北航數(shù)值分析大作業(yè)第二題(fortran)

1、“數(shù)值分析“計(jì)算實(shí)習(xí)大作業(yè)第二題SY1415215孔維鵬一、計(jì)算說(shuō)明本程序采用帶雙步位移的QR方法求解矩陣A的所有特征值，然后采用反冪法求解矩陣A的實(shí)特征值對(duì)應(yīng)的特征向量。在采用帶雙步位移的QR方法求解特征值時(shí)，對(duì)教材上所提供的具體算法作稍微的改動(dòng)，以簡(jiǎn)化程序，具體算法如下所示：1、計(jì)算出A擬上三角化后的矩陣A(n-1)，給定精度水平=10-12和最大迭代次數(shù)L；2、記A1=A(n-1)=aij(1)nn，令k=1，m=n；3、如果m2，則可直接計(jì)算出最后1或2個(gè)特征值，轉(zhuǎn)8，否則轉(zhuǎn)4；4、如果am,m-1(k)，則可得一個(gè)特征值，置m=m-1；轉(zhuǎn)3，否則轉(zhuǎn)5；5、如果am-1,m-2(k)，

2、則可得兩個(gè)特征值，置m=m-2；轉(zhuǎn)3，否則轉(zhuǎn)6；6、記Ak=aij1mm(1i,jm)，計(jì)算s=am-1,m-1(k)+am,m(k)t=am-1,m-1(k)am,m(k)-am,m-1(k)am-1,m(k)Mk=Ak2-sAk+tI (I是m階單位矩陣)Mk=QkRk (對(duì)Mk作QR分解)Ak+1=QkTAkQk7、k=k+1,轉(zhuǎn)38、A的全部特征值已經(jīng)求出，停止計(jì)算。二、計(jì)算源程序（FORTRAN）PROGRAM SY1415215_2PARAMETER (N=10)DIMENSION A(N,N),A1(N,N),A2(N,N),C(2,N),Q(N,N),R(N,N),CR(N),

3、CM(N)!C為存儲(chǔ)特征值的數(shù)組,1為實(shí)部，為虛部REAL(8) A,A1,A2,C,Q,R,CME=1E-12 !精度水平L=1000 !迭代最大次數(shù)OPEN(1,FILE=數(shù)值分析大作業(yè)第二題計(jì)算結(jié)果.TXT)DO I=1,N DO J=1,N IF(I=J) THEN A(I,J)=1.52*COS(I+1.2*J) ELSE A(I,J)=SIN(0.5*I+0.2*J) ENDIF ENDDOENDDOA1=AWRITE(*,(矩陣A為：)WRITE(1,(矩陣A為：)DO I=1,N DO J=1,N WRITE(*,(2X,E20.13,2X,) A(I,J) WRITE(1,(

4、2X,E20.13,2X,) A(I,J) ENDDO WRITE(*,( ) WRITE(1,( )ENDDO!使用矩陣的擬上三角化的算法將矩陣A化為擬上三角矩陣A（n-1）CALL HESSENBERG(A,N)WRITE(*,(擬上三角化后矩陣A（n-1）為：)WRITE(1,(擬上三角化后矩陣A（n-1）為：)DO I=1,N DO J=1,N WRITE(*,(2X,E20.13,2X,) A(I,J) WRITE(1,(2X,E20.13,2X,) A(I,J) ENDDO WRITE(*,() WRITE(1,()ENDDO!計(jì)算對(duì)矩陣A（n-1）實(shí)行QR方法迭代結(jié)束后所得矩陣A

5、2=ACALL QRD(A2,N,Q,R)WRITE(*,(對(duì)矩陣A（n-1）實(shí)行QR方法迭代結(jié)束后所得Q為：)WRITE(1,(對(duì)矩陣A（n-1）實(shí)行QR方法迭代結(jié)束后所得Q為：)DO I=1,N DO J=1,N WRITE(*,(2X,E20.13,2X,) Q(I,J) WRITE(1,(2X,E20.13,2X,) Q(I,J) ENDDO WRITE(*,() WRITE(1,()ENDDOWRITE(*,(對(duì)矩陣A（n-1）實(shí)行QR方法迭代結(jié)束后所得R為：)WRITE(1,(對(duì)矩陣A（n-1）實(shí)行QR方法迭代結(jié)束后所得R為：)DO I=1,N DO J=1,N WRITE(*,(

6、2X,E20.13,2X,) R(I,J) WRITE(1,(2X,E20.13,2X,) R(I,J) ENDDO WRITE(*,() WRITE(1,()ENDDO!使用帶雙步位移的QR方法求解矩陣A（n-1）的特征值K=1M=NDO WHILE(K=L) IF(M=2) THEN IF(M=1) THEN C(1,M)=A(M,M) ELSE IF(M=2) THEN CALL CALCUS(A,N,M,C) ENDIF EXIT ELSE IF(ABS(A(M,M-1)E) THEN C(1,M)=A(M,M) M=M-1 ELSE IF(ABS(A(M-1,M-2)E) THEN

7、CALL CALCUS(A,N,M,C) M=M-2 ELSE CALL CALM(A,M,N) ENDIF K=K+1ENDDO WRITE(*,(矩陣A的全部特征值為：)WRITE(1,(矩陣A的全部特征值為：)DO J=1,N WRITE(*,(E20.13,+,E20.13,i) C(1,J),C(2,J) WRITE(1,(E20.13,+,E20.13,i) C(1,J),C(2,J)ENDDO !使用反冪法求解A的相應(yīng)于實(shí)特征值的特征向量J=1DO I=1,N IF(C(2,I)=0)THEN CR(J)=C(1,I) J=J+1 ENDIFENDDOJC=J-1WRITE(*,

8、(矩陣A的實(shí)特征值為：)WRITE(1,(矩陣A的實(shí)特征值為：)DO I=1,JC WRITE(*,(E20.13) CR(I) WRITE(1,(E20.13) CR(I)ENDDODO II=1,JC DO I=1,N DO J=1,N IF(I=J) THEN A(I,J)=A1(I,J)-CR(II) ELSE A(I,J)=A1(I,J) ENDIF ENDDO ENDDO CALL INPOVERMETHOD(A,N,CM) WRITE(*,(與實(shí)特征值,E20.13,對(duì)應(yīng)的特征向量為：) CR(II) WRITE(1,(與實(shí)特征值,E20.13,對(duì)應(yīng)的特征向量為：) CR(II)

9、 DO I=1,N WRITE(*,(2X,E20.13,2X,) CM(I) WRITE(1,(2X,E20.13,2X,) CM(I) ENDDO WRITE(*,() WRITE(1,()ENDDO CLOSE(1) END!*擬上三角化子函數(shù)*！SUBROUTINE HESSENBERG(A,N)DIMENSION A(N,N),P(N),Q(N),W(N),U(N),AT(N,N)REAL(8) A,P,Q,W,U,ATREAL(8) S0,S1,S2,S3,S4,TDO L=1,N-2 JUDGE=0 DO I=L+2,N IF(A(I,L)/=0) THEN JUDGE=1 EX

10、IT ENDIF ENDDO IF(JUDGE=0) THEN A=A CYCLE ELSE IF(JUDGE/=0) THEN !計(jì)算DR S0=0 DO I=L+1,N S0=S0+A(I,L)*2 ENDDO DR=SQRT(S0) !計(jì)算CR IF(A(L+1,L)=0)THEN CR=DR ELSE CR=-SGN(A(L+1,L)*DR ENDIF !計(jì)算HR HR=CR*2-CR*A(L+1,L) !給u賦值 DO I=1,N IF(IL+1) THEN U(I)=A(I,L) ENDIF ENDDO !計(jì)算P DO I=1,N DO J=1,N AT(I,J)=A(J,I) E

11、NDDO ENDDO DO I=1,N S1=0 DO J=1,N S1=S1+AT(I,J)*U(J) ENDDO P(I)=S1/HR ENDDO !計(jì)算Q DO I=1,N S2=0 DO J=1,N S2=S2+A(I,J)*U(J) ENDDO Q(I)=S2/HR ENDDO !計(jì)算T S3=0 DO I=1,N S3=S3+P(I)*U(I) ENDDO T=S3/HR !計(jì)算W DO I=1,N W(I)=Q(I)-T*U(I) ENDDO !計(jì)算A（r+1） DO I=1,N DO J=1,N A(I,J)=A(I,J)-W(I)*U(J)-U(I)*P(J) ENDDO E

12、NDDO ENDIFENDDO RETURN END!*符號(hào)函數(shù)子程序*！FUNCTION SGN(X)REAL(8) XIF(X0) THENSGN=1ELSE IF(X=0) THEN Y(1,M)=(-B-SQRT(D)/2 Y(1,M-1)=(-B+SQRT(D)/2ELSEIF(D0) THEN Y(1,M)=-B/2 Y(1,M-1)=-B/2 Y(2,M)=-SQRT(-D)/2 Y(2,M-1)=-SQRT(-D)/2ENDIFRETURNEND!*計(jì)算Mk，Ak+1子函數(shù)*！SUBROUTINE CALM(A,M,N)DIMENSION A(N,N),MK(M,M),X(M,

13、M),QK(M,M),RK(M,M),S1(M,M),S2(M,M),QKT(M,M)REAL(8) A,MK,X,QK,RK,QKTREAL(8) S0,S1,S2DO I=1,M DO J=1,M IF(I=J) THEN X(I,J)=1 ELSE X(I,J)=0 ENDIF ENDDOENDDO S=A(M-1,M-1)+A(M,M)T=A(M-1,M-1)*A(M,M)-A(M,M-1)*A(M-1,M)DO I=1,M DO J=1,M S0=0 DO K=1,M S0=S0+A(I,K)*A(K,J) ENDDO MK(I,J)=S0-S*A(I,J)+T*X(I,J) END

14、DOENDDO!對(duì)Mk做QR分解CALL QRD(MK,M,QK,RK) DO I=1,M DO J=1,M QKT(I,J)=QK(J,I) ENDDOENDDODO I=1,M DO J=1,M S1(I,J)=0 DO K=1,M S1(I,J)=S1(I,J)+QKT(I,K)*A(K,J) ENDDO ENDDOENDDOA=S1DO I=1,M DO J=1,M S2(I,J)=0 DO K=1,M S2(I,J)=S2(I,J)+A(I,K)*QK(K,J) ENDDO ENDDOENDDOA=S2RETURNEND !*QR分解子程序*！SUBROUTINE QRD(A,N,Q

15、,R)DIMENSION A(N,N),AT(N,N),Q(N,N),U(N),W(N),P(N),R(N,N)REAL(8) A,AT,Q,U,W,P,RREAL(8) DR,S0,CR,HR,S1,S2DO I=1,N DO J=1,N IF(I=J) THEN Q(I,J)=1 ELSE Q(I,J)=0 ENDIF ENDDOENDDODO L=1,N-1 JUDGE=0 DO I=L+1,N IF(A(I,L)/=0) THEN JUDGE=1 EXIT ENDIF !A(I,L)中有一個(gè)不為零,判斷條件為真，跳出循環(huán)轉(zhuǎn) ENDDO IF(JUDGE=0) THEN Q=Q A=A

16、CYCLE !A(I,L)全為零，結(jié)束本循環(huán)，進(jìn)入下一個(gè) ELSE IF(JUDGE/=0) THEN !計(jì)算DR S0=0 DO I=L,N S0=S0+A(I,L)*2 ENDDO DR=SQRT(S0) !計(jì)算CR IF(A(L,L)=0)THEN CR=DR ELSE CR=-SGN(A(L,L)*DR ENDIF !計(jì)算HR HR=CR*2-CR*A(L,L) !給u賦值 DO I=1,N IF(IL) THEN U(I)=A(I,L) ENDIF ENDDO !計(jì)算W DO I=1,N S1=0 DO J=1,N S1=S1+Q(I,J)*U(J) ENDDO W(I)=S1 EN

17、DDO !計(jì)算Q（r+1） DO I=1,N DO J=1,N Q(I,J)=Q(I,J)-W(I)*U(J)/HR ENDDO ENDDO !計(jì)算P DO I=1,N DO J=1,N AT(I,J)=A(J,I) ENDDO ENDDO DO I=1,N S2=0 DO J=1,N S2=S2+AT(I,J)*U(J) ENDDO P(I)=S2/HR ENDDO !計(jì)算A（r+1） DO I=1,N DO J=1,N A(I,J)=A(I,J)-U(I)*P(J) ENDDO ENDDO ENDIFENDDOQ=QR=ARETURN END !*運(yùn)用反冪法求解矩陣A實(shí)特征值的特征向量*！

18、 SUBROUTINE INPOVERMETHOD(A,N,Y)DIMENSION A(N,N),U(N),Y(N),U1(N,N),L1(N,N)REAL(8) E,Z,Z1,Z2,S1,S2,BREAL(8) A,U,Y,U1,L1DO I=1,N U(I)=1ENDDO !任取非零向量UCALL DETA(A,N,U1,L1)Z2=EIZ1=1.0E=1K=1DO WHILE (E1E-12) S1=0 DO I=1,N S1=S1+U(I)*2 ENDDO B=SQRT(S1) !1 DO I=1,N Y(I)=U(I)/B ENDDO !2 CALL DOOLITTLE(U1,L1,

19、Y,N,U) !3利用DOOLITTLE分解法法求解Au=y S2=0 DO I=1,N S2=S2+Y(I)*U(I) ENDDO Z1=Z2 Z2=S2 !4 E=ABS(1/Z2-1/Z1)/ABS(1/Z2) !判斷是否滿足精度 K=K+1ENDDORETURN ENDSUBROUTINE DOOLITTLE(U,L,B1,N,X)DIMENSION B(N),U(N,N),X(N),Y(N),B1(N)REAL(8) L(N,N)REAL(8) B,U,X,Y,B1REAL(8) S1,S2,S3,S4B=B1Y(1)=B(1)DO I=2,NS3=0DO M=1,I-1S3=S3+

20、L(I,M)*Y(M)ENDDOY(I)=B(I)-S3ENDDOX(N)=Y(N)/U(N,N)DO I=N-1,1,-1S4=0DO M=I+1,NS4=S4+U(I,M)*X(M)ENDDOX(I)=(Y(I)-S4)/U(I,I)ENDDORETURNENDSUBROUTINE DETA(A1,N,U,L)DIMENSION A(N,N),U(N,N),A1(N,N)REAL(8) L(N,N)REAL(8) X,S1,S2REAL(8) A,U,A1X=1A=A1!對(duì)矩陣A進(jìn)行Doolittle分解DO K=1,NDO J=K,NS1=0DO M=1,K-1S1=S1+L(K,M)*

21、U(M,J)ENDDOU(K,J)=A(K,J)-S1A(K,J)=U(K,J)ENDDOIF (K=N) THENEXITELSEDO I=K+1,NS2=0DO M=1,K-1S2=S2+L(I,M)*U(M,K)ENDDOL(I,K)=(A(I,K)-S2)/U(K,K)A(I,K)=L(I,K)ENDDOENDIFENDDORETURNEND三、計(jì)算結(jié)果矩陣A為：-0.8945217728615E+00 0.7833269238472E+00 0.8912073969841E+00 0.9635581970215E+00 0.9974949955940E+00 0.9916648268

22、700E+00 0.9463000893593E+00 0.8632094264030E+00 0.7457050681114E+00 0.5984721183777E+00 0.9320390820503E+00 -0.4671458303928E+00 0.9995735883713E+00 0.9738476276398E+00 0.9092974066734E+00 0.8084963560104E+00 0.6754630804062E+00 0.5155014395714E+00 0.3349879682064E+00 0.1411200016737E+00 0.991664826

23、8700E+00 0.9463000893593E+00 0.1444353342056E+01 0.7457052469254E+00 0.5984721183777E+00 0.4273798465729E+00 0.2392492294312E+00 0.4158075898886E-01 -0.1577458828688E+00 -0.3507832288742E+00 0.8084963560104E+00 0.6754630804062E+00 0.5155014395714E+00 -0.1232861518860E+01 0.1411200016737E+00 -0.58374

24、19256568E-01 -0.2555412054062E+00 -0.4425203502178E+00 -0.6118580698967E+00 -0.7568024992943E+00 0.4273798465729E+00 0.2392492294312E+00 0.4158075898886E-01 -0.1577456444502E+00 0.6727060768753E-02 -0.5298361778259E+00 -0.6877662539482E+00 -0.8182770609856E+00 -0.9161660075188E+00 -0.9775301218033E+

25、00 -0.5837419256568E-01 -0.2555412054062E+00 -0.4425203502178E+00 -0.6118578314781E+00 -0.7568024992943E+00 0.1224942922592E+01 -0.9516021013260E+00 -0.9936909675598E+00 -0.9961646199226E+00 -0.9589242935181E+00 -0.5298361778259E+00 -0.6877662539482E+00 -0.8182770609856E+00 -0.9161660075188E+00 -0.9

26、775301218033E+00 -0.9999232292175E+00 -0.1448488712311E+01 -0.9258147478104E+00 -0.8322673439980E+00 -0.7055402994156E+00 -0.8715756535530E+00 -0.9516021013260E+00 -0.9936909675598E+00 -0.9961646199226E+00 -0.9589242935181E+00 -0.8834547400475E+00 -0.7727644443512E+00 0.4799310266972E+00 -0.46460202

27、33631E+00 -0.2794154882431E+00 -0.9999232292175E+00 -0.9824525713921E+00 -0.9258147478104E+00 -0.8322673439980E+00 -0.7055402994156E+00 -0.5506857037544E+00 -0.3738765716553E+00 -0.1821625977755E+00 0.8836100697517E+00 0.2151199877262E+00 -0.8834547400475E+00 -0.7727644443512E+00 -0.6312667131424E+0

28、0 -0.4646020233631E+00 -0.2794154882431E+00 -0.8308959007263E-01 0.1165492981672E+00 0.3115412592888E+00 0.4941135048866E+00 -0.1519940495491E+01 擬上三角化后矩陣A（n-1）為：-0.8945217728615E+00 -0.9933137953325E-01 -0.1099831636616E+01 -0.7665050102665E+00 0.1707594469998E+00 -0.1934882894244E+01 -0.8390134390

29、705E-01 0.9132556516637E+00 -0.6407974994717E+00 0.1946715019429E+00-0.2347878320167E+01 0.2372058080829E+01 0.1827998576666E+01 0.3266566437117E+00 0.2082368675377E+00 0.2088987417740E+01 0.1847851643235E+00 -0.1263014392786E+01 0.6790698873535E+00 -0.4672130067887E+000.3226931170760E-07 0.17359545

30、35701E+01 -0.1165022873713E+01 -0.1246745323208E+01 -0.6298232266879E+00 -0.1984820078643E+01 0.2975743603486E+00 0.6339292078743E+00 -0.1308509012927E+00 0.3040284203485E+000.1423586330828E-07 0.9209743857214E-09 -0.1292937522755E+01 -0.1126240301657E+01 0.1190782136896E+01 -0.1308773854722E+01 0.1

31、860152393829E+00 0.4236729462899E+00 -0.1019591572985E+00 0.1943652598126E+00-0.1604833588908E-08 -0.2121194294804E-07 0.8533227584783E-09 0.1577711603212E+01 0.8169354953886E+00 0.4461530106988E+00 -0.4365089732955E-01 -0.4665975603472E+00 0.2941230066159E+00 -0.1034409078751E+00-0.3477340203987E-0

32、7 0.4951800147030E-08 -0.1163098578700E-08 0.6139091525187E-08 -0.7728980255203E+00 -0.1601026529821E+01 -0.2912710054588E+00 -0.2434335314476E+00 0.6736293096855E+00 0.2624776772240E+00-0.3470636131521E-07 0.5153701712282E-07 0.5466085271163E-09 0.4042739259524E-07 -0.2172883892180E-08 -0.729678498

33、8040E+00 -0.7963940110270E-02 0.9710720841706E+00 -0.1298962616680E+00 0.2780184160906E-010.2824279413454E-07 0.1552714184100E-07 -0.1493776248626E-08 0.5462159606108E-08 -0.6804315955054E-09 -0.2605399790245E-07 0.7945528832850E+00 -0.4525155066528E+00 0.5048915772314E+00 -0.1211208421619E+00-0.856

34、0265006517E-08 -0.1746383679003E-07 0.1238687231355E-08 0.2479480585694E-07 -0.9877219097781E-09 -0.1138665066640E-07 0.1651955742740E-07 0.7039926664890E+00 0.1267533554989E+00 -0.3714708484034E+00-0.1181033699336E-08 0.3402393384483E-07 0.2721445674400E-09 0.9979965496699E-07 -0.4011949378052E-08

35、-0.7236569816358E-08 -0.1149301577382E-07 -0.5885757992097E-09 -0.4919593043220E+00 0.4081502835024E+00對(duì)矩陣A（n-1）實(shí)行QR方法迭代結(jié)束后所得Q為：-0.3560272815910E+00 0.4439874197723E+00 -0.6935938843844E+00 0.6597508877265E-01 0.3701042113892E+00 0.1873679534840E+00 -0.1616901005278E-01 0.1142210689327E+00 0.4846176

36、222781E-01 -0.5435299347356E-01-0.9344755613513E+00 -0.1691554621234E+00 0.2642533921785E+00 -0.2513595147466E-01 -0.1410065819368E+00 -0.7138558660925E-01 0.6160244663687E-02 -0.4351726812555E-01 -0.1846352196332E-01 0.2070803053804E-010.1284346080176E-07 -0.8799213605304E+00 -0.4007708824585E+00 0

37、.3812159427358E-01 0.2138528122276E+00 0.1082645332603E+00 -0.9342714756167E-02 0.6599896425979E-01 0.2800204178411E-01 -0.3140612519156E-010.5665994801374E-08 -0.6731378914494E-08 -0.5371036846272E+00 -0.1260095704391E+00 -0.7068830118277E+00 -0.3578646320818E+00 0.3088206840900E-01 -0.218157293586

38、5E+00 -0.9255984012850E-01 0.1038118582492E+00-0.6387374319990E-09 0.1145813249974E-07 -0.1078228631015E-08 0.9887789458786E+00 -0.1266091196147E+00 -0.6409675331588E-01 0.5531265008227E-02 -0.3907396459740E-01 -0.1657835486362E-01 0.1859359513712E-01-0.1384011007393E-07 0.1279221992471E-07 -0.92625

39、58908976E-08 0.7942414467386E-08 0.5307480849561E+00 -0.6851608956975E+00 0.5912622247311E-01 -0.4176799031642E+00 -0.1772133811242E+00 0.1987561902979E+00-0.1381342729472E-07 -0.1085041551280E-07 -0.6302351300011E-08 0.3663011930258E-07 0.1752482576120E-07 -0.5886044488414E+00 -0.9581624758180E-01

40、0.6768661964240E+00 0.2871810369554E+00 -0.3220919956398E+000.1124087252576E-07 -0.2029877134119E-07 0.7446927387208E-08 0.4535651412684E-08 -0.1010647131559E-07 -0.3402353082044E-07 -0.9929513420376E+00 -0.9993987729170E-01 -0.4240249703029E-01 0.4755713950966E-01-0.3407058355014E-08 0.126190594822

41、2E-07 -0.2542051664776E-08 0.1266690552996E-07 0.1278109511219E-07 -0.1144195534285E-09 -0.3032310997717E-07 0.5375799694997E+00 -0.5611567807748E+00 0.6293733739071E+00-0.4700614677014E-09 -0.1672634638944E-07 0.1437403000058E-08 0.6833811586949E-07 0.2558255838771E-07 0.6874219112542E-08 0.8036560

42、338531E-08 0.1656475356181E-07 0.7463992503745E+00 0.6654984290293E+00對(duì)矩陣A（n-1）實(shí)行QR方法迭代結(jié)束后所得R為：0.2512509066339E+01 -0.2181265603313E+01 -0.1316649950576E+01 -0.3235597877207E-01 -0.2553872765746E+00 -0.1263236593769E+01 -0.1428060347911E+00 0.8551121499445E+00 -0.4064328268943E+00 0.3672907719171E+0

43、0-0.2109953755478E-15 -0.1972851940621E+01 0.2276011662676E+00 0.7014635294177E+00 0.5947855446945E+00 0.5340582895718E+00 -0.3303506185987E+00 0.6131194880252E-01 -0.2842358922417E+00 -0.1020577798422E+000.3296154263567E-15 0.0000000000000E+00 0.2407240074437E+01 0.1722530351127E+01 -0.450569066201

44、0E+00 0.3392450326905E+01 -0.1121450352289E+00 -0.1448801049644E+01 0.7311036152624E+00 -0.4847256225157E+00-0.3135322751998E-16 0.0000000000000E+00 0.0000000000000E+00 0.1595616091532E+01 0.6397404386507E+00 0.3502374325905E+00 -0.6543692816387E-01 -0.3985830660960E+00 0.2393364523032E+00 -0.905946

45、8782884E-01-0.1758839859323E-15 0.0000000000000E+00 0.0000000000000E+00 0.3763787648836E-15 -0.1456242740813E+01 -0.1416207451897E+01 -0.2740269988274E+00 0.2820470970623E+00 0.3146397887171E-01 0.2179587784814E+00-0.8904254938570E-16 0.0000000000000E+00 0.0000000000000E+00 0.1905444662310E-15 -0.17

46、95055574840E-15 0.1239675436578E+01 0.1437900209104E+00 -0.1965884558516E+00 -0.5501589478330E+00 -0.1563869764441E+000.7683972019840E-17 0.0000000000000E+00 0.0000000000000E+00 -0.1644310936739E-16 0.1549050548437E-16 0.0000000000000E+00 -0.8001931693942E+00 0.3239215548033E+00 -0.4348124850648E+00 0.1296865621794E+00-0.5428108139367E-16 0.0000000000000E+00 0.0000000000000E+00 0.1161575150373E-15 -0.1094281165003E-15 0.0000000000000E+00 0.0000000000000E+00 0.1309558979373E+01 -0.4522318426591E+00 -0.2541313