"CODE" 34138;
"PROCEDURE" LSQREFSOL(A, QR, N, M, N1, AUX, AID, CI, B,LDX,X,RES);
"VALUE"N,M,N1;"INTEGER"N,M,N1;"INTEGER""ARRAY"CI;"REAL"LDX;
"ARRAY"QR,A,AID,AUX,X,RES,B;
"BEGIN""INTEGER"I,J,K,S;
       "REAL"C1,NEXVE,NDX,NDR,D,DD,OP,OPL,CORRNORM;
       "ARRAY"F[1:N],G[1:M];
       "PROCEDURE" HOUSEHOLDER(P, Q, R, E);
       "VALUE" P,Q,R,E;"INTEGER" P,Q,R,E;
       "BEGIN" "FOR" S:=P "STEP" Q "UNTIL" R "DO"
               ELMVECCOL(S, E, S, F, QR,TAMVEC(S, E, S,QR, F)/(QR[S,S]*
               AID[S]))
       "END";
       "FOR" J:=1 "STEP" 1 "UNTIL" M "DO"
       "BEGIN" S:=CI[J];"IF" S^=J"THEN" ICHCOL(1,N,J,S,A) "END";
       "FOR"J:=1"STEP"1"UNTIL"M"DO"X[J]:=G[J]:=0;
       "FOR"I:=1"STEP"1"UNTIL"N"DO"
       "BEGIN"RES[I]:=0;F[I]:=B[I]"END";
       "FOR"K:=0,1,K+1
          "WHILE" (CORRNORM>AUX[2]*NEXVE & K<=AUX[6])
       "DO"
       "BEGIN"NDX:=NDR:=0;
          "IF"K^=0"THEN"
          "BEGIN""FOR"I:=1"STEP"1"UNTIL"N"DO"RES[I]:=RES[I]+F[I];
                 "FOR"S:=1"STEP"1"UNTIL"M"DO"
                 "BEGIN" X[S]:=X[S]+G[S];
                        LNGTAMVEC(1,N,S,A,RES,0,0,D,DD);
                        G[S]:=(-D-TAMVEC(1,S-1,S,QR,G))/AID[S]
                 "END";
                 "FOR"I:=1"STEP"1"UNTIL"N"DO"
                 "BEGIN" LNGMATVEC(1, M, I, A, X,
                         "IF" I>N1 "THEN" RES[I] "ELSE" 0, 0, D, DD);
                        LNG SUB(B[I],0,D,DD,OP,OPL);
                        F[I]:=OP
                 "END"
          "END";
          NEXVE:=SQRT(VECVEC(1,M,0,X,X)+VECVEC(1,N,0,RES,RES));
          HOUSEHOLDER(1, 1, N1, N1);
          "FOR" I:=N1+1 "STEP" 1 "UNTIL" N "DO"
          F[I]:=F[I]-MATVEC(1,N1, I, QR, F);
          HOUSEHOLDER(N1+1, 1, M, N);
          "FOR" I:=1 "STEP" 1 "UNTIL" M "DO"
          "BEGIN" C1:=F[I];F[I]:=G[I];
              G[I]:="IF" I>N1 "THEN" C1-G[I] "ELSE" C1
          "END";
          "FOR"S:=M"STEP"-1"UNTIL"1"DO"
          "BEGIN"G[S]:=(G[S]-MATVEC(S+1,M,S,QR,G))/AID[S];
                 NDX:=NDX+G[S]**2
          "END";
          HOUSEHOLDER(M, -1, N1+1, N);
          "FOR" S:=1 "STEP" 1 "UNTIL" N1 "DO"
          F[S]:=F[S]-TAMVEC(N1+1, N, S, QR, F);
          HOUSEHOLDER(N1, -1, 1, N1);
          AUX[7]:=K;
          "FOR"I:=1"STEP"1"UNTIL"N"DO"NDR:=NDR+F[I]**2;
          CORRNORM:=SQRT(NDX+NDR)
       "END"FOR K;
       LDX:=SQRT(NDX);
       "FOR" S:=M "STEP" -1 "UNTIL" 1 "DO"
       "BEGIN" J:=CI[S];"IF" J^=S "THEN"
          "BEGIN" C1:=X[J];X[J]:=X[S];X[S]:=C1;ICHCOL(1,N,J,S,A)"END"
       "END"
"END" LSQREFSOL;
        "EOP"