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