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subroutine subbak ( w, ipivot, nrow, ncol, last, x )
c carries out backsubstitution for current block.
c
c parameters
c w, ipivot, nrow, ncol, last are as on return from factrb.
c x(1),...,x(ncol) contains, on input, the right side for the
c equations in this block after backsubstitution has been
c carried up to but not including equation ipivot(last).
c means that x(j) contains the right side of equation ipi-
c vot(j) as modified during elimination, j=1,...,last, while
c for j .gt. last, x(j) is already a component of the solut-
c ion vector.
c x(1),...,x(ncol) contains, on output, the components of the solut-
c ion corresponding to the present block.
c
integer nrow, ncol
integer ipivot(nrow),last, ip,j,k,kp1
real w(nrow,ncol),x(ncol), sum
k = last
ip = ipivot(k)
sum = 0.
if (k .eq. ncol) go to 4
kp1 = k+1
2 do 3 j=kp1,ncol
3 sum = w(ip,j)*x(j) + sum
4 x(k) = (x(k) - sum)/w(ip,k)
if (k .eq. 1) return
kp1 = k
k = k-1
ip = ipivot(k)
sum = 0.
go to 2
end
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