subroutine balbak(nm,n,low,igh,scale,m,z) c integer i,j,k,m,n,ii,nm,igh,low double precision scale(n),z(nm,m) double precision s c c this subroutine is a translation of the algol procedure balbak, c num. math. 13, 293-304(1969) by parlett and reinsch. c handbook for auto. comp., vol.ii-linear algebra, 315-326(1971). c c this subroutine forms the eigenvectors of a real general c matrix by back transforming those of the corresponding c balanced matrix determined by balanc. 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 balanc. c c scale contains information determining the permutations c and scaling factors used by balanc. 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 if (igh .eq. low) go to 120 c do 110 i = low, igh s = scale(i) c .......... left hand eigenvectors are back transformed c if the foregoing statement is replaced by c s=1.0d0/scale(i). .......... do 100 j = 1, m 100 z(i,j) = z(i,j) * s c 110 continue c ......... for i=low-1 step -1 until 1, c igh+1 step 1 until n do -- .......... 120 do 140 ii = 1, n i = ii if (i .ge. low .and. i .le. igh) go to 140 if (i .lt. low) i = low - ii k = scale(i) if (k .eq. i) go to 140 c do 130 j = 1, m s = z(i,j) z(i,j) = z(k,j) z(k,j) = s 130 continue c 140 continue c 200 return end