subroutine ortran(nm,n,low,igh,a,ort,z) c integer i,j,n,kl,mm,mp,nm,igh,low,mp1 real a(nm,igh),ort(igh),z(nm,n) real g c c this subroutine is a translation of the algol procedure ortrans, 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 orthogonal similarity c transformations used in the reduction of a real general c matrix to upper hessenberg form by orthes. 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 information about the orthogonal trans- c formations used in the reduction by orthes c in its strict lower triangle. c c ort contains further information about the trans- c formations used in the reduction by orthes. 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 orthes. c c ort has been altered. 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) = 0.0e0 c z(j,j) = 1.0e0 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 if (a(mp,mp-1) .eq. 0.0e0) go to 140 mp1 = mp + 1 c do 100 i = mp1, igh 100 ort(i) = a(i,mp-1) c do 130 j = mp, igh g = 0.0e0 c do 110 i = mp, igh 110 g = g + ort(i) * z(i,j) c .......... divisor below is negative of h formed in orthes. c double division avoids possible underflow .......... g = (g / ort(mp)) / a(mp,mp-1) c do 120 i = mp, igh 120 z(i,j) = z(i,j) + g * ort(i) c 130 continue c 140 continue c 200 return end