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|
subroutine matlu
c ====================================================================
c
c evaluate functions involving gaussian elimination
c
c ====================================================================
c
c Copyright INRIA
include '../stack.h'
integer id(nsiz),io
c
c fonction / fin
c -2 -1 1 2 3 4 5 6 7
c \ / inv det rcond lu chol rref
c
if (ddt .eq. 4) then
write(buf(1:4),'(i4)') fin
call basout(io,wte,' matlu '//buf(1:4))
endif
c
if(rhs.le.0) then
call error(39)
return
endif
c
go to (20,10,99,30,40,50,60,99,80,85),fin+3
c
10 continue
c matrix right division, a/a2
call intrdiv
goto 99
c
20 continue
call intldiv
goto 99
c
30 continue
c inv
call intinv
goto 99
c
40 continue
c det
call intdet
return
c
50 continue
c rcond
call intrcond
goto 99
c
60 continue
c lu
call intlu
goto 99
c
80 continue
c cholesky
call intchol
go to 99
c
85 continue
c rref
call intrref
go to 99
99 return
end
subroutine intlu
c lu
include '../stack.h'
integer iadr,sadr
c
iadr(l)=l+l-1
sadr(l)=(l/2)+1
c
c Check number of arguments
if (rhs .ne. 1) then
call error(39)
return
endif
if (lhs .ne. 2 .and.lhs .ne. 3) then
call error(41)
return
endif
c Check input argument type
il=iadr(lstk(top-rhs+1))
if (istk(il).ne.1) then
call putfunnam('lu',top-rhs+1)
fun=-1
return
endif
m=istk(il+1)
n=istk(il+2)
it=istk(il+3)
l=sadr(il+4)
nn=n*n
if (m .ne. n) then
err=rhs
call error(20)
return
endif
c form output matrices
top = top+1
ilu=iadr(lstk(top))
lu=sadr(ilu+4)
lstk(top+1)=lu+nn*(it+1)
if(lhs.eq.3) then
top = top+1
ile=iadr(lstk(top))
le=sadr(ile+4)
lstk(top+1)=le+nn
endif
ilp=iadr(lstk(top+1))
c check for space
err = sadr(ilp+n) -lstk(bot)
if (err .gt. 0) then
call error(17)
return
endif
c
istk(ilu)=1
istk(ilu+1)=n
istk(ilu+2)=n
istk(ilu+3)=it
if(lhs.eq.3) then
istk(ile)=1
istk(ile+1)=n
istk(ile+2)=n
istk(ile+3)=0
endif
if(nn.le.0) then
c lu of an empty matrix
go to 99
endif
c Compute factorisation
if(it.eq.0) then
call dgefa(stk(l),m,n,istk(ilp),info)
else
call wgefa(stk(l),stk(l+nn),m,n,istk(ilp),info)
endif
c Form output matrices
call dset(nn*(it+1),0.0d0,stk(lu),1)
do 12 kb = 1, n
k = n+1-kb
ll=l+(k-1)*n
luk=lu+(k-1)*n
c . copy upper triangle in U
call dcopy(k,stk(ll),1,stk(luk),1)
if(k.ne.n) then
call dscal(n-k,-1.0d+0,stk(ll+k),1)
endif
c . set lower triangle of L to 0
call dset(k,0.0d+0,stk(ll),1)
stk(ll+k-1)=1.0d+0
c
i = istk(ilp+k-1)
if (i .ne. k) then
li = l+i-1+(k-1)*n
lk = l+k-1+(k-1)*n
call dswap(n-k+1,stk(li),n,stk(lk),n)
endif
12 continue
if(it.eq.1) then
c L and U Imaginary part
do 14 kb = 1, n
k = n+1-kb
ll=l+nn+(k-1)*n
luk=lu+nn+(k-1)*n
call dcopy(k,stk(ll),1,stk(luk),1)
if(k.ne.n) then
call dscal(n-k,-1.0d+0,stk(ll+k),1)
endif
call dset(k,0.0d0,stk(ll),1)
14 continue
i = istk(ilp+k-1)
if (i .ne. k) then
li = l+i-1+(k-1)*n
lk = l+k-1+(k-1)*n
call dswap(n-k+1,stk(li),n,stk(lk),n)
endif
endif
if(lhs.eq.3) then
call dset(nn,0.0d0,stk(le),1)
call dset(n,1.0d0,stk(le),n+1)
do 16 kb = 1, n
k = n+1-kb
i = istk(ilp+k-1)
if (i .ne. k) then
call dswap(n,stk(le+(i-1)*n),1,stk(le+(k-1)*n),1)
endif
16 continue
do 17 k = 1, n
i = istk(ilp+k-1)
if (i .ne. k) then
call dswap(n,stk(l+(i-1)),n,stk(l+(k-1)),n)
if(it.eq.1) then
call dswap(n,stk(l+nn+(i-1)),n,stk(l+nn+(k-1)),n)
endif
endif
17 continue
endif
99 continue
return
end
subroutine intchol
c Cholesky
include '../stack.h'
integer iadr,sadr
c
iadr(l)=l+l-1
sadr(l)=(l/2)+1
c
c Check number of arguments
if (rhs .ne. 1) then
call error(39)
return
endif
if (lhs .ne. 1) then
call error(41)
return
endif
c Check argument type
il=iadr(lstk(top-rhs+1))
if (istk(il).ne.1) then
call putfunnam('chol',top-rhs+1)
fun=-1
return
endif
m=istk(il+1)
n=istk(il+2)
it=istk(il+3)
l=sadr(il+4)
nn=n*n
c Check argument dimension
if (m .ne. n) then
err=rhs
call error(20)
return
endif
c
if(nn.le.0) return
if(it.eq.1) call wpofa(stk(l),stk(l+nn),m,n,err)
if(it.eq.0) call dpofa(stk(l),m,n,err)
if (err .ne. 0) then
call error(29)
return
endif
do 81 j = 1, n
ll = l+j+(j-1)*m
call dcopy(m-j,0.0d+0,0,stk(ll),1)
if(it.eq.1) call dcopy(m-j,0.0d+0,0,stk(ll+nn),1)
81 continue
return
end
subroutine intrref
include '../stack.h'
double precision eps
integer iadr,sadr
c
iadr(l)=l+l-1
sadr(l)=(l/2)+1
c
eps=stk(leps)
c
c Check number of arguments
if (rhs .ne. 1) then
call error(39)
return
endif
if (lhs .ne. 1) then
call error(41)
return
endif
c Check argument type
il=iadr(lstk(top-rhs+1))
if (istk(il).ne.1) then
call putfunnam('rref',top-rhs+1)
fun=-1
return
endif
m=istk(il+1)
n=istk(il+2)
it=istk(il+3)
l=sadr(il+4)
mn=m*n
if(mn.le.0) return
c
if(it.eq.0) then
call drref(stk(l),m,m,n,eps)
else
call wrref(stk(l),stk(l+mn),m,m,n,eps)
endif
return
end
subroutine intrcond
include '../stack.h'
double precision sr,si,rcond
integer iadr,sadr
c
iadr(l)=l+l-1
sadr(l)=(l/2)+1
c
c Check number of arguments
if (rhs .ne. 1) then
call error(39)
return
endif
if (lhs .gt. 2) then
call error(41)
return
endif
c
c Check argument type
il=iadr(lstk(top-rhs+1))
if (istk(il).ne.1) then
call putfunnam('rcond',top-rhs+1)
fun=-1
return
endif
m=istk(il+1)
n=istk(il+2)
it=istk(il+3)
l=sadr(il+4)
nn=n*n
c Check argument size
if (m .ne. n) then
err=rhs
call error(20)
return
endif
l3 = l + nn*(it+1)
err = l3+n*(it+1)+sadr(n) - lstk(bot)
if (err .gt. 0) then
call error(17)
return
endif
if(nn.le.0) then
c empty matrix case
rcond=1.0d0
else
if(it.eq.0) then
call dlslv(stk(l),m,n,sr,0,0,stk(l3),rcond,ierr,0)
else
call wlslv(stk(l),stk(l+nn),m,n,sr,si,0,0,stk(l3),
$ rcond,ierr,0)
endif
endif
stk(l) = rcond
istk(il+1)=1
istk(il+2)=1
istk(il+3)=0
lstk(top+1)=l+1
if (lhs .gt. 1) then
top=top+1
il=iadr(lstk(top))
istk(il)=1
if(nn.eq.0) then
istk(il+1)=0
istk(il+2)=0
istk(il+3)=0
lstk(top+1)=sadr(il+4)+1
else
istk(il+1)=n
istk(il+2)=1
istk(il+3)=it
l=sadr(il+4)
call dcopy(n*(it+1),stk(l3+sadr(n)),1,stk(l),1)
lstk(top+1)=l+n*(it+1)
endif
endif
return
end
subroutine intdet
include '../stack.h'
double precision dtr(2),dti(2),sr,si,t
integer iadr,sadr
c
iadr(l)=l+l-1
sadr(l)=(l/2)+1
c
if (rhs .ne. 1) then
call error(39)
return
endif
if (lhs .gt. 2) then
call error(41)
return
endif
c
il=iadr(lstk(top-rhs+1))
if (istk(il).ne.1) then
call putfunnam('det',top-rhs+1)
fun=-1
return
endif
c
m=istk(il+1)
n=istk(il+2)
it=istk(il+3)
l=sadr(il+4)
mn=m*n
nn=n*n
if (m .ne. n) then
err=1
call error(20)
return
endif
if(mn.le.0) goto 47
ilp=iadr(l+mn*(it+1))
lw=sadr(ilp+n)
err=lw-lstk(bot)
if(err.gt.0) then
call error(17)
return
endif
if(it.eq.0) then
call dgefa(stk(l),m,n,istk(ilp),info)
call dgedi(stk(l),m,n,istk(ilp),dtr,sr,10)
else
call wgefa(stk(l),stk(l+mn),m,n,istk(ilp),info)
call wgedi(stk(l),stk(l+mn),m,n,istk(ilp),dtr,dti,
& sr,si,10)
endif
k = int(dtr(2))
if(lhs.eq.1) then
stk(l) = dtr(1)*10.0d+0**int(dtr(2))
if(it.eq.1) stk(l+1) = dti(1)*10.0d+0**int(dtr(2))
istk(il+1)=1
istk(il+2)=1
lstk(top+1)=l+it+1
else
stk(l) = dtr(2)
istk(il+1)=1
istk(il+2)=1
istk(il+3)=0
lstk(top+1)=l+1
top=top+1
il=iadr(lstk(top))
istk(il)=1
istk(il+1)=1
istk(il+2)=1
istk(il+3)=it
l=sadr(il+4)
stk(l)=dtr(1)
if(it.eq.1) stk(l+1)=dti(1)
lstk(top+1)=l+(it+1)
endif
go to 99
c cas de la matrice vide
47 continue
if(lhs.eq.1) then
istk(il+1)=1
istk(il+2)=1
lstk(top+1)=l+it+1
stk(l)=1.0d+0
if (it.eq.1) stk(l+1)=0.0d+0
else
stk(l) = 0.0d0
istk(il+1)=1
istk(il+2)=1
istk(il+2)=0
lstk(top+1)=l+1
top=top+1
il=iadr(lstk(top))
istk(il)=1
istk(il+1)=1
istk(il+2)=1
istk(il+3)=it
l=sadr(il+4)
stk(l)=1.0d+0
if (it.eq.1) stk(l+1)=0.0d+0
lstk(top+1)=l+(it+1)
endif
go to 99
99 continue
return
end
subroutine intinv
include '../stack.h'
double precision sr,si,rcond,t
integer iadr,sadr
c
iadr(l)=l+l-1
sadr(l)=(l/2)+1
c
if (rhs .ne. 1) then
call error(39)
return
endif
if (lhs .ne. 1) then
call error(41)
return
endif
c
il=iadr(lstk(top-rhs+1))
if (istk(il).ne.1) then
call putfunnam('inv',top-rhs+1)
fun=-1
return
endif
m=istk(il+1)
n=istk(il+2)
it=istk(il+3)
l=sadr(il+4)
mn=m*n
nn=n*n
if (m .ne. n) then
err=rhs
call error(20)
return
endif
c
n=abs(n)
if(mn.le.0) return
l3 = l + nn*(it+1)
err = l3+n*(it+1)+sadr(n) - lstk(bot)
if (err .gt. 0) then
call error(17)
return
endif
if(it.eq.0) then
call dlslv(stk(l),n,n,sr,0,0,stk(l3),rcond,err,3)
else
call wlslv(stk(l),stk(l+nn),n,n,sr,si,0,0,stk(l3),
$ rcond,err,3)
endif
if (rcond .eq. 0.0d+0) then
call error(19)
return
endif
t = 1.0d+0 + rcond
if (t .eq. 1.0d+0) then
write(buf(1:13),'(1pd13.4)') rcond
c matrice est quasi singuliere ou mal normalisee')
call msgs(5,0)
endif
return
end
subroutine intldiv
c matrix left division a backslash a2
include '../stack.h'
double precision sr,si,rcond,t
integer iadr,sadr
c
iadr(l)=l+l-1
sadr(l)=(l/2)+1
c
il=iadr(lstk(top-rhs+1))
if (istk(il).ne.1) then
err=rhs
call error(53)
return
endif
c
m=istk(il+1)
n=istk(il+2)
it=istk(il+3)
l=sadr(il+4)
mn=m*n
nn=n*n
top=top-1
il2=iadr(lstk(top+1))
if(istk(il2).ne.1) then
err=rhs
call error(53)
return
endif
m2=istk(il2+1)
n2=istk(il2+2)
it2=istk(il2+3)
l2=sadr(il2+4)
mn2=m2*n2
c
if (m .ne. n) then
err=rhs
call error(20)
return
endif
if (mn2 .eq. 1) go to 26
if (mn2.le.0) then
err=rhs
call error(45)
return
endif
if (mn.le.0) then
lstk(top+1)=l
return
endif
if (m2 .ne. n) then
call error(12)
return
endif
l3=l2+(max(it,it2)+1)*mn2
err = l3+n*(it+1)+sadr(n) - lstk(bot)
if (err .gt. 0) then
call error(17)
return
endif
c
if(it.eq.1) then
if(it2.eq.0) call dcopy(mn2,0.0d+0,0,stk(l2+mn2),1)
call wlslv(stk(l),stk(l+mn),m,n,stk(l2),stk(l2+mn2),
& m2,n2,stk(l3),rcond,err,1)
else
call dlslv(stk(l),m,n,stk(l2),m2,n2*(it2+1),stk(l3),
& rcond,err,1)
endif
c
if (rcond .eq. 0.0d+0) then
call error(19)
return
endif
t = 1.0d+0 + rcond
c
if (t .eq. 1.0d+0) then
write(buf(1:13),'(1pd13.4)') rcond
call msgs(5,0)
endif
c
istk(il+2)=n2
it=max(it,it2)
istk(il+3)=it
lstk(top+1)=l+mn2*(it+1)
call dcopy(mn2*(it+1),stk(l2),1,stk(l),1)
go to 99
26 sr = stk(l2)
si=0.0d+0
if(it2.eq.1) si = stk(l2+1)
if (m .ne. n) then
err=rhs
call error(20)
return
endif
n=abs(n)
if(mn.le.0) return
l3 = l + nn*(it+1)
err = l3+n*(it+1)+sadr(n) - lstk(bot)
if (err .gt. 0) then
call error(17)
return
endif
if(it.eq.0) then
call dlslv(stk(l),n,n,sr,0,0,stk(l3),rcond,err,3)
else
call wlslv(stk(l),stk(l+nn),n,n,sr,si,0,0,stk(l3),
$ rcond,err,3)
endif
if (rcond .eq. 0.0d+0) then
call error(19)
return
endif
t = 1.0d+0 + rcond
if (t .eq. 1.0d+0) then
write(buf(1:13),'(1pd13.4)') rcond
c matrice est quasi singuliere ou mal normalisee')
call msgs(5,0)
endif
goto(33,34,35) (it+2*it2)
33 call dscal(nn*(it+1),sr,stk(l),1)
istk(il+3)=it
lstk(top+1)=l+m*n*(it+1)
goto 99
34 call dcopy(nn,stk(l),1,stk(l+nn),1)
call dscal(nn,sr,stk(l),1)
call dscal(nn,si,stk(l+nn),1)
istk(il+3)=1
lstk(top+1)=l+2*nn
goto 99
35 call wscal(nn,sr,si,stk(l),stk(l+nn),1)
go to 99
99 continue
return
end
subroutine intrdiv
include '../stack.h'
double precision eps,sr,si,rcond,t
integer iadr,sadr
c
iadr(l)=l+l-1
sadr(l)=(l/2)+1
c
eps=stk(leps)
il=iadr(lstk(top-rhs+1))
if (istk(il).ne.1) then
err=rhs
call error(53)
return
endif
m=istk(il+1)
n=istk(il+2)
it=istk(il+3)
l=sadr(il+4)
mn=m*n
nn=n*n
c
top=top-1
il2=iadr(lstk(top+1))
if(istk(il2).ne.1) then
err=rhs
call error(53)
return
endif
m2=istk(il2+1)
n2=istk(il2+2)
it2=istk(il2+3)
itr=max(it,it2)
l2=sadr(il2+4)
mn2=m2*n2
c
if (m2 .ne. n2) then
err=rhs
call error(20)
return
endif
if (mn .eq. 1) go to 16
if (mn2.le.0) then
err=2
call error(45)
return
endif
if (mn.le.0) then
lstk(top+1)=l
return
endif
if (n .ne. n2) then
call error(11)
return
endif
l3=max(l+(itr+1)*mn,l2)+(it2+1)*mn2
err=l3+n2*(it2+1)+(n2+1)/2-lstk(bot)
if(err.gt.0) then
call error(17)
return
endif
c
if(it.eq.1.or.it2.eq.0) goto 9
inc=1
if(l2.le.l+2*mn) inc=-1
call dcopy(mn2*(it2+1),stk(l2),inc,stk(l+2*mn),inc)
call dcopy(mn,0.0d+0,0,stk(l+mn),1)
istk(il+3)=1
l2=l+2*mn
lstk(top+1)=l2
9 continue
if(it2.eq.1) call wlslv(stk(l2),stk(l2+mn2),m2,n2,
$ stk(l),stk(l+mn),m,m,stk(l3),rcond,err,2)
if(it2.eq.0) call dlslv(stk(l2),m2,n2,stk(l),m,m,stk(l3),
$ rcond,err,2)
if(it2.eq.0.and.it.eq.1) call dlslv(stk(l2),m2,n2,stk(l+mn),m,m,
$ stk(l3),rcond,err,-2)
if (rcond.eq.0.0d+0) then
call error(19)
return
endif
t = 1.0d+0 + rcond
if (t.eq.1.0d+0 .and. fun.ne.21) then
write(buf(1:13),'(1pd13.4)') rcond
call msgs(5,0)
endif
if (t.eq.1.0d+0 .and. fun.eq.21) then
write(buf(1:13),'(1pd13.4)') rcond
call msgs(6,0)
endif
c
c check for imaginary roundoff in matrix functions
if(it2.eq.0.and.it.eq.0) goto 99
do 13 i=1,nn
sr=abs(stk(l+i-1))
si=abs(stk(l+mn+i-1))
if(si.gt.eps*sr) goto 99
13 continue
istk(il+3)=0
lstk(top+1)=l+mn
go to 99
c
16 sr = stk(l)
si=0.0d+0
if(it.eq.1) si = stk(l+1)
n = n2
m = n
mn=m*n
nn=n*n
istk(il+1)=n
istk(il+2)=n
istk(il+3)=it2
lstk(top+1)=l+nn*(it2+1)
call dcopy(nn*(it2+1),stk(l2),1,stk(l),1)
it2=it
it=istk(il+3)
if (m .ne. n) then
err=rhs
call error(20)
return
endif
n=abs(n)
if(mn.le.0) return
l3 = l + nn*(it+1)
err = l3+n*(it+1)+sadr(n) - lstk(bot)
if (err .gt. 0) then
call error(17)
return
endif
if(it.eq.0) then
call dlslv(stk(l),n,n,sr,0,0,stk(l3),rcond,err,3)
else
call wlslv(stk(l),stk(l+nn),n,n,sr,si,0,0,stk(l3),
$ rcond,err,3)
endif
if (rcond .eq. 0.0d+0) then
call error(19)
return
endif
t = 1.0d+0 + rcond
if (t .eq. 1.0d+0) then
write(buf(1:13),'(1pd13.4)') rcond
c matrice est quasi singuliere ou mal normalisee')
call msgs(5,0)
endif
goto(33,34,35) (it+2*it2)
33 call dscal(nn*(it+1),sr,stk(l),1)
istk(il+3)=it
lstk(top+1)=l+m*n*(it+1)
goto 99
34 call dcopy(nn,stk(l),1,stk(l+nn),1)
call dscal(nn,sr,stk(l),1)
call dscal(nn,si,stk(l+nn),1)
istk(il+3)=1
lstk(top+1)=l+2*nn
goto 99
35 call wscal(nn,sr,si,stk(l),stk(l+nn),1)
go to 99
99 continue
return
end
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