subroutine balbak(nm,n,low,igh,scale,m,z)
c
integer i,j,k,m,n,ii,nm,igh,low
double precision scale(n),z(nm,m)
double precision s
c
c this subroutine is a translation of the algol procedure balbak,
c num. math. 13, 293-304(1969) by parlett and reinsch.
c handbook for auto. comp., vol.ii-linear algebra, 315-326(1971).
c
c this subroutine forms the eigenvectors of a real general
c matrix by back transforming those of the corresponding
c balanced matrix determined by balanc.
c
c on input
c
c nm must be set to the row dimension of two-dimensional
c array parameters as declared in the calling program
c dimension statement.
c
c n is the order of the matrix.
c
c low and igh are integers determined by balanc.
c
c scale contains information determining the permutations
c and scaling factors used by balanc.
c
c m is the number of columns of z to be back transformed.
c
c z contains the real and imaginary parts of the eigen-
c vectors to be back transformed in its first m columns.
c
c on output
c
c z contains the real and imaginary parts of the
c transformed eigenvectors in its first m columns.
c
c questions and comments should be directed to burton s. garbow,
c mathematics and computer science div, argonne national laboratory
c
c this version dated august 1983.
c
c ------------------------------------------------------------------
c
if (m .eq. 0) go to 200
if (igh .eq. low) go to 120
c
do 110 i = low, igh
s = scale(i)
c .......... left hand eigenvectors are back transformed
c if the foregoing statement is replaced by
c s=1.0d0/scale(i). ..........
do 100 j = 1, m
100 z(i,j) = z(i,j) * s
c
110 continue
c ......... for i=low-1 step -1 until 1,
c igh+1 step 1 until n do -- ..........
120 do 140 ii = 1, n
i = ii
if (i .ge. low .and. i .le. igh) go to 140
if (i .lt. low) i = low - ii
k = scale(i)
if (k .eq. i) go to 140
c
do 130 j = 1, m
s = z(i,j)
z(i,j) = z(k,j)
z(k,j) = s
130 continue
c
140 continue
c
200 return
end