PROGRAM EOF
!C THIS PROGRAM USES EOF FOR ANALYSING TIME SERIES OF METEOROLOGICAL FIELD
!C M:LENTH OF TIME SERIES !!!!!!!!!! m:时间序列长度
!C N:NUMBER OF GRID-POINTS !!!!!!!!!! n:格点数
!C KS=-1:SELF; KS=0:DEPATURE; KS=1:STANDERDLIZED DEPATURE
!C KV:NUMBER OF EIGENVALUES WILL BE OUTPUT
!C KVT:NUMBER OF EIGENVECTORS AND TIME SERIES WILL BE OUTPUT
!C MNH=MIN(M,N)
!C EGVT=EIGENVACTORS, ECOF=TIME COEFFICIENTS FOR EGVT.
!C ER(KV,1)=LAMDA,LAMDA EIGENVALUE
!C ER(KV,2)=ACCUMULATE LAMDA
!C ER(KV,3)=THE SUM OF COMPONENTS VECTORS PROJECTED ONTO EIGENVACTOR.
!C ER(KV,4)=ACCUMULATE ER(KV,3)
integer countit,k,i,j,M,N,NN,nx,ny,MNH,ks,kv,kvt
real pi,f,er,sum1
PARAMETER(M=22,N=144*73,NN=144*73,nx=144,ny=73,MNH=22,KS=-1,KV=4,KVT=4,pi=3.1415926)
real,dimension(nx,ny,M)::ps
real,dimension(MNH)::v,ave1,sum2
real,dimension(N)::DF,AVF
real,dimension(N,KVT)::EGVT2
real,dimension(NN,KVT)::EGVT
real,dimension(M,KVT)::ECOF,SECOF
real,dimension(MNH,MNH)::a,s
DIMENSION F(NN,M),ER(MNH,4)
open(1,file='d:\da\data\ps.grd',form='binary')
open(20,file='d:\da\data\eof\egvt.grd',form='binary')
open(21,file='d:\da\data\eof\egvt.txt')
open(30,file='d:\da\data\eof\t.grd',form='binary')
open(31,file='d:\da\data\eof\t.txt')
open(16,file='d:\da\data\eof\eof.txt')
!cccccccccccccccccc读数据
do it=1,m
do j=1,ny
do i=1,nx
read(1)ps(i,j,it)
enddo;enddo;enddo
!print*,ps(:,:,1)
write(*,*)'read data ok'
!cccccccccccccccc 处理数据 从ps到f的转换
do it=1,m
count=0
do j=1,ny
do i=1,nx
count=count+1
f(count,it)=ps(i,j,it)
enddo;enddo;enddo
!CCCCCCCCCCCCCCCC INPUT DATA CCCCCCCCCCCCCCCCCCC
CALL TRANSF(NN,M,F,AVF,DF,KS)
write(*,*)'ok program 1'
CALL FORMA(NN,M,MNH,F,A)
write(*,*)'ok program 2'
CALL JCB(MNH,A,S,0.00001)
write(*,*)'ok program 3'
CALL ARRANG(KV,MNH,A,ER,S)
write(*,*)'ok program 4'
CALL TCOEFF(KVT,KV,NN,M,MNH,S,F,V,ER)
write(*,*)'ok program 5'
CALL OUTER(KV,ER,MNH)
write(*,*)'ok program 6'
CALL OUTVT(KVT,NN,M,MNH,S,F,EGVT,ECOF,EGVT2,n)
write(*,*)'ok program 7'
!ccccccccccccc存储数据
!print*,ecof
!标准化时间系数
do i=1,kvt
sum1=0
do j=1,m
sum1=sum1+ecof(j,i)
enddo;
ave1(i)=1.0*sum1/m
enddo
do i=1,kvt
sum2(i)=0
do j=1,m
sum2(i)=sum2(i)+(ecof(j,i)-ave1(i))**2
enddo;
sum2(i)=sqrt(1.0/m*sum2(i))
enddo
do i=1,kvt
do j=1,m
secof(j,i)=(ecof(j,i)-ave1(i))/sum2(i)
!print*,secof(j,i)
enddo;enddo
do j=1,m
do i=1,kvt
write(30)secof(j,i)
enddo;enddo
do j=1,m
do i=1,kvt
write(31,*)secof(j,i)
enddo;enddo
!CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC储存特征向量场egvt
do it=1,kvt
do j=1,n
write(20)egvt(j,it)
enddo
enddo
do it=1,kvt
do j=1,n
write(21,*)egvt(j,it)
enddo
enddo
write(*,*)'ok 8'
!cccccccccccc
END
!ccccccccccccccccccccccccc子程序1~7
SUBROUTINE TRANSF(NN,M,F,AVF,DF,KS)
! THIS SUBROUTINE PROVIDES INITIAL F BY KS
DIMENSION F(NN,M),AVF(NN),DF(NN)
DO 5 I=1,NN
AVF(I)=0.0
5 DF(I)=0.0
IF(KS) 30,10,10
10 DO 14 I=1,NN
DO 12 J=1,M
12 AVF(I)=AVF(I)+F(I,J)
AVF(I)=AVF(I)/M
DO 14 J=1,M
F(I,J)=F(I,J)-AVF(I)
14 CONTINUE
!print*,F
IF(KS.EQ.0) THEN
RETURN
ELSE
DO 24 I=1,NN
DO 22 J=1,M
22 DF(I)=DF(I)+F(I,J)*F(I,J)
DF(I)=SQRT(DF(I)/M)
DO 24 J=1,M
F(I,J)=F(I,J)/DF(I)
24 CONTINUE
ENDIF
30 CONTINUE
RETURN
END
SUBROUTINE FORMA(NN,M,MNH,F,A)
! THIS SUBROUTINE FORMS A BY F
DIMENSION F(NN,M),A(MNH,MNH)
IF(M-NN) 40,50,50
40 DO 44 I=1,MNH
DO 44 J=I,MNH
A(I,J)=0.0
DO 42 IS=1,NN
42 A(I,J)=A(I,J)+F(IS,I)*F(IS,J)
A(J,I)=A(I,J)
44 CONTINUE
RETURN
50 DO 54 I=1,MNH
DO 54 J=I,MNH
A(I,J)=0.0
DO 52 JS=1,M
52 A(I,J)=A(I,J)+F(I,JS)*F(J,JS)
A(J,I)=A(I,J)
54 CONTINUE
RETURN
END
SUBROUTINE JCB(NN,A,S,EPS)
! THIS SUBROUTINE COMPUTS EIGENVALUES AND standard EIGENVECTORS OF A
DIMENSION A(NN,NN),S(NN,NN)
DO 30 I=1,NN
DO 30 J=1,I
IF(I-J) 20,10,20
10 S(I,J)=1.
GO TO 30
20 S(I,J)=0.
S(J,I)=0.
30 CONTINUE
G=0.
DO 40 I=2,NN
I1=I-1
DO 40 J=1,I1
40 G=G+2.*A(I,J)*A(I,J)
S1=SQRT(G)
S2=EPS/FLOAT(NN)*S1
S3=S1
L=0
50 S3=S3/FLOAT(NN)
60 DO 130 IQ=2,NN
IQ1=IQ-1
DO 130 IP=1,IQ1
IF(ABS(A(IP,IQ)).LT.S3) GOTO 130
L=1
V1=A(IP,IP)
V2=A(IP,IQ)
V3=A(IQ,IQ)
U=0.5*(V1-V3)
IF(U.EQ.0.0) G=1.
IF(ABS(U).GE.1E-10) G=-SIGN(1.,U)*V2/SQRT(V2*V2+U*U)
ST=G/SQRT(2.*(1.+SQRT(1.-G*G)))
CT=SQRT(1.-ST*ST)
DO 110 I=1,NN
G=A(I,IP)*CT-A(I,IQ)*ST
A(I,IQ)=A(I,IP)*ST+A(I,IQ)*CT
A(I,IP)=G
G=S(I,IP)*CT-S(I,IQ)*ST
S(I,IQ)=S(I,IP)*ST+S(I,IQ)*CT
110 S(I,IP)=G
DO 120 I=1,NN
A(IP,I)=A(I,IP)
120 A(IQ,I)=A(I,IQ)
G=2.*V2*ST*CT
A(IP,IP)=V1*CT*CT+V3*ST*ST-G
A(IQ,IQ)=V1*ST*ST+V3*CT*CT+G
A(IP,IQ)=(V1-V3)*ST*CT+V2*(CT*CT-ST*ST)
A(IQ,IP)=A(IP,IQ)
130 CONTINUE
IF(L-1) 150,140,150
140 L=0
GO TO 60
150 IF(S3.GT.S2) GOTO 50
RETURN
END
SUBROUTINE ARRANG(KV,MNH,A,ER,S)
! THIS SUBROUTINE PROVIDES A SERIES OF EIGENVALUES FROM MAX TO MIN
DIMENSION A(MNH,MNH),ER(MNH,4),S(MNH,MNH)
TR=0.0
DO 200 I=1,MNH
TR=TR+A(I,I)
200 ER(I,1)=A(I,I)
MNH1=MNH-1
DO 210 K1=MNH1,1,-1
DO 210 K2=K1,MNH1
IF(ER(K2,1).LT.ER(K2+1,1)) THEN
C=ER(K2+1,1)
ER(K2+1,1)=ER(K2,1)
ER(K2,1)=C
DO 205 I=1,MNH
C=S(I,K2+1)
S(I,K2+1)=S(I,K2)
S(I,K2)=C
205 CONTINUE
ENDIF
210 CONTINUE
ER(1,2)=ER(1,1)
DO 220 I=2,KV
ER(I,2)=ER(I-1,2)+ER(I,1)
220 CONTINUE
DO 230 I=1,KV
ER(I,3)=ER(I,1)/TR
ER(I,4)=ER(I,2)/TR
230 CONTINUE
!WRITE(*,250) TR
250 FORMAT(/5X,'TOTAL SQUARE ERROR=',F20.5)
RETURN
END
SUBROUTINE TCOEFF(KVT,KV,NN,M,MNH,S,F,V,ER)
! THIS SUBROUTINE PROVIDES STANDARD EIGENVECTORS (M.GE.N,SAVED IN S;M.LT.N,SAVED IN F) AND
! ITS TIME COEFFICENTS SERIES (M.GE.NSAVED IN F; M.LT.N,SAVED IN S)
DIMENSION S(MNH,MNH),F(NN,M),V(MNH),ER(MNH,4)
IF(NN.LE.M) THEN
DO 390 J=1,M
DO 370 I=1,NN
V(I)=F(I,J)
F(I,J)=0.
370 CONTINUE
DO 380 IS=1,KVT
DO 380 I=1,NN
380 F(IS,J)=F(IS,J)+V(I)*S(I,IS)
390 CONTINUE
ELSE
DO 410 I=1,NN
DO 400 J=1,M
V(J)=F(I,J)
F(I,J)=0.
400 CONTINUE
DO 410 JS=1,KVT
DO 410 J=1,M
F(I,JS)=F(I,JS)+V(J)*S(J,JS)
410 CONTINUE
DO 430 JS=1,KVT
DO 420 J=1,M
S(J,JS)=S(J,JS)*SQRT(ER(JS,1))
420 CONTINUE
DO 430 I=1,N
F(I,JS)=F(I,JS)/SQRT(ER(JS,1))
430 CONTINUE
ENDIF
RETURN
END
SUBROUTINE OUTER(KV,ER,MNH)
! THIS SUBROUTINE PRINTS ARRAY ER
! ER(KV,1) FOR SEQUENCE OF EIGENVALUE FROM BIG TO SMALL
! ER(KV,2) FOR EIGENVALUE FROM BIG TO SMALL
! ER(KV,3) FOR SMALL LO=(LAMDA/TOTAL VARIANCE)
! ER(KV,4) FOR BIG LO=SUM OF SMALL LO)
DIMENSION ER(MNH,4)
WRITE(16,510)
510 FORMAT(/10X,'EIGENVALUE AND ANALYSIS ERROR')
WRITE(16,520)
520 FORMAT(10X,1HH,8X,5HLAMDA,10X,6HSLAMDA,11X,2HPH,12X,3HSPH)
WRITE(16,530) (IS,(ER(IS,J),J=1,4),IS=1,KV)
530 FORMAT(1X,I10,4F15.5)
WRIT
