利用sirt、art、kaczmarz、奇异值分解方法解地震层析成像方程组
温柔似野鬼°
547次浏览
2020年07月29日 00:36
最佳经验
本文由作者推荐
附和拼音-自言自语的近义词
**************************************************************************
*程序功能：利用sirt、art、kaczmarz、奇异值分解方法解地震层析成像方程组 *
*参量说明： *
*A-系数矩阵 *
*B-方程右端项 *
*X-方程解向量 *
*M,N-A的维数 *
*EPS-精度要求 *
*说明：sirt和art算法基于地震波射线理论。在使用时，必须注意射线路径的合理 *
* 性，若射线路径不合实际，将不能得到正确的解。 *
**************************************************************************
PROGRAM TOPOG
IMPLICIT NONE
INTEGER M,N
PARAMETER(M=10,N=9)
DIMENSION A(M,N)
DIMENSION B(M),X(N)
DOUBLE PRECISION A,EPS,B,X
DATA A/1.,0.,0.,1.,0.,0.,1.41421,0.,0.,0.,
&1.,0.,0.,0.,1.,0.,0.,0.,0.,1.41421,
&1.,0.,0.,0.,0.,1.,0.,0.,1.41421,0.,
&0.,1.,0.,1.,0.,0.,0.,0.,0.,0.,
&0.,1.,0.,0.,1.,0.,1.41421,0.,1.41421,0.,
&0.,1.,0.,0.,0.,1.,0.,0.,0.,0.,
&0.,0.,1.,1.,0.,0.,0.,0.,1.41421,0.,
&0.,0.,1.,0.,1.,0.,0.,0.,0.,0.,
&0.,0.,1.,0.,0.,1.,1.41421,1.41421,0.,0./
DATA B/2.2,1.4,2.5,2.3,1.7,2.1,4.24263,1.41421,4.24263,0.282842/
EPS=1e-12
CALL SIRT(M,N,A,X,B,EPS)
PRINT 100,X
CALL ART(M,N,A,X,B,EPS)
PRINT 100,X
CALL KACZMARZ(M,N,A,X,B,EPS)
PRINT 100,X
CALL SVD(M,N,A,X,B,EPS)
PRINT 100,X
100tFORMAT(<n>F8.3)
ENDPROGRAM
!****SIRT方法**************************************************
SUBROUTINE SIRT(M,N,A,X,B,EPS)
IMPLICIT NONE
EXTERNAL NORM2
INTEGER M,N,I,J,K,ITS
DOUBLE PRECISION A(M,N),X(N),B(M)
DOUBLE PRECISION KJ(N),NI(M),LI(M),QI,DM(N)
DOUBLE PRECISION EPS,NORM2
X=0.
DO J=1,N
KJ(J)=0.
DO I=1,M
IF(ABS(A(I,J))>1E-15) KJ(J)=KJ(J)+1
ENDDO
ENDDO
DO I=1,M
NI(I)=0.
LI(I)=0.
DO J=1,N
IF(ABS(A(I,J))>1E-15) THEN
NI(I)=NI(I)+1
LI(I)=LI(I)+A(I,J)
ENDIF
ENDDO
ENDDO
ITS=0
DO WHILE(NORM2(MATMUL(A,X)-B,M)><100000)
ITS=ITS+1
DM=0.
DO I=1,M
QI=0.
DO J=1,N
IF(ABS(A(I,J))>1E-15) QI=QI+X(J)
ENDDO
DO J=1,N
IF(ABS(A(I,J))>1E-15) DM(J)=DM(J)+B(I)/LI(I)-QI/NI(I)
ENDDO
ENDDO
DO J=1,N
IF(ABS(KJ(J))>1E-15) X(J)=X(J)+DM(J)/KJ(J)
ENDDO
ENDDO
ENDSUBROUTINE
!****ART方法***************************************************
SUBROUTINE ART(M,N,A,X,B,EPS)
IMPLICIT NONE
EXTERNAL NORM2
INTEGER M,N,I,J,K,ITS
DOUBLE PRECISION A(M,N),X(N),B(M)
DOUBLE PRECISION NI(M),LI(M),QI
DOUBLE PRECISION EPS,NORM2
DO I=1,M
LI(I)=0
NI(I)=0
DO J=1,N
IF(ABS(A(I,J))>1E-15) THEN
NI(I)=NI(I)+1
LI(I)=LI(I)+A(I,J)
ENDIF
ENDDO
ENDDO
X=0.
ITS=0
DO WHILE(NORM2(MATMUL(A,X)-B,M)><100000)
ITS=ITS+1
DO I=1,M
QI=0
DO J=1,N
IF(ABS(A(I,J))>1E-15) QI=QI+X(J)
ENDDO
DO J=1,N
IF(ABS(A(I,J))>1E-15) X(J)=X(J)+B(I)/LI(I)-QI/NI(I)
ENDDO
ENDDO
ENDDO
ENDSUBROUTINE
!****kaczmarz方法**********************************************
SUBROUTINE KACZMARZ(M,N,A,X,B,EPS)
IMPLICIT NONE
EXTERNAL NORM2
INTEGER M,N,I,J,K,ITS
DOUBLE PRECISION A(M,N),X(N),B(M),EPS,GM,GGT,NORM2
X=0.
DO WHILE(NORM2(MATMUL(A,X)-B,M)><100000)
ITS=ITS+1
DO I=1,M
GM=0
GGT=0
DO J=1,N
GM=A(I,J)*X(J)+GM
GGT=A(I,J)**2+GGT
ENDDO
GM=(B(I)-GM)/GGT
DO J=1,N
X(J)=X(J)+GM*A(I,J)
ENDDO
ENDDO
ENDDO
ENDSUBROUTINE
!****奇异值分解方法********************************************
SUBROUTINE SVD(M,N,A,X,B,EPS)
IMPLICIT NONE
INTEGER M,N,i,j
DOUBLE PRECISION A(M,N),A0(M,N),AA(N,M),X(N),B(M),EPS
A0=A
CALL BGINV(M,N,A0,AA,EPS,MAX(M,N)+1)
X=MATMUL(AA,B)
ENDSUBROUTINE
!****奇异值分解子程序******************************************
SUBROUTINE BGINV(M,N,A,AA,EPS,KA)
IMPLICIT NONE
INTEGER M,N,I,J,K,II,KA,L
DIMENSION A(M,N),U(M,M),V(N,N),AA(N,M)
DIMENSION S(KA),E(KA),WORK(KA)
DOUBLE PRECISION A,U,V,AA,S,E,WORK,EPS
CALL BMUAV(A,M,N,U,V,L,EPS,KA,S,E,WORK)
IF (.0) THEN
K=1
10t IF (A(K,K).NE.0.0) THEN
K=K+1
IF ((M,N)) GOTO 10
END IF
K=K-1
IF (.0) THEN
DO 40 I=1,N
DO 40 J=1,M
AA(I,J)=0.0
DO 30 II=1,K
30t AA(I,J)=AA(I,J)+V(II,I)*U(J,II)/A(II,II)
40t CONTINUE
END IF
END IF
RETURN
ENDSUBROUTINE
SUBROUTINE BMUAV(A,M,N,U,V,L,EPS,KA,S,E,WORK)
IMPLICIT NONE
INTEGER M,N,I,IT,J,K,KK,KA,KL,L,LL,MM,NN,KS,M1
DIMENSION A(M,N),U(M,M),V(N,N),S(KA),E(KA),WORK(KA)
DOUBLE PRECISION A,U,V,S,E,D,WORK,DD,F,G,CS,SN,
* SHH,SK,EK,B,C,SM,SM1,EM1,EPS
IT=60
K=N
IF (.N) K=M-1
L=M
IF (.M) L=N-2
IF (.0) L=0
LL=K
IF (.K) LL=L
IF (.1) THEN
DO 150 KK=1,LL
IF (.K) THEN
D=0.0
DO 10 I=KK,M
10t D=D+A(I,KK)*A(I,KK)
S(KK)=SQRT(D)
IF (S(KK).NE.0.0) THEN
IF (A(KK,KK).NE.0.0) S(KK)=SIGN(S(KK),A(KK,KK))
DO 20 I=KK,M
20t A(I,KK)=A(I,KK)/S(KK)
A(KK,KK)=1.0+A(KK,KK)
END IF
S(KK)=-S(KK)
END IF
IF (+1) THEN
DO 50 J=KK+1,N
IF ((.K).AND.(S(KK).NE.0.0)) THEN
D=0.0
DO 30 I=KK,M
30t D=D+A(I,KK)*A(I,J)
D=-D/A(KK,KK)
DO 40 I=KK,M
40t A(I,J)=A(I,J)+D*A(I,KK)
END IF
E(J)=A(KK,J)
50t CONTINUE
END IF
IF (.K) THEN
DO 60 I=KK,M
60t U(I,KK)=A(I,KK)
END IF
IF (.L) THEN
D=0.0
DO 70 I=KK+1,N
70t D=D+E(I)*E(I)
E(KK)=SQRT(D)
IF (E(KK).NE.0.0) THEN
IF (E(KK+1).NE.0.0) E(KK)=SIGN(E(KK),E(KK+1))
DO 80 I=KK+1,N
80t E(I)=E(I)/E(KK)
E(KK+1)=1.0+E(KK+1)
END IF
E(KK)=-E(KK)
IF ((KK+.M).AND.(E(KK).NE.0.0)) THEN
DO 90 I=KK+1,M
90t WORK(I)=0.0
DO 110 J=KK+1,N
DO 100 I=KK+1,M
100t WORK(I)=WORK(I)+E(J)*A(I,J)
110t
CONTINUE
DO 130 J=KK+1,N
DO 120 I=KK+1,M
120t A(I,J)=A(I,J)-WORK(I)*E(J)/E(KK+1)
130t CONTINUE
END IF
DO 140 I=KK+1,N
140t V(I,KK)=E(I)
END IF
150t CONTINUE
END IF
MM=N
IF (M+.N) MM=M+1
IF (.N) S(K+1)=A(K+1,K+1)
IF () S(MM)=0.0
IF (L+) E(L+1)=A(L+1,MM)
E(MM)=0.0
NN=M
IF (.N) NN=N
IF (.K+1) THEN
DO 190 J=K+1,NN
DO 180 I=1,M
180t U(I,J)=0.0
U(J,J)=1.0
190t CONTINUE
END IF
IF (.1) THEN
DO 250 LL=1,K
KK=K-LL+1
IF (S(KK).NE.0.0) THEN
IF (+1) THEN
DO 220 J=KK+1,NN
D=0.0
DO 200 I=KK,M
200t D=D+U(I,KK)*U(I,J)/U(KK,KK)
D=-D
DO 210 I=KK,M
210t U(I,J)=U(I,J)+D*U(I,KK)
220t CONTINUE
END IF
DO 225 I=KK,M
225t U(I,KK)=-U(I,KK)
U(KK,KK)=1.0+U(KK,KK)
IF (.1) THEN
DO 230 I=1,KK-1
230t U(I,KK)=0.0
END IF
ELSE
DO 240 I=1,M
240t U(I,KK)=0.0
U(KK,KK)=1.0
END IF
250t CONTINUE
END IF
DO 300 LL=1,N
KK=N-LL+1
IF ((.L).AND.(E(KK).NE.0.0)) THEN
DO 280 J=KK+1,N
D=0.0
DO 260 I=KK+1,N
260t D=D+V(I,KK)*V(I,J)/V(KK+1,KK)
D=-D
DO 270 I=KK+1,N
270t V(I,J)=V(I,J)+D*V(I,KK)
280t CONTINUE
END IF
DO 290 I=1,N
290t V(I,KK)=0.0
V(KK,KK)=1.0
300tCONTINUE
DO 305 I=1,M
DO 305 J=1,N
305tA(I,J)=0.0
M1=MM
IT=60
310tIF (.0) THEN
L=0
IF (.N) THEN
I=N
ELSE
I=M
END IF
DO 315 J=1,I-1
A(J,J)=S(J)
A(J,J+1)=E(J)
315t CONTINUE
A(I,I)=S(I)
IF (.N) A(I,I+1)=E(I)
DO 314 I=1,N-1
DO 313 J=I+1,N
D=V(I,J)
V(I,J)=V(J,I)
V(J,I)=D
313t CONTINUE
314t CONTINUE
RETURN
END IF
IF (.0) THEN
L=MM
IF (.N) THEN
I=N
ELSE
I=M
END IF
DO 316 J=1,I-1
A(J,J)=S(J)
A(J,J+1)=E(J)
316t CONTINUE
A(I,I)=S(I)
IF (.N) A(I,I+1)=E(I)
DO 318 I=1,N-1
DO 317 J=I+1,N
D=V(I,J)
V(I,J)=V(J,I)
V(J,I)=D
317t CONTINUE
318t CONTINUE
RETURN
END IF
KK=MM
320 tKK=KK-1
IF (.0) THEN
D=ABS(S(KK))+ABS(S(KK+1))
DD=ABS(E(KK))
IF (*D) GOTO 320
E(KK)=0.0
END IF
IF (-1) THEN
KK=KK+1
IF (S(KK).LT.0.0) THEN
S(KK)=-S(KK)
DO 330 I=1,N
330t V(I,KK)=-V(I,KK)
END IF
335t IF (.M1) THEN
IF
(S(KK).LT.S(KK+1)) THEN
D=S(KK)
S(KK)=S(KK+1)
S(KK+1)=D
IF (.N) THEN
DO 340 I=1,N
D=V(I,KK)
V(I,KK)=V(I,KK+1)
V(I,KK+1)=D
340t CONTINUE
END IF
IF (.M) THEN
DO 350 I=1,M
D=U(I,KK)
U(I,KK)=U(I,KK+1)
U(I,KK+1)=D
350t CONTINUE
END IF
KK=KK+1
GOTO 335
END IF
END IF
IT=60
MM=MM-1
GOTO 310
END IF
KS=MM+1
360tKS=KS-1
IF () THEN
D=0.0
IF () D=D+ABS(E(KS))
IF (+1) D=D+ABS(E(KS-1))
DD=ABS(S(KS))
IF (*D) GOTO 360
S(KS)=0.0
END IF
IF () THEN
KK=KK+1
D=ABS(S(MM))
IF (ABS(S(MM-1)).GT.D) D=ABS(S(MM-1))
IF (ABS(E(MM-1)).GT.D) D=ABS(E(MM-1))
IF (ABS(S(KK)).GT.D) D=ABS(S(KK))
IF (ABS(E(KK)).GT.D) D=ABS(E(KK))
SM=S(MM)/D
SM1=S(MM-1)/D
EM1=E(MM-1)/D
SK=S(KK)/D
EK=E(KK)/D
B=((SM1+SM)*(SM1-SM)+EM1*EM1)/
2.0
C=SM*EM1
C=C*C
SHH=0.0
IF ((.0.0).OR.(.0.0)) THEN
SHH=SQRT(B*B+C)
IF (.0.0) SHH=-SHH
SHH=C/(B+SHH)
END IF
F=(SK+SM)*(SK-SM)-SHH
G=SK*EK
DO 400 I=KK,MM-1
CALL SSS(F,G,CS,SN)
IF () E(I-1)=F
F=CS*S(I)+SN*E(I)
E(I)=CS*E(I)-SN*S(I)
G=SN*S(I+1)
S(I+1)=CS*S(I+1)
IF ((.1.0).OR.(.0.0)) THEN
DO 370 J=1,N
D=CS*V(J,I)+SN*V(J,I+1)
V(J,I+1)=-SN*V(J,I)+CS*V(J,I+1)
V(J,I)=D
370t CONTINUE
END IF
CALL SSS(F,G,CS,SN)
S(I)=F
F=CS*E(I)+SN*S(I+1)
S(I+1)=-SN*E(I)+CS*S(I+1)
G=SN*E(I+1)
E(I+1)=CS*E(I+1)
IF (.M) THEN
IF ((.1.0).OR.(.0.0)) THEN
DO 380 J=1,M
D=CS*U(J,I)+SN*U(J,I+1)
U(J,I+1)=-SN*U(J,I)+CS*U(J,I+1)
U(J,I)=D
380t CONTINUE
END IF
END IF
400t CONTINUE
E(MM-1)=F
IT=IT-1
GOTO 310
END IF
IF () THEN
KK=KK+1
F=E(MM-1)
E(MM-1)=0.0
DO 420 LL=KK,MM-1
I=MM+KK-LL-1
G=S(I)
CALL SSS(G,F,CS,SN)
S(I)=G
IF () THEN
F=-SN*E(I-1)
E(I-1)=CS*E(I-1)
END IF
IF ((.1.0).OR.(.0.0)) THEN
DO 410 J=1,N
D=CS*V(J,I)+SN*V(J,MM)
V(J,MM)=-SN*V(J,I)+CS*V(J,MM)
V(J,I)=D
410t CONTINUE
END IF
420t CONTINUE
GOTO 310
END IF
KK=KS+1
F=E(KK-1)
E(KK-1)=0.0
DO 450 I=KK,MM
G=S(I)
CALL SSS(G,F,CS,SN)
S(I)=G
F=-SN*E(I)
E(I)=CS*E(I)
IF ((.1.0).OR.(.0.0)) THEN
DO 430 J=1,M
D=CS*U(J,I)+SN*U(J,KK-1)
U(J,KK-1)=-SN*U(J,I)+CS*U(J,KK-1)
U(J,I)=D
430t CONTINUE
END IF
450tCONTINUE
GOTO 310
END
SUBROUTINE SSS(F,G,CS,SN)
DOUBLE PRECISION F,G,CS,SN,D,R
IF ((ABS(F)+ABS(G)).EQ.0.0) THEN
CS=1.0
SN=0.0
D=0.0
ELSE
D=SQRT(F*F+G*G)
IF (
ABS(F).(G)) D=SIGN(D,F)
IF (ABS(G).(F)) D=SIGN(D,G)
CS=F/D
SN=G/D
END IF
R=1.0
IF (ABS(F).(G)) THEN
R=SN
ELSE
IF (.0.0) R=1.0/CS
END IF
F=D
G=R
RETURN
ENDSUBROUTINE
!****求向量范数子函数******************************************
FUNCTION NORM2(A,M)
IMPLICIT NONE
INTEGER M,I
DOUBLE PRECISION A(M),NORM2
NORM2=0.
DO I=1,M
NORM2=NORM2+A(I)**2
ENDDO
ENDFUNCTION