"CODE" 34441;
    "PROCEDURE" GSSNEWTON(M, N, PAR, RV, JJINV, FUNCT, JACOBIAN,
      IN, OUT);
    "VALUE" M, N; "INTEGER" M, N;
    "ARRAY" PAR, RV, JJINV, IN, OUT;
    "BOOLEAN" "PROCEDURE" FUNCT;
    "PROCEDURE" JACOBIAN;

    "BEGIN" "INTEGER" I, J, INR, MIT, TEXT,
        IT, ITMAX, INRMAX, TIM, FEVAL, FEVALMAX;
        "REAL" RHO, RES1, RES2, RN, RELTOLPAR, ABSTOLPAR, ABSTOLRES,
           STAP, NORMX;
        "BOOLEAN" CONV, TESTTHF, DAMPING ON;
        "ARRAY" JAC[1:M + 1,1:N], PR, AID, SOL[1 : N], FU2[1 : M],
           AUX[2 : 5];
        "INTEGER""ARRAY" CI[1:N];

        "BOOLEAN""PROCEDURE" LOC FUNCT(M, N, PAR, RV);
        "VALUE" M, N; "INTEGER" M, N; "ARRAY" PAR, RV;
        "BEGIN" LOC FUNCT:= TEST THF:= FUNCT(M, N, PAR, RV)
            "AND" TEST THF; FEVAL:= FEVAL + 1
        "END" LOC FUNCT;

        ITMAX:= FEVALMAX:= IN[5]; AUX[2]:= N * IN[0]; TIM:= IN[7];
        RELTOLPAR:= IN[1] ** 2; ABSTOLPAR:= IN[2] ** 2;
        ABSTOLRES:= IN[4] ** 2; INRMAX:= IN[6];
        DUPVEC(1, N, 0, PR, PAR);
        "IF" M < N "THEN"
        "FOR" I:= 1 "STEP" 1 "UNTIL" N "DO" JAC[M + 1, I]:= 0;
        TEXT:= 4; MIT:= 0; TEST THF:= "TRUE";
        RES2:= STAP:= OUT[5]:= OUT[6]:= OUT[7]:= 0;
        FUNCT(M, N, PAR, FU2); RN:= VECVEC(1, M, 0, FU2, FU2);
        OUT[3]:= SQRT(RN); FEVAL:= 1; DAMPING ON:= "FALSE";
        "FOR" IT:= 1, IT + 1 "WHILE" IT <= ITMAX "AND"
               FEVAL < FEVALMAX "DO"
        "BEGIN" OUT[5]:= IT; JACOBIAN(M, N, PAR, FU2, JAC, LOCFUNCT);
           "IF" "NOT" TEST THF "THEN"
           "BEGIN" TEXT:= 7; "GO TO" FAIL "END";
           LSQORTDEC(JAC, M, N, AUX, AID, CI);
           "IF" AUX[3] ^= N "THEN"
           "BEGIN" TEXT:= 5; "GO TO" FAIL "END";
           LSQSOL(JAC, M, N, AID, CI, FU2); DUPVEC(1, N, 0, SOL, FU2);
           STAP:= VECVEC(1, N, 0, SOL, SOL);
           RHO:= 2; NORMX:= VECVEC(1, N, 0, PAR, PAR);
           "IF" STAP > RELTOLPAR * NORMX + ABSTOLPAR
              "OR" IT = 1 "AND" STAP > 0 "THEN"
           "BEGIN""FOR" INR:= 0, INR + 1
              "WHILE""IF" INR = 1 "THEN" DAMPING ON "OR" RES2 >= RN
              "ELSE""NOT" CONV "AND" (RN <= RES1 "OR" RES2 < RES1) "DO"
              "BEGIN""COMMENT" DAMPING STOPS WHEN
                 R0 > R1 "AND" R1 <= R2 (BEST RESULT IS X1, R1)
                 WITH  X1 = X0 + I * DX, I:= 1, .5, .25, .125, ETC.  ;
                 RHO:= RHO / 2; "IF" INR > 0 "THEN"
                 "BEGIN" RES1:= RES2; DUPVEC(1, M, 0, RV, FU2);
                    DAMPING ON:= INR > 1
                 "END";
                 "FOR" I:= 1 "STEP" 1 "UNTIL" N "DO"
                 PR[I]:= PAR[I] - SOL[I] * RHO;
                 FEVAL:= FEVAL + 1;
                 "IF" "NOT" FUNCT(M, N, PR, FU2) "THEN"
                 "BEGIN" TEXT:= 6; "GO TO" FAIL "END";
                 RES2:= VECVEC(1, M, 0, FU2, FU2); CONV:= INR >= INRMAX
              "END" DAMPING OF STEP VECTOR;
              "IF" CONV "THEN"
              "BEGIN""COMMENT" RESIDUE CONSTANT; MIT:= MIT + 1;
                 "IF" MIT < TIM "THEN" CONV:= "FALSE"
              "END" "ELSE" MIT:= 0;
              "IF" INR > 1 "THEN"
              "BEGIN" RHO:= RHO * 2; ELMVEC(1, N, 0, PAR, SOL, - RHO);
                 RN:= RES1; "IF" INR > 2 "THEN" OUT[7]:= IT
              "END""ELSE"
              "BEGIN" DUPVEC(1, N, 0, PAR, PR); RN:= RES2;
                 DUPVEC(1, M, 0, RV, FU2)
              "END";

              "IF" RN <= ABSTOLRES "THEN"
              "BEGIN" TEXT:= 1; ITMAX:= IT "END""ELSE"
              "IF" CONV "AND" INRMAX > 0 "THEN"
              "BEGIN" TEXT:= 3; ITMAX:= IT "END"
              "ELSE" DUPVEC(1, M, 0, FU2, RV)
           "END" ITERATION WITH DAMPING AND TESTS "ELSE"
           "BEGIN" TEXT:= 2; RHO:= 1; ITMAX:= IT "END"
        "END" OF ITERATIONS;

        LSQINV(JAC, N, AID, CI);
        "FOR" I:= 1 "STEP" 1 "UNTIL" N "DO"
        "BEGIN" JJINV[I,I]:= JAC[I,I];
            "FOR" J:= I + 1 "STEP" 1 "UNTIL" N "DO"
            JJINV[I,J]:= JJINV[J,I]:= JAC[I,J]
        "END" CALCULATION OF INVERSE MATRIX OF NORMAL EQUATIONS;
    FAIL :
        OUT[6]:= SQRT(STAP) * RHO; OUT[2]:= SQRT(RN); OUT[4]:= FEVAL;
        OUT[1]:= TEXT; OUT[8]:= AUX[3]; OUT[9]:= AUX[5]
    "END" GSSNEWTON;
        "EOP"