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subroutine matdsc
C ====================================================================
C
C evaluate functions involving eigenvalues and eigenvectors
C
C ====================================================================
C
include '../stack.h'
C
double precision sr,si,powr,powi,t,rmax,eps,tt(1,1)
logical herm,vect,fail
C
sadr(l) = (l/2) + 1
iadr(l) = l + l - 1
C
if (ddt .eq. 4) then
write (buf(1:4),'(i4)') fin
call basout(io,wte,' matdsc '//buf(1:4))
endif
C
C functions/fin
C 1 2 3 4 5 6
C 0 hess schur spectre blocdia balanc
C
if (top+lhs-rhs .ge. bot) then
call error(18)
return
endif
if (rhs .le. 0) then
call error(39)
return
endif
C
if (istk(iadr(lstk(top+1-rhs))) .ne. 1) then
err = 1
call error(53)
return
endif
C
lw = lstk(top+1)
eps = stk(leps)
C
if (fin .eq. 6) goto 310
C
if (fin.eq.2 .and. rhs.eq.2) then
call error(43)
return
endif
C
vect = (lhs.eq.2.and.fin.ne.3)
it2 = 0
if (rhs .eq. 1) goto 5
if (rhs.lt.1.or.rhs.gt.2.or.fin.ne.2.and.fin.ne.4) then
call error(39)
return
endif
il = iadr(lstk(top))
if (istk(il+1)*istk(il+2) .ne. 1) then
call error(30)
return
endif
l = sadr(il+4)
it2 = istk(il+3)
powi = 0.0d+0
powr = stk(l)
if (it2 .eq. 1) powi = stk(l+1)
top = top - 1
5 continue
C acquisition des parametre de la matrice
il = iadr(lstk(top))
m = istk(il+1)
n = istk(il+2)
l = sadr(il+4)
mn = m * n
if (mn .ne. 0) goto 6
C
C matrice de taille nulle
C
if (fin.ne.3 .or. lhs.gt.1) then
err = 1
call error(89)
return
endif
return
C
6 continue
C
C
C test si la matrice est carree
ld = l
if (m .ne. n) then
err = 1
call error(20)
return
endif
nn = n * n
if (fin .eq. 4) goto 200
C
C decomposition spectrale de la matrice
C
C la matrice est-elle symetrique?
herm = .false.
if (n .eq. 1) goto 21
do 20 j = 2,n
j1 = j - 1
do 20 i = 1,j1
ls = l + (i-1) + j1*n
ll = l + (i-1)*n + j1
sr = abs(stk(ll)-stk(ls))
si = abs(stk(ll+nn)+stk(ls+nn))
if (stk(ll)+sr.gt.stk(ll) .or. stk(ll+nn)+si.gt.stk(ll+nn))
& goto 23
20 continue
21 do 22 j = 1,n
ll = l + (j-1) + (j-1)*n
if (stk(ll)+abs(stk(ll+nn)) .gt. stk(ll)) goto 23
22 continue
herm = .true.
23 continue
if (herm) goto 100
if (fin .gt. 3) goto 900
C
C equilibrage
low = 1
igh = n
if (fin .ne. 3) goto 24
lw = l + nn + nn
err = lw + n - lstk(bot)
if (err .gt. 0) then
call error(17)
return
endif
call cbal(n,n,stk(l),stk(l+nn),low,igh,stk(lw))
C
C calcul de la forme de hessenberg
24 lv = l
if (vect) l = lstk(top+1)
if (lhs .eq. 1) goto 25
C on cree une nouvelle variable
top = top + 1
il = iadr(lstk(top))
istk(il) = 1
istk(il+1) = n
istk(il+2) = n
istk(il+3) = 1
l = sadr(il+4)
lstk(top+1) = l + nn*2
25 continue
lw = l + nn*2
err = lw + n*2 - lstk(bot)
if (err .gt. 0) then
call error(17)
return
endif
if (vect) call dcopy(nn*2,stk(lv),1,stk(l),1)
call corth(n,n,low,igh,stk(l),stk(l+nn),stk(lw),stk(lw+n))
if (vect)
& call cortr(n,n,low,igh,stk(l),stk(l+nn),stk(lw),stk(lw+n),
& stk(lv),stk(lv+nn))
if (fin .ne. 1) goto 40
C fin hess
if (n .lt. 3) goto 31
do 30 j = 3,n
call dset(j-2,0.0d+0,stk(l+j-1),n)
30 call dset(j-2,0.0d+0,stk(l+nn+j-1),n)
31 continue
goto 999
C
C calcul de la forme de schur
40 job = 0
if (vect) job = 1
lsr = lw
lsi = lw
if (fin.eq.2 .or. fin.eq.3) job = job + 10
lsi = lsr + n
err = lsi + n - lstk(bot)
if (err .gt. 0) then
call error(17)
return
endif
call comqr3(n,n,low,igh,stk(l),stk(l+nn),stk(lsr),stk(lsi),
& stk(lv),stk(lv+nn),ierr,job)
if (ierr .gt. 1) call msgs(2,ierr)
C
if (fin .eq. 3) goto 44
C
C fin schur
if (n .lt. 2) goto 999
do 42 i = 2,n
call dset(i-1,0.0d+0,stk(l-1+i),n)
call dset(i-1,0.0d+0,stk(l+nn-1+i),n)
42 continue
goto 999
C
44 continue
C fin spectre et root
call dcopy(2*n,stk(lsr),1,stk(l),1)
istk(il+1) = n
istk(il+2) = 1
istk(il+3) = 1
lstk(top+1) = l + 2*n
goto 999
C
C fin cas general
C cas d'une matrice hermitienne
100 continue
C calcul de la forme de hessenberg(tridagonale)
lv = l
if (vect) l = lstk(top+1)
if (lhs .eq. 1) goto 108
C on cree une nouvelle variable
top = top + 1
il = iadr(lstk(top))
istk(il) = 1
istk(il+1) = n
istk(il+2) = n
l = sadr(il+4)
istk(il+3) = 0
lstk(top+1) = l + n*n
108 continue
ld = l + nn*2
le = ld + n
le2 = le + n
lw = le2 + n
err = lw + 2*n - lstk(bot)
if (err .gt. 0) then
call error(17)
return
endif
if (vect) call dcopy(nn*2,stk(lv),1,stk(l),1)
call htridi(n,n,stk(l),stk(l+nn),stk(ld),stk(le),stk(le2),stk(lw))
if (fin .ne. 1) goto 120
C fin hess
if (.not. vect) goto 109
call dset(nn,0.0d+0,stk(lv),1)
call dset(n,1.0d+0,stk(lv),n+1)
call htribk(n,n,stk(l),stk(l+nn),stk(lw),n,stk(lv),stk(lv+nn))
109 istk(il+3) = 0
lstk(top+1) = l + nn
call dset(nn,0.0d+0,stk(l),1)
call dcopy(n,stk(ld),1,stk(l),n+1)
if (n .le. 1) goto 999
call dcopy(n-1,stk(le+1),1,stk(l+1),n+1)
call dcopy(n-1,stk(le+1),1,stk(l+n),n+1)
goto 999
C
C calcul de la forme diagonale
120 continue
job = 0
if (.not. vect) goto 121
job = 1
call dset(nn,0.0d+0,stk(lv),1)
call dset(n,1.0d+0,stk(lv),n+1)
121 continue
if (vect) job = 1
call imtql3(n,n,stk(ld),stk(le),stk(lv),ierr,job)
if (ierr .gt. 1) call msgs(2,ierr)
if (vect)
& call htribk(n,n,stk(l),stk(l+nn),stk(lw),n,stk(lv),stk(lv+nn))
mn = n
C
if (fin .eq. 3) goto 123
C
C fin schur et jordan
call dset(nn,0.0d+0,stk(l),1)
call dcopy(n,stk(ld),1,stk(l),n+1)
istk(il+3) = 0
lstk(top+1) = l + nn
goto 999
C
123 continue
C fin spectre
if (lhs .ne. 1) then
call error(41)
return
endif
call dcopy(n,stk(ld),1,stk(l),1)
istk(il+1) = n
istk(il+2) = 1
istk(il+3) = 0
lstk(top+1) = l + n
goto 999
C
C bloc diagonalisation
C
200 continue
if (rhs .gt. 2) then
call error(39)
return
endif
if (rhs .eq. 1) goto 201
C rmax est en argument
rmax = powr
if (powi .ne. 0.0d+0) then
err = 2
call error(52)
return
endif
goto 202
C calcul de rmax par defaut:norme l1
201 rmax = 0.0d+0
lj = l - 1
do 203 j = 1,n
t = 0.0d+0
do 204 i = 1,n
t = t + abs(stk(lj+i)) + abs(stk(lj+nn+i))
204 continue
if (t .gt. rmax) rmax = t
lj = lj + n
203 continue
202 continue
C preparation de la pile
top = top + 1
C
C changement de base
ilx = iadr(lstk(top))
istk(ilx) = 1
istk(ilx+1) = n
istk(ilx+2) = n
istk(ilx+3) = 1
lx = sadr(ilx+4)
lstk(top+1) = lx + 2*nn
C structure des blocs
top = top + 1
ilbs = iadr(lstk(top))
lbs = sadr(ilbs+4)
illbs = ilbs + 4
C er,ei:valeurs propres (tbl de travail)
ler = lbs + n
lei = ler + n
ilb = iadr(lei+n)
lw = sadr(ilb+n)
err = lw + n - lstk(bot)
if (err .gt. 0) then
call error(17)
return
endif
call wbdiag(n,n,stk(l),stk(l+nn),rmax,stk(ler),stk(lei),istk(ilb),
& stk(lx),stk(lx+nn),tt,tt,stk(lw),0,fail)
C sorties
C structure des blocs
nbloc = 0
ln = lbs - 1
do 222 k = 1,n
if (istk(ilb+k-1) .lt. 0) goto 222
nbloc = nbloc + 1
ln = ln + 1
stk(ln) = dble(istk(ilb+k-1))
222 continue
lstk(top+1) = sadr(ilbs+4) + nbloc
istk(ilbs) = 1
istk(ilbs+1) = nbloc
istk(ilbs+2) = 1
istk(ilbs+3) = 0
if (lhs .eq. 2) top = top - 1
if (lhs .eq. 1) top = top - 2
goto 999
C
C equilibrage (balanc)
C
310 continue
if (lhs .ne. 2) then
call error(41)
return
endif
if (rhs .ne. 1) then
call error(42)
return
endif
il = iadr(lstk(top))
m = istk(il+1)
n = istk(il+2)
it = istk(il+3)
l = sadr(il+4)
C test si la matrice est carree
if (m .ne. n) then
err = 1
call error(20)
return
endif
nn = n * n
if (nn .eq. 0) then
err = 1
call error(89)
return
endif
C equilibrage
low = 1
igh = n
ilv = iadr(lw)
lv = sadr(ilv+4)
lw = lv + nn
err = lw + n - lstk(bot)
if (err .gt. 0) then
call error(17)
return
endif
call cbal(n,n,stk(l),stk(l+nn),low,igh,stk(lw))
call dset(nn,0.0d+0,stk(lv),1)
call dset(n,1.0d+0,stk(lv),n+1)
call balbak(n,n,low,igh,stk(lw),n,stk(lv))
istk(ilv) = 1
istk(ilv+1) = n
istk(ilv+2) = n
istk(ilv+3) = 0
top = top + 1
lstk(top+1) = lv + nn
goto 999
C
999 return
900 call error(43)
return
end
|
