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subroutine eltran(nm,n,low,igh,a,int,z)
c
integer i,j,n,kl,mm,mp,nm,igh,low,mp1
double precision a(nm,igh),z(nm,n)
integer int(igh)
c
c this subroutine is a translation of the algol procedure elmtrans,
c num. math. 16, 181-204(1970) by peters and wilkinson.
c handbook for auto. comp., vol.ii-linear algebra, 372-395(1971).
c
c this subroutine accumulates the stabilized elementary
c similarity transformations used in the reduction of a
c real general matrix to upper hessenberg form 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 n is the order of the matrix.
c
c low and igh are integers determined by the balancing
c subroutine balanc. if balanc has not been used,
c set low=1, igh=n.
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 on output
c
c z contains the transformation matrix produced in the
c reduction by elmhes.
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
c .......... initialize z to identity matrix ..........
do 80 j = 1, n
c
do 60 i = 1, n
60 z(i,j) = 0.0d0
c
z(j,j) = 1.0d0
80 continue
c
kl = igh - low - 1
if (kl .lt. 1) go to 200
c .......... for mp=igh-1 step -1 until low+1 do -- ..........
do 140 mm = 1, kl
mp = igh - mm
mp1 = mp + 1
c
do 100 i = mp1, igh
100 z(i,mp) = a(i,mp-1)
c
i = int(mp)
if (i .eq. mp) go to 140
c
do 130 j = mp, igh
z(mp,j) = z(i,j)
z(i,j) = 0.0d0
130 continue
c
z(i,mp) = 1.0d0
140 continue
c
200 return
end
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