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subroutine fpbacp(a,b,z,n,k,c,k1,nest)
c subroutine fpbacp calculates the solution of the system of equations
c g * c = z with g a n x n upper triangular matrix of the form
c ! a ' !
c g = ! ' b !
c ! 0 ' !
c with b a n x k matrix and a a (n-k) x (n-k) upper triangular
c matrix of bandwidth k1.
c ..
c ..scalar arguments..
integer n,k,k1,nest
c ..array arguments..
real*8 a(nest,k1),b(nest,k),z(n),c(n)
c ..local scalars..
integer i,i1,j,l,l0,l1,n2
real*8 store
c ..
n2 = n-k
l = n
do 30 i=1,k
store = z(l)
j = k+2-i
if(i.eq.1) go to 20
l0 = l
do 10 l1=j,k
l0 = l0+1
store = store-c(l0)*b(l,l1)
10 continue
20 c(l) = store/b(l,j-1)
l = l-1
if(l.eq.0) go to 80
30 continue
do 50 i=1,n2
store = z(i)
l = n2
do 40 j=1,k
l = l+1
store = store-c(l)*b(i,j)
40 continue
c(i) = store
50 continue
i = n2
c(i) = c(i)/a(i,1)
if(i.eq.1) go to 80
do 70 j=2,n2
i = i-1
store = c(i)
i1 = k
if(j.le.k) i1=j-1
l = i
do 60 l0=1,i1
l = l+1
store = store-c(l)*a(i,l0+1)
60 continue
c(i) = store/a(i,1)
70 continue
80 return
end
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