"CODE" 36401;
"PROCEDURE" SYMEIGIMP(N,A,VEC,VAL1,VAL2,LBOUND,UBOUND,AUX);
"VALUE" N;"INTEGER" N;"ARRAY" A,VEC,VAL1,VAL2,LBOUND,UBOUND,AUX;
"BEGIN"
    "INTEGER" K,I,J,I0,I1,ITER,MAXITP1;"REAL" S,HEAD,TAIL,MAX,TOL,
    MATEPS,RELERRA,RELTOLR,NORMA;"INTEGER" "ARRAY" PERM[1:N];
    "ARRAY" R,P,Y[1:N,1:N],RQ,RQT,EPS,Z,VAL3,ETA[1:N];
    "PROCEDURE" BOUNDS(I0,I1,N,LBOUND,UBOUND);"VALUE" I0,I1,N;
    "INTEGER" I0,I1,N;"ARRAY" LBOUND,UBOUND;
    "BEGIN" "INTEGER" K,I,J,I01;"REAL" EPS2,DL,DR;
        "FOR" I:=I0,I01 "WHILE" I<=I1 "DO"
        "BEGIN" J:=I01:=I;
            "FOR" J:=J+1 "WHILE" "IF" J>I1 "THEN" "FALSE" "ELSE"
            RQ[J]-RQ[J-1]<=EPS[J]+EPS[J-1] "DO" I01:=J;
            "IF" I = I01 "THEN"
            "BEGIN"
                "IF" I<N "THEN"
                "BEGIN"
                    "IF" I=1 "THEN" DL:=DR:=RQ[I+1]-RQ[I]-EPS[I+1]
                    "ELSE" "BEGIN" DL:=RQ[I]-RQ[I-1]-EPS[I-1];
                                   DR:=RQ[I+1]-RQ[I]-EPS[I+1]
                           "END"
                "END" "ELSE" DL:=DR:=RQ[I]-RQ[I-1]-EPS[I-1];
                EPS2:=EPS[I]*EPS[I];LBOUND[I]:=EPS2/DR+MATEPS;
                UBOUND[I]:=EPS2/DL+MATEPS
            "END" "ELSE"
            "BEGIN" "FOR" K:=I "STEP" 1 "UNTIL" I01 "DO"
                LBOUND[K]:=UBOUND[K]:=EPS[K]+MATEPS
            "END";I01:=I01+1
        "END"
    "END" BOUNDS;
    "BOOLEAN" STOP;STOP:="FALSE";NORMA:=INFNRMMAT(1,N,1,N,J,A);
    RELERRA:=AUX[0];RELTOLR:=AUX[2];MAXITP1:=AUX[4]+1;
    MATEPS:=RELERRA*NORMA;TOL:=RELTOLR*NORMA;
    "FOR" ITER:=1 "STEP" 1 "UNTIL" MAXITP1 "DO"
    "BEGIN" STOP:="TRUE";MAX:=0;
        "FOR" J:=1 "STEP" 1 "UNTIL" N "DO"
        "FOR" I:=1 "STEP" 1 "UNTIL" N "DO"
        "BEGIN"
            LNGMATVEC(J,J,I,VEC,VAL1,0,0,HEAD,TAIL);
            LNGMATMAT(1,N,I,J,A,VEC,-HEAD,-TAIL,R[I,J],TAIL);
            "IF"ABS(R[I,J])>MAX "THEN" MAX:=ABS(R[I,J])
        "END";"IF" MAX > TOL "THEN" STOP:="FALSE";
        "IF" "NOT" STOP "AND" ITER<MAXITP1 "THEN"
        "BEGIN"
            "FOR" I:=1 "STEP" 1 "UNTIL" N "DO"
            LNGTAMMAT(1,N,I,I,VEC,R,VAL1[I],0,RQ[I],RQT[I]);
            "FOR" J:=1 "STEP" 1 "UNTIL" N "DO"
            "BEGIN" "FOR" I:=1 "STEP" 1 "UNTIL" N "DO"
                ETA[I]:=R[I,J]-(RQ[J]-VAL1[J])*VEC[I,J];
                Z[J]:=SQRT(VECVEC(1,N,0,ETA,ETA))
            "END";
            MERGESORT(RQ,PERM,1,N);VECPERM(PERM,1,N,RQ);
            "FOR" I:=1 "STEP" 1 "UNTIL" N "DO"
            "BEGIN" EPS[I]:=Z[PERM[I]];VAL3[I]:=VAL1[PERM[I]];
                ROWPERM(PERM,1,N,I,VEC);ROWPERM(PERM,1,N,I,R)
            "END";
            "FOR" I:=1 "STEP" 1 "UNTIL" N "DO"
            "FOR" J:=I "STEP" 1 "UNTIL" N "DO"
            P[I,J]:=P[J,I]:=TAMMAT(1,N,I,J,VEC,R);
        "END";
        "FOR"I0:=1,I1+1 "WHILE" I0<=N "DO"
        "BEGIN" J:=I1:=I0;
            "FOR" J:=J+1 "WHILE" "IF" J>N "THEN" "FALSE" "ELSE"
            RQ[J]-RQ[J-1]<=SQRT((EPS[J]+EPS[J-1])*NORMA) "DO" I1:=J;
            "IF" STOP "OR" ITER=MAXITP1 "THEN"
            BOUNDS(I0,I1,N,LBOUND,UBOUND) "ELSE"
            "BEGIN"
                "IF" I0=I1 "THEN"
                "BEGIN" "FOR" K:=1 "STEP" 1 "UNTIL" N "DO"
                    "IF" K=I0 "THEN" Y[K,I0]:=1 "ELSE"
                    R[K,I0]:=P[K,I0];
                    VAL1[I0]:=RQ[I0];VAL2[I0]:=RQT[PERM[I0]]
                "END" "ELSE"
                "BEGIN""INTEGER" N1,I0M1,I1P1;"REAL" M1;"ARRAY"EM[0:5];
                    N1:=I1-I0+1;EM[0]:=EM[2]:="-14;EM[4]:=10*N1;
                    "BEGIN" "ARRAY" PP[1:N1,1:N1],VAL4[1:N1];M1:=0;
                        "FOR" K:=I0 "STEP" 1 "UNTIL" I1 "DO"
                        M1:=M1+VAL3[K];M1:=M1/N1;
                        "FOR" I:=1 "STEP" 1 "UNTIL" N1 "DO"
                        "FOR" J:=1 "STEP" 1 "UNTIL" N1 "DO"
                        "BEGIN" PP[I,J]:=P[I+I0-1,J+I0-1];
                            "IF" I=J "THEN"
                            PP[I,J]:=PP[I,J]+VAL3[J+I0-1]-M1
                        "END";"FOR" I:=I0 "STEP" 1 "UNTIL" I1 "DO"
                        "BEGIN" VAL3[I]:=M1;VAL1[I]:=RQ[I];
                            VAL2[I]:=RQT[PERM[I]]
                        "END";
                        QRISYM(PP,N1,VAL4,EM);
                        MERGESORT(VAL4,PERM,1,N1);
                        "FOR" I:=1 "STEP" 1 "UNTIL" N1 "DO"
                        "FOR" J:=1 "STEP" 1 "UNTIL" N1 "DO"
                        P[I+I0-1,J+I0-1]:=PP[I,PERM[J]];
                        I0M1:=I0-1;I1P1:=I1+1;
                        "FOR" J:=I0 "STEP" 1 "UNTIL" I1 "DO"
                        "BEGIN" "FOR" I:=1 "STEP" 1 "UNTIL" I0M1,
                            I1P1 "STEP" 1 "UNTIL" N "DO"
                            "BEGIN" S:=0;
                                "FOR" K:=I0 "STEP" 1 "UNTIL" I1 "DO"
                                S:=S+P[I,K]*P[K,J];
                                R[I,J]:=S
                            "END";"FOR" I:=I0 "STEP" 1 "UNTIL" I1 "DO"
                            Y[I,J]:=P[I,J]
                        "END" FOR J
                    "END" INNERBLOCK
                "END" I1>I0
            "END" NOT STOP
        "END" FOR I0;
        "IF" "NOT" STOP "AND" ITER<MAXITP1 "THEN"
        "BEGIN"
            "FOR" J:=1 "STEP" 1 "UNTIL" N "DO"
            "FOR" I:=1 "STEP" 1 "UNTIL" N "DO"
            "IF" VAL3[I]^=VAL3[J] "THEN"
            Y[I,J]:=R[I,J]/(VAL3[J]-VAL3[I]);
            "FOR" I:=1 "STEP" 1 "UNTIL" N "DO"
            "BEGIN" "FOR" J:=1 "STEP" 1 "UNTIL" N "DO"
                Z[J]:=MATMAT(1,N,I,J,VEC,Y);
                "FOR" J:=1 "STEP" 1 "UNTIL" N "DO" VEC[I,J]:=Z[J]
            "END";ORTHOG(N,1,N,VEC)
        "END" "ELSE"
        "BEGIN" AUX[5]:=ITER-1;"GOTO" EXIT "END"
    "END" FOR ITER;
    EXIT: AUX[1]:=NORMA;AUX[3]:=MAX
"END" SYMEIGIMP;
        "EOP"