"CODE" 34214;
    "REAL" "PROCEDURE" RNK1MIN(N, X, G, H, FUNCT, IN, OUT);
    "VALUE" N;
    "INTEGER" N; "ARRAY" X, G, H, IN, OUT;
    "REAL" "PROCEDURE" FUNCT;
    "BEGIN" "INTEGER" I, IT, N2, CNTL, CNTE, EVL, EVLMAX;
        "BOOLEAN" OK;
        "REAL" F, F0, FMIN, MU, DG, DG0, GHG, GS, NRMDELTA, ALFA,
        MACHEPS, RELTOL, ABSTOL, EPS, TOLG, ORTH, AID;
        "ARRAY" V, DELTA, GAMMA, S, P[1:N];

        MACHEPS:= IN[0]; RELTOL:= IN[1]; ABSTOL:= IN[2];
        MU:= IN[3]; TOLG:= IN[4]; FMIN:= IN[5]; IT := 0;
        ALFA:= IN[6]; EVLMAX:= IN[7]; ORTH:= IN[8];
        N2:= N * (N + 1) // 2; CNTL:= CNTE:= 0; "IF" ALFA > 0 "THEN"
        "BEGIN" INIVEC(1, N2, H, 0); INISYMD(1, N, 0, H, ALFA) "END";
        F:= FUNCT(N, X, G); EVL:= 1; DG:= SQRT(VECVEC(1, N, 0, G, G));
        "FOR" I:= 1 "STEP" 1 "UNTIL" N "DO"
        DELTA[I]:= - SYMMATVEC(1, N, I, H, G);
        NRMDELTA:= SQRT(VECVEC(1, N, 0, DELTA, DELTA));
        DG0:= VECVEC(1, N, 0, DELTA, G); OK:= DG0 < 0;
        EPS:= SQRT(VECVEC(1, N, 0, X, X)) * RELTOL + ABSTOL;
        "FOR" IT:= IT + 1  "WHILE"
        (NRMDELTA > EPS "OR" DG > TOLG "OR" ^ OK) "AND" EVL < EVLMAX
        "DO"
        "BEGIN" "IF" ^OK "THEN"
            "BEGIN" "ARRAY" VEC[1:N,1:N], TH[1:N2], EM[0:9];
                EM[0]:= MACHEPS; EM[2]:= AID:= SQRT(MACHEPS * RELTOL);
                EM[4]:= ORTH; EM[6]:= AID * N; EM[8]:= 5;
                CNTE:= CNTE + 1; DUPVEC(1, N2, 0, TH, H);
                EIGSYM1(TH,N,N,V,VEC,EM);
                "FOR" I:= 1 "STEP" 1 "UNTIL" N "DO"
                "BEGIN" AID:= - TAMVEC(1, N, I, VEC, G);
                    S[I]:= AID * ABS(V[I]); V[I]:= AID * SIGN(V[I])
                "END"
                "FOR" I:= 1 "STEP" 1 "UNTIL" N "DO"
                "BEGIN" DELTA[I]:= MATVEC(1, N, I, VEC, S);
                    P[I]:= MATVEC(1, N, I, VEC, V)
                "END";
                DG0:= VECVEC(1, N, 0, DELTA, G);
                NRMDELTA:= SQRT(VECVEC(1, N, 0, DELTA, DELTA))
            "END" CALCULATING GREENSTADTS DIRECTION;
            DUPVEC(1, N, 0, S, X); DUPVEC(1, N, 0, V, G);
            "IF" IT > N "THEN" ALFA:= 1 "ELSE"
            "BEGIN" "IF" IT ^= 1 "THEN" ALFA:= ALFA / NRMDELTA "ELSE"
                "BEGIN" ALFA:= 2 * (FMIN - F) / DG0;
                "IF" ALFA > 1 "THEN" ALFA:= 1
                "END"
            "END";
            ELMVEC(1, N, 0, X, DELTA, ALFA);
            F0:= F; F:= FUNCT(N, X, G); EVL:= EVL +1 ;
            DG:= VECVEC(1, N, 0, DELTA, G);
            "IF" IT = 1 "OR" F0 - F < -MU * DG0 * ALFA "THEN"
            "BEGIN" I:= EVLMAX - EVL; CNTL:= CNTL +1 ;
                LINEMIN(N, S, DELTA, NRMDELTA, ALFA, G, FUNCT, F0, F,
                DG0, DG, I, "FALSE", IN); EVL:= EVL + I;
                DUPVEC(1, N, 0, X, S);
            "END" LINEMINIMIZATION;
            DUPVEC(1, N, 0, GAMMA, G); ELMVEC(1, N, 0, GAMMA, V, -1);
            "IF" ^ OK "THEN" MULVEC(1, N, 0, V, P, -1);
            DG:= DG - DG0; "IF" ALFA ^= 1 "THEN"
            "BEGIN" MULVEC(1, N, 0, DELTA, DELTA, ALFA);
                MULVEC(1, N, 0, V, V, ALFA);
                NRMDELTA:= NRMDELTA * ALFA; DG:= DG * ALFA
            "END";
            DUPVEC(1, N, 0, P, GAMMA); ELMVEC(1, N, 0, P, V, 1);
            "FOR" I:= 1 "STEP" 1 "UNTIL" N "DO"
            V[I]:= SYMMATVEC(1, N, I, H, GAMMA);
            DUPVEC(1, N, 0, S, DELTA); ELMVEC(1, N, 0, S, V, -1);
            GS:= VECVEC(1, N, 0, GAMMA, S);
            GHG:= VECVEC(1, N, 0, V, GAMMA);
            AID:= DG / GS;
            "IF" VECVEC(1, N, 0, DELTA, P) ** 2 > VECVEC(1, N, 0, P, P)
            * (ORTH * NRMDELTA) ** 2 "THEN" RNK1UPD(H, N, S, 1 / GS)
            "ELSE" "IF" AID >= 0 "THEN"
            FLEUPD(H, N, DELTA, V, 1 / DG, (1 + GHG / DG) / DG) "ELSE"
            DAVUPD(H, N, DELTA, V, 1 / DG, 1 / GHG);
            "FOR" I:= 1 "STEP" 1 "UNTIL" N "DO"
            DELTA[I]:= -SYMMATVEC(1, N, I, H, G);
            ALFA:= NRMDELTA;
            NRMDELTA:= SQRT(VECVEC(1, N, 0, DELTA, DELTA));
            EPS:= SQRT(VECVEC(1, N, 0, X, X)) * RELTOL + ABSTOL;
            DG:= SQRT(VECVEC(1, N, 0, G, G));
            DG0:= VECVEC(1, N, 0, DELTA, G); OK:= DG0 <= 0
        "END" ITERATION;
        OUT[0]:= NRMDELTA; OUT[1]:= DG; OUT[2]:= EVL;
        OUT[3]:= CNTL; OUT[4]:= CNTE; RNK1MIN:= F
    "END" RNK1MIN

        "EOP"