"CODE" 34186;
    "COMMENT" MCA 2416;
    "INTEGER" "PROCEDURE" REAQRI(A, N, EM, VAL, VEC); "VALUE" N;
    "INTEGER" N; "ARRAY" A, EM, VAL, VEC;
    "BEGIN" "INTEGER" M1, I, I1, M, J, Q, MAX, COUNT;
        "REAL" W, SHIFT, KAPPA, NU, MU, R, TOL, S, MACHTOL,
        ELMAX, T, DELTA, DET;
        "ARRAY" TF[1:N];

        MACHTOL:= EM[0] * EM[1]; TOL:= EM[1] * EM[2]; MAX:= EM[4];
        COUNT:= 0; ELMAX:= 0; M:= N;
        "FOR" I:= 1 "STEP" 1 "UNTIL" N "DO"
        "BEGIN" VEC[I,I]:= 1;
            "FOR" J:= I + 1 "STEP" 1 "UNTIL" N "DO"
            VEC[I,J]:= VEC[J,I]:= 0
        "END";
     IN: M1:= M - 1;
        "FOR" I:= M, I - 1 "WHILE" ("IF" I >= 1 "THEN"
        ABS(A[I + 1,I]) > TOL "ELSE" "FALSE") "DO" Q:= I;
        "IF" Q > 1 "THEN"
        "BEGIN" "IF" ABS(A[Q,Q - 1]) > ELMAX "THEN"
            ELMAX:= ABS(A[Q, Q - 1])
        "END";
        "IF" Q = M "THEN"
        "BEGIN" VAL[M]:= A[M,M]; M:= M1 "END"
        "ELSE"
        "BEGIN" DELTA:= A[M,M] - A[M1,M1]; DET:= A[M,M1] * A[M1,M];
            "IF" ABS(DELTA) < MACHTOL "THEN" S:= SQRT(DET) "ELSE"
            "BEGIN" W:= 2 / DELTA; S:= W * W * DET + 1;
                S:= "IF" S <= 0 "THEN" -DELTA * .5 "ELSE"
                W * DET / (SQRT(S) + 1)
            "END";
            "IF" Q = M1 "THEN"
            "BEGIN" A[M,M]:= VAL[M]:= A[M,M] + S;
                A[Q,Q]:= VAL[Q]:= A[Q,Q] - S;
                T:= "IF" ABS(S) < MACHTOL "THEN"
                (S + DELTA) / A[M,Q] "ELSE" A[Q,M] / S;
                R:= SQRT(T * T + 1); NU:= 1 / R;
                MU:= -T * NU; A[Q,M]:= A[Q,M] - A[M,Q];
                ROTROW(Q + 2, N, Q, M, A, MU, NU);
                ROTCOL(1, Q - 1, Q, M, A, MU, NU);
                ROTCOL(1, N, Q, M, VEC, MU, NU); M:= M - 2
            "END"

            "ELSE"
            "BEGIN" COUNT:= COUNT + 1;
                "IF" COUNT > MAX "THEN" "GOTO" END;
                SHIFT:= A[M,M] + S; "IF" ABS(DELTA) < TOL "THEN"
                "BEGIN" W:= A[M1,M1] - S;
                    "IF" ABS(W) < ABS(SHIFT) "THEN" SHIFT:= W
                "END";
                A[Q,Q]:= A[Q,Q] - SHIFT;
                "FOR" I:= Q "STEP" 1 "UNTIL" M1 "DO"
                "BEGIN" I1:= I + 1; A[I1,I1]:= A[I1,I1] - SHIFT;
                    KAPPA:= SQRT(A[I,I] ** 2 + A[I1,I] ** 2);
                    "IF" I > Q "THEN"
                    "BEGIN" A[I,I - 1]:= KAPPA * NU;
                        W:= KAPPA * MU
                    "END"
                    "ELSE" W:= KAPPA; MU:= A[I,I] / KAPPA;
                    NU:= A[I1,I] / KAPPA; A[I,I]:= W;
                    ROTROW(I1, N, I, I1, A, MU, NU);
                    ROTCOL(1, I, I, I1, A, MU, NU);
                    A[I,I]:= A[I,I] + SHIFT;
                    ROTCOL(1, N, I, I1, VEC, MU, NU)
                "END";
                A[M,M1]:= A[M,M] * NU; A[M,M]:= A[M,M] * MU + SHIFT
            "END"
        "END";
        "IF" M > 0 "THEN" "GOTO" IN;
        "FOR" J:= N "STEP" -1 "UNTIL" 2 "DO"
        "BEGIN" TF[J]:= 1; T:= A[J,J];
            "FOR" I:= J - 1 "STEP" -1 "UNTIL" 1 "DO"
            "BEGIN" DELTA:= T - A[I,I];
                TF[I]:= MATVEC(I + 1, J, I, A, TF) /
                ("IF" ABS(DELTA) < MACHTOL "THEN" MACHTOL "ELSE" DELTA)
            "END";
            "FOR" I:= 1 "STEP" 1 "UNTIL" N "DO"
            VEC[I,J]:= MATVEC(1, J, I, VEC, TF)
        "END";
     END: EM[3]:= ELMAX; EM[5]:= COUNT; REAQRI:= M
    "END" REAQRI

        "EOP"