9)
call icopy(4,istk(ilb+4),1,id,1)
endif
c
il1=iadr(lstk(top+1-rhs))
ilr=il1
if(istk(il1).lt.0) il1=iadr(istk(il1+1))
if(istk(il1).gt.2) then
fun=-1
call funnam(ids(1,pt+1),'bezout',il1)
return
endif
refa=ilr.ne.il1
it1=istk(il1+3)
if(it1.ne.0) then
fun=-1
call funnam(ids(1,pt+1),'bezout',il1)
return
endif
if(istk(il1+1)*istk(il1+2).ne.1) then
err=1
call error(89)
return
endif
mn1=1
if(istk(il1).eq.2) then
id1=il1+8
l1=sadr(id1+mn1+1)
vol=istk(id1+mn1)-1
na=vol-1
if(id(1).eq.0) call icopy(4,istk(il1+4),1,id,1)
else
l1=sadr(il1+4)
na=0
endif
if(id(1).eq.0) call iset(4,blank,id,1)
c
lf=lstk(top+1)+na+9
if(refa) lf=lw+na+9
c
lw=lf+2*(na+nb)+min(na,nb)+3
n0=max(na,nb)+1
err=lw+10*n0+3*n0*n0-lstk(bot)
if(err.gt.0) then
call error(17)
return
endif
call recbez(stk(l1),na,stk(lb),nb,stk(lf),ipb,stk(lw),er)
c pgcd
istk(ilr)=2
istk(ilr+1)=1
istk(ilr+2)=1
istk(ilr+3)=0
call icopy(4,id,1,istk(ilr+4),1)
l1=sadr(ilr+8+mn1+1)
istk(ilr+8)=1
np=ipb(2)-ipb(1)-1
istk(ilr+9)=2+np
call unsfdcopy(np+1,stk(lf+ipb(1)-1),1,stk(l1),1)
lstk(top)=l1+np+1
c matrice q
il=iadr(lstk(top))
istk(il)=2
istk(il+1)=2
istk(il+2)=2
istk(il+3)=0
call icopy(4,id,1,istk(il+4),1)
il=il+8
istk(il)=1
l=sadr(il+5)
do 71 i=1,4
ii=i+1
istk(il+1)=istk(il)+ipb(ii+1)-ipb(ii)
call unsfdcopy(istk(il+1)-istk(il),stk(lf+ipb(ii)-1),1,
$ stk(l),1)
l=l+istk(il+1)-istk(il)
il=il+1
71 continue
lstk(top+1)=l
if(lhs.eq.3) then
c retour de l'erreur
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)=er
lstk(top+1)=l+1
endif
goto 999
999 return
end
subroutine intsimp(id)
INCLUDE '../stack.h'
integer iadr, sadr
integer id(nsiz)
integer vol,v2,blank
double precision er
integer simpmd
common/csimp/ simpmd
c
iadr(l)=l+l-1
sadr(l)=(l/2)+1
c
if(simpmd.eq.0) then
call ref2val()
return
endif
if(rhs.eq.1) then
call intrsimp(id)
elseif(rhs.eq.2) then
call intpsimp(id)
else
call error(39)
endif
c
return
end
subroutine intpsimp(id)
INCLUDE '../stack.h'
integer iadr, sadr
integer id(nsiz)
integer vola,volb
logical chkvar,vcopyobj
c
iadr(l)=l+l-1
sadr(l)=(l/2)+1
c
c simp(num,den)
c
if(lhs.ne.2) then
call error(41)
return
endif
c
ila=iadr(lstk(top+1-rhs))
il=ila
if(istk(il).lt.0) il=iadr(istk(il+1))
if(istk(il).gt.2) then
fun=-1
call funnam(ids(1,pt+1),'simp',il)
return
endif
c
ilb=iadr(lstk(top))
il=ilb
if(istk(il).lt.0) il=iadr(istk(il+1))
if(istk(il).gt.2) then
fun=-1
call funnam(ids(1,pt+1),'simp',il)
return
endif
c
if(istk(ila).lt.0) then
c move b and copy value of a in place of its reference
k=istk(ila+2)
vola=lstk(k+1)-lstk(k)
volb=lstk(top+1)-lstk(top)
err=lstk(top)+vola+volb-lstk(bot)
if(err.gt.0) then
call error(17)
return
endif
call unsfdcopy(volb,stk(lstk(top)),-1,stk(lstk(top-1)+vola),-1)
call unsfdcopy(vola,stk(lstk(k)),1,stk(lstk(top-1)),1)
lstk(top)=lstk(top-1)+vola
ilb=iadr(lstk(top))
lstk(top+1)=lstk(top)+volb
endif
if(istk(ilb).lt.0) then
c copy value of b in place of its reference
k=istk(ilb+2)
volb=lstk(k+1)-lstk(k)
err=lstk(top)+volb-lstk(bot)
if(err.gt.0) then
call error(17)
return
endif
call unsfdcopy(volb,stk(lstk(k)),1,stk(lstk(top)),1)
lstk(top+1)=lstk(top)+volb
endif
lw=lstk(top+1)
c
if(istk(ila+3).ne.0.or.istk(ilb+3).ne.0) then
fun=-1
call funnam(ids(1,pt+1),'simp',ilb)
return
endif
c
mna=istk(ila+1)*istk(ila+2)
id(1)=0
if(istk(ila).eq.2) then
ida=ila+8
la=sadr(ida+mna+1)
call icopy(4,istk(ila+4),1,id,1)
else
la=sadr(ila+4)
ida=iadr(lw)
lw=sadr(ida+mna+1)
err=lw-lstk(bot)
if(err.gt.0) then
call error(17)
return
endif
do 74 i=1,mna+1
istk(ida+i-1)=i
74 continue
endif
c
mnb=istk(ilb+1)*istk(ilb+2)
if(istk(ilb).eq.2) then
idb=ilb+8
lb=sadr(idb+mnb+1)
if(id(1).eq.0) then
call icopy(4,istk(ilb+4),1,id,1)
else
if(.not.chkvar(id,istk(ilb+4))) then
call error(43)
return
endif
endif
else
lb=sadr(ilb+4)
idb=iadr(lw)
lw=sadr(idb+mna+1)
err=lw-lstk(bot)
if(err.gt.0) then
call error(17)
return
endif
do 75 i=1,mna+1
istk(idb+i-1)=i
75 continue
endif
if(mnb.ne.mna)then
call error(60)
return
endif
c
c determine max of the degrees
na=0
nb=0
do 76 i=1,mna
na=max(na,istk(ida+i)-istk(ida-1+i))
nb=max(nb,istk(idb+i)-istk(idb-1+i))
76 continue
c preserve adress of the beginning of a and b coefficients
lar=la
lbr=lb
c allocate memory for intermediate results
law=lw
lbw=law+na+1
lw=lbw+nb+1
c simplify
la1=la
lb1=lb
do 79 i=1,mna
na=istk(ida+i)-istk(ida-1+i)-1
nb=istk(idb+i)-istk(idb-1+i)-1
ierr=lstk(bot)-lw
call dpsimp(stk(la),na,stk(lb),nb,stk(law),nnum,
$ stk(lbw),nden,stk(lw),ierr)
if(ierr.eq.1) then
call error(27)
return
elseif(ierr.eq.2) then
call msgs(43,i)
endif
c . copy overwrite initial polynomials with simplified ones
call dcopy(nnum,stk(law),1,stk(la1),1)
call dcopy(nden,stk(lbw),1,stk(lb1),1)
la=la+na+1
lb=lb+nb+1
la1=la1+nnum
lb1=lb1+nden
istk(ida-1+i)=nnum
istk(idb-1+i)=nden
79 continue
c
c form vector of pointers from vector of degrees+1
ma=1
mb=1
do 80 i=1,mna+1
na=istk(ida-1+i)
nb=istk(idb-1+i)
istk(ida-1+i)=ma
istk(idb-1+i)=mb
ma=ma+na
mb=mb+nb
80 continue
c
c compute position of the a and b simplified in the result
lstk(top)=lar+istk(ida+mna)-1
il=iadr(lstk(top))
c
c put new b variable in place
if(istk(ilb).eq.2) then
c b matrice de polynome
l=sadr(il+9+mna)
c . move b data up
call icopy(9+mna,istk(ilb),1,istk(il),1)
call unsfdcopy(istk(il+8+mna),stk(lbr),1,stk(l),1)
l=l+istk(il+8+mna)-1
else
c b matrice de scalaires
call icopy(4,istk(ilb),1,istk(il),1)
l=sadr(il+4)
call unsfdcopy(mna,stk(lbr),1,stk(l),1)
l=l+mna
endif
lstk(top+1)=l
end
subroutine intrsimp(id)
INCLUDE '../stack.h'
integer iadr, sadr
integer id(nsiz)
integer vola,volb,vol
double precision er
logical refr,chkvar,israt,ok
data blank/40/
c
iadr(l)=l+l-1
sadr(l)=(l/2)+1
c
lw=lstk(top+1)
c simplification of a transfer function
if(lhs.ne.1) then
call error(41)
return
endif
il1=iadr(lstk(top))
ilr=il1
if(istk(il1).lt.0) il1=iadr(istk(il1+1))
refr=il1.ne.ilr
if(.not.israt(il1,ila,ilb,ildom)) then
fun=-1
call funnam(ids(1,pt+1),'simp',il1)
return
endif
c
if(istk(ila+3).ne.0.or.istk(ilb+3).ne.0) then
fun=-1
call funnam(ids(1,pt+1),'simp',il1)
return
endif
c
if(refr) then
k=istk(ilr+2)
vol=lstk(k+1)-lstk(k)
err=lstk(top)+vol-lstk(bot)
if(err.gt.0) then
call error(17)
return
endif
call unsfdcopy(vol,stk(lstk(k)),1,stk(lstk(top)),1)
lstk(top+1)=lstk(top)+vol
lw=lstk(top+1)
il1=ilr
ok=israt(il1,ila,ilb,ildom)
endif
c
mna=istk(ila+1)*istk(ila+2)
id(1)=0
if(istk(ila).eq.2) then
ida=ila+8
la=sadr(ida+mna+1)
call icopy(4,istk(ila+4),1,id,1)
else
la=sadr(ila+4)
ida=iadr(lw)
lw=sadr(ida+mna+1)
err=lw-lstk(bot)
if(err.gt.0) then
call error(17)
return
endif
do 74 i=1,mna+1
istk(ida+i-1)=i
74 continue
endif
c
mnb=istk(ilb+1)*istk(ilb+2)
if(istk(ilb).eq.2) then
idb=ilb+8
lb=sadr(idb+mnb+1)
if(id(1).eq.0) then
call icopy(4,istk(ilb+4),1,id,1)
else
if(.not.chkvar(id,istk(ilb+4))) then
call error(43)
return
endif
endif
else
lb=sadr(ilb+4)
idb=iadr(lw)
lw=sadr(idb+mna+1)
err=lw-lstk(bot)
if(err.gt.0) then
call error(17)
return
endif
do 75 i=1,mna+1
istk(idb+i-1)=i
75 continue
endif
if(mnb.ne.mna)then
call error(60)
return
endif
c
c determine max of the degrees
na=0
nb=0
do 76 i=1,mna
na=max(na,istk(ida+i)-istk(ida-1+i))
nb=max(nb,istk(idb+i)-istk(idb-1+i))
76 continue
c
c set adress where to put the results
ll=sadr(il1+7)
ill=iadr(ll)
la1=la
lb1=lb
ida1=ida
idb1=idb
c
c allocate memory for intermediate results
law=lw
lbw=law+na+1
lw=lbw+nb+1
c beginning of numerator in resulting structure
l0=ll+istk(ilr+4)-1
c
lar=la1
lbr=lb1
nta=istk(ida+mna)
ntb=istk(idb+mnb)
c simplify
do 79 i=1,mna
na=istk(ida+i)-istk(ida-1+i)-1
nb=istk(idb+i)-istk(idb-1+i)-1
ierr=lstk(bot)-lw
call dpsimp(stk(la),na,stk(lb),nb,stk(law),nnum,
$ stk(lbw),nden,stk(lw),ierr)
if(ierr.eq.1) then
call error(27)
return
elseif(ierr.eq.2) then
call msgs(43,i)
endif
c . copy overwrite initial polynomials with simplified ones
call dcopy(nnum,stk(law),1,stk(la1),1)
call dcopy(nden,stk(lbw),1,stk(lb1),1)
la=la+na+1
lb=lb+nb+1
la1=la1+nnum
lb1=lb1+nden
istk(ida1-1+i)=nnum
istk(idb1-1+i)=nden
79 continue
c
c form vector of pointers from vector of degrees+1
ma=1
mb=1
do 80 i=1,mna+1
na=istk(ida1-1+i)
nb=istk(idb1-1+i)
istk(ida1-1+i)=ma
istk(idb1-1+i)=mb
ma=ma+na
mb=mb+nb
80 continue
c
c update size of numerator
vola=istk(ilr+4)-istk(ilr+3)+istk(ida1+mna)-nta
istk(ilr+4)=istk(ilr+3)+vola
c compute position of new denominator in the result
ll0=ll+istk(ilr+4)-1
il=iadr(ll0)
c
c put new b variable in place
if(istk(ilb).eq.2) then
c b matrice de polynome
call icopy(9+mna,istk(ilb),1,istk(il),1)
idb1=il+8
l=sadr(il+9+mna)
call unsfdcopy(istk(idb1+mna)-1,stk(lbr),1,stk(l),1)
l=l+istk(idb1+mna)-1
else
c b matrice de scalaires
call icopy(4,istk(ilb),1,istk(il),1)
l=sadr(il+4)
call unsfdcopy(mna,stk(lbr),1,stk(l),1)
l=l+mna
endif
volb=l-ll0
c copy 4th entry of the list
mb=istk(ilr+6)-istk(ilr+5)
call unsfdcopy(mb,stk(ll+istk(ilr+5)-1),1,stk(l),1)
l=l+mb
lstk(top+1)=l
c adjust components sizes
istk(ilr+5)=istk(ilr+4)+volb
istk(ilr+6)=istk(ilr+5)+mb
end
subroutine intsfact(id)
INCLUDE '../stack.h'
integer iadr, sadr
integer id(nsiz)
integer vol
logical ref
c
iadr(l)=l+l-1
sadr(l)=(l/2)+1
c
maxit=100
lw=lstk(top+1)
if(lhs.ne.1) then
call error(41)
return
endif
if(rhs.ne.1) then
call error(42)
return
endif
il1=iadr(lstk(top))
ilr=il1
if(istk(il1).lt.0) il1=iadr(istk(il1+1))
ref=ilr.ne.il1
if(istk(il1).ne.2) then
fun=-1
call funnam(ids(1,pt+1),'sfact',il1)
return
endif
m1=istk(il1+1)
n1=istk(il1+2)
it1=istk(il1+3)
if(it1.ne.0) then
err=1
call error(52)
return
endif
mn1=m1*n1
id1=il1+8
l1=sadr(id1+mn1+1)
lr=l1
vol=istk(id1+mn1)-1
if(mn1.eq.1) then
c
c sfact of a polynomial
if(ref) then
c . sfact1 modifies its input argument
lr=sadr(ilr+8+mn1+1)
lstk(top+1)=lr+vol
err=lstk(top+1)-lstk(bot)
if(err.gt.0) then
call error(17)
return
endif
call icopy(8+mn1+1,istk(il1),1,istk(ilr),1)
call unsfdcopy(vol,stk(l1),1,stk(lr),1)
lstk(top+1)=lr+vol
endif
c
c . check symmetry
n1=istk(id1+1)-2
if (2*int(n1/2).ne.n1) then
call error(88)
return
endif
n=1+n1/2
do 81 i=0,n-1
if(stk(lr+i).ne.stk(lr+n1-i)) then
call error(88)
return
endif
81 continue
c
lw=lstk(top+1)
err=lw+6*n-lstk(bot)
if(err.gt.0) then
call error(17)
return
endif
call sfact1(stk(lr),n-1,stk(lw),maxit,ierr)
if(ierr.eq.2) then
write(buf,82) n-1
82 format('No real solution: degree ',i2,' entry is negative!')
call error(999)
return
else if(ierr.eq.1) then
call error(24)
return
else if(ierr.lt.0) then
c convergence incomplete
write(buf(1:4),'(i3)') ierr
call msgs(22,0)
endif
lstk(top+1)=lr+n
istk(ilr+8+1)=n+1
else
c multivariable case
if(m1.ne.n1) then
err=1
call error(20)
return
endif
c . convert matrix of polynomials to a polynomial matrix
n1=0
do 87 i=1,mn1
n1=max(n1,istk(id1+i)-istk(id1+i-1))
87 continue
c
n1=1+(n1-1)/2
l2=lstk(top+1)
if(ref) l2=l2+mn1+9+mn1*n1
lw=l2+mn1*n1
err=lw+sadr((n1+1)*m1*((n1+1)*m1)+1)-lstk(bot)
if(err.gt.0) then
call error(17)
return
endif
c
call dset(mn1*n1,0.0d+0,stk(l2),1)
do 88 i1=0,mn1-1
lij=l1-1+istk(id1+i1)
mij=2+istk(id1+i1+1)-istk(id1+i1)-1-n1
if(mij.gt.0) call unsfdcopy(mij,stk(lij+n1-1),1,
$ stk(l2+i1),mn1)
88 continue
c
maxit=maxit+n1
call sfact2(stk(l2),m1,n1-1,stk(lw),maxit,ierr)
if(ierr.lt.0) then
call error(24)
return
endif
if(ierr.gt.0) then
call error(88)
return
endif
c . convert polynomial matrix to matrix of polynomials
id1=ilr+8
lr=sadr(id1+mn1+1)
l1=lr
do 89 i=0,mn1-1
call unsfdcopy(n1,stk(l2+i),mn1,stk(l1),1)
l1=l1+n1
89 continue
do 90 i=0,mn1
istk(id1+i)=1+n1*i
90 continue
if(ref) call icopy(8,istk(il1),1,istk(ilr),1)
lstk(top+1)=l1
endif
return
end
subroutine intvarn(id)
INCLUDE '../stack.h'
integer iadr, sadr
integer id(nsiz)
integer vol,blank
logical ref
data blank/40/
c
iadr(l)=l+l-1
sadr(l)=(l/2)+1
c
if(lhs.ne.1) then
call error(41)
return
endif
c
il1=iadr(lstk(top+1-rhs))
ilr=il1
if(istk(il1).lt.0) il1=iadr(istk(il1+1))
ref=ilr.ne.il1
if(istk(il1).ne.2) then
if(rhs.eq.2.and.istk(il1).eq.1) then
top=top-1
if (ref) then
k=istk(ilr+2)
vol=lstk(k+1)-lstk(k)
err=lstk(top)+vol-lstk(bot)
if(err.gt.0) then
call error(17)
return
endif
call unsfdcopy(vol,stk(lstk(k)),1,stk(lstk(top)),1)
lstk(top+1)=lstk(top)+vol
endif
return
endif
fun=-1
call funnam(ids(1,pt+1),'varn',il1)
return
endif
call icopy(4,istk(il1+4),1,id,1)
if(rhs.eq.1) then
c get formal variable name
if(ref) then
err=sadr(ilr+10)-lstk(bot)
if(err.gt.0) then
call error(17)
return
endif
endif
c extraction du nom de la variable muette
istk(ilr)=10
istk(ilr+1)=1
istk(ilr+2)=1
istk(ilr+3)=0
do 10 ii=4,1,-1
if(istk(il1+3+ii).ne.blank) then
nv=ii
goto 11
endif
10 continue
11 call icopy(nv,istk(il1+4),-1,istk(ilr+6),-1)
istk(ilr+4)=1
istk(ilr+5)=nv+1
lstk(top+1)=sadr(ilr+10)
elseif(rhs.eq.2) then
c change formal variable name
c . get new variable name
il=iadr(lstk(top))
if(istk(il).lt.0) il=iadr(istk(il+1))
if(istk(il).ne.10) then
err=2
call error(55)
return
endif
if(istk(il+1)*istk(il+2).ne.1) then
err=2
call error(36)
return
endif
nc=istk(il+5)-1
if(istk(il1).eq.1) goto 106
call icopy(max(4,nc),istk(il+6),1,id,1)
if(nc.lt.4) call iset(4-nc,blank,id(nc+1),1)
106 top=top-1
if(ref) then
c . variable is passed by reference copy it on the top of the
c stack
k=istk(ilr+2)
vol=lstk(k+1)-lstk(k)
err=lstk(top)+vol-lstk(bot)
if(err.gt.0) then
call error(17)
return
endif
call unsfdcopy(vol,stk(lstk(k)),1,stk(lstk(top)),1)
lstk(top+1)=lstk(top)+vol
endif
ilr=iadr(lstk(top))
call icopy(4,id,1,istk(ilr+4),1)
else
call error(42)
return
endif
return
end
subroutine intpclean(id)
INCLUDE '../stack.h'
integer iadr, sadr
integer id(nsiz)
integer vol
logical ref
double precision epsa,epsr
c
iadr(l)=l+l-1
sadr(l)=(l/2)+1
c
if(lhs.ne.1) then
call error(41)
return
endif
if (rhs.lt.1.or.rhs.gt.3) then
call error(42)
return
endif
c
il1=iadr(lstk(top+1-rhs))
ilr=il1
if(istk(il1).lt.0) il1=iadr(istk(il1+1))
if(istk(il1).ne.2) then
fun=-1
call funnam(ids(1,pt+1),'clean',il1)
return
endif
ref=il1.ne.ilr
c get relative and absolute tolerances
epsr=1.0d-10
epsa=1.0d-10
if (rhs.eq.3) then
il=iadr(lstk(top))
if(istk(il).lt.0) il=iadr(istk(il+1))
if(istk(il).ne.1) then
err=3
call error(52)
return
endif
if(istk(il+1)*istk(il+2).ne.1) then
err=3
call error(60)
return
endif
if(istk(il+3).ne.0) then
err=3
call error(52)
return
endif
epsr=stk(sadr(il+4))
top=top-1
endif
if (rhs.ge.2) then
il=iadr(lstk(top))
if(istk(il).lt.0) il=iadr(istk(il+1))
if(istk(il).ne.1) then
err=3
call error(52)
return
endif
if(istk(il+1)*istk(il+2).ne.1) then
err=3
call error(60)
return
endif
if(istk(il+3).ne.0) then
err=3
call error(52)
return
endif
epsa=stk(sadr(il+4))
top=top-1
endif
if(ref) then
k=istk(ilr+2)
vol=lstk(k+1)-lstk(k)
err=lstk(top)+vol-lstk(bot)
if(err.gt.0) then
call error(17)
return
endif
call unsfdcopy(vol,stk(lstk(k)),1,stk(lstk(top)),1)
lstk(top+1)=lstk(top)+vol
il1=ilr
endif
it1=istk(il1+3)
m1=istk(il1+1)
n1=istk(il1+2)
mn1=m1*n1
id1=il1+8
l1=sadr(id1+mn1+1)
vol=istk(id1+mn1)-1
id2=iadr(lstk(top+1))
err=sadr(id2+mn1+1)-lstk(bot)
if(err.gt.0) then
call error(17)
return
endif
if(it1.eq.0) then
call dmpcle(stk(l1),istk(id1),m1,n1,istk(id2),epsr,epsa)
else
call wmpcle(stk(l1),stk(l1+vol),istk(id1),m1,n1,
& istk(id2),epsr,epsa)
endif
lstk(top+1)=l1+(istk(id1+mn1)-1)*(it1+1)
return
end
subroutine intsimpmd(id)
INCLUDE '../stack.h'
integer iadr, sadr
integer id(nsiz)
integer simpmd
common/csimp/ simpmd
c
iadr(l)=l+l-1
sadr(l)=(l/2)+1
c
if(rhs.gt.1) then
call error(39)
return
endif
if(rhs.le.0) then
top=top+1
il=iadr(lstk(top))
istk(il)=4
istk(il+1)=1
istk(il+2)=1
istk(il+3)=simpmd
lstk(top+1)=sadr(il+4)
else
il=iadr(lstk(top))
if(istk(il).lt.0) il=iadr(istk(il+1))
if(istk(il).ne.4) then
err=1
call error(208)
return
endif
if(istk(il+1)*istk(il+2).ne.1) then
err=1
call error(36)
return
endif
simpmd=istk(il+3)
il=iadr(lstk(top))
istk(il)=0
lstk(top+1)=sadr(il+1)
endif
return
end
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