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|
subroutine matsvd
c ================================== ( Inria ) =============
c evaluate functions involving singular value decomposition
c
c =============================================================
c Copyright INRIA
include '../stack.h'
c
double precision s,t,tol,eps
double precision ddot,dlamch
integer rang, iadr,sadr
c
c fin 1 2 3 4 5 6
c svd pinv cond norm rank sva
c
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,' matsvd '//buf(1:4))
endif
c
if(rhs.le.0) then
call error(39)
return
endif
if(top+lhs-rhs+1.ge.bot) then
call error(18)
return
endif
c
eps=stk(leps)
c
go to (50,70,10,30,70,80), fin
c
c cond
c
10 continue
il=iadr(lstk(top+1-rhs))
if(istk(il).ne.1) then
call putfunnam('cond',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
m1=min(m+1,n)
if(mn.le.0) then
k=1
goto 78
endif
ld = l + mn*(it+1)
l1 = ld + m1*(it+1)
l2 = l1 + n*(it+1)
err = l2+m*(it+1) - lstk(bot)
if (err .gt. 0) then
call error(17)
return
endif
if(it.eq.0) goto 11
call wsvdc(stk(l),stk(l+mn),m,m,n,stk(ld),stk(ld+m1),
1 stk(l1),stk(l1+n),t,t,1,t,t,1,stk(l2),stk(l2+m),0,ierr)
goto 12
11 call dsvdc(stk(l),m,m,n,stk(ld),stk(l1),t,1,t,1,stk(l2),0,ierr)
12 continue
c
if (ierr.gt.1) call msgs(3,ierr)
s = stk(ld)
ld = ld + min(m,n) - 1
t = stk(ld)
if (t .eq. 0.0d+0) then
t=dlamch('o')
else
t=s/t
endif
stk(l) = t
istk(il+1)=1
istk(il+2)=1
istk(il+3)=0
lstk(top+1)=l+1
go to 99
c
c vector and matrix norm
c
30 continue
call intnorm("norm")
goto 99
c
c svd
c
50 continue
il=iadr(lstk(top+1-rhs))
if(istk(il).ne.1) then
call putfunnam('svd',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
m1=min(m+1,n)
c
tol = -1.0d+0
if (rhs.eq.2) then
il1=iadr(lstk(top))
if(istk(il1).ne.1) then
err=2
call error(53)
return
endif
if(istk(il1+3).ne.0) then
err=2
call error(52)
return
endif
l1=sadr(il1+4)
tol=stk(l1)
top = top-1
endif
if(mn.le.0) then
c empty matrix
c svd([])=[]
if(lhs.eq.1) return
c [u,s,v]=svd([]) -> u=[],v=[],s=[]
if(lhs.ge.3) then
istk(il)=1
istk(il+1)=0
istk(il+2)=0
istk(il+3)=0
lstk(top+1)=sadr(il+4)
c
top = top+1
il=iadr(lstk(top))
istk(il)=1
istk(il+1)=0
istk(il+2)=0
istk(il+3)=0
lstk(top+1)=sadr(il+4)
c
top = top+1
il=iadr(lstk(top))
istk(il)=1
istk(il+1)=0
istk(il+2)=0
istk(il+3)=0
lstk(top+1)=sadr(il+4)
if(lhs.eq.3) return
top=top+1
il=iadr(lstk(top))
l=sadr(il+4)
istk(il)=1
istk(il+1)=1
istk(il+2)=1
istk(il+3)=0
stk(l)=0.d0
lstk(top+1)=l+1
return
endif
endif
if (lhs .lt. 3) go to 52
k = m
if (rhs .eq. 2 .and. lhs .ne. 4) k = min(m,n)
lu=l
ld=lu+m*k*(it+1)+sadr(5)-1
lv=ld+k*n+sadr(5)-1
l=lv+n*n*(it+1)
l1=l+m*n*(it+1)
l2=l1+n*(it+1)
lsv=l2+m*(it+1)
c
err = lsv+m1*(it+1) - lstk(bot)
if (err .gt. 0) then
call error(17)
return
endif
c
call dcopy(m*n*(it+1),stk(lu),1,stk(l),1)
job = 11
if (rhs .eq. 2 .and. lhs .ne. 4) job = 21
if(it.eq.0) call dsvdc(stk(l),m,m,n,stk(lsv),stk(l1),
1 stk(lu),m,stk(lv),n,stk(l2),job,ierr)
if(it.eq.1) call wsvdc(stk(l),stk(l+m*n),m,m,n,stk(lsv),
1 stk(lsv+m1),stk(l1),stk(l1+n),stk(lu),stk(lu+m*k),m,stk(lv),
2 stk(lv+n*n),n,stk(l2),stk(l2+m),job,ierr)
c set matrix of singular values
c
if (ierr.gt.1) call msgs(3,ierr)
c
if(rhs.eq.1) tol=dble(max(m,n))*eps*stk(lsv)
rang=0
do 51 j = 1, n
do 51 i = 1, k
ll = ld+i-1+(j-1)*k
ls = lsv+i-1
if (i.eq.j) then
stk(ll) = stk(ls)
if(stk(ls).gt.tol) rang=i
else
stk(ll)=0.0d+0
endif
51 continue
c
c set headers for lhs
istk(il+1)=m
istk(il+2)=k
istk(il+3)=it
lstk(top+1)=lu+m*k*(it+1)
c
top = top+1
il=iadr(lstk(top))
istk(il)=1
istk(il+1)=k
istk(il+2)=n
istk(il+3)=0
lstk(top+1)=ld+k*n
c
top = top+1
il=iadr(lstk(top))
istk(il)=1
istk(il+1)=n
istk(il+2)=n
istk(il+3)=it
lstk(top+1)=lv+n*n*(it+1)
if(lhs.eq.3) goto 99
top=top+1
il=iadr(lstk(top))
istk(il)=1
istk(il+1)=1
istk(il+2)=1
istk(il+3)=0
lr=lv+n*n*(it+1)+sadr(5)-1
stk(lr)=dble(rang)
lstk(top+1)=lr+1
go to 99
c
52 ld = l + m*n*(it+1)
l1 = ld + m1*(it+1)
l2 = l1 + n*2
err = l2+m*(it+1) - lstk(bot)
if (err .gt. 0) then
call error(17)
return
endif
if(it.eq.0) call dsvdc(stk(l),m,m,n,stk(ld),
$ stk(l1),t,1,t,1,stk(l2),
$ 0,ierr)
if(it.eq.1) call wsvdc(stk(l),stk(l+m*n),m,m,n,
1 stk(ld),stk(ld+m1),stk(l1),stk(l1+n),t,t,1,t,t,1,
2 stk(l2),stk(l2+m),0,ierr)
c
if (ierr.gt.1) call msgs(3,ierr)
k = min(m,n)
call dcopy(k,stk(ld),1,stk(l),1)
istk(il+1)=k
istk(il+2)=1
istk(il+3)=0
lstk(top+1)=l+k
go to 99
c
c pinv and rank
c
70 continue
il=iadr(lstk(top+1-rhs))
if(istk(il).ne.1) then
if(fin.eq.5) then
call putfunnam('rank',top-rhs+1)
else
call putfunnam('pinv',top-rhs+1)
endif
fun=-1
return
endif
m=istk(il+1)
n=istk(il+2)
it=istk(il+3)
l=sadr(il+4)
mn = m*n
m1=min(m+1,n)
tol = -1.0d+0
if (rhs.eq.2) then
il1=iadr(lstk(top))
if(istk(il1).ne.1) then
err=2
call error(53)
return
endif
if(istk(il1+3).ne.0) then
err=2
call error(52)
return
endif
l1=sadr(il1+4)
tol=stk(l1)
top = top-1
endif
if (mn.le.0 ) then
if (fin.eq.2) then
c pinv([])=[]
c err=1
c call error(45)
return
endif
k=0
goto 78
endif
lu = l + m*n*(it+1)
ld = lu + m*m*(it+1)
if (fin .eq. 5) ld = l + m*n*(it+1)
lv = ld + m1*(it+1)
l1 = lv + n*n*(it+1)
if (fin .eq. 5) l1 = ld + n*(it+1)
l2 = l1 + n*(it+1)
err = l2+m*(it+1) - lstk(bot)
if (err .gt. 0) then
call error(17)
return
endif
if (fin .eq. 2) job = 11
if (fin .eq. 5) job = 0
if(it.eq.0) call dsvdc(stk(l),m,m,n,stk(ld),
$ stk(l1),stk(lu),m,stk(lv),
$ n,stk(l2),job,ierr)
if(it.eq.1) call wsvdc(stk(l),stk(l+m*n),m,m,n,
1 stk(ld),stk(ld+m1),stk(l1),stk(l1+n),
2 stk(lu),stk(lu+m*m),m,stk(lv),stk(lv+n*n),n,
3 stk(l2),stk(l2+m),job,ierr)
c
if (ierr.gt.1) call msgs(3,ierr)
if (tol .lt. 0.0d+0) tol = dble(max(m,n))*eps*stk(ld)
mn = min(m,n)
k = 0
do 72 j = 1, mn
ls = ld+j-1
s = stk(ls)
if (s .le. tol) go to 73
k = j
ll = lv+(j-1)*n
if (fin.eq.2) call dscal(n,1.0d+0/s,stk(ll),1)
if (fin.eq.2.and.it.eq.1) call dscal(n,1.0d+0/s,stk(ll+n*n),1)
72 continue
73 if (fin .eq. 5) go to 78
do 74 j=1,m
do 74 i=1,n
ll=l+i-1+(j-1)*n
l1=lv+i-1
l2=lu+j-1
stk(ll)=ddot(k,stk(l2),m,stk(l1),n)
74 continue
if(it.eq.0) goto 77
do 76 j = 1, m
do 76 i = 1, n
ll = l+i-1+(j-1)*n
l1 = lv+i-1
l2 = lu+j-1
stk(ll) = stk(ll)+ddot(k,stk(l2+m*m),m,stk(l1+n*n),n)
stk(ll+m*n)=ddot(k,stk(l2),m,stk(l1+n*n),n)
1 -ddot(k,stk(l2+m*m),m,stk(l1),n)
76 continue
77 continue
istk(il+1)=n
istk(il+2)=m
istk(il+3)=it
lstk(top+1)=l+m*n*(it+1)
go to 99
78 stk(l) = dble(k)
istk(il+1)=1
istk(il+2)=1
istk(il+3)=0
lstk(top+1)=l+1
go to 99
c
c sva
c
80 continue
il=iadr(lstk(top+1-rhs))
if(istk(il).ne.1) then
call putfunnam('sva',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
m1=min(m+1,n)
c
tol = -1.0d+0
if (rhs.eq.2) then
il1=iadr(lstk(top))
if(istk(il1).ne.1) then
err=2
call error(53)
return
endif
if(istk(il1+3).ne.0) then
err=2
call error(52)
return
endif
l1=sadr(il1+4)
tol=stk(l1)
top = top-1
endif
c
if(lhs.ne.3) then
call error(41)
return
endif
k=min(m,n)
lu=l
ld=lu+m*k*(it+1)+sadr(5)-1
lv=ld+k*n+sadr(5)-1
l=lv+n*n*(it+1)
l1=l+m*n*(it+1)
l2=l1+n*(it+1)
lsv=l2+m*(it+1)
c
err = lsv+m1*(it+1) - lstk(bot)
if (err .gt. 0) then
call error(17)
return
endif
c
call dcopy(m*n*(it+1),stk(lu),1,stk(l),1)
job=21
if(it.eq.0) call dsvdc(stk(l),m,m,n,stk(lsv),stk(l1),
1 stk(lu),m,stk(lv),n,stk(l2),job,ierr)
if(it.eq.1) call wsvdc(stk(l),stk(l+m*n),m,m,n,stk(lsv),
1 stk(lsv+m1),stk(l1),stk(l1+n),stk(lu),stk(lu+m*k),m,stk(lv),
2 stk(lv+n*n),n,stk(l2),stk(l2+m),job,ierr)
if(tol.ge.1.0d+0) goto 81
c calcul du rang numerique
if(rhs.eq.1) tol=dble(max(m,n))*eps*stk(lsv)
rang=0
do 82 j=1,k
ls=lsv+j-1
s=stk(ls)
if(s.le.tol) goto 83
rang=j
82 continue
81 if(tol.ge.1.0d+0) rang=int(tol)
83 continue
c set matrix of singular values
ld=lu+m*rang*(it+1)+sadr(5)-1
do 84 jb = 1, rang
do 84 i = 1, rang
j = rang+1-jb
ll = ld+i-1+(j-1)*rang
if (i.ne.j) stk(ll) = 0.0d+0
ls = lsv+i-1
if (i.eq.j) stk(ll) = stk(ls)
84 continue
c
if (ierr.gt.1) call msgs(3,ierr)
c
c set headers for lhs
istk(il+1)=m
istk(il+2)=rang
istk(il+3)=it
lstk(top+1)=lu+m*rang*(it+1)
c
top = top+1
il=iadr(lstk(top))
istk(il)=1
istk(il+1)=rang
istk(il+2)=rang
istk(il+3)=0
lst=ld+n*k
lstk(top+1)=ld+rang*rang
c
lvn=ld+rang*rang+sadr(5)-1
call dcopy(n*rang*(it+1),stk(lv),1,stk(lvn),1)
top = top+1
il=iadr(lstk(top))
istk(il)=1
istk(il+1)=n
istk(il+2)=rang
istk(il+3)=it
lstk(top+1)=lvn+n*rang*(it+1)
go to 99
99 return
end
subroutine intnorm(fname)
c -------------------------------
c norm of matrix or vector
c -------------------------------
character*(*) fname
character*(4) type
INCLUDE '../stack.h'
logical checkrhs,checklhs,getsmat,getscalar,cremat,getmat
logical inf,fro
integer gettype,itype,topk,isanan
double precision p,wnrm2
double precision dnrm2,dasum,dlamch,dres,t
ires=0
inf = .false.
fro = .false.
p=2.0d+0
topk=top
if (.not.checklhs(fname,1,1)) return
if (.not.checkrhs(fname,1,2)) return
c second argument : optional 'inf','fro' or p ( p: double
c or %inf or %nan )
c --------------------------------
if ( rhs.eq.2 ) then
itype=gettype(topk)
if ( itype.eq.10 ) then
if(.not.getsmat(fname,topk,top,m2,n2,1,1,lr2,nlr2))return
call cvstr(min(nlr2,3),istk(lr2),type,1)
if ( type(1:1).eq.'i') then
inf = .true.
else if ( type(1:1).eq.'f') then
fro = .true.
else
buf=fname//' : second argument string inf or fro '
call error(999)
return
endif
else if (itype.eq.1) then
if(.not.getscalar(fname,topk,top,lr2))return
p=stk(lr2)
else
buf=fname
$ //' : second argument string inf or fro or integer '
call error(999)
return
endif
top=top-1
endif
c the first argument matrix or vector
c ---------------------------------
itype = gettype(top)
if ( itype.ne.1 ) then
call putfunnam('norm',top)
top=topk
fun=-1
return
endif
if(.not.getmat(fname,topk,top,it1,m,n,lr1,lc1)) return
mn = m*n
if (mn.eq.0.or. m.eq.1.or.n.eq.1) then
c ==============================vector case
if (mn.eq.0) then
dres = 0.0d+0
else if ( isanan(p).eq.1) then
dres = p
else if (p.gt.dlamch('o').or.inf) then
if (it1.eq.1) call vpythag(mn,stk(lr1),stk(lc1))
i = idamax(mn,stk(lr1),1)
dres= abs(stk(lr1+i-1))
else if ( p.eq.1.0d+0) then
if (it1.eq.1) call vpythag(mn,stk(lr1),stk(lc1))
dres = dasum(mn,stk(lr1),1)
else if (fro.or. p.eq.2.0d+0) then
if (it1.eq.1) then
dres= wnrm2(mn,stk(lr1),stk(lc1),1)
else
dres= dnrm2(mn,stk(lr1),1)
endif
else
if (it1.eq.1) call vpythag(mn,stk(lr1),stk(lc1))
i=idamax(mn,stk(lr1),1)+lr1-1
dres =abs(stk(i))
if ( dres .ne.0.0d+0) then
t=0.0d+0
do 12 i=0,mn-1
t = t + (abs(stk(lr1+i))/dres)** p
12 continue
if (p.ne.0.0d+0) then
dres = dres*t**(1.0d+0/p)
else
c Must return %inf :
dres = 10000.0d0**1000.0d0
endif
endif
endif
if (.not.cremat(fname,top,0,1,1,lr1,lc1)) return
stk(lr1)=dres
else
c ==============================Matrix case
if ( isanan(p).eq.1) then
dres = p
else if (p.gt.dlamch('o').or.inf) then
if (it1.eq.1) call vpythag(mn,stk(lr1),stk(lc1))
dres = 0.0d+0
do 45 i = 1, m
li = lr1+i-1
t = dasum(n,stk(li),m)
dres = max(dres,t)
45 continue
else if (fro) then
if (it1.eq.1) then
dres= wnrm2(mn,stk(lr1),stk(lc1),1)
else
dres= dnrm2(mn,stk(lr1),1)
endif
else if ( p.eq.1.0d+0) then
if (it1.eq.1) call vpythag(mn,stk(lr1),stk(lc1))
dres=0.0d+0
do 48 j = 1, n
lj = lr1+(j-1)*m
t = dasum(m,stk(lj),1)
dres = max(dres,t)
48 continue
else if ( p.eq.2.0d+0) then
m1=min(m+1,n)
if (.not.cremat(fname,topk+1,it1,1,m1,ld,lcd)) return
if (.not.cremat(fname,topk+2,it1,1,n,l1,l1c)) return
if (.not.cremat(fname,topk+3,it1,1,m,l2,l2c)) return
ierr=1
if(it1.eq.0) then
call dsvdc(stk(lr1),m,m,n,stk(ld),stk(l1),
$ t,1,t,1,stk(l2),0,ierr)
else
call wsvdc(stk(lr1),stk(lc1),m,m,n,stk(ld),stk(lcd),
$ stk(l1),stk(l1c),t,t,1,t,t,1,
$ stk(l2),stk(l2c),0,ierr)
endif
if (ierr.gt.1) call msgs(3,ierr)
dres = stk(ld)
else
call error(23)
return
endif
if (.not.cremat(fname,top,0,1,1,lr1,lc1)) return
stk(lr1)=dres
endif
return
end
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