PROCEDURE svbksb(u: glmpbynp; w: glnparray; v: glnpbynp;
       m,n,mp,np: integer; b: glmparray; VAR x: glnparray);
{

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(* Programs using SVBKSB must define the types
TYPE
   glnparray = ARRAY [1..np] OF real;
   glmparray = ARRAY [1..mp] OF real;
   glnpbynp = ARRAY [1..np,1..np] OF real;
   glmpbynp = ARRAY [1..mp,1..np] OF real;
in the main routine. *)
VAR
   jj,j,i: integer;
   s: real;
   tmp: glnparray;
BEGIN
   FOR j := 1 TO n DO BEGIN
      s := 0.0;
      IF (w[j] <> 0.0) THEN BEGIN
         FOR i := 1 TO m DO BEGIN
            s := s+u[i,j]*b[i]
         END;
         s := s/w[j]
      END;
      tmp[j] := s
   END;
   FOR j := 1 TO n DO BEGIN
      s := 0.0;
      FOR jj := 1 TO n DO BEGIN
         s := s+v[j,jj]*tmp[jj];
      END;
      x[j] := s
   END
END;