@process directive('" (') subroutine combak(nm,low,igh,ar,ai,int,m,zr,zi) c integer i,j,m,mp,nm,igh,low real ar(nm,igh),ai(nm,igh),zr(nm,m),zi(nm,m) real xr,xi integer int(igh) c c this subroutine is a translation of the algol procedure combak, 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 complex general c matrix by back transforming those of the corresponding c upper hessenberg matrix determined by comhes. 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 cbal. if cbal has not been used, c set low=1 and igh equal to the order of the matrix. c c ar and ai contain the multipliers which were used in the c reduction by comhes in their lower triangles c below the subdiagonal. c c int contains information on the rows and columns c interchanged in the reduction by comhes. c only elements low through igh are used. c c m is the number of eigenvectors to be back transformed. c c zr and zi contain the real and imaginary parts, c respectively, of the eigenvectors to be c back transformed in their first m columns. c c on output c c zr and zi contain the real and imaginary parts, c respectively, of the transformed eigenvectors c in their first m columns. c c Questions and comments should be directed to Alan K. Cline, c Pleasant Valley Software, 8603 Altus Cove, Austin, TX 78759. c Electronic mail to cline@cs.utexas.edu. c c this version dated january 1989. (for the IBM 3090vf) c c ------------------------------------------------------------------ c call xuflow(0) if (m .eq. 0) go to 200 c .......... for mp=igh-1 step -1 until low+1 do -- .......... do 140 mp = igh-1, low+1, -1 c" ( ignore recrdeps do 110 i = mp+1, igh xr = ar(i,mp-1) xi = ai(i,mp-1) c do 100 j = 1, m zr(i,j) = zr(i,j) + xr * zr(mp,j) - xi * zi(mp,j) zi(i,j) = zi(i,j) + xr * zi(mp,j) + xi * zr(mp,j) 100 continue c 110 continue c i = int(mp) c c" ( prefer vector do 130 j = 1, m xr = zr(i,j) zr(i,j) = zr(mp,j) zr(mp,j) = xr xi = zi(i,j) zi(i,j) = zi(mp,j) zi(mp,j) = xi 130 continue c 140 continue c 200 return end