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PARAMETER(M=52,N=19,MNH=13,KS=1,KV=8,KVT=3)!N为站点数,若N>M,则MNH=M
DIMENSION F(N,M),A(MNH,MNH),S(MNH,MNH),ER(MNH,4),t(n,m)
dimension err(kvt,2)
DIMENSION DF(N),V(MNH),AVF(N)
real EGVT(N,KVT),ECOF(M,KVT)
dimension H(N),U(N),VR(N),WT(N),WK(N)
dimension WBT(M),WBK(M),R(KVT),ST(KVT)
dimension fc(kvt)
INTEGER iSTa(n)
CCCCCCCCCCCCCCCCCCCCCC input data CCCCCCCCCCCCCCCCCCCCCCCCCCCCC
open(2,file='D:\lw\eof\winter.txt')
do i=1,n
do it=1,m
READ(2,*)f(i,it)
enddo
enddo
print*,'read OK OK oK'
close(2)
CCCCCCCCCCCCCCCC INPUT DATA CCCCCCCCCCCCCCCCCCC
CALL TRANSF(N,M,F,AVF,DF,KS)
CALL FORMA(N,M,MNH,F,A)
CALL JCB(MNH,A,S,0.00001)
write(*,*)'call 3 ok'
CALL ARRANG(KV,MNH,A,ER,S,TR0)
call jy(KV,M,ER)
write(*,*)'jian yan OK'
CALL TCOEFF(KVT,KV,N,M,MNH,S,F,V,ER)
C CALL OUTER(KV,KVT,ER,R)
CALL OUTER(KV,KVT,MNH,ER,R)
CALL OUTVT(KVT,N,M,MNH,S,F,EGVT,ECOF)
cccccccccccccccccc output unrotatted time cooficience cccccccccc
do 131 js=1,kvt
fc(js)=0.0
do 132 j=1,M
132 fc(js)=fc(js)+ecof(j,js)*ecof(j,js)/float(M)
fc(js)=sqrt(fc(js))
131 print*,'fc= ',js,' ',fc(js)
open(16,file='D:\lw\eof\winteruntmc.grd',form='binary')
do 348 j=1,m
348 write(16)(ecof(j,is)/fc(is),is=1,kvt)
close(16)
cccccccccccccc output unrotatted eigenvectors cccccccccccccc
open(25,file='D:\lw\eof\winterunvec.grd',form='binary')
write(25) ((fc(js)*egvt(i,js),i=1,n),js=1,kvt)
close(25)
print*,' EOF OK !'
ccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
CALL rotation(EGVT,ECOF,R,H,ST,N,M,KVT,U,VR,WT,WK,WBT,WBK)
call rarrange(KVT,N,M,TR0,EGVT,ECOF,ERr)
cccccccccccccccccc output rotatted time cooficience cccccccccc
do 133 js=1,kvt
fc(js)=0.0
do 134 j=1,M
134 fc(js)=fc(js)+ecof(j,js)*ecof(j,js)/float(M)
fc(js)=sqrt(fc(js))
133 print*,'fc= ',js,' ',fc(js)
open(26,file='D:\lw\eof\winterrtmc.grd',form='binary')
do 449 j=1,M
449 write(26)(ecof(j,is)/fc(is),is=1,kvt)
close(26)
cccccccccccccc output rotatted eigenvectors cccccccccccccc
OPEN(25,file='D:\lw\eof\winterrvec.grd',
&form='binary')
write(25) ((fc(js)*egvt(i,js),i=1,n),js=1,kvt)
close(25)
ccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
STOP
END
!----------------------将资料标准化或距平----------------------!
!ks=1将资料标准化,即均值为零,方差为1;ks=0将资料化为距平值;ks=-1原始资料不变化
!avf(i)为第i个格点的多年均值,df(i)为方差;m为时间长度,n为格点数。
SUBROUTINE TRANSF(N,M,F,AVF,DF,KS)
DIMENSION F(N,M),AVF(N),DF(N)
DO I=1,N
AVF(I)=0.0
DF(I)=0.0
enddo
IF(KS.eq.0)then
DO I=1,N
DO J=1,M
AVF(I)=AVF(I)+F(I,J)
enddo
AVF(I)=AVF(I)/M
DO J=1,M
F(I,J)=F(I,J)-AVF(I)
enddo
enddo
elseif(KS.EQ.-1) then
RETURN
ELSE
DO I=1,N
DO J=1,M
AVF(I)=AVF(I)+F(I,J)
enddo
AVF(I)=AVF(I)/M
DO j=1,M
F(I,J)=F(I,J)-AVF(I)
enddo
enddo
DO I=1,N
DO J=1,M
DF(I)=DF(I)+F(I,J)*F(I,J)
enddo
DF(I)=SQRT(DF(I)/M)
DO J=1,M
F(I,J)=F(I,J)/DF(I)
enddo
enddo
ENDIF
RETURN
END
! ------------- 计算相关矩阵A(mnh,mnh)------------!
SUBROUTINE FORMA(N,M,MNH,F,A)
DIMENSION F(N,M),A(MNH,MNH)
IF(M-N) 40,50,50
40 DO 44 I=1,MNH
DO 44 J=I,MNH
A(I,J)=0.0
DO 42 IS=1,N
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
!----------计算相关矩阵A(mnh,mnh)的特征值和特征向量---------!
SUBROUTINE JCB(N,A,S,EPS)
DIMENSION A(N,N),S(N,N)
DO 30 I=1,N
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,N
I1=I-1
DO 40 J=1,I1
40 G=G+2.*A(I,J)*A(I,J)
S1=SQRT(G)
S2=EPS/real(N)*S1
S3=S1
L=0
50 S3=S3/real(N)
60 DO 130 IQ=2,N
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,N
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,N
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
!---------------特征值从大到小排序---------------!
SUBROUTINE ARRANG(KV,MNH,A,ER,S,TR)
c DIMENSION A(MNH,MNH),ER(KV,4),S(MNH,MNH)
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
RETURN
END
!--------------------计算标准化特征向量及其时间系数-----------------------!
SUBROUTINE TCOEFF(KVT,KV,N,M,MNH,S,F,V,ER)
C THIS SUBROUTINE PROVIDES STANDARD EIGENVECTORS (M.GE.N,SAVED IN S;
C M.LT.N,SAVED IN F) AND ITS TIME COEFFICENTS SERIES (M.GE.N,
C SAVED IN F; M.LT.N,SAVED IN S)
c DIMENSION S(MNH,MNH),F(N,M),V(MNH),ER(KV,4)
DIMENSION S(MNH,MNH),F(N,M),V(MNH),ER(MNH,4)
DO 360 J=1,KVT
C=0.
DO 350 I=1,MNH
350 C=C+S(I,J)*S(I,J)
C=SQRT(C)
DO 160 I=1,MNH
160 S(I,J)=S(I,J)/C
360 CONTINUE
IF(N.LE.M) THEN
DO 390 J=1,M
DO 370 I=1,N
V(I)=F(I,J)
F(I,J)=0.
370 CONTINUE
DO 380 IS=1,KVT
DO 380 I=1,N
380 F(IS,J)=F(IS,J)+V(I)*S(I,IS)
390 CONTINUE
ELSE
DO 410 I=1,N
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
C SUBROUTINE OUTER(KV,KVT,ER,R)
SUBROUTINE OUTER(KV,KVT,MNH,ER,R)
C THIS SUBROUTINE PRINTS ARRAY ER
C ER(KV,1) FOR SEQUENCE OF EIGENVALUE FROM BIG TO SMALL
C ER(KV,2) FOR EIGENVALUE FROM BIG TO SMALL
C ER(KV,3) FOR SMALL LO=(LAMDA/TOTAL VARIANCE)
C ER(KV,4) FOR BIG LO=sum OF SMALL LO)
C DIMENSION ER(KV,4),R(KVT)
DIMENSION ER(MNH,4),R(KVT)
open(26,file='D:\lw\eof\unrvalue.dat')
WRITE(26,510)
510 FORMAT(/30X,'EIGENVALUE AND ANALYSIS ERROR',/)
WRITE(26,520)
520 FORMAT(10X,1HH,8X,5HLAMDA,10X,6HSLAMDA,11X,2HPH,12X,3HSPH)
WRITE(26,530) (IS,(ER(IS,J),J=1,4),IS=1,KV)
530 FORMAT(1X,I10,4F15.5)
WRITE(26,540)
540 FORMAT(//)
DO I=1,KVT
R(I)=ER(I,1)
ENDDO
RETURN
END
SUBROUTINE OUTVT(KVT,N,M,MNH,S,F,EGVT,ECOF)
C THIS SUBROUTINE PRINTS STANDARD EIGENVECTORS
C AND ITS TIME-COEFFICENT SERIES
DIMENSION F(N,M),S(MNH,MNH),EGVT(N,KVT),ECOF(M,KVT)
DO 550 I=1,N
IF(M.GE.N) THEN
DO 11 JS=1,KVT
EGVT(I,JS)=S(I,JS)
11 CONTINUE
ELSE
DO 12 JS=1,KVT
EGVT(I,JS)=F(I,JS)
12 CONTINUE
ENDIF
550 CONTINUE
DO 600 J=1,M
IF(M.GE.N) THEN
DO 13 IS=1,KVT
ECOF(J,IS)=F(IS,J)
13 CONTINUE
ELSE
DO 14 IS=1,KVT
ECOF(J,IS)=S(J,IS)
14 CONTINUE
ENDIF
600 CONTINUE
RETURN
END
subroutine rotation(a,b,r,h,st,mm,nn,np,u,vr,wt,wk,wbt,wbk)
c-----------------------------------------------------------------c
c a(mm,np): eigenvector in unrotated origin field c
c b(nn,np): time coefficient(PC) in unrotated origin field c
c r(np): eigenvalue in unrotated origin field c
c-----------------------------------------------------------------c
dimension a(mm,np),b(nn,np),h(mm),u(mm),vr(mm),wt(mm),wk(mm)
dimension wbt(nn),wbk(nn),r(np),st(np),vrlv(40)
integer t,k
do 333 j=1,np
do 333 i=1,mm
a(i,j)=a(i,j)*sqrt(r(j))
333 continue
do 321 j=1,np
do 321 it=1,nn
b(it,j)=b(it,j)/sqrt(r(j))
321 continue
do 20 i=1,mm
h(i)=0.0
do 21 j=1,np
21 h(i)=h(i)+a(i,j)**2
20 continue
do 23 i=1,mm
23 h(i)=sqrt(h(i))
lll=0
vrlv0=0.0
do 230 k=1,np
g1=0.0
g2=0.0
do 434 i=1,mm
g1=g1+(a(i,k)**2/h(i)**2)**2/real(mm)
434 g2=g2+(a(i,k)**2/h(i)**2)/real(mm)
g2=g2**2
vrlv0=vrlv0+g1-g2
230 continue
800 continue
do 505 t=1,np
do 505 k=1,np
if(t.ge.k) goto 505
call rot(a,b,h,t,k,mm,nn,np,u,vr,wt,wk,wbt,wbk)
505 continue
lll=lll+1
vrlv(lll)=0.0
do 530 k=1,np
g1=0.0
g2=0.0
do 534 i=1,mm
g1=g1+(a(i,k)**2/h(i)**2)**2/real(mm)
534 g2=g2+(a(i,k)**2/h(i)**2)/real(mm)
g2=g2**2
vrlv(lll)=vrlv(lll)+g1-g2
530 continue
if(lll.lt.2) goto 800
ci=(vrlv(lll)-vrlv(lll-1))/vrlv0
if(ci.lt.0.01) goto 600
if(lll.ge.40) goto 600
goto 800
600 continue
write(6,538)
write(6,549)
write(6,539) vrlv0,(vrlv(k),k=1,lll)
538 format(//1x,'sum of variance of squared element of each colum of
1 rotated loding martix ')
549 format(1x,'at each circulation')
539 format((1x,10f8.3))
return
end
subroutine rot(a,b,h,t,k,mm,nn,np,u,vr,wt,wk,wbt,wbk)
dimension a(mm,np),b(nn,np),h(mm),u(mm),vr(mm),wt(mm),wk(mm),
1 wbt(nn),wbk(nn)
integer t,k
c write(6,*)((b(it,j),it=1,nn),j=1,np)
do 25 i=1,mm
u(i)=(a(i,t)/h(i))**2-(a(i,k)/h(i))**2
25 vr(i)=2.0*(a(i,t)/h(i))*(a(i,k)/h(i))
c=0.0
d=0.0
s=0.0
g=0.0
do 30 i=1,mm
c=c+(u(i)**2-vr(I)**2)
d=d+2.0*u(i)*vr(i)
s=s+u(i)
30 g=g+vr(i)
tg1=d-2.0*s*g/mm
tg2=c-(s**2-g**2)/mm
fi=atan2(tg1,tg2)/4.0
do 75 i=1,mm
wt(i)=a(i,t)
75 wk(i)=a(i,k)
do 84 kk=1,nn
wbt(kk)=b(kk,t)
84 wbk(kk)=b(kk,k)
do 78 i=1,mm
a(i,t)=wt(i)*cos(fi)+wk(i)*sin(fi)
78 a(i,k)=wt(i)*(-sin(fi))+wk(i)*cos(fi)
do 89 it=1,nn
b(it,t)=wbt(it)*cos(fi)+wbk(it)*sin(fi)
89 b(it,k)=wbt(it)*(-sin(fi))+wbk(it)*cos(fi)
return
end
SUBROUTINE rarrange(KVT,N,M,TR,a,b,ER)
C THIS SUBROUTINE PROVIDES A SERIES OF EIGENVALUES
C FROM MAX TO MIN
DIMENSION a(N,KVT),b(M,KVT),ER(KVT,2)
do 802 I=1,KVT
ER(I,1)=0.0
do 803 J=1,N
803 ER(I,1)=ER(I,1)+a(J,I)**2
802 continue
KVT1=KVT-1
DO 210 K1=KVT1,1,-1
DO 210 K2=K1,KVT1
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,N
C=a(I,K2+1)
a(I,K2+1)=a(I,K2)
a(I,K2)=C
205 CONTINUE
DO 305 I=1,M
C=b(I,K2+1)
b(I,K2+1)=b(I,K2)
b(I,K2)=C
305 CONTINUE
ENDIF
210 CONTINUE
DO 230 I=1,KVT
ER(I,2)=ER(I,1)/TR
230 CONTINUE
ee=0.0
do i=1,KVT
ee=ee+ER(i,2)
enddo
open(16,file='D:\lw\eof\rvalue.dat')
do I=1,KVT
write(16,*) er(i,1),ER(I,2)
enddo
write(16,*) ee
RETURN
END
SUBROUTINE jy(KV,M,ER)
DIMENSION ER(KV,4),wc(kv)
open(1,file='D:\lw\eof\jy.dat')
do i=1,kv
wc(i)=er(i,1)*sqrt(2./real(m))
enddo
do i=1,kv-1
a=er(i,1)-er(i+1,1)
if(a.ge.wc(i))then
b=i+1
write(1,*)i,b,'you jia zhi'
endif
enddo
close(1)
end
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