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subroutine lydsr(n,a,na,c,ierr)
c%But
c
c this routine solves the discrete lyapunov equation for the
c case where the matrix a has been transformed to quasi-
c triangular form.
c
c
c warning -this routine is intended to be called only from
c slice routine lybad .
c%
integer i,j,k,l,n,dk,dl,ii,ik,jj,kk,ll,l1,na,job,km1,
x ierr,info,ldim,nsys,ipvt(4)
double precision a(na,n),c(na,n)
double precision t(4,4),p(4)
double precision ddot
ierr = 0
ldim = 4
job = 0
l = 1
10 dl = 1
if (l .eq. n) go to 20
if (a(l+1,l) .ne. 0.0d+0) dl = 2
20 ll = l + dl - 1
k = l
30 km1 = k - 1
dk = 1
if (k .eq. n) go to 40
if (a(k+1,k) .ne. 0.0d+0) dk = 2
40 kk = k + dk - 1
l1 = l - 1
if (l1 .eq. 0) go to 70
ii = 0
c
do 50 i = k, kk
ii = ii + 1
jj = 0
c
do 50 j = l, ll
jj = jj + 1
t(ii,jj)=ddot(l1,c(i,1),na,a(1,j),1)
50 continue
c
do 60 i = k, kk
jj = 0
c
do 60 j = l, ll
jj = jj + 1
c(i,j)=c(i,j)-ddot(kk-k+1,a(k,i),1,t(1,jj),1)
60 continue
c
70 if (km1 .eq. 0) go to 100
c
do 90 j = l, ll
c
do 90 i = 1, km1
c
do 90 ik = k, kk
c(ik,j)=c(ik,j)-a(i,ik)*ddot(ll,c(i,1),na,a(1,j),1)
90 continue
c
100 if (dl .eq. 2) go to 120
if (dk .eq. 2) go to 110
t(1,1) = a(k,k) * a(l,l) - 1.0d+0
if (t(1,1) .eq. 0.0d+0) go to 180
c(k,l) = c(k,l) / t(1,1)
go to 150
110 t(1,1) = a(k,k) * a(l,l) - 1.0d+0
t(1,2) = a(l,l) * a(kk,k)
t(2,1) = a(l,l) * a(k,kk)
t(2,2) = a(kk,kk) * a(l,l) - 1.0d+0
p(1) = c(k,l)
p(2) = c(kk,l)
nsys = 2
call dgefa(t,ldim,nsys,ipvt,info)
if (info .ne. 0) go to 180
call dgesl(t,ldim,nsys,ipvt,p,job)
c(k,l) = p(1)
c(kk,l) = p(2)
go to 150
120 if (dk .eq. 2) go to 130
t(1,1) = a(l,l) * a(k,k) - 1.0d+0
t(2,1) = a(l,ll) * a(k,k)
t(1,2) = a(ll,l) * a(k,k)
t(2,2) = a(ll,ll) * a(k,k) - 1.0d+0
p(1) = c(k,l)
p(2) = c(k,ll)
nsys = 2
call dgefa(t,ldim,nsys,ipvt,info)
if (info .ne. 0) go to 180
call dgesl(t,ldim,nsys,ipvt,p,job)
c(k,l) = p(1)
c(k,ll) = p(2)
go to 150
130 if (k .ne. l) go to 140
t(1,1) = a(l,l) * a(l,l) - 1.0d+0
t(1,2) = a(l,l) * a(ll,l) + a(l,l) * a(ll,l)
t(1,3) = a(ll,l) * a(ll,l)
t(2,1) = a(l,l) * a(l,ll)
t(2,2) = a(l,l) * a(ll,ll) + a(l,ll) * a(ll,l) - 1.0d+0
t(2,3) = a(ll,ll) * a(ll,l)
t(3,1) = a(l,ll) * a(l,ll)
t(3,2) = a(l,ll) * a(ll,ll) + a(l,ll) * a(ll,ll)
t(3,3) = a(ll,ll) * a(ll,ll) - 1.0d+0
p(1) = c(l,l)
p(2) = c(ll,l)
p(3) = c(ll,ll)
nsys = 3
call dgefa(t,ldim,nsys,ipvt,info)
if (info .ne. 0) go to 180
call dgesl(t,ldim,nsys,ipvt,p,job)
c(l,l) = p(1)
c(l,ll) = p(2)
c(ll,l) = p(2)
c(ll,ll) = p(3)
go to 150
140 t(1,1) = a(l,l) * a(k,k) - 1.0d+0
t(1,2) = a(l,l) * a(kk,k)
t(1,3) = a(ll,l) * a(k,k)
t(1,4) = a(ll,l) * a(kk,k)
t(2,1) = a(l,l) * a(k,kk)
t(2,2) = a(l,l) * a(kk,kk) - 1.0d+0
t(2,3) = a(ll,l) * a(k,kk)
t(2,4) = a(ll,l) * a(kk,kk)
t(3,1) = a(l,ll) * a(k,k)
t(3,2) = a(l,ll) * a(kk,k)
t(3,3) = a(ll,ll) * a(k,k) - 1.0d+0
t(3,4) = a(ll,ll) * a(kk,k)
t(4,1) = a(l,ll) * a(k,kk)
t(4,2) = a(l,ll) * a(kk,kk)
t(4,3) = a(ll,ll) * a(k,kk)
t(4,4) = a(ll,ll) * a(kk,kk) - 1.0d+0
p(1) = c(k,l)
p(2) = c(kk,l)
p(3) = c(k,ll)
p(4) = c(kk,ll)
nsys = 4
call dgefa(t,ldim,nsys,ipvt,info)
if (info .ne. 0) go to 180
call dgesl(t,ldim,nsys,ipvt,p,job)
c(k,l) = p(1)
c(kk,l) = p(2)
c(k,ll) = p(3)
c(kk,ll) = p(4)
150 if (k .eq. l) go to 170
c
do 160 i = k, kk
c
do 160 j = l, ll
c(j,i) = c(i,j)
160 continue
c
170 k = k + dk
if (k .le. n) go to 30
l = l + dl
if (l .le. n) go to 10
go to 190
180 ierr = 1
190 return
end
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