"CODE" 34601;
"PROCEDURE" QZI(N,A,B,X,ALFR,ALFI,BETA,ITER,EM);
"VALUE" N;"INTEGER" N;"ARRAY"A,B,X,ALFR,ALFI,BETA,EM;
"INTEGER" "ARRAY" ITER;
"BEGIN" "REAL" DWARF,EPS,EPSA,EPSB;
"PROCEDURE" QZIT(N,A,B,X,EPS,EPSA,EPSB,ITER);"VALUE"N,EPS;
"REAL" EPS,EPSA,EPSB;"INTEGER" N;"INTEGER" "ARRAY" ITER;"ARRAY" A,B,X;
"BEGIN" "REAL" ANORM,BNORM,ANI,BNI,CONST,A10,A20,A30,B11,
    B22,B33,B44,A11,A12,A21,A22,A33,A34,A43,A44,B12,B34,OLD1,OLD2;
    "INTEGER" I,Q,M,M1,Q1,J,K,K1,K2,K3,KM1;"BOOLEAN" STATIONARY;
    ANORM:=BNORM:=0;"FOR" I:=1 "STEP" 1 "UNTIL" N "DO"
    "BEGIN" BNI:=0;ITER[I]:=0;ANI:="IF" I>1"THEN"ABS(A[I,I-1])"ELSE" 0;
        "FOR" J:=I "STEP" 1 "UNTIL" N "DO"
        "BEGIN" ANI:=ANI+ABS(A[I,J]);BNI:=BNI+ABS(B[I,J])
        "END";"IF" ANI>ANORM "THEN" ANORM:=ANI;"IF" BNI>BNORM"THEN"
        BNORM:=BNI
    "END";"IF" ANORM=0 "THEN" ANORM:=EPS;"IF"BNORM=0 "THEN" BNORM:=EPS;
    EPSA:=EPS*ANORM;EPSB:=EPS*BNORM;
    "FOR" M:=N,M "WHILE" M>=3 "DO"
  "BEGIN"
    "FOR" I:=M+1,I-1 "WHILE"("IF" I>1 "THEN"ABS(A[I,I-1])>EPSA "ELSE"
    "FALSE") "DO" Q:=I-1;
    "IF" Q>1 "THEN" A[Q,Q-1]:=0;
 L: "IF" Q>=M-1 "THEN" M:=Q-1 "ELSE"
    "BEGIN"
        "IF" ABS(B[Q,Q])<=EPSB "THEN"
        "BEGIN" B[Q,Q]:=0;Q1:=Q+1;
            HSH2COL(Q,Q,N,Q,A[Q,Q],A[Q1,Q],A,B);A[Q1,Q]:=0;
            Q:=Q1;"GOTO" L
        "END" "ELSE" M1:=M-1;Q1:=Q+1;CONST:=0.75;ITER[M]:=ITER[M]+1;
        STATIONARY:="IF" ITER[M]=1 "THEN" "TRUE" "ELSE"
        ABS(A[M,M-1])>=CONST*OLD1"AND"ABS(A[M-1,M-2])>=CONST*OLD2;
        "IF" ITER[M]>30"AND"STATIONARY "THEN"
        "BEGIN" "FOR" I:=1 "STEP" 1 "UNTIL" M "DO" ITER[I]:=-1;
            "GOTO" OUT
        "END";
        "IF" ITER[M]=10"AND"STATIONARY "THEN"
        "BEGIN" A10:=0;A20:=1;A30:=1.1605
        "END" "ELSE"
        "BEGIN" B11:=B[Q,Q];B22:="IF" ABS(B[Q1,Q1])<EPSB "THEN"EPSB
            "ELSE" B[Q1,Q1];
            B33:="IF" ABS(B[M1,M1])<EPSB "THEN" EPSB "ELSE"B[M1,M1];
            B44:="IF" ABS(B[M,M])<EPSB "THEN" EPSB "ELSE" B[M,M] ;
            A11:=A[Q,Q]/B11;A12:=A[Q,Q1]/B22;A21:=A[Q1,Q]/B11;
            A22:=A[Q1,Q1]/B22;A33:=A[M1,M1]/B33;A34:=A[M1,M]/B44;
            A43:=A[M,M1]/B33;A44:=A[M,M]/B44;B12:=B[Q,Q1]/B22;
            B34:=B[M1,M]/B44;
            A10:=((A33-A11)*(A44-A11)-A34*A43+A43*B34*A11)/A21
                 +A12-A11*B12;
            A20:=(A22-A11-A21*B12)-(A33-A11)-(A44-A11)+A43*B34;
            A30:=A[Q+2,Q1]/B22
        "END";OLD1:=ABS(A[M,M-1]);OLD2:=ABS(A[M-1,M-2]);
        "FOR" K:=Q "STEP" 1 "UNTIL" M1 "DO"
        "BEGIN" K1:=K+1;K2:=K+2;K3:="IF" K+3>M "THEN" M "ELSE" K+3;
            KM1:="IF" K-1<Q "THEN" Q "ELSE" K-1;
            "IF" K^=M1 "THEN"
            "BEGIN" "IF" K=Q "THEN"
                HSH3COL(KM1,KM1,N,K,A10,A20,A30,A,B) "ELSE"
                "BEGIN"
                 HSH3COL(KM1,KM1,N,K,A[K,KM1],A[K1,KM1],A[K2,KM1],A,B);
                  A[K1,KM1]:=A[K2,KM1]:=0
                "END";
                HSH3ROW3(1,K3,N,K,B[K2,K2],B[K2,K1],B[K2,K],A,B,X);
                B[K2,K]:=B[K2,K1]:=0 ;
            "END" "ELSE"
            "BEGIN" HSH2COL(KM1,KM1,N,K,A[K,KM1],A[K1,KM1],A,B);
                A[K1,KM1]:=0
            "END";
            HSH2ROW3(1,K3,K3,N,K,B[K1,K1],B[K1,K],A,B,X);B[K1,K]:=0
        "END"
    "END"
  "END"; OUT:
"END" QZIT;
"PROCEDURE" QZVAL(N,A,B,X,EPSA,EPSB,ALFR,ALFI,BETA);"VALUE" N;
"REAL" EPSA,EPSB;"INTEGER" N;"ARRAY" ALFR,ALFI,BETA,A,B,X;
"BEGIN" "INTEGER" M,L,J;"REAL" AN,BN,A11,A12,A21,A22,B11,B12,B22,E,C,D,
    ER,EI,A11R,A11I,A12R,A12I,A21R,A21I,A22R,A22I,CZ,SZR,SZI,
    CQ,SQR,SQI,SSR,SSI,TR,TI,BDR,BDI,R;
    "FOR" M:=N,M "WHILE" M>0 "DO"
    "IF"("IF" M>1 "THEN" A[M,M-1]=0 "ELSE" "TRUE")"THEN"
    "BEGIN" ALFR[M]:=A[M,M];BETA[M]:=B[M,M];ALFI[M]:=0;M:=M-1
    "END" "ELSE"
    "BEGIN" L:=M-1;"IF" ABS(B[L,L])<=EPSB "THEN"
        "BEGIN" B[L,L]:=0;HSH2COL(L,L,N,L,A[L,L],A[M,L],A,B);
            A[M,L]:=B[M,L]:=0;ALFR[L]:=A[L,L];ALFR[M]:=A[M,M];
            BETA[L]:=B[L,L];BETA[M]:=B[M,M];ALFI[M]:=ALFI[L]:=0;
        "END" "ELSE" "IF" ABS(B[M,M])<=EPSB "THEN"
        "BEGIN"B[M,M]:=0;HSH2ROW3(1,M,M,N,L,A[M,M],A[M,L],A,B,X);
            A[M,L]:=B[M,L]:=0;ALFR[L]:=A[L,L];ALFR[M]:=A[M,M];
            BETA[L]:=B[L,L];BETA[M]:=B[M,M];ALFI[M]:=ALFI[L]:=0;
        "END""ELSE"
      "BEGIN"
        AN:=ABS(A[L,L])+ABS(A[L,M])+ABS(A[M,L])+ABS(A[M,M]);
        BN:=ABS(B[L,L])+ABS(B[L,M])+ABS(B[M,M]);
        A11:=A[L,L]/AN;A12:=A[L,M]/AN;A21:=A[M,L]/AN;A22:=A[M,M]/AN;
        B11:=B[L,L]/BN;B12:=B[L,M]/BN;B22:=B[M,M]/BN;
        E:=A11/B11;
        C:=((A22-E*B22)/B22-(A21*B12)/(B11*B22))/2;
        D:=C*C+(A21*(A12-E*B12))/(B11*B22);
        "IF" D>=0 "THEN"
        "BEGIN"E:=E+("IF"C<0"THEN"C-SQRT(D)"ELSE"C+SQRT(D));
            A11:=A11-E*B11;A12:=A12-E*B12;A22:=A22-E*B22;
            "IF" ABS(A11)+ABS(A12)>=ABS(A21)+ABS(A22) "THEN"
            HSH2ROW3(1,M,M,N,L,A12,A11,A,B,X)"ELSE"
            HSH2ROW3(1,M,M,N,L,A22,A21,A,B,X);
            "IF"AN>=ABS(E)*BN"THEN"
            HSH2COL(L,L,N,L,B[L,L],B[M,L],A,B) "ELSE"
            HSH2COL(L,L,N,L,A[L,L],A[M,L],A,B);
            A[M,L]:=B[M,L]:=0;
            ALFR[L]:=A[L,L];ALFR[M]:=A[M,M];BETA[L]:=B[L,L];
            BETA[M]:=B[M,M];ALFI[M]:=ALFI[L]:=0;
        "END""ELSE"
        "BEGIN"
            ER:=E+C;EI:=SQRT(-D);A11R:=A11-ER*B11;A11I:=EI*B11;
            A12R:=A12-ER*B12;A12I:=EI*B12;A21R:=A21;A21I:=0;
            A22R:=A22-ER*B22;A22I:=EI*B22;
            "IF"ABS(A11R)+ABS(A11I)+ABS(A12R)+ABS(A12I)>=
            ABS(A21R)+ABS(A22R)+ABS(A22I)"THEN"
            CHSH2(A12R,A12I,-A11R,-A11I,CZ,SZR,SZI)"ELSE"
            CHSH2(A22R,A22I,-A21R,-A21I,CZ,SZR,SZI);
            "IF"AN>=(ABS(ER)+ABS(EI))*BN"THEN"
            CHSH2(CZ*B11+SZR*B12,SZI*B12,SZR*B22,SZI*B22,CQ,SQR,SQI)
            "ELSE"CHSH2(CZ*A11+SZR*A12,SZI*A12,CZ*A21+SZR*A22,SZI*A22,
            CQ,SQR,SQI);SSR:=SQR*SZR+SQI*SZI;SSI:=SQR*SZI-SQI*SZR;
            TR:=CQ*CZ*A11+CQ*SZR*A12+SQR*CZ*A21+SSR*A22;
            TI:=CQ*SZI*A12-SQI*CZ*A21+SSI*A22;
            BDR:=CQ*CZ*B11+CQ*SZR*B12+SSR*B22;
            BDI:=CQ*SZI*B12+SSI*B22;
            R:=SQRT(BDR*BDR+BDI*BDI);BETA[L]:=BN*R;
            ALFR[L]:=AN*(TR*BDR+TI*BDI)/R;
            ALFI[L]:=AN*(TR*BDI-TI*BDR)/R;
            TR:=SSR*A11-SQR*CZ*A12-CQ*SZR*A21+CQ*CZ*A22;
            TI:=-SSI*A11-SQI*CZ*A12+CQ*SZI*A21;
            BDR:=SSR*B11-SQR*CZ*B12+CQ*CZ*B22;
            BDI:=-SSI*B11-SQI*CZ*B12;
            R:=SQRT(BDR*BDR+BDI*BDI);BETA[M]:=BN*R;
            ALFR[M]:=AN*(TR*BDR+TI*BDI)/R;
            ALFI[M]:=AN*(TR*BDI-TI*BDR)/R;
        "END"
      "END";M:=M-2
    "END"
"END" QZVAL

"PROCEDURE" QZVEC(N,A,B,X,EPSA,EPSB,ALFR,ALFI,BETA);"VALUE"N,EPSA,EPSB;
"INTEGER" N;"REAL" EPSA,EPSB;"ARRAY" A,B,ALFR,ALFI,BETA,X;
"BEGIN""INTEGER" M,MR,MI,L,L1,J,K;"REAL" BETM,ALFM,SL,SK,D,TKK,TKL,TLK,
    TLL,ALMI,ALMR,TR,TI,SLR,SLI,SKR,SKI,DR,DI,TKKR,TKKI,TKLR,TKLI,TLKR,
    TLKI,TLLR,TLLI,S,R;
    "FOR" M:=N "STEP" -1 "UNTIL" 1 "DO"
    "IF" ALFI[M]=0 "THEN"
    "BEGIN" "COMMENT" M-TH REAL VECTOR;
        ALFM:=ALFR[M];BETM:=BETA[M];B[M,M]:=1;L1:=M;
        "FOR" L:=M-1 "STEP" -1 "UNTIL" 1 "DO"
        "BEGIN" SL:=0;
            "FOR" J:=L1 "STEP" 1 "UNTIL" M "DO"
            SL:=SL+(BETM*A[L,J]-ALFM*B[L,J])*B[J,M];
            "IF"("IF"L^=1"THEN"BETM*A[L,L-1]=0"ELSE""TRUE")"THEN"
            "BEGIN""COMMENT" 1-1 BLOCK;
                D:=BETM*A[L,L]-ALFM*B[L,L];
                "IF" D=0 "THEN" D:=(EPSA+EPSB)/2;B[L,M]:=-SL/D
            "END""ELSE"
            "BEGIN" "COMMENT" 2-2 BLOCK;K:=L-1;SK:=0;
                "FOR"J:=L1 "STEP" 1 "UNTIL" M "DO"
                SK:=SK+(BETM*A[K,J]-ALFM*B[K,J])*B[J,M];
                TKK:=BETM*A[K,K]-ALFM*B[K,K];
                TKL:=BETM*A[K,L]-ALFM*B[K,L];
                TLK:=BETM*A[L,K];
                TLL:=BETM*A[L,L]-ALFM*B[L,L];
                D:=TKK*TLL-TKL*TLK;"IF" D=0 "THEN" D:=(EPSA+EPSB)/2;
                B[L,M]:=(TLK*SK-TKK*SL)/D;
               B[K,M]:="IF"ABS(TKK)>=ABS(TLK)"THEN"-(SK+TKL*B[L,M])/TKK
                "ELSE" -(SL+TLL*B[L,M])/TLK;L:=L-1
            "END";L1:=L
        "END"
    "END""ELSE"
    "BEGIN" "COMMENT" COMPLEX VECTOR;
        ALMR:=ALFR[M-1];ALMI:=ALFI[M-1];BETM:=BETA[M-1];MR:=M-1;MI:=M;
        B[M-1,MR]:=ALMI*B[M,M]/(BETM*A[M,M-1]);
        B[M-1,MI]:=(BETM*A[M,M]-ALMR*B[M,M])/(BETM*A[M,M-1]);
        B[M,MR]:=0;B[M,MI]:=-1;L1:=M-1;
        "FOR" L:=M-2 "STEP" -1 "UNTIL" 1 "DO"
        "BEGIN" SLR:=SLI:=0;
            "FOR" J:=L1 "STEP" 1 "UNTIL" M "DO"
            "BEGIN" TR:=BETM*A[L,J]-ALMR*B[L,J];
                TI:=-ALMI*B[L,J];
                SLR:=SLR+TR*B[J,MR]-TI*B[J,MI];
                SLI:=SLI+TR*B[J,MI]+TI*B[J,MR]
            "END";
            "IF"("IF"L^=1"THEN"BETM*A[L,L-1]=0"ELSE""TRUE")"THEN"
            "BEGIN"DR:=BETM*A[L,L]-ALMR*B[L,L];
                DI:=-ALMI*B[L,L];
                COMDIV(-SLR,-SLI,DR,DI,B[L,MR],B[L,MI]);
            "END""ELSE"
            "BEGIN" K:=L-1;SKR:=SKI:=0;
                "FOR" J:=L1 "STEP" 1 "UNTIL" M "DO"
                "BEGIN" TR:=BETM*A[K,J]-ALMR*B[K,J];
                    TI:=-ALMI*B[K,J];
                    SKR:=SKR+TR*B[J,MR]-TI*B[J,MI];
                    SKI:=SKI+TR*B[J,MI]+TI*B[J,MR]
                "END";
                TKKR:=BETM*A[K,K]-ALMR*B[K,K];
                TKKI:=-ALMI*B[K,K];
                TKLR:=BETM*A[K,L]-ALMR*B[K,L];
                TKLI:=-ALMI*B[K,L];
                TLKR:=BETM*A[L,K];TLKI:=0;
                TLLR:=BETM*A[L,L]-ALMR*B[L,L];
                TLLI:=-ALMI*B[L,L];
                DR:=TKKR*TLLR-TKKI*TLLI-TKLR*TLKR;
                DI:=TKKR*TLLI+TKKI*TLLR-TKLI*TLKR;
                "IF"DR=0"AND"DI=0"THEN"DR:=(EPSA+EPSB)/2;
                COMDIV(TLKR*SKR-TKKR*SLR+TKKI*SLI,TLKR*SKI-TKKR*SLI-
                TKKI*SLR,DR,DI,B[L,MR],B[L,MI]);
                "IF"ABS(TKKR)+ABS(TKKI)>=ABS(TLKR)"THEN"
                COMDIV(-SKR-TKLR*B[L,MR]+TKLI*B[L,MI],-SKI-TKLR*B[L,MI]
                -TKLI*B[L,MR],TKKR,TKKI,B[K,MR],B[K,MI])"ELSE"
                COMDIV(-SLR-TLLR*B[L,MR]+TLLI*B[L,MI],-SLI-TLLR*B[L,MI]
                -TLLI*B[L,MR],TLKR,TLKI,B[K,MR],B[K,MI]);L:=L-1
            "END";L1:=L
        "END";M:=M-1
    "END";
    "FOR" M:=N "STEP" -1 "UNTIL" 1 "DO"
    "FOR" K:=1 "STEP" 1 "UNTIL" N "DO"
    X[K,M]:=MATMAT(1,M,K,M,X,B);
    "FOR" M:=N "STEP" -1 "UNTIL" 1 "DO"
    "BEGIN" S:=0;"IF" ALFI[M]=0 "THEN"
        "BEGIN" "FOR" K:=1 "STEP" 1 "UNTIL" N "DO"
            "BEGIN" R:=ABS(X[K,M]);
                "IF" R>=S "THEN""BEGIN" S:=R;D:=X[K,M] "END"
            "END";"FOR" K:=1 "STEP" 1 "UNTIL" N "DO"
            X[K,M]:=X[K,M]/D
        "END""ELSE"
        "BEGIN" "FOR" K:=1 "STEP" 1 "UNTIL" N "DO"
            "BEGIN" R:=ABS(X[K,M-1])+ABS(X[K,M]);
                R:=R*SQRT((X[K,M-1]/R)**2+(X[K,M]/R)**2);
                "IF" R>=S"THEN"
                "BEGIN" S:=R;DR:=X[K,M-1];DI:=X[K,M] "END"
            "END";"FOR" K:=1 "STEP" 1 "UNTIL" N "DO"
            COMDIV(X[K,M-1],X[K,M],DR,DI,X[K,M-1],X[K,M]);M:=M-1
        "END"
    "END"
"END" QZVEC;
DWARF:=EM[0];EPS:=EM[1];
HSHDECMUL(N,A,B,DWARF);
HESTGL3(N,A,B,X);
QZIT(N,A,B,X,EPS,EPSA,EPSB,ITER);
QZVAL(N,A,B,X,EPSA,EPSB,ALFR,ALFI,BETA);
QZVEC(N,A,B,X,EPSA,EPSB,ALFR,ALFI,BETA)
"END" QZI;
        "EOP"