subbak.f

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      subroutine subbak ( w, ipivot, nrow, ncol, last, x )

c*********************************************************************72
c
cc SUBBAK carries out back substitution for the current block.
c
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
      implicit none

      integer ncol
      integer nrow

      integer ipivot(nrow),last,  ip,j,k,kp1
      double precision w(nrow,ncol),x(ncol), sum
      k = last
      ip = ipivot(k)
      sum = 0.0d+00
      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 = 0.0d+00
                                        go to 2
      end