北航数值分析报告大作业第三题(fortran)

“数值分析“计算实习大作业第三题
——SY1415215
孔维鹏
一、计算说明
1、将x i=0.08i，y j=0.5+0.05j分别代入方程组（A.3）得到关于t，u，v，w的的方程组，调用离散牛顿迭代子函数求出与x i，y j对应的t i，u j。

2、调用分片二次代数插值子函数在点(t i,u j)处插值得到z(x i,y j)=f(x i,y j)，得到数表(x i,y j,f(x i,y j))。

3、对于k=1,2,3,4⋯，分别调用最小二乘拟合子函数计算系数矩阵c rs及误差σ，直到满足精度，即求得最小的k值及系数矩阵c rs。

4、将x i∗=0.1i，y j∗=0.5+0.2j分别代入方程组（A.3）得到关于t∗，u∗，v∗，w∗的的方程组，调用离散牛顿迭代子函数求出与x i∗，y j∗对应的t i∗，u j∗，调用分片二次代数插值子函数在点(t i∗,u j∗)处插值得到z∗(x i∗,y j∗)=f(x i∗,y j∗)；调用步骤3中求得的系数矩阵c rs求得p(x i∗,y j∗)，打印数表(x i∗,y j∗,f(x i∗,y j∗),p(x i∗,y j∗))。

二、源程序（FORTRAN）
PROGRAM SY1415215
DIMENSION X(11),Y(21),T(6),U(6),Z(6,6),UX(11,21),TY(11,21),FXY(11,21),C(6,6) DIMENSION X1(8),Y1(5),FXY1(8,5),PXY1(8,5),UX1(8,5),TY1(8,5)
REAL(8) X,Y,T,U,Z,FXY,UX,TY,C,E,X1,Y1,FXY1,PXY1,UX1,TY1
OPEN (1,FILE='第三题计算结果.TXT')
DO I=1,11
X(I)=0.08*(I-1)
ENDDO
DO I=1,21
Y(I)=0.5+0.05*(I-1)
ENDDO
!*****求解非线性方程组，得到z=f（t，u）的函数*******
DO I=1,11
DO J=1,21
CALL DISNEWTON_NONLINEAR(X(I),Y(J),UX(I,J),TY(I,J)) ENDDO
ENDDO
!*************分片二次插值得到z=f（x，y）***********
DO I=1,11
DO J=1,21
CALL INTERPOLATION(UX(I,J),TY(I,J),FXY(I,J))
ENDDO
ENDDO
WRITE (1,"('数表(x,y,f(x,y)):')")
WRITE (1,"(3X,'X',7X,'Y',10X,'F(X,Y)')")
DO I=1,11
DO J=1,21
WRITE(1,'(1X,F5.2,2X,F5.3,2X,E20.13)') X(I),Y(J),FXY(I,J) ENDDO
WRITE (1,"('')")
ENDDO
!***********最小二乘拟合得到P（x，y）**************
N=11
M=21
WRITE (1,'(" ","K和σ分别为：")')
DO K=1,20
CALL LSFITTING(X,Y,FXY,C,N,M,K,K,E)
WRITE (1,'(I3,2X,E20.13)') K-1,E
IF(E<10E-7) EXIT
ENDDO
WRITE(1,'(" ")')
WRITE(1,'("系数矩阵Crs（按行）为：")')
DO I=1,K
DO J=1,K
WRITE (1,'(E20.13,2X,\)') C(I,J)
ENDDO
WRITE (1,"('')")
WRITE (*,"('')")
ENDDO
DO I=1,8
X1(I)=0.1*I
ENDDO
DO J=1,5
Y1(J)=0.5+0.2*J
ENDDO
DO I=1,8
DO J=1,5
CALL DISNEWTON_NONLINEAR(X1(I),Y1(J),UX1(I,J),TY1(I,J))
ENDDO
ENDDO
DO I=1,8
DO J=1,5
CALL INTERPOLATION(UX1(I,J),TY1(I,J),FXY1(I,J))
ENDDO
ENDDO
PXY1=0
DO I=1,8
DO J=1,5
DO II=1,K
DO JJ=1,K
PXY1(I,J)=PXY1(I,J)+C(II,JJ)*(X1(I)**(II-1))*(Y1(J)**(JJ-1)) ENDDO
ENDDO
ENDDO
ENDDO
WRITE(1,'(" ")')
WRITE(1,'("数表（x,y,f(x,y),p(x,y)):")')
WRITE(1,"(2X,'X',6X,'Y',12X,'F(X,Y)',14X,'P(X,Y)')")
DO I=1,8
DO J=1,5
WRITE(1,'(F5.3,2X,F5.3,2X,E20.13,2X,E20.13)') X1(I),Y1(J),FXY1(I,J),PXY1(I,J) ENDDO
WRITE (1,"('')")
ENDDO
CLOSE (1)
END
!***********用离散牛顿法求解非线性方程组****************
SUBROUTINE DISNEWTON_NONLINEAR(X1,Y1,U,T)
PARAMETER (N=4)
REAL EPS !EPS为迭代精度，M为最大迭代次数
DIMENSION X(N),H(N),Y(N),JA(N,N),E(N),XK(N)
REAL(8) JA,X,H,Y,E,XK,U,T,V,W,X1,Y1,E1,E2
F1(T,U,V,W)=0.5*COS(T)+U+V+W-X1-2.67
F2(T,U,V,W)=T+0.5*SIN(U)+V+W-Y1-1.07
F3(T,U,V,W)=0.5*T+U+COS(V)+W-X1-3.74
F4(T,U,V,W)=T+0.5*U+V+SIN(W)-Y1-0.79
EPS=10E-12
M=100
X=1.0
DO K=1,M
H=1
!计算Y=F（x）
Y(1)=F1(X(1),X(2),X(3),X(4))
Y(2)=F2(X(1),X(2),X(3),X(4))
Y(3)=F3(X(1),X(2),X(3),X(4))
Y(4)=F4(X(1),X(2),X(3),X(4))
!计算JA（N,N）
E=0.0
DO I=1,N
DO J=1,N
DO JJ=1,N
IF(JJ==J) THEN
E(JJ)=X(JJ)+H(JJ)
ELSE
E(JJ)=X(JJ)
ENDIF
ENDDO
IF(I==1) THEN
JA(I,J)=(F1(E(1),E(2),E(3),E(4))-F1(X(1),X(2),X(3),X(4)))/H(J) ELSEIF(I==2) THEN
JA(I,J)=(F2(E(1),E(2),E(3),E(4))-F2(X(1),X(2),X(3),X(4)))/H(J) ELSEIF(I==3) THEN
JA(I,J)=(F3(E(1),E(2),E(3),E(4))-F3(X(1),X(2),X(3),X(4)))/H(J) ELSEIF(I==4) THEN
JA(I,J)=(F4(E(1),E(2),E(3),E(4))-F4(X(1),X(2),X(3),X(4)))/H(J) ENDIF
ENDDO
ENDDO
!求解线性方程组
CALL GAUSS(JA,XK,-Y,N)
!判断精度
CALL NORM(XK,N,E1)
CALL NORM(X,N,E2)
IF(E1/E2<=EPS) THEN
T=X(1)
U=X(2)
EXIT
ELSE
DO I=1,N
X(I)=X(I)+XK(I)
ENDDO
ENDIF
ENDDO
RETURN
END
!**********列主元高斯消去法求解线性方程组********* SUBROUTINE GAUSS(A,X,B,N)
DIMENSION A(N,N),B(N),X(N),T(N,N),TB(N)
REAL M(N,N)
REAL(8) A,B,X,T
!消元过程
DO K=1,N-1
TA=A(K,K)
TL=K
DO L=K+1,N
IF ((A(L,K)>TA).OR.(A(L,K)==TA)) THEN
TA=A(L,K)
TL=L
DO J=K,N
T(K,J)=A(K,J)
A(K,J)=A(TL,J)
A(TL,J)=T(K,J)
ENDDO
TB(K)=B(K)
B(K)=B(TL)
B(TL)=TB(K)
ENDIF
ENDDO
DO I=K+1,N
M(I,K)=A(I,K)/A(K,K)
A(I,K)=0
DO J=K+1,N
A(I,J)=A(I,J)-M(I,K)*A(K,J)
ENDDO
B(I)=B(I)-M(I,K)*B(K)
ENDDO
ENDDO
!回代过程
X(N)=B(N)/A(N,N)
DO K=N-1,1,-1
S=0.0
DO J=K+1,N
S=S+A(K,J)*X(J)
ENDDO
X(K)=(B(K)-S)/A(K,K)
ENDDO
RETURN
END
!***********求向量的无穷数************ SUBROUTINE NORM(X,N,A)
DIMENSION X(N)
REAL(8) X,A
A=ABS(X(1))
DO I=2,N
IF(ABS(X(I))>ABS(X(I-1))) THEN
A=ABS(X(I))
ENDIF
ENDDO
RETURN
END
!**************分片二次代数插值************** SUBROUTINE INTERPOLATION(U,V,W) PARAMETER (N=6,M=6)
DIMENSION X(N),Y(M),Z(M,N),LK(3),LR(3)
REAL(8) X,Y,Z,H,T
REAL(8) U,V,W,LK,LR !U,V分别为插值点处的坐标，W为插值结果INTEGER R
!**********************数据赋值********************** DATA Y/0.0,0.2,0.4,0.6,0.8,1.0/
DATA X/0.0,0.4,0.8,1.2,1.6,2.0/
DATA Z/-0.5,-0.42,-0.18,0.22,0.78,1.5,&
&-0.34,-0.5,-0.5,-0.34,-0.02,0.46,&
&0.14,-0.26,-0.5,-0.58,-0.5,-0.26,&
&0.94,0.3,-0.18,-0.5,-0.66,-0.66,&
&2.06,1.18,0.46,-0.1,-0.5,-0.74,&
&3.5,2.38,1.42,0.62,-0.02,-0.5/
H=0.4
T=0.2
!******************计算K,R*************************
IF(U<=X(2)+H/2) THEN
K=2
ELSEIF(U>X(N-1)-H/2) THEN
K=N-1
ELSE
DO I=3,N-2
IF((U>X(I)-H/2).AND.(U<=X(I)+H/2)) THEN
K=I
ENDIF
ENDDO
ENDIF
IF(V<=Y(2)+T/2) THEN
R=2
ELSEIF(V>Y(M-1)-T/2) THEN
R=M-1
ELSE
DO J=3,M-2
IF((V>Y(J)-T/2).AND.(V<=Y(J)+T/2)) THEN
R=J
ENDIF
ENDDO
ENDIF
I=K
J=R
LK(1)=(U-X(I))*(U-X(I+1))/(X(I-1)-X(I))/(X(I-1)-X(I+1))
LK(2)=(U-X(I-1))*(U-X(I+1))/(X(I)-X(I-1))/(X(I)-X(I+1)) LK(3)=(U-X(I))*(U-X(I-1))/(X(I+1)-X(I))/(X(I+1)-X(I-1)) LR(1)=(V-Y(J))*(V-Y(J+1))/(Y(J-1)-Y(J))/(Y(J-1)-Y(J+1)) LR(2)=(V-Y(J-1))*(V-Y(J+1))/(Y(J)-Y(J-1))/(Y(J)-Y(J+1)) LR(3)=(V-Y(J))*(V-Y(J-1))/(Y(J+1)-Y(J))/(Y(J+1)-Y(J-1))
W=0
DO K=1,3
DO R=1,3
W=W+LK(K)*LR(R)*Z(J+R-2,I+K-2)
ENDDO
ENDDO
RETURN
END
!*******************最小二乘拟合子函数************** SUBROUTINE LSFITTING(X,Y,Z,A,N,M,P,Q,DT1)
INTEGER P,Q
DIMENSION X(N),Y(M),Z(N,M),A(P,Q)
DIMENSION APX(20),APY(20),BX(20),BY(20),U(20,20),V(20,M) DIMENSION T(20),T1(20),T2(20)
REAL(8) X,Y,Z,A,DT1
DO I=1,P
DO J=1,Q
A(I,J)=0.0
ENDDO
ENDDO
IF(P>N) P=N
IF(P>20) P=20
IF(Q>M) Q=M
IF(Q>20) Q=20
XX=0
YY=0
D1=N
APX(1)=0.0
DO I=1,N
APX(1)=APX(1)+X(I)
ENDDO
APX(1)=APX(1)/D1
DO J=1,M
V(1,J)=0.0
DO I=1,N
V(1,J)=V(1,J)+Z(I,J)
ENDDO
V(1,J)=V(1,J)/D1
ENDDO
IF(P>1) THEN
D2=0.0
APX(2)=0.0
DO I=1,N
G=X(I)-APX(1)
D2=D2+G*G
APX(2)=APX(2)+(X(I)-XX)*G*G ENDDO
APX(2)=APX(2)/D2
BX(2)=D2/D1
DO J=1,M
V(2,J)=0.0
DO I=1,N
G=X(I)-APX(1)
V(2,J)=V(2,J)+Z(I,J)*G
ENDDO
V(2,J)=V(2,J)/D2
ENDDO
D1=D2
ENDIF
DO K=3,P
D2=0.0
APX(K)=0.0
DO J=1,M
V(K,J)=0.0
ENDDO
DO I=1,N
G1=1.0
G2=X(I)-APX(1)
DO J=3,K
G=(X(I)-APX(J-1))*G2-BX(J-1)*G1 G1=G2
G2=G
ENDDO
D2=D2+G*G
APX(K)=APX(K)+X(I)*G*G
DO J=1,M
V(K,J)=V(K,J)+Z(I,J)*G
ENDDO
ENDDO
DO J=1,M
V(K,J)=V(K,J)/D2
ENDDO
APX(K)=APX(K)/D2
BX(K)=D2/D1
D1=D2
ENDDO
D1=M
APY(1)=0.0
DO I=1,M
APY(1)=APY(1)+Y(I)
ENDDO
APY(1)=APY(1)/D1
DO J=1,P
U(J,1)=0.0
DO I=1,M
U(J,1)=U(J,1)+V(J,I) ENDDO
U(J,1)=U(J,1)/D1
ENDDO
IF(Q>1)THEN
D2=0.0
APY(2)=0.0
DO I=1,M
G=Y(I)-APY(1)
D2=D2+G*G
APY(2)=APY(2)+(Y(I))*G*G ENDDO
APY(2)=APY(2)/D2
BY(2)=D2/D1
DO J=1,P
U(J,2)=0.0
DO I=1,M
G=Y(I)-APY(1)
U(J,2)=U(J,2)+V(J,I)*G
ENDDO
U(J,2)=U(J,2)/D2
ENDDO
D1=D2
ENDIF
DO K=3,Q
D2=0.0
APY(K)=0.0
DO J=1,P
U(J,K)=0.0
ENDDO
DO I=1,M
G1=1.0
G2=Y(I)-APY(1)
DO J=3,K
G=(Y(I)-APY(J-1))*G2-BY(J-1)*G1 G1=G2
G2=G
ENDDO
D2=D2+G*G
APY(K)=APY(K)+Y(I)*G*G
DO J=1,P
U(J,K)=U(J,K)+V(J,I)*G
ENDDO
ENDDO
DO J=1,P
U(J,K)=U(J,K)/D2
ENDDO
APY(K)=APY(K)/D2
BY(K)=D2/D1
D1=D2
ENDDO
V(1,1)=1.0
V(2,1)=-APY(1)
V(2,2)=1.0
DO I=1,P
DO J=1,Q
A(I,J)=0.0
ENDDO
ENDDO
DO I=3,Q
V(I,I)=V(I-1,I-1)
V(I,I-1)=-APY(I-1)*V(I-1,I-1)+V(I-1,I-2)
IF(I>=4) THEN
DO K=I-2,2,-1
V(I,K)=-APY(I-1)*V(I-1,K)+V(I-1,K-1)-BY(I-1)*V(I-2,K) ENDDO
ENDIF
V(I,1)=-APY(I-1)*V(I-1,1)-BY(I-1)*V(I-2,1)
ENDDO
DO I=1,P
IF(I==1) THEN
T(1)=1.0
T1(1)=1.0
ELSEIF(I==2) THEN
T(1)=-APX(1)
T(2)=1.0
T2(1)=T(1)
T2(2)=T(2)
ELSE
T(I)=T2(I-1)
T(I-1)=-APX(I-1)*T2(I-1)+T2(I-2)
IF(I>=4) THEN
DO K=I-2,2,-1
T(K)=-APX(I-1)*T2(K)+T2(K-1)-BX(I-1)*T1(K)
ENDDO
ENDIF
T(1)=-APX(I-1)*T2(1)-BX(I-1)*T1(1)
T2(I)=T(I)
DO K=I-1,1,-1
T1(K)=T2(K)
T2(K)=T(K)
ENDDO
ENDIF
DO J=1,Q
DO K=I,1,-1
DO L=J,1,-1
A(K,L)=A(K,L)+U(I,J)*T(K)*V(J,L)
ENDDO
ENDDO
ENDDO
ENDDO
DT1=0.0
DO I=1,N
X1=X(I)
DO J=1,M
Y1=Y(J)
X2=1.0
DD=0.0
DO K=1,P
G=A(K,Q)
DO KK=Q-1,1,-1
G=G*Y1+A(K,KK)
ENDDO
G=G*X2
DD=DD+G
X2=X2*X1
ENDDO
DT=DD-Z(I,J)
DT1=DT1+DT*DT
ENDDO
ENDDO
RETURN
END
三、计算结果
数表(x,y,f(x,y)):
X Y UX TY F(X,Y) 0.00 0.500 1.345 0.243 0.17E+00
0.00 0.550 1.322 0.269 0.66E+00
0.00 0.600 1.299 0.295 0.35E+00
0.00 0.650 1.277 0.322 0.94E+00
0.00 0.700 1.255 0.350 0.30E-02
0.00 0.750 1.235 0.377 -0.87E-01
0.00 0.800 1.215 0.406 -0.58E+00
0.00 0.850 1.196 0.434 -0.72E+00
0.00 0.900 1.177 0.463 -0.54E+00
0.00 0.950 1.159 0.492 -0.86E+00
0.00 1.050 1.125 0.550 -0.74E+00 0.00 1.100 1.109 0.580 -0.06E+00 0.00 1.150 1.093 0.609 -0.00E+00 0.00 1.200 1.079 0.639 -0.18E+00 0.00 1.250 1.064 0.669 -0.52E+00 0.00 1.300 1.050 0.699 -0.19E+00 0.00 1.350 1.037 0.729 -0.48E+00 0.00 1.400 1.024 0.759 -0.68E+00 0.00 1.450 1.011 0.790 -0.52E+00 0.00 1.500 1.000 0.820 -0.29E+00
0.08 0.500 1.415 0.228 0.67E+00 0.08 0.550 1.391 0.253 0.08E+00 0.08 0.600 1.368 0.279 0.02E+00 0.08 0.650 1.346 0.306 0.47E+00 0.08 0.700 1.325 0.333 0.57E+00 0.08 0.750 1.304 0.360 0.48E-01 0.08 0.800 1.284 0.388 -0.73E-01 0.08 0.850 1.265 0.416 -0.16E+00 0.08 0.900 1.246 0.444 -0.29E+00 0.08 0.950 1.229 0.473 -0.36E+00 0.08 1.000 1.211 0.502 -0.08E+00 0.08 1.050 1.194 0.531 -0.29E+00 0.08 1.100 1.178 0.560 -0.78E+00 0.08 1.150 1.163 0.589 -0.93E+00 0.08 1.200 1.148 0.619 -0.44E+00 0.08 1.250 1.133 0.649 -0.92E+00 0.08 1.300 1.119 0.679 -0.71E+00
0.08 1.400 1.093 0.739 -0.37E+00 0.08 1.450 1.080 0.769 -0.83E+00 0.08 1.500 1.068 0.799 -0.92E+00
0.16 0.500 1.483 0.214 0.31E+00 0.16 0.550 1.460 0.239 0.64E+00 0.16 0.600 1.437 0.264 0.91E+00 0.16 0.650 1.414 0.290 0.06E+00 0.16 0.700 1.393 0.316 0.70E+00 0.16 0.750 1.372 0.343 0.59E+00 0.16 0.800 1.352 0.370 0.12E+00 0.16 0.850 1.333 0.398 0.77E-02 0.16 0.900 1.315 0.426 -0.83E-01 0.16 0.950 1.297 0.454 -0.58E+00 0.16 1.000 1.279 0.483 -0.20E+00 0.16 1.050 1.262 0.512 -0.11E+00 0.16 1.100 1.246 0.541 -0.74E+00 0.16 1.150 1.231 0.570 -0.09E+00 0.16 1.200 1.216 0.600 -0.59E+00 0.16 1.250 1.201 0.629 -0.66E+00 0.16 1.300 1.187 0.659 -0.71E+00 0.16 1.350 1.174 0.689 -0.32E+00 0.16 1.400 1.161 0.718 -0.56E+00 0.16 1.450 1.148 0.748 -0.31E+00 0.16 1.500 1.136 0.778 -0.75E+00
0.24 0.500 1.551 0.201 0.66E+01 0.24 0.550 1.527 0.225 0.03E+00
0.24 0.650 1.482 0.275 0.64E+00 0.24 0.700 1.460 0.301 0.47E+00 0.24 0.750 1.439 0.327 0.34E+00 0.24 0.800 1.419 0.354 0.24E+00 0.24 0.850 1.400 0.381 0.69E+00 0.24 0.900 1.381 0.409 0.04E-01 0.24 0.950 1.363 0.437 -0.42E-01 0.24 1.000 1.346 0.465 -0.06E+00 0.24 1.050 1.329 0.494 -0.59E+00 0.24 1.100 1.313 0.523 -0.83E+00 0.24 1.150 1.297 0.552 -0.15E+00 0.24 1.200 1.282 0.581 -0.19E+00 0.24 1.250 1.267 0.610 -0.84E+00 0.24 1.300 1.253 0.640 -0.66E+00 0.24 1.350 1.240 0.669 -0.30E+00 0.24 1.400 1.227 0.699 -0.86E+00 0.24 1.450 1.214 0.729 -0.84E+00 0.24 1.500 1.202 0.759 -0.77E+00
0.32 0.500 1.617 0.188 0.28E+01 0.32 0.550 1.593 0.212 0.49E+01 0.32 0.600 1.570 0.236 0.68E+00 0.32 0.650 1.547 0.261 0.75E+00 0.32 0.700 1.526 0.286 0.60E+00 0.32 0.750 1.505 0.312 0.77E+00 0.32 0.800 1.485 0.339 0.05E+00 0.32 0.850 1.466 0.365 0.99E+00 0.32 0.900 1.447 0.393 0.27E+00
0.32 1.000 1.411 0.448 -0.01E-02 0.32 1.050 1.395 0.477 -0.41E-01 0.32 1.100 1.378 0.505 -0.18E+00 0.32 1.150 1.363 0.534 -0.25E+00 0.32 1.200 1.347 0.563 -0.29E+00 0.32 1.250 1.333 0.592 -0.90E+00 0.32 1.300 1.319 0.621 -0.00E+00 0.32 1.350 1.305 0.650 -0.40E+00 0.32 1.400 1.292 0.680 -0.54E+00 0.32 1.450 1.279 0.710 -0.79E+00 0.32 1.500 1.267 0.739 -0.91E+00
0.40 0.500 1.681 0.177 0.91E+01 0.40 0.550 1.658 0.199 0.00E+01 0.40 0.600 1.634 0.223 0.83E+01 0.40 0.650 1.612 0.247 0.02E+01 0.40 0.700 1.591 0.272 0.94E+00 0.40 0.750 1.570 0.298 0.49E+00 0.40 0.800 1.550 0.324 0.94E+00 0.40 0.850 1.530 0.350 0.40E+00 0.40 0.900 1.512 0.377 0.33E+00 0.40 0.950 1.493 0.405 0.99E+00 0.40 1.000 1.476 0.432 0.68E+00 0.40 1.050 1.459 0.460 0.08E-01 0.40 1.100 1.443 0.488 -0.84E-01 0.40 1.150 1.427 0.517 -0.98E+00 0.40 1.200 1.412 0.545 -0.27E+00 0.40 1.250 1.397 0.574 -0.06E+00
0.40 1.350 1.369 0.632 -0.66E+00 0.40 1.400 1.356 0.662 -0.37E+00 0.40 1.450 1.343 0.691 -0.43E+00 0.40 1.500 1.331 0.721 -0.12E+00
0.48 0.500 1.745 0.166 0.69E+01 0.48 0.550 1.721 0.188 0.02E+01 0.48 0.600 1.698 0.211 0.74E+01 0.48 0.650 1.676 0.235 0.40E+01 0.48 0.700 1.654 0.259 0.23E+01 0.48 0.750 1.634 0.284 0.56E+00 0.48 0.800 1.613 0.310 0.28E+00 0.48 0.850 1.594 0.336 0.49E+00 0.48 0.900 1.575 0.363 0.31E+00 0.48 0.950 1.557 0.390 0.66E+00 0.48 1.000 1.539 0.417 0.30E+00 0.48 1.050 1.522 0.444 0.34E+00 0.48 1.100 1.506 0.472 0.07E-01 0.48 1.150 1.490 0.500 -0.62E-01 0.48 1.200 1.475 0.529 -0.45E+00 0.48 1.250 1.460 0.557 -0.86E+00 0.48 1.300 1.446 0.586 -0.39E+00 0.48 1.350 1.432 0.615 -0.22E+00 0.48 1.400 1.419 0.644 -0.67E+00 0.48 1.450 1.406 0.674 -0.55E+00 0.48 1.500 1.394 0.703 -0.14E+00
0.56 0.500 1.808 0.156 0.48E+01
0.56 0.600 1.761 0.200 0.10E+01 0.56 0.650 1.739 0.223 0.68E+01 0.56 0.700 1.717 0.247 0.94E+01 0.56 0.750 1.696 0.272 0.33E+01 0.56 0.800 1.676 0.297 0.11E+00 0.56 0.850 1.657 0.323 0.63E+00 0.56 0.900 1.638 0.349 0.97E+00 0.56 0.950 1.620 0.375 0.52E+00 0.56 1.000 1.602 0.402 0.56E+00 0.56 1.050 1.585 0.429 0.47E+00 0.56 1.100 1.568 0.457 0.20E+00 0.56 1.150 1.552 0.485 0.13E+00 0.56 1.200 1.537 0.513 0.09E-01 0.56 1.250 1.522 0.541 -0.47E-01 0.56 1.300 1.508 0.570 -0.99E+00 0.56 1.350 1.494 0.599 -0.82E+00 0.56 1.400 1.481 0.627 -0.26E+00 0.56 1.450 1.468 0.657 -0.71E+00 0.56 1.500 1.455 0.686 -0.98E+00
0.64 0.500 1.870 0.147 0.74E+01 0.64 0.550 1.846 0.168 0.10E+01 0.64 0.600 1.823 0.190 0.54E+01 0.64 0.650 1.801 0.213 0.42E+01 0.64 0.700 1.779 0.236 0.56E+01 0.64 0.750 1.758 0.260 0.03E+01 0.64 0.800 1.738 0.285 0.42E+01 0.64 0.850 1.718 0.310 0.41E+01
0.64 0.950 1.681 0.362 0.36E+00 0.64 1.000 1.664 0.388 0.18E+00 0.64 1.050 1.646 0.415 0.28E+00 0.64 1.100 1.630 0.443 0.07E+00 0.64 1.150 1.614 0.470 0.66E+00 0.64 1.200 1.598 0.498 0.09E+00 0.64 1.250 1.584 0.526 0.50E-01 0.64 1.300 1.569 0.554 -0.88E-01 0.64 1.350 1.555 0.583 -0.76E+00 0.64 1.400 1.542 0.611 -0.66E+00 0.64 1.450 1.529 0.640 -0.33E+00 0.64 1.500 1.516 0.669 -0.56E+00
0.72 0.500 1.931 0.139 0.94E+01 0.72 0.550 1.907 0.159 0.84E+01 0.72 0.600 1.884 0.181 0.36E+01 0.72 0.650 1.862 0.203 0.40E+01 0.72 0.700 1.840 0.226 0.47E+01 0.72 0.750 1.819 0.249 0.56E+01 0.72 0.800 1.799 0.273 0.19E+01 0.72 0.850 1.779 0.298 0.37E+01 0.72 0.900 1.760 0.323 0.86E+01 0.72 0.950 1.742 0.349 0.76E+00 0.72 1.000 1.724 0.375 0.24E+00 0.72 1.050 1.707 0.402 0.55E+00 0.72 1.100 1.691 0.429 0.97E+00 0.72 1.150 1.675 0.456 0.27E+00 0.72 1.200 1.659 0.484 0.31E+00
0.72 1.250 1.644 0.511 0.51E+00 0.72 1.300 1.630 0.539 0.49E+00 0.72 1.350 1.616 0.568 0.72E-02 0.72 1.400 1.602 0.596 -0.69E-01 0.72 1.450 1.589 0.625 -0.67E+00 0.72 1.500 1.576 0.653 -0.20E+00
0.80 0.500 1.992 0.131 0.31E+01 0.80 0.550 1.968 0.151 0.44E+01 0.80 0.600 1.945 0.172 0.41E+01 0.80 0.650 1.922 0.193 0.45E+01 0.80 0.700 1.900 0.216 0.00E+01 0.80 0.750 1.879 0.239 0.10E+01 0.80 0.800 1.859 0.263 0.16E+01 0.80 0.850 1.840 0.287 0.52E+01 0.80 0.900 1.821 0.312 0.02E+01 0.80 0.950 1.802 0.337 0.38E+01 0.80 1.000 1.784 0.363 0.89E+01 0.80 1.050 1.767 0.389 0.28E+00 0.80 1.100 1.751 0.416 0.09E+00 0.80 1.150 1.734 0.443 0.23E+00 0.80 1.200 1.719 0.470 0.93E+00 0.80 1.250 1.704 0.498 0.15E+00 0.80 1.300 1.689 0.525 0.86E+00 0.80 1.350 1.675 0.553 0.64E+00 0.80 1.400 1.662 0.582 0.74E-01 0.80 1.450 1.649 0.610 -0.37E-01 0.80 1.500 1.636 0.638 -0.81E+00
K和σ分别为：
0 0.93E+03
1 0.61E+01
2 0.92E-02
3 0.53E-03
4 0.16E-05
5 0.77E-07
系数矩阵Crs（按行）为：
0.00E+01 -0.83E+01 0.56E+00 0.97E+00 -0.03E+00 0.70E-01
0.91E+01 -0.99E+00 -0.96E+01 0.17E+01 -0.66E+00 0.10E-01
0.77E+00 0.42E+01 -0.10E+00 -0.81E+00 0.81E+00 -
0.62E-01
-0.25E+00 -0.21E+00 0.97E+00 -0.18E+00 0.49E+00 -
0.63E-01
0.34E+00 -0.56E+00 0.69E-01 0.51E+00 -0.77E-01 0.27E-01
-0.94E-01 0.94E+00 -0.58E+00 0.69E-01 -0.50E-01 0.53E-02
数表（x,y,f(x,y),p(x,y)):
X Y F(X,Y) P(X,Y)
0.100 0.700 0.58E+00 0.05E+00
0.100 1.100 -0.66E+00 -0.26E+00 0.100 1.300 -0.68E+00 -0.31E+00 0.100 1.500 -0.52E+00 -0.49E+00
0.200 0.700 0.54E+00 0.19E+00 0.200 0.900 -0.63E-01 -0.65E-01 0.200 1.100 -0.90E+00 -0.90E+00 0.200 1.300 -0.84E+00 -0.90E+00 0.200 1.500 -0.03E+00 -0.04E+00
0.300 0.700 0.82E+00 0.09E+00 0.300 0.900 0.48E+00 0.11E+00 0.300 1.100 -0.63E+00 -0.88E+00 0.300 1.300 -0.72E+00 -0.96E+00 0.300 1.500 -0.34E+00 -0.84E+00
0.400 0.700 0.79E+00 0.89E+00 0.400 0.900 0.56E+00 0.63E+00 0.400 1.100 -0.83E-01 -0.04E-01 0.400 1.300 -0.72E+00 -0.71E+00 0.400 1.500 -0.85E+00 -0.07E+00
0.500 0.700 0.56E+01 0.92E+01 0.500 0.900 0.51E+00 0.23E+00 0.500 1.100 0.59E+00 0.27E+00 0.500 1.300 -0.53E+00 -0.11E+00 0.500 1.500 -0.67E+00 -0.33E+00
0.600 0.900 0.14E+00 0.75E+00 0.600 1.100 0.19E+00 0.32E+00 0.600 1.300 -0.70E-01 -0.82E-01 0.600 1.500 -0.08E+00 -0.75E+00
0.700 0.700 0.89E+01 0.29E+01 0.700 0.900 0.91E+01 0.11E+01 0.700 1.100 0.60E+00 0.97E+00 0.700 1.300 0.22E-01 0.06E-01 0.700 1.500 -0.53E+00 -0.80E+00
0.800 0.700 0.09E+01 0.06E+01 0.800 0.900 0.32E+01 0.50E+01 0.800 1.100 0.03E+00 0.79E+00 0.800 1.300 0.25E+00 0.50E+00 0.800 1.500 -0.14E+00 -0.28E+00。