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|
subroutine matqr
C ================================== ( Inria ) =============
C evaluate functions involving qr decomposition (least squares)
C ====================================================================
c Copyright INRIA
include '../stack.h'
integer iadr,sadr
C
double precision t(1),tol,eps,sr,si,tt
integer vol
C
C fin -2 -1 1
C a\a2 a/a2 qr
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,' matqr '//buf(1:4))
endif
C
eps = stk(leps)
C
il = iadr(lstk(top-rhs+1))
if (istk(il) .ne. 1) then
if(fin.eq.1) then
call putfunnam('qr',top-rhs+1)
fun=-1
return
else
err = rhs
call error(53)
return
endif
endif
m = istk(il+1)
n = istk(il+2)
it = istk(il+3)
l = sadr(il+4)
C
goto (14,10,99,40) fin+3
C
C rectangular matrix right division, a/a2
C call left division for a2'\a
C
10 continue
C on interverti l'ordre de a et a2
l1 = lstk(top-1)
l2 = lstk(top)
l3 = lstk(top+1)
ll = l1 + l3 - l2
err = ll + l3 - l1 - lstk(bot)
if (err .gt. 0) then
call error(17)
return
endif
call unsfdcopy(l3-l1,stk(l1),-1,stk(ll),-1)
call unsfdcopy(l3-l2,stk(ll+l2-l1),1,stk(l1),1)
lstk(top) = ll
lstk(top+1) = ll + l2 - l1
C transposition a2
lw = lstk(top+1)
il1 = iadr(lstk(top))
m1 = istk(il1+1)
n1 = istk(il1+2)
it1 = istk(il1+3)
mn1 = m1 * n1
l1 = sadr(il1+4)
if (mn1.eq.0 .or. istk(il1).eq.0) goto 11
vol = mn1 * (it1+1)
ll = lw
err = ll + vol - lstk(bot)
if (err .gt. 0) then
call error(17)
return
endif
C
istk(il1+1) = n1
istk(il1+2) = m1
C
call unsfdcopy(vol,stk(l1),1,stk(ll),1)
call mtran(stk(ll),m1,stk(l1),n1,m1,n1)
if (it1 .eq. 0) goto 11
call mtran(stk(ll+mn1),m1,stk(l1+mn1),n1,m1,n1)
call dscal(mn1,-1.0d+0,stk(l1+mn1),1)
C
C transposition a
11 continue
il1 = iadr(lstk(top-1))
m1 = istk(il1+1)
n1 = istk(il1+2)
it1 = istk(il1+3)
mn1 = m1 * n1
l1 = sadr(il1+4)
if (mn1.eq.0 .or. istk(il1).eq.0) goto 12
vol = mn1 * (it1+1)
ll = lw
err = ll + vol - lstk(bot)
if (err .gt. 0) then
call error(17)
return
endif
C
istk(il1+1) = n1
istk(il1+2) = m1
C
call unsfdcopy(vol,stk(l1),1,stk(ll),1)
call mtran(stk(ll),m1,stk(l1),n1,m1,n1)
if (it1 .eq. 0) goto 12
call mtran(stk(ll+mn1),m1,stk(l1+mn1),n1,m1,n1)
call dscal(mn1,-1.0d+0,stk(l1+mn1),1)
C
12 top = top - 1
il = iadr(lstk(top))
m = istk(il+1)
n = istk(il+2)
it = istk(il+3)
l = sadr(il+4)
goto 15
C
C rectangular matrix left division a backslash a2
C
14 top = top - 1
15 il2 = iadr(lstk(top+1))
m2 = istk(il2+1)
n2 = istk(il2+2)
it2 = istk(il2+3)
l2 = sadr(il2+4)
if (m2*n2 .gt. 1) goto 16
C scalar divided by a matrix
m2 = m
n2 = m
err = l2 + m*m*(it2+1) - lstk(bot)
if (err .gt. 0) then
call error(17)
return
endif
sr = stk(l2)
if (it2 .eq. 1) si = stk(l2+1)
call dset(m*m*(it2+1),0.0d+0,stk(l2),1)
call dset(m,sr,stk(l2),m+1)
if (it2 .eq. 1) call dset(m,si,stk(l2+m*m),m+1)
C
16 if (m2 .ne. m) then
call error(10-fin)
return
endif
it1 = max(it,it2)
nn2 = max(m,n) * n2
l3 = l2 + nn2*(it1+1)
l4 = l3 + n*(it+1)
ilb = iadr(l4+n*(it+1))
err = sadr(ilb+n) - lstk(bot)
if (err .gt. 0) then
call error(17)
return
endif
if (m .ge. n) goto 23
C on plonge a2 dans une matrice ayant des lignes de longueur n
mn2 = m * n2
ls = l2 + mn2*(it2+1)
ll = l2 + nn2*(it2+1)
mn = n2 * (it2+1)
do 22 j = 1,mn
ll = ll - n
ls = ls - m
call unsfdcopy(m,stk(ls),-1,stk(ll),-1)
22 continue
C factorisation qr
23 do 24 j = 1,n
istk(ilb+j-1) = 0
24 continue
if (it .eq. 0)
& call dqrdc(stk(l),m,m,n,stk(l4),istk(ilb),stk(l3),1)
if (it .eq. 1)
& call wqrdc(stk(l),stk(l+m*n),m,m,n,stk(l4),stk(l4+n),istk(ilb),
& stk(l3),stk(l3+n),1)
C determination du rang
k = 0
tt = abs(stk(l))
if (it .eq. 1) tt = tt + abs(stk(l+m*n))
tol = dble(max(m,n)) * eps * tt
mn = min(m,n)
do 25 j = 1,mn
ls = l + j - 1 + (j-1)*m
tt = abs(stk(ls))
if (it .eq. 1) tt = tt + abs(stk(ls+m*n))
if (tt .gt. tol) k = j
25 continue
if (k .lt. mn) then
write (buf(1:17),'(i4,1pd13.4)') k, tol
call basout(io,wte,
& ' deficient rank: rank ='//buf(1:4)//' - tol ='//
& buf(5:17))
endif
mn = max(m,n)
C resolution
if (it .eq. 1) goto 28
C a est reelle
ls = l2
do 27 j = 1,n2
call dqrsl(stk(l),m,m,k,stk(l4),stk(ls),t,stk(ls),stk(ls),t,t,
& 100,info)
call dset(n-k,0.0d+0,stk(ls+k),1)
if (it2 .eq. 0) goto 27
call dqrsl(stk(l),m,m,k,stk(l4),stk(ls+nn2),t,stk(ls+nn2),
& stk(ls+nn2),t,t,100,info)
call dset(n-k,0.0d+0,stk(ls+nn2+k),1)
27 ls = ls + mn
goto 30
28 continue
C cas a complexe
if (it2 .eq. 0) call dset(nn2,0.0d+0,stk(l2+nn2),1)
do 29 j = 1,n2
ls = l2 + (j-1)*mn
call wqrsl(stk(l),stk(l+m*n),m,m,k,stk(l4),stk(l4+n),stk(ls),
& stk(ls+nn2),t,t,stk(ls),stk(ls+nn2),stk(ls),
& stk(ls+nn2),t,t,t,t,100,info)
ll = ls + k
call dset(n-k,0.0d+0,stk(ll),1)
call dset(n-k,0.0d+0,stk(ll+nn2),1)
29 continue
C permutations
30 continue
do 31 j = 1,n
istk(ilb+j-1) = -istk(ilb+j-1)
31 continue
do 35 j = 1,n
if (istk(ilb+j-1) .gt. 0) goto 35
k = -istk(ilb+j-1)
istk(ilb+j-1) = k
33 continue
if (k .eq. j) goto 34
ls = l2 + j - 1
ll = l2 + k - 1
call dswap(n2,stk(ls),mn,stk(ll),mn)
if (it1 .eq. 1) call dswap(n2,stk(ls+nn2),mn,stk(ll+nn2),mn)
istk(ilb+k-1) = -istk(ilb+k-1)
k = istk(ilb+k-1)
goto 33
34 continue
35 continue
do 36 j = 1,n2
ls = l2 + (j-1)*mn
ll = l + (j-1)*n
call unsfdcopy(n,stk(ls),1,stk(ll),1)
36 continue
if (it1 .eq. 0) goto 38
do 37 j = 1,n2
ls = l2 + (j-1)*mn + mn*n2
ll = l + n*n2 + (j-1)*n
call unsfdcopy(n,stk(ls),1,stk(ll),1)
37 continue
38 continue
istk(il+1) = n
istk(il+2) = n2
istk(il+3) = it1
lstk(top+1) = l + n*n2*(it1+1)
rhs = 1
if (fin .eq. -1) then
il1 = iadr(lstk(top))
m1 = istk(il1+1)
n1 = istk(il1+2)
it1 = istk(il1+3)
mn1 = m1 * n1
l1 = sadr(il1+4)
if (mn1.eq.0 .or. istk(il1).eq.0) goto 99
vol = mn1 * (it1+1)
ll = lstk(top+1)
err = ll + vol - lstk(bot)
if (err .gt. 0) then
call error(17)
return
endif
C
istk(il1+1) = n1
istk(il1+2) = m1
C
call unsfdcopy(vol,stk(l1),1,stk(ll),1)
call mtran(stk(ll),m1,stk(l1),n1,m1,n1)
if (it1 .eq. 0) goto 99
call mtran(stk(ll+mn1),m1,stk(l1+mn1),n1,m1,n1)
call dscal(mn1,-1.0d+0,stk(l1+mn1),1)
endif
goto 99
C
C qr
40 if (top+lhs .ge. bot) then
call error(18)
return
endif
if (rhs .eq. 2) then
il = iadr(lstk(top))
tol = stk(sadr(il+4))
top = top - 1
endif
C
if (fin.eq.1 .and. (lhs.lt.2.or.lhs.gt.4.or.
$ rhs.eq.2.and.lhs.eq.3)) then
call error(41)
return
endif
C
mn = m * n
mm = m * m
job = 0
C implantation des resultats et tableaux de travail
ilq = iadr(lstk(top))
lq = l
lstk(top+1) = lq + mm*(it+1)
C
top = top + 1
ilr = iadr(lstk(top))
lr = sadr(ilr+4)
lstk(top+1) = lr + mn*(it+1)
C
if (lhs .eq. 4) then
top = top + 1
ilrk = iadr(lstk(top))
lrk = sadr(ilrk+4)
lstk(top+1) = lrk + 1
endif
C
if (lhs .ge. 3) then
C on calcule et on stocke e
top = top + 1
nn = n * n
job = 1
ile = iadr(lstk(top))
le = sadr(ile+4)
lstk(top+1) = le + nn
endif
C
laux = lstk(top+1)
lw = laux + n*(it+1)
ilb = iadr(lw+n*(it+1))
err = sadr(ilb+n) - lstk(bot)
if (err .gt. 0) then
call error(17)
return
endif
C
C calcul de la dcomposition qr
call unsfdcopy(mn*(it+1),stk(l),-1,stk(lr),-1)
do 43 j = 1,n
istk(ilb+j-1) = 0
43 continue
if (it .eq. 0)
& call dqrdc(stk(lr),m,m,n,stk(laux),istk(ilb),stk(lw),job)
if (it .eq. 1)
& call wqrdc(stk(lr),stk(lr+mn),m,m,n,stk(laux),stk(laux+n),
& istk(ilb),stk(lw),stk(lw+n),job)
C
C affectation des resultats
C
C affectation de q
call dset(mm*(it+1),0.0d+0,stk(lq),1)
call dset(m,1.0d+0,stk(lq),m+1)
ll = lq
do 44 j = 1,m
if (it .eq. 0)
& call dqrsl(stk(lr),m,m,n,stk(laux),stk(ll),stk(ll),t,t,t,t,
& 10000,info)
if (it .eq. 1)
& call wqrsl(stk(lr),stk(lr+mn),m,m,n,stk(laux),stk(laux+n),
& stk(ll),stk(ll+mm),stk(ll),stk(ll+mm),t,t,t,t,t,t,
& t,t,10000,info)
ll = ll + m
44 continue
istk(ilq+1) = m
istk(ilq+2) = m
m1 = min(m-1,n)
ll = lr + 1
do 51 j = 1,m1
call dset(m-j,0.0d+0,stk(ll),1)
if (it .eq. 1) call dset(m-j,0.0d+0,stk(ll+mn),1)
ll = ll + m + 1
51 continue
istk(ilr) = 1
istk(ilr+1) = m
istk(ilr+2) = n
istk(ilr+3) = it
C
if (lhs .eq. 2) goto 99
if (lhs .eq. 4) then
C ############# calcul du rang
tt = abs(stk(lr))
if (it .eq. 1) tt = tt + abs(stk(lr+mn))
if(rhs.eq.1) tol = dble(max(m,n)) * eps * tt
k = 0
ls = lr
m1 = min(m,n)
do 450 j = 1,m1
tt = abs(stk(ls))
if (it .eq. 1) tt = tt + abs(stk(ls+mn))
if (tt .le. tol) goto 460
k = j
ls = ls + m + 1
450 continue
460 istk(ilrk) = 1
istk(ilrk+1) = 1
istk(ilrk+2) = 1
istk(ilrk+3) = 0
stk(lrk) = dble(k)
endif
C ############# affectation de e
call dset(nn,0.0d+0,stk(le),1)
ll = le - 1
do 52 j = 1,n
stk(ll+istk(ilb+j-1)) = 1.0d+0
ll = ll + n
52 continue
istk(ile) = 1
istk(ile+1) = n
istk(ile+2) = n
istk(ile+3) = 0
goto 99
C
99 return
end
|
