!---------------------------------------------------------------------------! !输入的有: ! ! 1.RH(nn,mm),需作旋转EOF的矩阵,注意nn代表时间,mm代表站点或格点; ! ! 2.NP(整形):需要作旋转EOF的特征向量的个数;(一般对RH作EOF后由一定 ! ! 的规则来确定; ! !输出的有: ! ! 1.对RH作EOF的特征值和方差贡献; ! ! 2.对RH作EOF的特征向量和时间系数; ! ! 3.选择前NP个特征向量作旋转EOF的特征向量和时间系数; ! ! 4.旋转前后主分量的相关矩阵; ! !---------------------------------------------------------------------------! PROGRAM reof parameter(nn=47,mm=286) parameter(np= 15) DIMENSION RH(nn,mm),B(nn,np),reco(nn,mm) DIMENSION A(mm,mm),V(mm,mm),RAMDA(mm),RC(np,np),X(nn),Y(nn),h(mm), & MX(mm),XW(mm),D(mm),RR(np,np),ST(np) DIMENSION U(mm),VR(mm),WT(mm),WK(mm), & WBT(nn),WBK(nn) DIMENSION VRLV(50) INTEGER T,K,yr(100) REAL MX,rh,soi(100,12),so(nn),a1(nn) REAL asm(mm),sigma(mm),sm(mm) OPEN(66,FILE='rpca500.DAT') !旋转EOF的结果输出 open(7,file='e:\data2\sst\sst1') !读取原始资料 read(7,*)((rh(i,j),i=1,nn),j=1,mm) close(7) ccccc 682 format(1x,'original data') ! 683 format(1x,'Number station',i3) ! 686 format((1x,10f8.2)) ! CALL STANDARD(NN,MM,RH) ccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc c 原始资料 c CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCccccccccccccccccccccccccccccccccccCCCCC open(16,file='bzh_dat') !输出原始资料的标准化资料 do 786 i=1,nn c write(66,683) j 786 write(16,1686) (rh(i,j),j=1,mm) 1686 format(286f6.2) !按格点数目改动 ccccccccccccccccccccccccccccccccccccccccc rnn=real(nn) DO 12 J=1,mm DO 12 J1=1,mm A(J,J1)=0.0 DO 13 I=1,nn 13 A(J,J1)=A(J,J1)+RH(I,J)*RH(I,J1)/rnn 12 continue write(66,101) write(66,102) ((A(i,j),j=1,mm),i=1,mm) 101 format(/1x,'原始资料的相关矩阵A') 102 format((1X,286f6.2)) !按格点数目改动 sum=0.0 do 80 k=1,mm sum=sum+A(k,k) 80 continue write(66,103) sum 103 format(1x,' 相关矩阵A的维数 ==',f15.4) call jcb(mm,a,v,0.00001) call jcb1(mm,a,v) write(66,104) write(66,204)(a(i,i),i=1,mm) 104 format(//1x,' Eigenvalue(lambad)') 204 format((1x,4f20.12)) do 145 i=1,mm 145 ramda(i)=a(i,i) c write(66,104) ramda sum2=0.0 do 222 k=1,mm 222 sum2=sum2+A(k,k) write(66,106) sum2 write(66,909) 909 format(/3x,'特征值的总和必须等于相关矩阵A的维数!') err=abs(sum-sum2) if(err.lt.0.001) write(66,681) err if(err.ge.0.001) write(66,482) err 681 format(//1x,' ok 1 err= ',f9.4) 482 format(//1x,' in error err= ',f9.4) 106 format(1x,'THE SUM OF LAMBAD',f12.4) do 25 k=1,mm 25 mx(k)=100.0*a(k,k)/sum write(66,108) write(66,208) mx 108 format(//1x,'The percentage of lambad') 208 format((1x,10f8.2)) do 112 j=1,np write(66,110) j 112 write(66,210) (v(I,j),i=1,mm) 110 format(1x,'旋转前的特征向量或荷载.order:',I3) 210 format((1x,10f8.2)) do 50 it=1,nn do 47 jj=1,mm 47 xw(jj)=rh(it,jj) do 50 j=1,mm rh(it,j)=0.0 do 54 k=1,mm 54 rh(it,j)=rh(it,j)+xw(k)*v(k,j) 50 continue do 400 j=1,np write(66,125) j 400 write(66,805) (rh(i,j),i=1,nn) cccccccccccccccccccccccccccccccccccccccc C 未旋转前时间系数 C CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC open(18,file='unrot_time.dat') do 787 i=1,nn 787 write(18,1688)i+1899,(rh(i,j),j=1,np) 1688 format(i4,15f8.3) ccccccccccccccccccccccccccccccccccccccccc 125 format(/1x,'旋转前的时间系数(PC).order',i3) do 772 j=1,mm do 772 it=1,nn reco(it,j)=0.0 do 773 k=1,mm 773 reco(it,j)=reco(it,j)+v(j,k)*rh(it,k) 772 continue write(66,982) do 986 j=1,mm write(66,683) j 986 write(66,686) (reco(i,j),i=1,nn) 982 format(/1x,'Reconstructed data(for inspect) ') write(66,238) 238 format(//3x,'To inspect perpendicularty and variance of PC') write(66,258) 258 format(/1X,'The covariance martix of first NP principal companent *:') do 234 j1=1,np do 234 j2=1,np rr(j1,j2)=0.0 do 235 it=1,nn rr(j1,j2)=rr(j1,j2)+rh(it,j1)*rh(it,j2)/rnn 235 continue 234 continue do 366 j1=1,np 366 write(66,266) (rr(j1,j2),j2=1,np) 266 format(3x,10f8.3) write(66,269) write(66,469) write(66,669) write(66,869) 269 format(//4x,'Variance of each time coefficient(PC) must be equal') 469 format(/1x,'to corresponding eigenvalue.') 669 format(/4x,'The covariance between PC each other must be equal ') 869 format(/1x,' to zero.') DO 333 J=1,np DO 333 I=1,mm V(I,J)=V(I,J)*SQRT(RAMDA(J)) 333 CONTINUE write(66,782) 782 format(//1x,' ok 2') do 321 j=1,np do 323 i=1,mm 323 a(i,j)=v(i,j) do 325 it=1,nn 325 rh(it,j)=rh(it,j)/sqrt(ramda(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)) do 702 j=1,np st(j)=0.0 do 703 i=1,mm 703 st(j)=st(j)+a(i,j)**2 702 continue su=0.0 do 704 j=1,np 704 su=su+st(j) write(66,801) 801 format(/1x,'Sum of squared element of each colum of the loading *martix(first NPcolum)') write(66,805) st 805 format((1x,10f8.3)) write(66,901) 901 format(/1x,'Sum of squared element of first NP colum of loading &matrix') write(66,905) su 905 format((1x,f12.3)) do 346 j=1,np do 346 it=1,nn 346 b(it,j)=rh(it,j) 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(66,538) write(66,549) write(66,539) vrlv0,(vrlv(k),k=1,lll) 538 format(//1x,'Sum of variance of squared element of each colum of & rotated loding martix ') 549 format(1x,'at each circulation') 539 format((1x,10f8.3)) do 802 j=1,np st(j)=0.0 do 803 i=1,mm 803 st(j)=st(j)+a(i,j)**2 802 continue su=0.0 do 804 j=1,np 804 su=su+st(j) write(66,701) 701 format(/5x,'Sum of squared element of each of the first NP rotated * loading vector') write(66,805) st write(66,472) 472 format(/1x,'Sum of squared element of rotated loading matrix') write(66,905) su do 971 j=1,np write(66,117) j 971 write(66,805) (a(i,j),i=1,mm) 117 format(1x,'旋转后的荷载（ROTATED LOADING VECTOR， *简称RLV) ordre:',i3) cccccccccccccccccccccccccccccccccccccccccc C 旋转后时间系数 C CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC open(2,file='rot_time.dat') do 401 i=1,nn write(2,809)(b(i,j),j=1,np) 401 continue 809 format(15f8.3) close(2) close(18) do 906 j=1,np write(66,127) j 906 write(66,805) (b(i,j),i=1,nn) 127 format(/1x,'旋转主分量(RPC).order:',i3) do 945 i=1,np do 945 j=1,np do 966 it=1,nn x(it)=rh(it,i) 966 y(it)=b(it,j) 945 rc(i,j)=sokan(nn,x,y) write(66,888) 888 format(//1X,'旋转前后主分量的相关距阵') do 977 i=1,np 977 write(66,988) (rc(i,j),j=1,np) ccccccccccc 988 format((1X,15f6.2)) close(6) stop end ccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc c**************************************************************************** function sokan(n,xx,yy) dimension xx(n),yy(n) sx=0.0 sy=0.0 sxy=0.0 sxx=0.0 syy=0.0 do 10 i=1,n sx=sx+xx(i) sy=sy+yy(i) sxy=sxy+xx(i)*yy(i) sxx=sxx+xx(i)**2 syy=syy+yy(i)**2 10 continue fn=real(n) xmean=sx/fn ymean=sy/fn sokan=(sxy-fn*xmean*ymean)/ 1(sqrt(sxx-fn*xmean**2)*sqrt(syy-fn*ymean**2)) return end c**************************************************************************** subroutine rot(a,b,h,t,k,mm,nn,np,u,vr,wt,wk,wbt,wbk) dimension A(mm,mm),B(nn,np),H(mm),U(mm),VR(mm),WT(mm),WK(mm), 1WBT(nn),WBK(nn) integer t,k 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 c************************************************************************** subroutine jcb1(n,a,s) dimension a(n,n),s(n,n) do 20 i=1,n-1 w=a(i,i) k=i do 30 j=i+1,n if(a(j,j).le.w) go to 30 W=A(J,J) K=J 30 CONTINUE A(K,K)=A(I,I) A(I,I)=W DO 70 L=1,N W1=S(L,I) S(L,I)=S(L,K) S(L,K)=W1 70 CONTINUE 20 CONTINUE RETURN END C*************************************************************************** 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)=1.0 GO TO 30 20 S(I,J)=0.0 S(J,I)=0.0 30 CONTINUE G=0.0 DO 40 I=2,N I1=I-1 DO 40 J=1,I1 40 G=G+2.0*A(I,J)*A(I,J) S1=SQRT(G) S2=EPS/FLOAT(N)*S1 S3=S1 L=0 50 S3=S3/FLOAT(N) 60 DO 130 IQ=2,N IQ1=IQ-1 DO 130 IP=1,IQ1 IF(ABS(A(IP,IQ)).LT.S3) GO TO 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 GOTO 60 150 IF(S3.GT.S2)GOTO 50 RETURN END C**************************************************************************** C SUBROUTINE AB(RR,RMIN,RMAX,PP) C DIMENSION RR(10,8) C CALL OPNGKS C CALL DEFCON(1) C CALL MAPSTI('I1',2) C CALL MAPSTI('I2',2) C CALL MAPSTI('I3',2) C CALL MAPSTI('I4',2) C CALL MAPSTI('I5',2) C CALL MAPSTI('I6',2) C CALL MAPSTI('I7',2) C CALL MAPSTI('EL',1) C CALL MAPPOS(0.2,0.65,0.2,0.65) C CALL SUPMAP(1,90.0,0.0,-90.0,90.0,90.0,90.0,90.0,4,20,2,0,IERR) C CALL CONREC(RR,10,10,8,RMIN,RMAX,PP,2,0,-682) C CALL CLSGKS C RETURN C END C*************************************************************************** C FUNCTION FX(X,Y) C CALL MAPTRN(10.0*(Y-1.0)+10.0,40.0*(X-1.0)+00.0,XX,YY) C FX=XX C RETURN C END C************************************************************************** C FUNCTION FY(X,Y) C CALL MAPTRN(10.0*(Y-1.0)+10.0,40.0*(X-1.0)+00.0,XX,YY) C FY=YY C RETURN C END C************************************************************************** subroutine coff(x,y,n0) real x(n0),y(n0) ax=0 ay=0 xy=0 xx=0 yy=0 do 11 i=1,n0 ax=ax+x(i) ay=ay+y(i) xy=xy+x(i)*y(i) xx=xx+x(i)**2 yy=yy+y(i)**2 11 continue ax=ax/n0 ay=ay/n0 if((yy-n0*ay**2).eq.0)then r=0.0 else r=(xy-n0*ax*ay)/(sqrt(xx-n0*ax**2)*sqrt(yy-n0*ay**2)) endif write(*,*)r end subroutine standard(n,m,x) !m为格点数，n为时间长度 dimension x(n,m) do j=1,m ave=0.0 do i=1,n ave=ave+x(i,j)/float(n) enddo xigma=0.0 do i=1,n xigma=xigma+(x(i,j)-ave)**2/float(n) enddo xigma=sqrt(xigma) do i=1,n x(i,j)=(x(i,j)-ave)/xigma enddo enddo end