subroutine elmbak(nm,low,igh,a,int,m,z)
c
integer i,j,m,la,mm,mp,nm,igh,kp1,low,mp1
double precision a(nm,igh),z(nm,m)
double precision x
integer int(igh)
c
c this subroutine is a translation of the algol procedure elmbak,
c num. math. 12, 349-368(1968) by martin and wilkinson.
c handbook for auto. comp., vol.ii-linear algebra, 339-358(1971).
c
c this subroutine forms the eigenvectors of a real general
c matrix by back transforming those of the corresponding
c upper hessenberg matrix determined by elmhes.
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 low and igh are integers determined by the balancing
c subroutine balanc. if balanc has not been used,
c set low=1 and igh equal to the order of the matrix.
c
c a contains the multipliers which were used in the
c reduction by elmhes in its lower triangle
c below the subdiagonal.
c
c int contains information on the rows and columns
c interchanged in the reduction by elmhes.
c only elements low through igh are used.
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
la = igh - 1
kp1 = low + 1
if (la .lt. kp1) go to 200
c .......... for mp=igh-1 step -1 until low+1 do -- ..........
do 140 mm = kp1, la
mp = low + igh - mm
mp1 = mp + 1
c
do 110 i = mp1, igh
x = a(i,mp-1)
if (x .eq. 0.0d0) go to 110
c
do 100 j = 1, m
100 z(i,j) = z(i,j) + x * z(mp,j)
c
110 continue
c
i = int(mp)
if (i .eq. mp) go to 140
c
do 130 j = 1, m
x = z(i,j)
z(i,j) = z(mp,j)
z(mp,j) = x
130 continue
c
140 continue
c
200 return
end