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subroutine elmhes(nm,n,low,igh,a,int)
c
integer i,j,m,n,la,nm,igh,kp1,low,mm1,mp1
double precision a(nm,n)
double precision x,y
integer int(igh)
c
c this subroutine is a translation of the algol procedure elmhes,
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 given a real general matrix, this subroutine
c reduces a submatrix situated in rows and columns
c low through igh to upper hessenberg form by
c stabilized elementary similarity transformations.
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 input matrix.
c
c on output
c
c a contains the hessenberg matrix. the multipliers
c which were used in the reduction are stored in the
c remaining triangle under the hessenberg matrix.
c
c int contains information on the rows and columns
c interchanged in the reduction.
c only elements low through igh are used.
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
la = igh - 1
kp1 = low + 1
if (la .lt. kp1) go to 200
c
do 180 m = kp1, la
mm1 = m - 1
x = 0.0d0
i = m
c
do 100 j = m, igh
if (dabs(a(j,mm1)) .le. dabs(x)) go to 100
x = a(j,mm1)
i = j
100 continue
c
int(m) = i
if (i .eq. m) go to 130
c .......... interchange rows and columns of a ..........
do 110 j = mm1, n
y = a(i,j)
a(i,j) = a(m,j)
a(m,j) = y
110 continue
c
do 120 j = 1, igh
y = a(j,i)
a(j,i) = a(j,m)
a(j,m) = y
120 continue
c .......... end interchange ..........
130 if (x .eq. 0.0d0) go to 180
mp1 = m + 1
c
do 160 i = mp1, igh
y = a(i,mm1)
if (y .eq. 0.0d0) go to 160
y = y / x
a(i,mm1) = y
c
do 140 j = m, n
140 a(i,j) = a(i,j) - y * a(m,j)
c
do 150 j = 1, igh
150 a(j,m) = a(j,m) + y * a(j,i)
c
160 continue
c
180 continue
c
200 return
end
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